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 MUSIC 
 
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ATJGENER'S EDITION No. 9198 
 
 
 HARMONY SIMPLIFIED 
 
 OR 
 
 THE THEORY OF THE 
 
 TONAL FUNCTIONS OF CHORDS. 
 
 BV 
 
 DR. HUGO RIEMANN, 
 
 Professor of Musical Science at Leipzig University 
 
 TRANSLATED FROM THE GERMAN. 
 
 THIRD IMPRESSION 
 
 AUGENER LTD. 
 LONDON 
 
Printed in England 
 
 by 
 
 AUGENER Ltd., 
 287 Acton Lane, London, W. 4. 
 
©e&tcatefc 
 
 TO 
 
 PROFESSOR EBENEZER PROUT. B.A., 
 
 Professor of Music in the University of Dublin, etc. 
 THE DISTINGUISHED PIONEER OF MUSICAL PROGRESS. 
 
 THE AUTHOR 
 
CONTENTS. 
 
 Introduction page i. 
 
 (Harmony — Melody — Tone relationship — Overtones — Undertones — Majoi 
 chord and minor chord — The three functions — Modulation.) 
 
 CHAPTER I. — Writing Confined to Pure Principal Harmonies 
 (Tonic and Dominants) page 10. 
 
 § I. Overclangs and Underclangs. §2. Four-part writing — The writing of 
 single chords. §3. Plain-fifth step (T—D and °T— ° S)— The con- 
 nection of chords — Consecutive octaves — Chords of six-four (-Z?Jand S\i)- 
 §4. Contra-fifth step (T—S and "T— °D)— Complete (bi-lateral) 
 cadences. § 5. The whole-tone step (S — D and °D — °S) — Consecu- 
 tive fifths — The tritone— Score. § 6. The turn of harmony ( + T — "J? and 
 °T— + D)— Contra-fifth change {°S— Z> + ) and fifth-change (°S — + S 
 and "D — + -D) — Diminished and augmented part-progressions — False 
 relation — Modulation. 
 
 CHAPTER II. — Characteristic Dissonances — Parallel-Clangs 
 —Leading-Tone-Change Clangs page 55. 
 
 § 7. The characteristic dissonances {D 1 , S vn , S 6 , D vl ) — Treatment of 
 dissonant tones — Alto clef— Figuration with passing and auxiliary notes. 
 § 8. Chords of seven-three (IP 1 — $ vu ) and parallel clangs (Tp, Sp, Dp, 
 "Sp ; °Tp, °Sp, °Dp, + -Dp) — Treatment of feigning consonances — 
 Doubling of the third allowed — Third change — Leading-tone change — 
 Minor-third change — Whole-tone change — Tritone change — Tenor clef — 
 Third step — Minor-third step — Leading-tone step. §9. Dorian sixth, 
 Mixolydian seventh, Neapolitan sixth, Phrygian second, Lydian fourth — 
 The church modes — Revival of these as means of expression — Close — 
 Half-close — Deceptive-close — Contra-whole-tone change — Tritone step — 
 Chromatic-semitone change — Augmented-sixth change — Double-third 
 change — Chromatic-semitone step. 
 
vi Contents. 
 
 CHAPTER III.— The Theory of Dissonance — Sequences- 
 Intermediate Cadences page 107. 
 
 § 10. Completion of the Theory of Dissonance — Passing dissonances — Prepared 
 dissonances — Altered chords — Unprepared dissonances — Syncopated 
 figuration. § II. Sequences — The sequence as melodic imitation of har- 
 mony formations — Five-part writing, § 12. Intermediate cadences — 
 (Inserted) and [omitted] harmonies — The notation for transposing instru- 
 ments. 
 
 CHAPTER IV.— The Change of Tonal Functions (Modula- 
 tion) page 141. 
 
 § 13. Change of meaning of the simplest harmony steps — Characteristic 
 figuration. § 14. Modulating power of harmony steps. § 15. Modula- 
 tions by means of chords of seven-three and of minor nine-three — 
 Enharmonic Change. § 16. Modulations by means of the third-change 
 clangs. § 17. Modulations by means of bolder harmonic progressions 
 (leading-tone steps, third steps, etc.). § 18. Modulation by means of the 
 most far-reaching harmony steps (tritone step, etc.). § 19. Independent 
 creation of musical sentences — Period formation. § 20. Pedal-point and 
 modulating sequence. 
 
 Exercises : pages 11, 16, 20, 21, 23, 25-28, 30-34, 39-43. 5°-54. 64-69, 
 82-83, 85-87, 104-106, 1 18-120, 126-127, I 33 -, 4°> 180-187. 
 
 Explanation of the Terminology and the Chord Signs 
 in Alphabetical Order ... page 191 
 
 Alphabetical Index ... ._ page 196, 
 
HARMONY SIMPLIFIED. 
 
 INTRODUCTION. 
 
 The Theory of Harmony is that of the logically rational and 
 technically correct connection of chords (the simultaneous sounding of 
 several notes of different pitch). The natural laws for such 
 connection can be indicated with certainty only if the notes of 
 single chords be regarded not as isolated phenomena, but rather 
 as resulting from the motions of the parts ; chord successions arise 
 from simultaneous melodic motion of several parts. The history of 
 music teaches us that simultaneous melodic progression in several 
 parts was practised and more and more perfected for centuries 
 before the idea of harmony in the modern sense (chord) was even 
 conceived. Thus harmony, in so far as it may be defined as 
 composition in several parts (polyphony), takes root in melody. 
 
 Melody is the logically rational and aesthetically satisfactory 
 motion of a part through notes of different pitch. With regard to 
 the aesthetic laws for melody formation, we refer the student to 
 the philosophy of music (cf the author's " Catechism of Musical 
 .-Esthetics " [ f ' Wie horen wir Musik "]). As the foundation of 
 rational motion in melody common to all ages and all races, the 
 history of music suggests the diatonic scale, the simple step succes- 
 sion of the natural notes of our present note system : 
 
 with its regular insertion of a semitone step {b c, e /), alternately 
 
 after two and three whole-tone steps. The age of tbisfundamental 
 scale, counting by thousands of years, and the respect in which it 
 has been held, are a sufficient guarantee that it is a demand of 
 nature, that it is logical and necessary; indeed, even irregular 
 constructions of melody may be traced back to this foundation. 
 The notes of this fundamental scale stand in such relation to one 
 another as the ear can apprehend with certainty, and as are 
 expressed in acoustics and mathematics by certain simple 
 numerical ratios. These ratios, are the same as those which 
 exist between the numbers of vibrations of elastic bodies that 
 
2 Introduction. 
 
 produce the notes, and of the air that conveys them to our ear. 
 Such simple ratios of vibrating strings or columns of air enclosed 
 in tubes, or — if we put aside reasoning on physical grounds and 
 only take into consideration perception by hearing — such relations 
 of notes to one another (recognised by the ear) as allow of their 
 appearing musically intelligible and rational when sounded in 
 succession, are called harmonic (from the Greek apfiofaiv = to join), 
 and, indeed, these are after all the same relations which have to 
 be regarded as standard in viewing the combinations of several 
 parts, harmonies in the sense recognised nowadays. Just as 
 harmony, then, (as chord succession) has referred us to the melody 
 of single voices, so melody (as a succession of notes standing in 
 harmonic relation to one another) refers us again to the original 
 laws of harmony, so that we must say : Every note of a melody 
 owes its cBsthetic effect in great measure (viz., abstracting from the 
 effect produced by its absolute pitch, or by the fact that it repre- 
 sents a rising or falling of the melody-line) to its harmonic 
 meaning. And by the harmonic meaning of a note we understand 
 its relation, as accurately perceived by the ear, to other notes of the 
 same melody or — in composition in several parts — to notes of 
 other accompanying melodies. 
 
 One note compared with other notes (we shall speak now 
 only of notes whose relation is recognised by the ear as har- 
 monic and intelligible) is either itself the fixed point, the prima 
 ratio, starting from which the others are considered, or, con- 
 versely, it is in its turn cofisidered in its relation to some other 
 note ; in the former case it is, therefore, the starting point of 
 reference for other notes — the prime ; in the latter, a note to be 
 referred to the prime, and whose distance from it is expressed by 
 the ordinal number corresponding to the degree in the funda- 
 mental scale which the note occupies, counting from the prime. 
 So, e.g., if we compare c with g, either c is the prime and then 
 g the fifth step measured from c upwards ; or g is the prime, 
 and then c is the fifth step measured downwards from g (under- 
 fifth). The general name for the distance of notes from each 
 other, measured by the degrees of the fundamental scale, is 
 Interval. 
 
 The verdict of the ear declares those intervals simplest — i.e., 
 understands them with the greatest certainty, and requires pure 
 intonation for them most inexorably — which mathematics and 
 physics reduce to the simplest numerical ratios, either by 
 measuring the duration of vibrations in time or the extent of 
 sound-waves in space, or by dividing a tightly stretched string 
 in various ways. Starting with the latter as more convenient and 
 more easily intelligible, we shall find that the simplest division of 
 the string is into two halves ; each half of the string then gives the 
 octave of the note sounded by the whole string, and both halves 
 yield one and the same note. But it is evident that the ratio of 
 
Introduction. 3 
 
 the unison, 1 : 1, will be more easily understood than that of the 
 whole to the half, 1 : '/,. Next to these two comes the ratio of 
 the whole to the third part (1 : '/ 3 )> to which the musical interval 
 of the twelfth (fifth of the octave) corresponds; then follow 
 1 : 7 4 = double octave, 1 : 1 / 5 (major) third of the double octave, 
 1 : '/e fifth of the double octave, or octave of the twelfth ; in notes, 
 if we take c for the whole string : 
 
 If, conversely, we start with a higher note, e.g., thrice-accented 
 e (<? 3 ), and try to find those easily understood notes which lie 
 below e\ then doubling the length of the string will have to take 
 the place of halving, i.e., if we take the length of e 3 as = 1, the 
 note which corresponds to twice the length of the string (2) will 
 be the under-octave of e 3 , therefore e' ; a' will correspond to three 
 times the length, e x to four times, c< to five times, and a to six 
 times the length of the string : in notes, — 
 
 Intervals which are greater than the octave the musician does not 
 conceive in their total extent, but divides them with the help of 
 the octave, e.g., twelfth = octave -+- fifth, fifteenth = octave -f- 
 octave, seventeenth = octave + octave + (major) third, etc. 
 The octave is the most easily understood of all intervals (for the 
 unison is not really an interval, as the distance between the two 
 notes is equal to zero) ; notes which stand at the distance of an 
 octave from each other are similarly named in our modern note 
 system, as has been the custom for thousands of years, and are 
 regarded as repetitions of the same note in another region of the 
 domain of sound. The melodic fundamental scale (see above) 
 passes through a set of six strange notes and at the 8th degree 
 reaches the octave, the most easily intelligible note ; but the 
 fragments of the two harmonic natural scales, i.e., the two series 
 of notes having the closest harmonic relation, the so-called 
 overtone series and undertone series, which we have already con- 
 sidered, prove that even if the intermediate degrees of the 
 melodic fundamental scale are not all directly related to one 
 particular note, still they are connected with one another by 
 the relations found in the harmonic natural scales. If, in- 
 stead of referring the notes from \ to \, or from 2 to 6, to 1, 
 we compare the notes of each series with one another, we 
 
4 Introduction. 
 
 immediately find a number of the intervals of the fundamental 
 scale. 
 
 Fifth. Fourth. Major Minor 
 Third. Third. 
 
 Fifth. Fourth. Major Minor 
 Third. Third. 
 
 And if we follow up the division of the string beyond \, or the 
 multiplication beyond six times, we find the missing smaller 
 intervals, the major and minor second, and besides these, indeed, 
 an abundance of intervals which our note-system ignores : 
 
 and 
 
 from c=i : Whole tones. 
 
 * 
 
 Semitone. 
 
 h h (9 l"> /" /n /«3 /« /"S '■« 
 
 from e 3 =i : Whole tones. 
 * 
 
 Semitone. 
 
 In the overtone series the notes marked * are, according to 
 the verdict of our ears, too flat compared with the corresponding 
 ones in our note-system ; in the undertone series they are too 
 sharp. It is, therefore, evident that the attempt to fill up the 
 octave with the intermediate degrees thus gained, must have a 
 result contradictory to that of our musical experience ; the fourth 
 octave of the harmonic natural scale deviates in three notes and 
 in five intervals from the melodic fundamental scale : 
 
 and 
 
 8th to 16th Overtone. ^ 
 
 8th to 1 6th Undertone, j. 
 
 # * 
 
Introduction. 
 
 5 
 
 The ear entirely rejects the replacing of the fundamental scale 
 by either of the above, because in both the seconds from the &th to 
 the 16th partial tone continually become smaller (/), while the 
 fundamental scale, as already remarked, is a mixture of major 
 and minor seconds. The ear altogether fails to understand the 
 7th, nth, 13th, and 14th tones of the harmonic natural scales, 
 and refuses to recognise the intervals, formed by them with their 
 neighbouring notes and their fundamental note (1), as fit for 
 musical use. The rise and foundation of the natural melodic 
 scale cannot be fathomed in this manner (the attempt was made 
 first by F. A. Vallotti). 
 
 If we examine the two harmonic natural scales passing away 
 into infinity with their intervals continually becoming smaller, it 
 is clear that if our musical system is to be derived from them 
 at all, we must make a stop somewhere ; for our system knows no 
 quarter-tones, which the next octave must introduce. Let us, then, 
 first sharpen our gaze, and eliminate those notes from each series 
 which are related to other notes in the series, just as the latter are 
 to the fundamental note, i.e., let us distinguish between notes 
 related in the first and second degree, and regard the notes 
 3 . 2 = 6, 3 . 3 = 9, 3 . 4 = 12, 3 . s = 15, etc., and '/ 3 . 7,=7 6) 
 Vs • Vs = Vs. U ■ U = 7«» Vs • Vs = 'In; respectively, as nearest 
 related to the notes 3 and 7 3 > as belonging to them and derived 
 from them, and similarly with notes found by division by '/ t or '/ s 
 and multiplication by 4, 5, etc. : 
 
 !"-e-1 
 
 1 '/. Vs [V. • VJ 'Is [V. • V 3 ] 7, [V. • '/. • '/., Vs • V 3 > 
 
 1 * 
 
 r 1 * 
 
 Bes. \a. ■S - etc. 
 
 fen-*-- 
 
 
 - 
 
 S 5= — 1 
 
 J 
 
 L. ' 
 
 'Is •'/•I V« LV»" /■• m /13 L h • if /3 • In /•• /••7> , 7i 
 
 and: 
 
 1 z 3tz-aJ 5 ts-3) 7 [2. a. 2, 3-3. 
 
6 Introduction. 
 
 Only the following then, remain as the directly related notes 
 of each series : 
 
 and : 
 
 5 7 ii ij 
 
 Of all the primary related notes, our ears recognise only the 
 first ones (up to \ and 5 respectively), as the asterisks show, and 
 refuse to recognise all the following ones, which appear out of 
 tune. Those thus remaining are : the octave, fifth of the octave, 
 and third of the double octave in each direction ; if we shift 
 these into the nearest position to one another, which we may do 
 on account of the similar sound of octave-notes, there remain in 
 each case only two notes towards the filling up of the octave 
 interval, viz., the (major !) third, and the fifth : 
 
 i.e., of the overtone series only a major chord (overclang) is left, 
 of the undertone series only a minor chord (underclang), both 
 consisting of prime, major third, and perfect fifth, the former 
 measured upwards, the latter downwards. 
 
 " There are only three directly intelligible intervals : octave, 
 [major] third, and [perfect] fifth " (Moritz Hauptmann). All 
 other intervals are to be explained musically and mathematically as the 
 results of multiplication and involution of these three, e.g., the minor 
 
 third as -=-. -j-( 3 L : S L = ,a L = 6 /s)> the whole tone as- — 
 
 third ' * ' ' 5/ octave 
 
 / 3 L • 3 L \ .i, v third-fifth /*/, . 3 L 
 
 1 h — /» _ 9/ \ t he semitone as ( -L* — 12-— n . 
 
 \ 2 —'*/ octave V 2 h6 
 
 These secondary relationships now disclose the significance of 
 those degrees in the melodic fundamental scale which hitherto 
 seemed enigmatical : for the scale consists not only of direct 
 relatives of one note, but of relatives in the second degree as 
 well as in the first, and is, therefore, explicable not only in one 
 single way, but in various ways. The ancient Greek theorists 
 (Pythagoras) looked upon the scale as a chain of fifths • 
 f c, g, d, a, e, b, and as such it contains relatives even to the 
 sixth degree, according to the note that is taken as starting point 
 
Introduction, ^ 
 
 (3JY 720 
 (prime), (b as sixth fifth of / = ~- = 1—?). Since the signi 
 
 2 ^ I 2 
 
 ficance of the third-relationship of notes has been recognised 
 (cf. the author's " Katechismus der Musikwissenschaft," p. g 
 and following), it is simpler to refer the melodic fundamental 
 scale to one principal note (prime) with its third and fifth, and 
 its upper and under fifths with their thirds and fifths : 
 
 I 4 , 
 
 C I 
 
 g 
 
 
 7* 
 a 
 
 7< i 
 
 f a c 
 
 i 7 5 7, 
 
 g b d 
 
 i V, % 
 
 or 
 
 d f a 
 
 V. 7, ' 
 
 « i 
 
 V. 7< 
 
 7%« ear comprehends a lone with its direct relatives (third and fifth 
 or their octaves) o# rt* j-0#z<t side — therefore prime, over-third, and 
 over-fifth, or prime, under-third, and under-fifth, — as belonging to- 
 gether in closer unity, and distinguishes them from all more distant 
 relatives as forming one compound sound, which we will call a 
 clang ; each of the three tones can represent the clang, and even if 
 the prime be not sounded itself, it is possible to understand the 
 third or fifth as representing the clang. Tones which belong 
 to one and the same clang and represent it, are consonant (they 
 blend together, appearing only as the component parts of that one 
 clang). Tones which represent different clangs are dissonant. In 
 such cases one clang must be regarded as principal (prime-clang), 
 while the tones representing other clangs are to be considered as 
 merely disturbing its consonance. Thus dissonant chords arise 
 from the circumstance that, besides tones which represent one 
 clang (prime, third, or fifth), other tones (one or more) are sounded 
 which do not belong to the same clang, and can be under- 
 stood only mediately, as representatives of another clang (naturally 
 of one standing in comprehensible relationship to the principal 
 clang). 
 
 Just as one tone may be either principal tone (prime) or 
 derived tone (and then either directly related, i.e., plain third or 
 plain fifth of the clang represented, or a secondary relative, i.e., 
 prime, third, or fifth of another clang, and then dissonant), so 
 also a clang may be either principal clang — in which case it is 
 called tonic* — or derived clang ; and in the latter case it is either 
 nearest related clang on the overtone side or nearest related clang on 
 the undertone side, or again only a secondary relative, and then must 
 be indicated as nearest relative of a nearest related clang (ac- 
 cessory clang of the latter). Nearest related clangs are in the 
 first place only those known under the name of dominants. 
 Starting with an overclang (major chord), the overclang (major 
 chord) of its upper fifth is the so-called upper- dominant (or 
 simply dominant, indicated briefly by D), and the overclang of 
 
 • Indicated briefly by T. 
 
8 Introduction. 
 
 the under-fifth is the so-called under-dominant or subdominant 
 (indicated briefly by S) ; but also the contra-clang of the tonic, 
 i.e., the underclang of the same principal tone, may appear as 
 subdominant. We always indicate underclangs by a nought; 
 thus ° 5 is the under-dominant when a minor chord ; in c major, — 
 
 Similarly, starting with an underclang (minor chord), the. under- 
 clang of its under-fifth is under-dominant (°S) and the under- 
 clang of its upper-fifth is upper-dominant ("£>), but also the 
 contra-clang of the tonic (the overclang of its prime) may appear 
 as upper-dominant (D + ); the overclang we generally indicate by 
 the simple chord-signs, T, D, S, without any index, but in doubt- 
 ful cases take the precaution to indicate it by a + in opposition 
 to the ° : thus in a minor, — 
 
 While our musical system, as we have seen, admits partial 
 tones as representatives of a clang only as far as the interval of 
 the third (cf. p. 6), it does not recognise a representation of a 
 key by a clang beyond the fifth-clangs, i.e., although the natural 
 relationship of the upper- and under-third clangs is beyond doubt 
 (e.g., the e major chord is easily intelligible beside the c major 
 chord as overclang of its third), yet it is not possible for the 
 e major chord to represent the key of c major, and it generally 
 makes its appearance, as we shall see, as a secondary relative 
 (dominant of the parallel key, which we shall be able to explain 
 more fully later on). We may therefore state the following prin- 
 ciples, which explain and develop the title of the book : 
 
Introduction. g 
 
 I. There are only two kinds of clangs : overclangs and under- 
 clangs ; all dissonant chords are to be conceived, explained, and indi- 
 cated as modifications of overclangs and underclangs. 
 
 II. There are only three kinds of tonal functions {significance 
 within tfie key), namely, tonic, dominant, and subdominant. In the 
 change of these functions lies the essence of modulation. 
 
 By keeping both these principles well in mind, we succeed in 
 giving the theory of harmony a form thoroughly simple and 
 easily comprehensible, and in formulating the prescriptions and 
 prohibitions for the progression of parts in a much more definite 
 and binding fashion than was hitherto possible. 
 
Harmony Simplified. [Chap, i 
 
 CHAPTER I. 
 
 WRITING CONFINED TO PURE PRINCIPAL HARMONIES 
 
 (tonic AND dominants). 
 
 § I. OVERCLANGS AND UNDERCLANGS. 
 
 From the combination of a tone {prime) with its {major) upper- 
 third and upper-fifth arises the overciang {major chord) ; from its 
 combination with its (major) under-third and under-fifth, the under- 
 clang {minor chord). 
 
 To learn with certainty to know and to treat all overclangs 
 and underclangs, with which alone we are at present occupied, 
 and to which all that remains is easily attached as bywork, we 
 must impress firmly on our minds the fifth-succession of the 
 natural notes : 
 
 f c g d a e b 
 
 {to be learnt by heart fluently backwards and forwards), and also 
 the three {major) thirds without chromatic signs : 
 
 f a, c e, and g b. 
 
 The series of fifths is extended by repeating them with sharps, 
 flats, double sharps, and double flats (/#, c%, g\, etc., b\f, e\>, aP, 
 etc. fx, cx,g*, etc., i>bb, ebb, «bb, etc.), in addition to which 
 we need remark only that the connecting fifths of these series 
 (viz., those arrived at by correction of the fifth bfi which is too 
 small by a semitone, namely, b : /$ and bfy : f and also b% : /* 
 and b$b ■ fib, which are derived from the same degrees) are 
 the only fifths with unequal signature. In the case of thirds 
 we have to consider whether the particular third is one of those 
 indicated above as to be learnt by heart, or one derived from 
 them : for naturally all those on the same degrees {c% : e\, c*p ; efy, 
 g$ : bjjf, gb :bb, f% : a%, fO : a\>, etc.) must have similar sig- 
 nature, while those derived from the four remaining (d :f a: c, 
 e : g, b:d), which are too small by a semitone, must have unequal 
 signature, just like the fifth b : f (a % before the upper note or 
 a 1? before the lower, or again a f before the lower note and a x 
 before the upper, or a b before the upper note and a bb before 
 the lower). 
 
chap, i.] Tonic and Dominant Harmonies. i i 
 
 ist Exercise. — All the thirds arrived at in this manner 
 {in all 31) are to be completed as over clangs by adding the upper- 
 fifth of the lower note, and as underclangs by adding the under 
 fifth of the upper note ; e.g., the third c : e = 
 
 c e g = c overclang (c + , also indicated simply by c), 
 
 a c e — e underclang (°e). 
 
 This first exercise is under no circumstances to be dispensed 
 with. Another very useful preparatory exercise (second exer- 
 cise) consists in the construction of all possible overclangs 
 and underclangs, starting with each element of the clang, 
 e.g., if e be given as the third of an underclang, the other 
 notes (prime g% and under-fifth c#) are to be supplemented ; 
 if by 1, 3, 5 we understand the prime, third, and fifth of 
 the overclang, and by I, III, V, the prime, third, and fifth 
 of the underclang, this exercise will be thoroughly carried 
 out by looking upon every note in turn as 1, 3, 5, I, III, 
 and V, and adding the other notes of the clangs (as far as 
 the boundaries of notation will allow, i.e., stopping where 
 threefold chromatic signs would become necessary), e.g., if we 
 take the note ^Jf as the starting-point : 
 
 13- B g=^r4£Eg:g E 
 
 in 
 
 The more thoroughly these preparatory exercises are worked out 
 the less we shall need to fear vague notions about keys and their 
 principal harmonies. 
 
 § 2. FOUR-PART WRITING. 
 
 In the introduction we pointed out, as the task of the theory of 
 harmony, instruction in "the logically rational and technically 
 correct connection of chords"; we must first of all make the 
 supplementary remark that four-part writing, in the course of 
 centuries, has proved itself the most appropriate form for exercises 
 in this connection, because of its being at the same time so 
 ample as not to make too many restrictions necessary, and 
 simple enough not to be overladen and unwieldy. The four 
 parts from whose simultaneous melodic progression chords result, 
 are appropriately represented as the four principal species of the 
 human voice, and are called after them soprano, alto, tenor, and 
 bass. The first exercises are to be noted down in the simplest 
 
r 2 Harmony Simplified. [Chap. i. 
 
 fashion with the two most familiar clefs, treble and bass, the 
 former for the two upper parts (soprano and alto), the latter for 
 the two lower parts (tenor and bass) ; two parts are to be written 
 on one stave, on the upper the soprano with the note stems turned 
 upwards and the alio with the stems downwards, on the lower the 
 tenor with stems upwards and the bass with stems downwards, e.g. : 
 
 More particular directions for the actual compass of each 
 single voice are not at present necessary, as it is not as yet a 
 matter of real composition for voices. If we confine the soprano 
 and bass as far as possible within the lines, so that only very 
 
 exceptionally the soprano proceeds as high as 
 
 the bass as low as & , then with the help of the rules 
 
 -»- 
 
 to be given directly for the distance of the parts from one 
 another, the motion of the parts in a range of pitch which corre- 
 sponds to their actual compass will naturally follow. 
 
 As we are to write in four parts, and as the concords (over- 
 clang and underclang), which for the present alone require con- 
 sideration, contain only three notes of different name, either one 
 part must always be silent (a possibility which we do not take 
 into account at all, as it would put a stop to the four-part writing), 
 or one note must be introduced in two parts — must, as it is 
 termed, be "doubled." This "doubling" may occur either in 
 the same tone region or in another octave ; the latter is generally 
 preferable, as it secures greater fulness of sound. The note best 
 adapted for doubling in the overclang is the prime — in the under- 
 clang, the under-fifth. The latter assertion requires a reason. A 
 singular acoustical phenomenon — the attendant sounding of over- 
 tones — accompanies every note of our musical instruments (also 
 voices) with the whole series of upper harmonics shown in the 
 introduction (pp. 3-4), and the first few of these in particular 
 sound with considerable force ; thus especially the third partial 
 tone, the twelfth (fifth of the octave), is distinctly audible, and in 
 such a measure that the omission of the corresponding chord- 
 note in writing is scarcely perceptible ; therefore in the minor chord 
 as well as in the major, if all three notes of the chord cannot 
 conveniently be introduced (for reasons to be discussed later on), 
 the upper note of the interval of the fifth may be omitted without 
 changing the effect materially. In consequence of this strong 
 
chap, i.] Tonic and Dominant Harmonies. 13 
 
 simultaneous production of the twelfth, the lower note of the 
 interval of the fifth is the best bass-note even in the underclang* 
 and may appropriately be doubled. The underclang, which, on 
 account of the peculiar dependence of its notes on a higher 
 principal note, appears to tend downwards, first receives a firm 
 basis through the choice of the under-fifth for its bass-note, 
 whence by way of the nearest overtones it projects upwards 
 again, without, however, its nature being disturbed by this assimi- 
 lation to the formation of the overclang. A certain contradiction, 
 indeed, cannot be denied between the third of the clang and the 
 5th partial tone of the bass-note thus chosen, which, though 
 comparatively weak, is still audible (e.g., in the e underclang 
 [a minor chord], the 5th partial tone of the bass-note a is c%, 
 which opposes the third of the chord (c), and somewhat detracts 
 from the physical euphony of the minor chord) ; but the peculiar 
 sadness in the character of the minor chord by no means arises 
 from the harshness of this sound, but rather from the indicated 
 
 * In order more fully to explain the somewhat strange-looking fact that in the 
 underclang the fifth forms the fundamental note, we submit the following short 
 considerations : — 
 
 Unless all signs are fallacious, there has been a time which did not understand 
 the third as part, or rather — because that remote age did not know music in parts — - 
 as representative of a harmony, but rather stopped short, in its recognition of 
 relations of tones, at the fifth, the simplest relation after the octave. The old 
 Chinese and Gaelic scales do not possess the semitone, which results from the 
 introduction of the third as representative of a harmony. Also the older en- 
 harmonic genus of the Greeks is probably to be explained as a restriction to the 
 fifth as representative of a harmony (cf. Riemann, "Dictionary of Music," under 
 " Pentatonic Scales''). For a music which does not understand the third as a 
 representative of a harmony, the double modality of harmony is, of course, an 
 unrevealed secret — for instance, the following group of tones : 
 
 Tonic. 
 
 Subdominant. Dominant. 
 
 is neither C major nor C minor, or, perhaps, the one as well as the other. Only 
 when the third became recognised as representative of a harmony, the distinction 
 of relations of tones as either upwards (overtones) or downwards (undertones) 
 received practical importance and theoretical consideration. It is impossible for 
 us here to develop this thought so fully as its importance would deserve : we only 
 remark that the fact of the fifth being a much older and naturally more prominent 
 representative of a harmony, exerts its influence in this, that the third, as it was 
 recognised much later as possible representative of a harmony, so even now is 
 regarded only as a sort of complementary and distinctive factor of harmony — as 
 a factor necessary, indeed, to make harmony complete and unambiguous, but one 
 which, all the same, appears only as accessory, if compared with the two funda- 
 mental pillars of harmony (prime and fifth, whether over-fifth or under-fifth), that 
 were much earlier recognised and stand in a much simpler relation to each 
 other. 
 
 There is yet another consideration to be taken into account. Tones that stand 
 at the distance of an octave from each other are considered by the musician as 
 identical. (No arithmetician has as yet solved the problem why it is that no 
 involution of the interval of the octave produces a dissonance, while we under- 
 stand even the second fifth as a dissonance) ; and hence theory and practice of all 
 times and nations agree in limiting melodies or parts of a melody by the octave 
 (which may have been suggested by the naturally limited compass of the human 
 
i4 Harmony Simplified. [Chap. i. 
 
 downward derivation of the notes. But this contradiction does, 
 indeed, explain the aversion of earlier composers to finishing a 
 musical piece with the complete minor chord ; their expedient, 
 however, in cases where they did not introduce the major chord — 
 omission of the third — is now no longer customary ; on the con- 
 trary, we nowadays desire to hear that note which alone decides 
 whether we have an overclang or an underclang before us. 
 Therefore the third must not be omitted either in the overclang or 
 underclang ; but it must also not be doubled, for then the clang 
 obtains a striking sharpness. This doubling of the third is 
 particularly bad when it is produced by two parts proceeding 
 in the same direction. Let us put these directions together so 
 as to be easily surveyed, and the result in the following form 
 will be easily remembered as equally applicable to overclang and 
 
 underclang (with @ an overclang, with m an underclang). 
 
 _ may be omitted, but may also be doubled. 
 =n must not be omitted, and generally not be doubled, 
 -good bass-note {fundamental note), best for doubling. 
 
 As the aim of plain four-part writing is the harmonious com- 
 bination of four parts progressing melodiously, a disagreeable effect 
 will be the result if the parts stand at too great a distance from 
 
 voice). The conception of the interval of the fifth as the prototype of harmony 
 produced by only two tone-, presupposes the identity of octave tones ; for simpler 
 than the ratio 2 : 3 (fifth) is the ratio 1 : 3 (twelfth). The third appears, in the 
 series of related notes, only after the second octave : 
 
 c . . c . . g . . c- . . e' 
 
 ia 345 
 and 
 
 Ei, . . G . . < . . g . . g> 
 
 5 4 3 3 1 
 
 Its absolutely simplest relation to the principal tone, accordingly, represents an 
 interval which transcends the range of an ordinary voice. There can be little 
 doubt, therefore, that the natural limitation of the human voice— that musical 
 instrument which is the oldest and the type and standard of all others— even in 
 primeval times, has suggested the vicarious use of octave tones in the repre- 
 sentation of tone relations ; and hence it is neither chance nor arbitrariness that we 
 are accustomed to conceive harmony in that form which places the constituent 
 notes in closest proximity, so that between the two more important tones— which, 
 without an inversion of the relation of above and below, cannot be placed closer 
 than at the interval of a. fifth— the third enters as a middle link, as-well in the 
 case of the overclang as in that of the underclang : 
 
 c . . g . . e and eg . . c . . g 
 3 3 5 532 
 
 Only this genesis — which must be considered not as excogitated arbitrarily or 
 as having grown by chance, but as resulting necessarily from nature— fully explains 
 the fact that also in the chord of C minor ihe c, although not prime, but fifth 
 forms the fundamental note. If the third were quite on the same level with 
 the fifth, it would seem proper to construct the minor chord on it as foundation ; 
 but this is refused by the ear as being altogether impossible. 
 
Chap, i.j Tonic and Dominant Harmonies. 
 
 15 
 
 one another. Observation of the practice of the great masters 
 and close examination of the sound of different combinations, 
 have led to the strict rule, that the greatest distance allowed 
 between the two highest parts (soprano and alto) is a?i octave, which, 
 however, is no longer admissible between the two inner parts, while 
 the bass, vvhich is added more for the sake of completeness and 
 good foundation, may at pleasure be removed further from the 
 tenor. Our exercises always keep to the natural relative position of 
 the higher and lower parts, i.e., a lower part must not cross over a 
 higher one (crossing of parts). 
 
 As has already been hinted several times, the bass part as 
 actual basis readily takes the fundamental notes of clangs, i.e., the 
 prime (1) in the overclang and the under-fifth (V) in the underclang ; 
 for the beginning of a period this is certainly to be recommended, 
 for the close it is strictly the rule, and also in the course of work it 
 is at any time good, unless the bass, which should also be a 
 melodious part, be by this means condemned to incoherent 
 groping about with large intervals (cf the directions for the 
 melodious connection of chords which follow below). There are 
 no rules directing the use of certain notes of the chord for the 
 other parts, though there can be no doubt that, at least in the 
 majo'r key, to begin and especially to close the melody with the 
 fundamental note (1, V) gives greater decision and repose, and is 
 therefore particularly appropriate for the special melody-part, the' 
 soprano, at least for the close of fairly long movements. 
 
 We are now in a position to arrange single chords in four 
 parts in such a manner that they will sound well, e.g., the c-major 
 chord in the following forms : 
 
 (a) Fundamental note in the Eass, and doubled. 
 
 -4-1 — I- 
 
 .<=!_,_<=!_ 
 
 (All good.) 
 
 r— '-t— T 
 
 (i) Third in the Bass. 
 
 (c) Fifth in the Cass. 
 
 (All good.) 
 
 (All good.) 
 
 Here at (b) in four cases the fifth has been doubled, to which 
 there is no objection. The doubling of the fifths at (c) is in fact 
 
16 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 mostly necessary ; temporary rule — if the fifth is in the bass, it 
 must be doubled. The following positions of the chord are not 
 good, but faulty : 
 
 J 
 
 17- \ 
 
 A few cases with omission of the fifth may also be given 
 
 , («) i i i i (*) i i i 
 
 (Good.) (Bad.) 
 
 Of 1 8 (b) we may remark that, in four-part writing, according 
 to our strict rules, doubling of the third, which for the present is 
 to be avoided altogether, sounds very bad if the fifth be omitted. 
 We shall come across further restrictions as regards third- 
 doubling and also fifth-doubling directly. 
 
 3RD Exercise. — Write out a number of major and minor 
 chords after the pattern of 16 — 18, adding the qualification 
 "good "or "bad." 
 
 § 3. PLAIN-FIFTH STEP (CONNECTING THE TONIC WITH THE 
 PLAIN-FIFTH CLANG I T— D AND °T—"S). 
 
 We now take a considerable step forward in attempting to 
 connect the two harmonies nearest related to each other, namely, 
 the harmony of a tonic and its plain-fifth clang. By plain-fifth 
 clang we understand that clang of the same mode as the first 
 clang, which has as its prime the fifth of the latter. In the 
 connection of these two clangs, the progression of the parts is quite 
 analogous in both major and minor modes, but the aesthetic signifi- 
 cance is very different, inasmuch as in major this connection entails 
 rising, in minor, falling, thus in the first case strengthening the 
 major character, in the latter, strengthening the minor character. 
 It would be a complete misunderstanding of the peculiar and 
 important aesthetic significance of the clang-mode, were we to 
 expect the downward movement in minor to have the same effect 
 as the upward movement in major. The plain-fifth clang is, in 
 major, the nearest related clang on the overtone side (the upper- 
 dominant), in minor, the nearest related clang on the undertone 
 
Chap. I.) 
 
 Tonic and Dominant Harmonies. 
 
 17 
 
 side (the under-dominant) ; the one, therefore, soars upwards, the 
 other dives downwards, the former case entailing, for the return to 
 the tonic, a sinking downwards, the latter, a rising aloft. 
 
 These two simplest combinations of harmonies lead directly 
 to the most important rules for the connection of chords. If we 
 chose to represent the harmonic relationship of these couples of 
 chords in such a manner that for the plain-fifth step in major 
 each part rose a fifth, and in minor fell a fifth : 
 
 we should be doing about all that custom, good taste, and 
 judgment forbid ; this would mean simply placing the two chords 
 side by side without any actual connection, and letting the parts 
 proceed so evenly together that not one of them would be really 
 independent ; but that, on the contrary, each would appear to be 
 dragged in the same direction by the others. But the principal 
 law of part-writing is that each part should go its own natural 
 road, and it should do this as melody, i.e., not by the degrees of 
 the natural harmonic scale (Introduction, p. 3), but by those of 
 the melodic (diatonic) scale. Since, as we know (cf. p. 1 2), every 
 note has its overtone series sounding with it, such parallel, con- 
 secutive progressions of two parts in octaves as above at 1 9 (a) 
 between soprano and bass, and 19 (b) between alto and bass, do 
 not really amount to two-part writing, but only to strengthened 
 unison. Therefore, it is strictly forbidden for two [real] parts 
 laying claim to independence (as is always the case with our four 
 parts) to proceed parallel to each other in octaves ; indeed, in 
 consequence of the similar sound of octave-notes, which easily 
 deceive the ear as regards tone region, it is not even allowable for 
 two real parts to proceed by contrary motion from notes of the 
 same name to notes of the same name (d) : 
 
 ,W ! , 8 'J, 15 1 1 (*) 
 
 (Wrong.) 
 
 But we must immediately remark that these consecutive octaves pro- 
 ceeding by leap are not nearly so disagreeable as those proceeding by 
 step (which we shall meet with directly) ; because parts proceeding 
 
i8 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 by step have in much greater measure the effect of real parts, i.e., 
 of melodies, and therefore disappoint us all the more, if their 
 course suddenly becomes identical, and they blend into one. 
 The same is true of consecutive fifths [cf. 19 (a) and 19 (b) between 
 tenor and bass] ; in the case of fifths proceeding by leap, it is less 
 the similarity of motion than the disconnectedness of the chords 
 and the want of melodious progression that strikes us disagree- 
 ably, whereas, in the case of fifths rising or falling by step, it is 
 the parallel motion itself which is the principal fault and causes 
 so disagreeable an effect. Fifths by leap in contrary motion : 
 
 21. i 
 
 indeed, often occur in the works of the best masters. No 
 recommendation, however, can be given to their use, nor to that 
 of octaves by leap in contrary motion, much less to that of 
 octaves and fifths by leap in parallel motion. The student who 
 wishes to get acquainted with the regular methods of part-writing, 
 to learn to know the normal paths, and to acquire and make a 
 habit of naturalness, smoothness, and fluency in the progression of 
 parts, so that he may judge for himself what he is doing when he 
 turns away from the straight road, must abstain from them entirely. 
 
 In the connection of harmonies with which we are at present 
 occupied, namely, the plain-fifth step and its inversion, the 
 "retrograde plain-fifth step," or "plain-fifth close," there is no 
 reason for making use of octaves and fifths, either in similar or 
 contrary motion, if the simplest fundamental law for the melodious 
 connection of chords be observed. This is : Every part should try 
 to reach a note of the new harmony by the nearest way. 
 
 From this main principle it follows that (1), when two 
 harmonies have notes in common, the latter most appropriately 
 remain in the same parts (" notes in common are kept in the same 
 part"); (2), progressions by step are always preferable to those by 
 leap, and steps of a mbior second (semitone progressions, leading- 
 tone steps) are specially to be recommended. 
 
 In progression by seconds rests the actual healthy life of melody 
 (therefore, the scale is really at all times the normal basis of 
 melody) ; and this is applicable even to the freest, boldest melody 
 formation. Leaps are not, indeed, excluded in melody ; on the 
 contrary, they form the most effective factors (vigorous arousing, 
 sudden collapse of energy, etc.); but they entail subsequent 
 complete, or, at least, partial, filling up of the gaps by means of 
 single-step progressions. 
 
 Only the bass part, whose exceptional position we have 
 
Chap. I. 
 
 Tonic and Dominant Harmonies. 
 
 »9 
 
 touched upon several times, is generally emancipated in greater 
 measure from the law of progression by seconds ; the bass readily 
 takes the fundamental notes of the harmonies (1, V), particularly at 
 the beginning and end (cf. p. 15), but may at all times correctly 
 proceed in seconds through other notes of the harmonies ; it may 
 also take the thirds of harmonies by leap, but then readily returns 
 (to fill up the gaps), for the specifically melodic reasons already 
 indicated. But it is altogether wrong for the bass to proceed by leap 
 from the fifth of the major chord or prime of the minor chord ; 
 proceeding by leap to this note (5, I), which is contradictory to the 
 fundamental note (therefore, not appropriate for the bass), should 
 also be avoided, particularly on the accented beat of the bar, 
 excepting in cases when this doubtful bass-note becomes funda- 
 mental note of the next chord (i.e., in the case of a "chord of 
 six-four," to which we shall refer further on ; cf. remarks about 
 Example 26). 
 
 If, after this rather detailed discussion, which, however, 
 exhausts pretty well all the rules for part-writing, we again attempt 
 to connect the tonic with its plain-fifth clang, the result will be 
 quite different from that reached at 19 (a)—(b) : 
 
 The seven progressions in this example are transitions from 
 the first form of the c-major chord given in Ex. 16, to the chord 
 of G-major ; they are all good, though the third (c) and the last 
 (g) only under the presupposition that the bass will not proceed 
 by leap from the fifth. The first (a) is absolutely normal, as the 
 bass proceeds from fundamental note to fundamental note, and in 
 both harmonies the latter is doubled, the note in common (g) 
 remains in the tenor (o), the leading-tone step (c—b) is made in 
 the soprano, and also the fourth part (alto) proceeds by second. 
 At (b)—(c) the bass moves melodically to the third and fifth 
 respectively, and the progression from fundamental to fundamental 
 is not made at all, as the other c also proceeds by second [at (l>) 
 soprano c"—d", at (c) soprano c" — b'}. Thus the doubling of the 
 fifth is brought about, which we know to be allowed. At (d) the 
 progression 1 — 1 (c" — g'), normal for the bass, is transposed into 
 the soprano, which is also at all times permissible. The cases 
 (e)—(g) are the freest ; at (e) and (/), the means of connection 
 by sustaining one note is missing ; at (<?) and (g) the leading-tone 
 step is also missing. But these progressions are also allowable 
 under the presupposition that the positions of the c-major chord 
 
Harmony Simplified. 
 
 [Chap. I. 
 
 were reached by stricter progression of the parts, and also that the 
 G-major chord proceed with better connection. Several such progres- 
 sions following one another without real melodic support would 
 be unwarrantable for the same reasons as those in Example 19. 
 On the other hand, the following progressions are faulty : 
 
 W <« 3 to . . <<0. , to . _ J (/) U ) 
 
 3 ' 8 '8 IS 
 
 (a) : consecutive octaves between soprano and bass : (b) : the 
 same fault, but aggravated by the doubling of the third of the 
 dominant. {Rule : Doubling the third of the major upper-dominant 
 and minor under-dominant, equivalent to the doubling of the 
 leading-note, is at all times — even in contrary motion — a bad 
 mistake] ; (c) : too great a distance between alto and tenor ; (d) 
 and (e) : the same between soprano and alto ; (/) : consecutive 
 octaves [by leap] between soprano and bass ; (g) : the same, but 
 in contrary motion [less striking, but not to be approved of]. 
 
 4TH Exercise. — Imitation of the seven different progressions 
 in Example 22, starting with the 11 other forms of the c-major 
 chord given in Example 16(a) (carrying out strictly the directions 
 for the distance of the parts from one another and for their total 
 compass). 
 
 The conditions for writing in minor are almost the same as 
 in major ; the plain-fifth clang (the under-dominant, °S) has one 
 note in common with the tonic (°T) (the A-minor chord [°e] with 
 the D-minor chord [°a~], the note a), and there is the possibility of 
 making a leading-tone step (e—f) ; on the other hand, it must be 
 noticed that the treatment of the V as fundamental note and as the 
 one best for doubling, stipulates a difference in the progression, as 
 not the V, but the I has the possibility of proceeding by second in 
 either direction (e — dund e—f). Therefore, in minor, doubling of 
 the I will occur more frequently than doubling of the 5 in major, 
 which only confirms the correctness of the view that the minor 
 and major chords are constructed on opposite principles. The 
 following are normal progressions in minor in imitation of the 
 first form of Example 16 (cf. Ex. 22) : 
 
 M (*) 1 to 1 W. to. (/) (?) 
 
Chap. I.] 
 
 Tonic and Dominant Harmonies. 
 
 Here at (d) — (/) the leading-tone step is missing ; a certain 
 disturbance of the facility of motion by the doubling of the V, 
 which arises from the imitation of the major, cannot be denied ; 
 for this reason, the doubling of the prime often occurs in minor, 
 excepting at the beginning and close ; also, in the course of 
 development, the bass often takes the third, by which means 
 greater mobility is gained : 
 
 STH Exercise. — Imitation of the progressions in Examples 
 24,25, starting with a considerable number of other minor chords. 
 
 We now proceed for the first time to the working out of a con- 
 tinuous example in 8 bars, which will give us occasion for a few 
 more observations. Take the exercise : 
 
 
 
 TD IT 7 .? \D ..\T..\DT\ 
 
 D T\ 
 
 5 
 
 5 
 
 In the first place, we must give a short explanation of this 
 figuring. The signs T, D we have explained (T= major tonic, 
 D = major upper-dominant) ; the numbers r, 3, 5, written below 
 or above, imply that the particular note (prime, third, fifth) is to 
 be in the lowest or highest part; the two dots (. .) indicate 
 repetition of the same harmony (but the alteration of the position 
 is always allowable and generally advisable) ; the perpendicular 
 strokes are the bar-lines, (P, the time-signature. No particular key 
 is prescribed ; on the contrary, all the examples given in this species 
 of notation are intended for working out i?i all keys (or at least 
 in a large number of keys). If we go to work, and choose for 
 the beginning the first position of 16 (a), in the key of A-major, the 
 attempt will probably turn out thus : 
 
 T D 
 
 26. < 
 
 (First model example.) 
 
 It should be well noted that the middle parts are here en- 
 trusted with the duty of keeping the other parts together, i.e., they 
 
2* Harmony Simplified. (Chap. I. 
 
 sustain notes as far as possible, and generally move within a 
 small circle. Only when the same harmony (. .) occurs twice in 
 succession [at (a) in the 2nd, 3rd, and 4th bars], progression 
 by seconds is naturally discontinued (as there can be no step of a 
 second between notes of the same clang), and all the parts (as in 
 bar 2), or at least several, move by leap. Such change of position 
 of a harmony should deliberately be made use of in order to gain a 
 good progression to the following/ the student should in such cases 
 always find out which position is rendered desirable by the bass-note 
 required for the next chord. — At (b) the bass leaps to the fifth, 
 which, on p. 19, we indicated as unadvisable in connecting 
 different harmonies. But when, as in this case, only the position 
 of harmony changes, it may be done without hesitation (also, 
 proceeding by leap from the fifth to the third or the fundamental 
 note of the same chord is admissible) ; but at the same time a 
 case occurs here, which we noted on page 19 as an exception, 
 when even with change of harmonies the bass may proceed by 
 leap to the fifth : the fifth is sustained and becomes fundamental 
 note (of the dominant). We will not delay the explanation of 
 this rule unnecessarily : the tonic with the fifth in the bass (T s ), 
 which generally appears as last chord but two (antepenultimate), and 
 which is follotved by the doininant leading to the closing tonic, is, in 
 reality, not tonic harmony, but rather a dissonant form of the 
 dominant, the so-called 
 
 Chord of six-four, 
 
 i.e., the dominant enters with two strange notes, namely, thi 
 fourth and sixth, which tend downwards to the third and fifth 
 of the chord, that is to say, with two suspensions. It is true 
 we shall not treat of suspensions till much later on; but this 
 chord formation is so indispensable, even for the simplest little 
 passages, that it seems imperatively necessary to introduce it at 
 the very beginning of the exercises, and to explain it properly. 
 The chord of six-four is the first of the examples of dissonant 
 chords under the cloak of consonance (feigning consonances), 
 which we shall often come across ; the doubling of the bass-note, 
 absolutely necessary in the chord of six-four, does not really mean 
 doubling of the fifth, but, on the contrary, doubling of the funda- 
 mental note (1 of the dominant). The student is to be warned, 
 in resolving the chord of six-four into the plain dominant harmony 
 (J f), against doubling the fifth, particularly in similar motion, 
 when it sounds simply horrible : 
 
 And thus the new numbers 4 and 6 appear in our chord 
 signs, the former indicating the (perfect) fourth lying a semi- 
 
chap, i.j Tonic and Dominant Harmonies. z$ 
 
 tone higher than the third, the latter the plain (major) sixth 
 lying a whole tone above the fifth. Finally, at (c), in the 
 closing chord, we have the first case of necessary omission of 
 the fifth before us, because the prime is prescribed for the highest 
 part. 
 
 Exercises 6 — n, in major (to be worked out in all major 
 keys up to c| major and c\> major). 
 
 (6) $ : T\D .. I T D\ T D\ T.. I D .. I T.. \-D*h TV J) 
 
 (7) '/« = TD T\ D .. T\ D . . A I T D T\D° .. * I T (J ) 
 
 5 3 I 3 I 3 I 3 I | ' 
 
 (8) $ : T x I D T I Z>' * I T . 3 . \D .. I T .. I Z>> D I T (a) 
 
 (9) $ z> I r d I r a I d . . I r . . i d t \ z>» * i r ( \j\ 
 
 '3 si 3 ' S 1 I 3 I I I Js 
 
 (10) ^^.T\DTD\T .. D*\?. TD\T..D\TDT\dAt( J I J) 
 I 3 '3 35I3 5 1^ (J •^.l' 
 
 1 1 
 
 (n) v 4 : ri.. Aiz>r|z>.. |rz'jrz)7'|.3 \o>h T(j) 
 
 N.B. — The note-signs after the last figure of each exercise 
 intimate the duration of the closing chord : those written under 
 the beginning of Exercise 1 1 indicate the rhythm to be carried 
 through. 
 
 Exercises 12 — 17, in minor (to be worked out in all minor 
 keys). 
 
 (12) $ : °T\°S°T I .'• °S\ T°S\°TS\ T ..\°S .. \°T( I J) 
 v ' ^ I I '" I 1 I in I 1 in I I \a±e*h 
 
 (13) %.: T 1 .". \°S.. IT.. \°S.. IT!'! I °S J 1 ! I TVS) 
 
 I in I hi I I I I * '" 
 
 (14) 3 A : °2" I °^ . . Tl 5 T"S\ T. . °S\T( J) 
 
 v *' " I III I III V I III I Ke3) 
 
 (15) »/ 4 : ^ '" .x I !s v ri ^ ».' A 1 t y _). 
 
 V ' ' 4 III I HI I I III I K ^ J 
 
 (17) $ : 'T'S I r '.'! I °S y. \T..\ S. . I 5.V „, I T (3,. 
 
 I III I I III I III I VI v I v • 
 
24 
 
 Harmony Simplified. 
 
 [Chap. i. 
 
 We must here, before all, supplement the explanation of the 
 figuring. As already indicated, the ° always demands an under- 
 clang ; Roman numbers, for indicating intervals measured down- 
 wards, likewise show that we have to do with an underclang, so 
 that the ° is then superfluous. In the last example the counterpart 
 in minor of the dominant chord of six-four in the major key, which 
 is well intelligible, is introduced ; naturally we must avoid placing 
 the i in the bass, for then the chord would appear merely as 
 tonic; similarly, the i must be doubled, for, as we shall see, 
 dissonant notes must never be doubled. This minor chord of 
 six-four is wanting in the principal means of effect of the chord 
 of six-four in major — the tension caused by the fourth and sixth 
 as suspensions from above of the third and fifth, and relaxed 
 by their downward resolution. It is just this higher or lower 
 position, this upward or downward relation, which produces 
 the different effect of major and minor, as the relations are not 
 congruent, but only symmetrical. 
 
 A second series of exercises will now follow (here and through 
 the course of the book) which are distinguished from the first, in 
 that one part is given completely (consequently also the key). One 
 given part often makes the best and most natural connection of har- 
 monies impossible ; if, e.g., for the harmony step tonic-dominant, 
 the melody step from third to third is given, then the leading-tone 
 step is made impossible (as the leading-note must not be doubled). 
 In these examples the harmonies are not indicated as tonic, 
 dominant, and subdominant, but by small italic letters (c, °e) indi- 
 cating their principal notes (1, I). In working out, the pupil is to 
 indicate the functions of the harmoies (viz., their significance as 
 tonic or dominant, etc., but without the numbers which refer 
 only to the progression of parts) ; in these first exercises this is a 
 very simple matter, but later on it will become more and more 
 difficult, and must, therefore, be made a duty from the very 
 beginning, if the attempt later on is not to prove a failure. Take 
 the following example : 
 
 (Soprano.) 
 
 N.B. — Where Only numbers, or + , or °, without clang-letter 
 or without . . , are placed by a note, it is itself (major or minor) 
 prime ; where there is no figuring at all (see the fifth note), it 
 is major prime ; the number, then, indicates the particular note 
 for the bass ; only where the latter is given, the number indicates 
 the note for the highest part. 
 
 The given part is so to be noted on the stave that the second 
 
Chap. I.] 
 
 Tonic and Dominant Harmonies. 
 
 -'5 
 
 part to be written on the same stave can be distinguished from 
 it (thus in the case in question all note-stems of the given soprano 
 are to be tinned upwards) ; when the soprano is given, the chord 
 signs are to be placed above the upper stave, when alto or tenor 
 are given, between the two staves, when bass, under the lower 
 stave ; also, at the beginning, above, or below the upper or lower 
 stave, it is to be indicated by cf. {cantus firmus, i.e., given part), 
 which part is given (these measures are necessary to spare the 
 teacher error in correcting [altering the cantus firmus]). The 
 example, worked out with the additional indication of functions, 
 would then look something like this : 
 
 28. A 
 
 T .. D .. 
 
 (Second model example.) 
 
 T D T D T D T 
 
 Z» 
 
 N.B. — Instead of \ after °, the abbreviated sign for the simple 
 overclang (major chord)" 1 " may be placed, as above, in the bar 
 before the last. This example is not wanting in progressions 
 which are deficient in smoothness (bars 1 — 2, 3, 5, 7); the student 
 should try to improve upon them ! 
 
 I. Major. 
 Exercises 18 — 20 (Soprano given). 
 
 g 5 3 d g 3 d g 3 d 
 
 bo f 3 5 3 f bo .. f A f 3 f b* J 
 
 3 a 
 
 a 5 3 5a 
 
26 
 
 Harmony Simplified. 
 Exercises 21 — 23 (Alto given). 
 
 [Chap. I. 
 
 / C 
 
 f c 
 
 3 c 
 1 
 
 Exercises 24 — 27 (Tenor given). 
 
 + fyb fy A 3 fy b ft ■■ ± fy b ft ■■ ± 
 
 Exercises 28 — 31 (Bass given). 
 
 ab .. di> ch J a\> db .. 
 
Tonic and Dominant Harmonies, 
 
 3^3 a gt * .. g%c%3g%\ +.. 
 4 4 
 
 II. Minor. 
 Exercises 32 — 34 (Soprano given). 
 
 Exercises 35 — 37 (Alto given). 
 
 IV III V I III I III 
 
 a - VIII III a o V. 1 .'. a a a d a °d .. a d .. . "a 
 I es » "iv 
 
 I I 
 
j8 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 Exercises 38 — 40 (Tenor given). 
 
 g B h /1 
 
 --&— - 
 
 -*—r 
 
 w-x-f- 
 
 ±x£z 
 
 1 I 
 
 1 I =t 
 
 Exercises 41 — 45 (Bass given). 
 
 °f °tn °f "bo O °fo °f . . °bo . . °f . . % °f °fo .. '/ 
 
 °dt 'as ■- °dt O "df "a; °d% ■■ °<z* °df V; .. °dt °ai°d% °a; 
 
 °et 'at .. O .. °as . . °et °aj "a °at o °at °es 
 
 § 4. CONTRA-FIFTH STEP (CONNECTING THE TONIC WITH THE 
 CONTRA-FIFTH CLANG: T — 5 AND °T — °D). 
 
 If, on the one hand, the transition from the tonic to the plain- 
 fifth clang appeared only like a natural continuation, a progression 
 to partial notes of the second order, making the fifth of the clang 
 
chap, ij Tonic and Dominant Harmonies. i<) 
 
 independent as the bearer of its own clang, on the other hand, 
 the transition to the contra-fifth clang (to the clang of the same 
 mode on the fifth of the opposite side) has an entirely different 
 significance. It must be defined as a forcible pressing back beyond 
 the starting-point of harmonic relations (the prime) : 
 
 T D < i 
 
 cTgTd and d JjJJ ~> * 
 
 v < 
 
 i > 
 
 "S T 
 
 The return from the plain-fifth clang to the tonic (D — T, 
 °S — °T) entirely coincides, indeed, in exterior, i.e., as regards the 
 means of melodious connection, with the contra-fifth step, but has 
 an entirely different meaning ; it is only a retrograde formation of 
 that which had grown out of the tonic prime, a simple return, 
 whereas the contra-fifth step — presupposing the consciousness of a 
 tonic as a fixed point in the change of harmonies — causes an 
 artificial suspense, which renders a marked forward motion neces- 
 sary. The contra-fifth clang is the stretched bow which slings 
 the arrow beyond the mark (the tonic). This applies to major as 
 well as minor. In major the contra-fifth clang (the under- 
 dominant, subdominant, abbreviated S) forms a receding down- 
 wards beyond the tonic, which itself strives upwards from its 
 fundamental note : therefore, a pressing down below the level, 
 whence it again powerfully forces the harmony upwards ; in minor 
 (as minor upper-dominant, abbreviated °D) it is as a pulling up- 
 wards, an artificial lifting beyond the starting-point (the minor prime) 
 from which the tonic develops downwards and generates the 
 plain-fifth clang : therefore the contra-fifth clang in minor presses 
 heavily downwards into the region of the dependencies of 
 the tonic. For this reason the contra-fifth clang is generally 
 not followed by the tonic itself; this simple solution of the 
 conflict caused by its introduction is not — at least at decisive 
 points of the harmonic development — satisfactory or sufficient ; 
 rather, the contra-fifth clang is generally followed by the plain- 
 fifth clang, which, then, leads back to the tonic in a thoroughly 
 satisfactory manner, and closes restfully. The clang successions 
 T—S—D—T and °r—°Z)—°S—°r are, therefore, really typical 
 for harmonic motion in general ; they are so-called complete (bilat- 
 eral) cadences. With the addition of this new element (the contra- 
 fifth clang), our exercises for the first time lose a certain stiffness 
 and one-sidedness — the latter in the full sense of the word, as, so 
 far, only one side of the tonic has been represented, whereas now 
 both will be represented. The following group of exercises still 
 abstains from connecting the two dominants directly (on account 
 of the risk of the worst consecutive fifths being incurred), 
 and either the tonic or the feigning consonant formation of 
 
3° 
 
 Harmony Simplified. 
 
 [Chap. 1. 
 
 the chord of six-four, already known to us, is inserted between 
 the contra-fifth clang and the plain-fifth clang. 
 
 The introduction of the contra-fifth clang after the tonic, its 
 return to the latter, and its transition to the chord of six-four, 
 give rise to no difficulties which would render new observations 
 necessary. 
 
 ^llippl!Sl 
 
 J] 
 
 Now, again, exercises without given part follow, only indicating 
 the harmonies as tonic, dominant, etc., in the fashion of the first 
 series in the last paragraph, which are to be worked out in all 
 keys ; these exercises, as already remarked, are the easier ones, 
 for, so long as the progression of parts is not restricted by the 
 fixing of certain notes for the bass or for the highest part, they 
 allow of the most normal ways of connection. 
 
 (46)$ 
 (47)$ 
 (48) % 
 
 (49) V. 
 
 (50) s 
 
 Exercises 46 — 51 (Major). 
 T D\T S\T D\T D\T S\D* " I T. 
 
 T S T\D T 
 
 6 + 
 
 3 
 
 r s .. I d< s 
 
 3 1 
 
 S \T .. S I T ,. S\T D T ID 
 
 I 3 1 3 I 5 3 I 3 '• 
 
 T \S T S 
 
 T S T\D t. ?. 
 
 S 5 I 
 
 T iJ). 
 
 T S\T 
 
 I 3 
 
 \D T\D „\T D\T S\D* " 
 
 3 I 5 3 I S ' i I 
 
Chap. I.J 
 
 Tonic and Dominant Harmonies. 
 
 3i 
 
 (si) V, 
 
 T D\T S T\S ?. T\S T \D T S\ 
 
 3 1 3 S 1 3 1 3 S 3 1 1 
 
 T D T 1 S J> * j T ( J) 
 
 5 3 1 1 y <="' 
 
 6 + 
 
 & " 
 
 3 
 
 (53) % 
 
 (54) % 
 
 o rr> 
 
 Exercises 52 — 57 (Minor). 
 
 (52) $ : °T\S .. I T D\°T S\ T D\ S I T S\.. .. I 
 I "I v I in 1 I I 1 v I iv in I 1 ml v in I 
 
 VI v 
 III 1 v 
 
 7 1 D T\S .. T\°D .. °T\'S °T °S\ .. .. "IT 
 
 I in V III I III I IV III I 
 
 VI V 
 
 "T "D I T °S I °T S\°T ..\°S ™\ T ..\S ,.\'T. 
 I hi I ml in I I in 1 I in v I 
 
 (55) 3 A : "T S I T . . °S I T . . . . I "D T °S\°T. 
 
 in I 1 in I in I in I 
 
 (56) § : T D\T S\T °S\ T °S\T °D\T °S\°T °S\°T. 
 
 I III I I | III I V I III I 
 
 III III 
 
 (57) $ : D I T S I "T °S I "T ™\°D ..\°T °Z>\S \°T. 
 
 I I" I I I III I I IV III I . 
 
 VI V 
 
 A second series of exercises with one given part and direct 
 indication of the clangs is intended for acquiring dexterity in 
 smoothing interruptions in the normal connection, caused by 
 abnormal steps in one part. The pupil is to indicate the func- 
 tions of the single clangs (as tonic, dominant, and subdominant) 
 in each exercise worked out, as was the case in Exercises 29 — 45 : 
 
 I. Major. 
 Exercises 58 — 60 (Soprano given). 
 
32 
 
 Harmony Simplified. 
 Exercises 6i — 63 (Alto given). 
 
 [Chap. 1 
 
 ea + + b*+eb b e a b* t 
 
 63. 
 
 
 mm 
 
 m^E^M^ 
 
 =2=S=zfl= 
 
 ^J 
 
 -5 ctf •• f% 
 
 Exercises 64 — 66 (Tenor given). 
 
 £•& di> c\> .. A 4 f. go dn 
 
 3 
 
 + 
 N.B. 
 
 «5- 
 
 »g^ 
 
 -4=45: 
 
 g^g ^% , (= 
 
 £=§ 
 
 J +..gSCS/t'rtgt-Ct+.. fy ..Ct + A 1../JCJ 
 
 335 s 4 v 1 
 
 i-^Eg 
 
 =t=li=f=?=|=fE: 
 
 Ei 
 
 S= 
 
 zt^fct 
 
 =t==t 
 
 3 g <l 
 
 5 ■■ d 
 
 Exercises 67 — 69 (Bass given). 
 
Chap, i.] Tonic and Dominant Harmonies. 33 
 
 69. 
 
 dt> ai 
 
 d\> + . . gb . . do 
 
 65 
 4 3 
 
 II. Minor. 
 Exercises 70 — 72 (Soprano given). 
 
 Exercises 73 — 75 (Alto given). 
 
 74- 
 
 j ■ J | 1 -p- i rn -r- -| 
 
 75- 
 
 yj °£ .. °c% .. °^ °ft a b °/ 
 
 
 -* ^> ~. • —• 
 
 ill III III 
 
 d g d "a "d °g o a °d o .. °d 
 
 Exercises 76 — 78 (Tenor given). 
 
 o .. o ..°gt .. °c% °g% o .. °g% . . d% °gt Vj . . o Vi o 
 in hi 1 
 
34 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 =t: 
 
 ia@^ 
 
 =t= r t=E 
 
 f °c f "to 'fib °f ..°c. °f .. O .. J 
 
 l HI 
 
 "at °d% o °e% "at °dt . . °a% °e% . . o °d$ .. o 
 Exercises 79 — 81 (Bass given). 
 
 °g °d °g " c O °c °g V °g o °g V °g °c "g 
 
 'c "/ o°z "c . . °g °e °f . , °c . . °f 
 
 o °gt °dt o °dt °gt O a%.. °dt °gt o °g$ .. "df 
 
 N.B. — For the first time in Exercise 65, a slur from the 1 in 
 the sign of the third chord from the end to the 1 of the last 
 chord is used to indicate that the bass-note (ct) is to be sustained. 
 There the c% is also an element of the middle chord (5 in/j + ) ; 
 later on we shall find this method of indication very useful in 
 expressing and explaining in a simple manner the most com- 
 plicated formations of the so-called Pedal-point. 
 
 § 5. THE WHOLE-TONE STEP (S — D AND °Z> — ° S). 
 
 The direct connection of the plain-fifth clang with the contra- 
 fifth clang, as has been pointed out, brings with it the risk of 
 the worst of all consecutive fifths, viz., fifths rising or falling a 
 
 whole tone while their notes have the significance $~? and v ~ v 
 
 respectively (actual harmonic consecutive fifths) : 
 
 C Major : A Minor : 
 
 32- 
 
 l^SESs 
 
 m 
 
 ^^m 
 
 S—D 
 
 °D—°S 
 
Chap. I.] 
 
 Tonic and Dominant Harmonies. 
 
 35 
 
 Our principal rules for the progression of parts form, indeed, 
 a pretty sure guarantee against such error ; why should we 
 take whole-tone steps in all the parts, and, as in Example 17, 
 introduce two harmonies in similar position after one another? 
 For in so doing, are we not neglecting the best possible step, 
 viz., the leading-tone step ? Let us make the leading-tone step, 
 and the other parts are immediately led into their proper paths, and 
 the danger of conseactive octaves and fifths disappears without trace : 
 
 As at (a) c proceeds to b, the alto cannot also take b, because 
 the latter may not be doubled; consequently it is forced down 
 to g. The tenor will have to take d, else this would be missing, 
 if we retain the desirable bass progression from fundamental note 
 to fundamental note. At (c) the relations are entirely similar : 
 /must not be doubled; if e proceed to f,g must go to a, and b 
 will be directed to d. At (b) and (d) an excellent connection of 
 the two chords is made by doubling the 5 in S, and the I in °Z>. 
 
 The state of matters is worse, however, if one given part 
 renders the above normal mode of connecting the harmonies 
 impossible, e.g., for/ + — g + : 
 
 («) 3 
 
 (i) 5 
 
 W 5 
 
 1 (d) 
 
 (<) 1 
 
 For, at 34 (a) and (e), and also at 35 (a) and (e), the leading-tone 
 step is made impossible ; since the leading-note itself (3 of the 
 I) and III of the °S respectively) may not be doubled, the c in 
 f + —g+ must not proceed to b, if a has proceeded to b [34 (a)], or 
 /to b [34 («)], and in °b—°a, e must not go to/ if g has gone to/ 
 [35 (a)], or b gone to / [35 (e)] ; therefore, in these four cases, the 
 leading-tone step must be sacrificed ; in major : 
 
36 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 [34 Ml 
 
 (/) N.B. O5 i.g) (h) bad 
 
 and similarly in minor : 
 bs(«)] 
 
 37- 
 
 (1) good (£) good 
 
 [35 Ml 
 
 / J* " J J 'II J = II 1 if 
 
 ■ , ,,,. . J..J ,.. 1 J.. 
 
 
 TTT^J— |flj^.-^ f j|J ffcf 
 
 Si*! rv r f- r 
 
 ■s- J J J 1 J 
 
 
 ft): p g- f* 1 p |-fj ^ 1 
 
 
 V 
 
 1 p. U_| p_. U_|- p — u -f <- — II 
 
 («) 
 
 (3) 
 
 W (<0 
 
 M 
 
 CO <*•) 
 
 But little need be added. At 36 (a) and (/) the bass part 
 leaps a third to the fifth of the dominant ; the effect is not 
 entirely good, for reasons already known to us (viz., because 
 taking the fifth in the bass part by leap readily gives it added 
 importance, and raises the impression that we have a chord of 
 six-four before us, cf. the remarks to Example 26), but it must 
 often be allowed for lack of better ways. Just in this very case, 
 however, the actual effect of a chord of six-four is excluded, as 
 coming after the under-dominant the upper-dominant in any 
 position marks the key very pointedly, and a resolution of the 
 chord of six-four into the chord of five-three (in this case the 
 resolution of d\ into d + ) must appear illogical, because it would 
 contradict the key again. At 36 (d) and 37 (d) the third of the 
 subdominant is doubled in order to open up other ways ; but it 
 must be presupposed that the third doubling was not the result 
 of parallel motion. At 36 (g) and (h) three parts proceed by leap, 
 an expedient to be resorted to only in extreme cases. 
 
 Such cases as 34 (3) and 35 (b) are also very disagreeable, 
 particularly when the step 5 — 5, or I — I respectively, is given in the 
 soprano or bass part ; in the former case, because then the 
 succession of the two fundamental notes is impossible (on 
 account of consecutive fifths necessarily arising), in the second 
 because the effect of two chords of six-four in succession is the 
 
Chap. I.J 
 
 Tonic and Dominant Harmonies. 
 
 37 
 
 result (that placing the minor prime in the bass may produce the 
 effect of six-four will be explained in the next chapter, which 
 introduces the contra-clang of the tonic). The ways of evading 
 the difficulty are : 
 
 [34 WJ 
 
 ia)lc/. 36 (i)l 
 
 135 (*H 
 
 Here at (e), (d), (e), (/), and («') even the leading-tone step could 
 be preserved. 
 
 There now remain the abnormal leaps given at 34(c) and (d), 
 and 35 {c) and (d), of which only 34 (d) gives rise to particular 
 difficulties : 
 
 b« <</»[«/ 36(A)] 
 
 I 
 
 
 In seven of these cases, indeed, the leading-tone step had to be 
 given up. 
 
 Another problem which this succession of harmonies for the 
 first time brings before our notice is the possibility of a part pro- 
 ceeding by an augmented interval ; the step from the prime of the 
 
33 
 
 Harmon^' Simplified. 
 
 [Chap. I. 
 
 contra-fifth clang to the third of the plain-fifth clang (/— 3 and b—f 
 respectively) is good only as fifth (diminished, i.e., too small by a 
 semitone) ; on the other hand, it is bad as a fourth (augmented, 
 i.e., too great by a semitone, tritone [three whole tones : 
 f . ■ g . ■ a . . fr\). Good melodious setting, which must always 
 be our norm, has to avoid the tritone under all circumstances (at 
 least with changing harmonies ; when possible within the same 
 harmony, it may be allowed without hesitation, so long as it does 
 not incur the violation of the most important melodic principle — 
 turning after leaps; i.e., f—b [rising], is good, while the same 
 harmony is sustained, if a can and does follow, an exception 
 which is of consequence in the treatment of the chord of the 
 under seventh, as we shall see later. For the present we must 
 accept the prohibition of augmented intervals without any 
 exception). 
 
 After this detailed examination of the difficulties which meet 
 us in writing the whole-tone step, and having settled the means of 
 overcoming them, we may introduce the direct connection of the 
 two dominants in our next exercises, which will thus gain in 
 variety. We again give two series, first, such as have no given 
 part and no key determined, in which so long as certain bass 
 progressions or notes for the highest part are not demanded, the 
 usual connecting of the two chords shown in Example 33 is 
 possible, and secondly, such as cause particular difficulties on 
 account of the given part. In working out the latter, the indica- 
 tions T, D, S, or °T, "D, °S, respectively, are to be added, as has 
 been done hitherto. 
 
 So as gradually to accustom the pupil to reading a score 
 consisting of many staves, and, foremost, to prepare him for writing 
 in the so-called " four clefs," the next exercises are no longer to 
 be worked out on two, but on four staves, in such a manner that 
 soprano and alto are noted, as hitherto, in the treble clef, and 
 tenor and bass in the bass clef, but every part on a separate stave, 
 as in the following model example : 
 
 6 S 
 
 40. \ 
 
 (Third model example.) 
 
Chap, i.j Tonic and Dominant Harmonies. 39 
 
 As in this case every part has a stave to itself, it is not 
 necessary for the soprano to have all the note-stems turned 
 upwards, etc. ; on the contrary, the calligraphic rules come into 
 force that all notes lying above the middle line should have their 
 stems turned downwards, all lying below, turned upwards, while 
 for notes on the middle line either way is equally good. 
 
 Exercises 82 — 93 (Major). 
 
 (82) %\ T\DT\ SD\ T .. I D.. I TS\D .. I T ( I J) 
 
 I I 3 ' 3 I 3I 31\ -J^ 
 
 (83) *l,\ T S D\T S T\D S T\S D ..\T S D\T S..\ 
 
 3 I 3 I 3 s I 3I I 3 I 
 
 /?' 5 D I T{ = .) 
 
 (84) 6: T\ 5 . . Z>' 3 I T S D T\ S .. D . . \TIJ \ 
 
 (85) 3 /„: T S D \T S D \T D T\D .. \TST\SDT\ 
 
 (rr) 
 
 5 £?** I T(J) 
 
 (86) %:T\D..\TS\..D\TD\TS\..£>\T*, I * (J) 
 
 I 3I I i I si I3 I I 
 
 (c r c-c) 
 
 (87) $: rz> i^ri 5 z? I rz> irjp5|Z)'»|r.( o ) 
 
 I I 3 I 3 s I 3I3 I ' 
 
 (88)»/ 4 : SD\T„\SD\TD\TS\D S^&If^T^.) 
 
 (f r r reto 3 
 
 (8 9 ) 3 / 4 : 2"| 5/> 3 | 7-.. I 5,0 I 7\. I 5/7 5 I DT\ SD\ T 
 
 (rrrrn (r r r r r) 
 
 (90) fi : r/)| T5Z> .. I TD TD\ 5.. Z* » I r Q) 
 
 V7/ 3 3 3 I S3 '3 l v/ 
 
4° 
 
 Harmony Simplified. (Chap. I 
 
 (91) »/«: T D\T S D T\D S T S\D i S D .. | 7* 
 
 (Ca* re Car re c*- rccsf r) 
 
 (9a)'/.: riszH r.. I5Z7I r^ir5ris..|z>..l r(j) 
 
 (e re re) 
 
 (93) -/ 4 : r.. J 0|rsi J p..riz>sirsz>|rsz>|rz>|ry) 
 
 (: r C) 3 (c r c) ( e r e c r c ) 3 
 
 Exercises 94 — 100 (Minor). 
 (94) &:°T\°S°T\ £>S\ T'S\T .. \°D°S\ T °S \°T ( |j 
 
 V7 ' I I ml 1 I in I I in I vt "x_L-" 
 
 (qc) i/ : °T \ S T °S \ T °D \ S °T °S \ T * °S \ °D °T °£> \ 
 V ' J I in 1 ! in I in I in I 1 
 
 rn 
 
 °S .. I °T(o.\o) 
 ( 9 6) 3 / 4 : T °Z> I T °S\ °T°D °S | °2" .. °S \ °T .. °D \ 
 
 (r r r r) 
 
 °^ •• r^(jjj.) 
 
 (f"D 
 
 (Q7) 3 /s : "^ I "-O "^ I T ^ I r°Z> I 5 . . I T°Z> I °£ . . I "T (J. |J\ 
 
 v I I I in I v in I 1 I \ - — / 
 
 (U I U I etc.) 
 
 (98) E: °T°S °T °£> I "5 . . T I °Z> °£ T "^ I f "S °7* 
 
 1 I in 
 
 1 > 1 i 1 1 r 1 & 1 1 ) r 
 
 (99) &: °T°S \ T S I r Z> I "S r I "£> "S I . . T I Z> °,S I °T 
 
 I III III I I V I III I I III I I V I 
 
 (ioo)7 4 : °T\°S'>T\°D'>SV'T°SV'T°S\ T°S\ T°D "S I T (J | J \ 
 
 (> I & etc.) £ I U 
 
 The notification of a certain rhythm (by means of ,^| J or 
 ^JTJIJ. etc., under the figures) scarcely requires any further 
 explanation. There would be no meaning in continuing to write 
 
chap, i.] Tonic and Dominant Harmonies. 41 
 
 exercises in equal notes after the manner of chorales ; on the 
 contrary, practice in four-part writing will be of the greatest 
 advantage, if so planned as to incite and fructify the talent of a 
 gifted pupil, instead of fettering it and sending it to sleep. 
 
 I. Major. 
 Exercises ioi — 103 (Soprano given). 
 
 b e ft .. 3 b .. e .. ft'f 
 
 do go J go do do do ao . . do. .go ao do ao + go . . + 
 
 Exercises 104 — 106 (Alto given). 
 
 eodo eo . .do 
 
 + db 5 do eo aodo .. do 
 
 bo c .. f bo c* bo c 
 
 Exercises 107 — 109 (Tenor given). 
 
 d e 3 e 3 e 
 
 e .. + d . . e .. 
 
42 
 
 Harmony Simplified. 
 
 [Chap. I 
 
 mzsE 
 
 i r 
 
 * a» + 
 
 bo 4> .. aobi J 
 
 6 5 
 4 3 
 
 * 
 
 /J +/f 01 J • • <^» .. + ../»+..<:» £ Of 4 A/j 
 
 Exercises iio — 112 (Bass given). 
 
 110. 
 
 
 
 
 ■ 1 , I 
 
 
 
 
 f. & 
 
 
 ^n 
 
 III. 
 
 J do do 
 
 •■ 
 
 g* ■ 
 
 
 1 
 
 do 
 
 65 
 ■43 
 
 + 
 
 — -11 
 
 112. 
 
 
 
 3Z= 
 
 d d 
 
 1 ' 1 1 ' ' 
 f 1 1 
 
 1 r* 1 
 
 
 a 
 
 .. d 
 
 a 
 
 m 
 
 -=NI 
 
 go 
 
 f bo & 
 
 II. Minor. 
 Exercises 113 — 115 (Soprano given). 
 
 "ft o °b "fy ■ ■ °b °ct °b o . . °b f% O b °fy V °b °fy 
 - — in - - 1 in v - 
 
Chap, i.) Tome and Dominant Harmonies. 
 
 43 
 
 Exercises 116 — 118 (Alto given). 
 
 °C% °fy O O °g% "f t O °g% O °CS O °g% "ft O 
 
 °g o °c 
 
 °d °c o . . "d V o V °d "c 
 
 °gt o o °g; "dt Vj o °ct o °d$ °c% o Yjj 
 Exercisfs 119 — 121 (Tenor given). 
 
 -!«- g- -m- 
 
 °dt"gi "dfas o . . d.'gi V; "at Cat o"gt"d}"a;"gt . "dt 
 
 §§££i^ 
 
 m 
 
 & 1 5 
 
 ' ' 1 
 
 ^£a 
 
 "/ V "bo f..V°fc°b> o °c bo .. / o 
 
 "f 
 
 O °df "at o V .. o 'dt "at "et III .. "at 
 
 Exercises 122 — 124 (Bass given). 
 
 % V °« °fo °eb "/ V> 'b> . . o o "bo "a °bb 
 
 °b .. o °e°b °e .. "ft "e .. .. °b "ft °e "b "ft °e °b °e .. °b 
 1=4- .„. 
 
44 Harmony Simplified. [Chap. I. 
 
 § 6. THE TURN OF HARMONY {T— °S AND °T— + D), CONTRA- 
 FIFTH CHANGE (°S — D + ) AND FIFTH-CHANGE (°S — +S AND 
 °Z>— Z>+). 
 
 If the contra-fifth clang coming after the tonic appeared like 
 proceeding in the opposite direction beyond the uniting point of 
 harmonic reference (pressing down below the level in major, 
 forcible drawing upwards in minor), therefore, in a measure, as a 
 step in the sense of the contrary clang principle (the contra-fifth is 
 under-Hfth of the major tonic and upper-fdth. of the minor tonic), 
 we cannot be surprised, if, beside the fifth of the contra-side, also 
 the third of that side be used, and the complete contra-clang be 
 placed in juxtaposition to the tonic, so that, in place of the direct 
 relatives of the overtone series, the direct ones of the undertone 
 series appear in company with the prime, and conversely : 
 
 Major : Minor : 
 
 N.B. °S D °S Z>+ N.B. 
 
 d f a c e g% b 
 
 • — r— ' > 
 
 In place of the marked tension peculiar to the contra- 
 fifth clang, the contra-clang (or " turn-of-harmony clang ") of 
 the tonic produces a transient contradiction of the mode, a 
 mixture of major and minor relations, which, it must be admitted, 
 is characterised by a certain artifkialness and excitement. After 
 the major tonic, the minor under-dominant — for the contra-clang 
 is that — appears like a sorrowful glimpse into the gloomy region 
 of minor relations, and, conversely, in the major upper-dominant 
 of the minor key, we must see a yearning straining upwards into 
 the bright domain of major relations. So much is certain — pure 
 minor as well as pure major, in opposition to these mixed modes 
 arising from the introduction of the contra-clangs (so to speak, 
 "minor-major" and "major-minor"), seem like healthier, more 
 original, simpler formations ; this is sufficiently indicated by the 
 fact that the contra-clang contradicts the scale: a\t is foreign to the 
 signature of c major, and g§ to that of a minor. The mixed 
 modes are an acquisition of modern times ; they were unknown 
 to antiquity and the middle ages. 
 
 The tonal function of this new harmonic formation must be 
 explained by its origin. Tlie contra-clang of the Tonic is really 
 a plain-fifth clang of the Tonic- Variant, i.e., of a tonic of the 
 other clang-mode*); the F-minor chord (°c) in c-major is really 
 
 * For this reason we do not indicate the contra-clang of the major tonic as 'T 
 (underclang of the tonic), but as "S, and the contra-clang of the minor tonic not 
 as T + but as D+, and in c major understand by 'T the c minor chord, and in 
 A minor by T+ the A-major chord (for which more reasons will be adduced 
 later on). 
 
chap, i.) Tonic and Dominant Harmonies. 45 
 
 the plain-fifth clang (subdominant) of the c-minor chord, the 
 E-major chord in A-minor is really the plain-fifth clang 
 (dominant) of the A-major chord, so that the introduction of 
 the contra-clang, strictly speaking, means borrowing a harmonic 
 relation which is obvious and quite natural in the other 
 mode. This is equivalent to saying that the contra-clang must 
 not be looked upon as taking the place of the contra-fifth 
 clang, but, on the contrary, as side by side with the plain-fifth 
 clang, as another means of making a perfect cadence borrowed 
 from the contrary mode [hence, also, the generally recognised pos- 
 sibility of closing with the tonic of the opposite mode after paving 
 the way by means of the contra-clang, at least in the minor key 
 [also possible in the major, but seldom used for aesthetic counter- 
 reasons]). To introduce the contra-clang simply in place of 
 the contra-fifth clang in the two perfect cadences T — S — D — T 
 and °T- — °Z> — °S — °T would not be right ; in so doing we should 
 simply be setting aside a highly important element of the cadence 
 (the tension caused by the contra-fifth clang cannot be replaced 
 by the contra- clang). We might sooner think of replacing the 
 plain-fifth clang by the contra-clang : 
 
 T—S—°S—T and "T— °D— Z>+— "T. 
 
 It cannot be denied that these two cadences still contain the 
 characteristic effects of motion towards a foreign clang (contra- 
 fifth clang) and satisfactory closing (by means of the step contra- 
 clang — tonic). The attempt at a contrary combination, viz., 
 deferring the contra-clang till after the plain-fifth clang : 
 
 T— D— °S— rand °T— °S— Z> + — T 
 
 even proves the cadential power of the contra-clang greater than 
 that of the plain-fifth clang, i.e., the contra-clang after the plain- 
 fifth clang already seems like a decided return towards the start- 
 ing-point ; all that remains to be done is to turn about the 
 prime as about a pivot. This form of cadence is generally 
 recognised for the minor. But there is no reason for dropping 
 either of the dominants proper to the scale in favour of those 
 foreign to ihe scale, i.e., ultimately the natural place for the contra- 
 clang is at the close of the cadence, even if the contra-fifth clang 
 and plain fifth clang have already been introduced : 
 
 T—S—D—°S— T and ° T—°B—°S— D +— ° T 
 
 Cadences are not, of course, musical pieces, and, therefore, 
 the importance of these remarks must not be overrated ; but, on 
 the other hand, it would be quite wrong to underrate them ; for 
 they are undoubtedly just as much types of harmonic develop- 
 ment as scales are types of melodic motion. 
 
 With the introduction of the major upper-dominant the minor 
 
4 6 
 
 Harmony Simplified. 
 
 [Chap, l 
 
 key acquires the chord of six-four, which is so important in 
 preparing cadences ; but the chord of six-four of the + dominant 
 of the minor key naturally has a minor sixth, corresponding to 
 the third of the tonic (chord of minor sixth and fourth). It is 
 distinguished in figuring by a > applied to the 6, which indi- 
 
 6> 
 
 cates that the sixth has to be lowered a semitone (e 4 = e a c ; 
 
 6 
 
 e 4 = e a c § !). 
 
 We must now, before proceeding to new exercises, examine 
 the connection of the contra-clang with the tonic and the other 
 clangs hitherto considered, in practical four-part writing. The 
 steps T 4 " — °S and °T — Z> + (turns of harmony) prove superior to 
 the plain-fifth step, firstly, in that they offer the possibility of two 
 leading-tone steps : 
 
 
 ■ Q z^g^r^^r [I — h 
 
 
 vt) — '■ — ,~^ r 
 
 1 — := ^ j - *-**?-~ 0m ^ ? — H 
 
 42.- 
 
 _-h-.-^_ . . 
 
 -G>-^ m - i=S ^&- 
 
 
 
 
 
 
 I— S £-£ '—*. U 
 
 
 
 
 
 
 ■&- 
 
 Besides, we have, as in the plain and contra-fifth-steps, a 
 
 111 III 
 sustained note (a note in common : c c c and e e e respectively), 
 
 and the unhindered succession of the two fundamental notes, 
 the doubling of which meets with no check. But this succession 
 of harmonies also brings a new problem with it, inasmuch as the 
 step from the third of the one clang to the third of the other is 
 allowable only under certain conditions : 
 
 e — a\> rising and c — %$ falling are diminished fourths (4 > ), e — «b 
 falling and c — g% rising are augmented fifths (5 < ; [ < , the inver- 
 sion of > , indicates raising a semitone] ) ; we have, therefore, 
 first an augmented interval (5 < ), which is altogether forbidden as 
 a part progression, and further a diminished one (4 > ), which is 
 only good if it can proceed correctly. All augmented and dimin- 
 ished part progressions necessitate a subsequent semitone step, the 
 augmented ones further away in the direction of the step already 
 made (for which reason they almost without exception contradict 
 the melody principle mentioned on page 18 — turning after leaps — 
 and are therefore bad), the diminished ones, on the other hand, 
 turning again (by which means they attain a specifically melodic 
 character). But diminished steps are good, only on the supposition 
 that a turning semitone step follows ; if the latter does not follow 
 
chap, i.) Tome and Dominant Harmonies. 47 
 
 or is impossible, the diminished step also is bad. The first con- 
 sequence of this is that the diminished step must be excluded in 
 cadences : 
 
 (bad) (bad) 
 
 But we must further remark that the rhythmical position is 
 of the greatest importance in estimating diminished as well as 
 augmented intervals ; as in the case of a real close, so in general 
 in progressionsfrom less accented to more accented beats, it is not goof 
 to introduce steps which call for subsequent proceeding by semi- 
 tone (namely, augmented and diminished steps) ; whereas, in going 
 from an accented to an unaccented beat, provided that the 
 subsequent semitone step takes place, even augmented intervals 
 are not very objectionable (but they must be avoided by the pupil, 
 as he must first acquire absolutely normal ways, naturalness, 
 smoothness, and fluency in writing). Therefore : 
 
 T °S T "T D + "T D T °S T °S °T D + °T 
 
 (good) (good) (not bad) (not bad) 
 
 The connection of the contra-clang with the plain-fifth clang 
 (Z> — "S and "S — Z>) meets with the same risks as the whole-tone 
 step (consecutive fifths and octaves), but a few new ones in 
 addition (augmented and diminished intervals). As, in the first 
 place, from the one clang to the principal note of the other there 
 is a contra-fifth step : 
 
 c < — g b d and d f a — > e 
 
 but the mode is also changed : 
 
 < — V . . . g — > and <£ — °a . . . e — > 
 
 we must indicate this succession of harmonies as a contra- 
 fifth change. The consecutive fifths which threaten us in writing 
 the contra-fifth change : 
 
 _s 1 
 46."* 
 
 are not, indeed, so very bad as those in the whole-tone step, 
 since the notes have not as in that case parallel significance 
 (here fZy, there fzf and v -v)> Dut they are, nevertheless, not good. 
 
*3 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 The other hindrances in writing are (besides the b—f in 
 common with the whole-tone-step, in both cases) : 
 
 another augmented fourth (bad) or diminished fifth (good), an 
 augmented second (2<, bad) or diminished seventh (7=-, good). 
 But as equivalent for these hindrances, we find two leading-tone 
 steps (3 — I and 1 — III) : 
 
 But any way, a great number of the progressions indicated for 
 the whole-tone-step become impossible, as a comparison, by no 
 means superfluous, with the last § (Examples 36-39) will show, 
 viz. : 
 
 NB. 
 
 [36(a)] [36 0)] 
 
 NB. H NB. 
 
 [36(c)] 
 
 \3T(<*)1 
 
 [37 (*)] 
 
 [37 Ml 
 
 I37OO] [38 0>] 
 
 NB. 4 . 
 
 (38(/)] 
 
 [38(f)] [38(*)| [ 3!) («)) 
 
 (39 Wl 
 
 [39(A)] 
 
 [39 (OJ 
 
 [» «1 
 
 t39(>«)] 
 
 [»<»)) 
 
 In four cases (at N.B.) even doubling of the third would occur, 
 which is altogether forbidden for the contra-clang. A few new 
 ways are opened to us by the step of the diminished seventh 
 
Chap. I.] 
 
 Tonic and Dominant Harmonies. 
 
 49 
 
 a step much better than that of the minor or major sevenths, 
 which, for that reason, we have altogether disregarded : 
 
 The result of connecting the contra-clang with the contra-fijth 
 clang is likewise a new harmony step, which we must call the 
 (plain) fifth-change, since the principal note of the second clang is 
 the plain fifth of the first, and the clang-mode changes : 
 
 / + ^ 
 
 >"£ 
 
 and 
 
 The clangs constituting the contra-fifth change appeared quite 
 foreign to each other (see above), but on the other hand, those of 
 the plain fifth-change are very closely connected, as they have 
 both notes of the interval of the fifth in common (though with 
 inverted meaning) and only differ in the third : 
 
 a 
 
 
 gt 
 
 f c 
 
 and 
 
 e b 
 
 ab 
 
 
 g 
 
 But with the introduction of this step we have a new part progres- 
 sion (the chromatic semitone) and also a new problem, that of 
 false relation. 
 
 The chromatic semitone step has even more undeniable claims 
 to consideration, than the diatonic (leading-tone step) ; if, in the 
 fifth-change, we neglect introducing both thirds in succession in the 
 same part, the result will be that ugly effect which is cried down 
 under the name of false relation (Ger. Querstand). Our ears 
 are then not able to perceive the change of harmony, and are rather 
 deceived into the belief that the same harmony is sustained ; and 
 so the chromatic note only appears out of tune. The effect is all 
 the more disagreeable, the less marked the part is which intro- 
 duces the second third, and the further the latter is distant from 
 the first as regards octave-position (real pitch) : 
 
 5'- 
 
5° 
 
 Harmony Simplified. 
 
 [Chap. 1. 
 
 Here (a) and (c) are particularly bad, as are also (Z>) and (d), 
 though the effect is somewhat mitigated at (c) and (d), because 
 the major chord appears second ; at («) and (/) another part 
 takes up the progression in the same octave-position, at (g) and 
 (h) the chromatic note appears in the highest part, and is, there- 
 fore, more easily recognised. The reason given above for the 
 bad effect of false relation also explains why the actual effect of 
 false relation is felt only in the fifth-change, and not, for example, 
 in third-steps of harmonies, etc., and why in certain harmony 
 successions (tritone-step) progressions with false relation may 
 even be normal. 
 
 The following exercises are to be worked out, similarly to 
 those of the last paragraph, on four staves, but the tenor is not to 
 be noted in the bass clef but in the treble clef, an octave higher 
 than it sounds — as is usual in modern vocal scores — like the 
 following model example : 
 
 °T°D "S 
 
 D .. °T°D D+°T D "S . . D °T 
 
 5M 
 
 (Fourth model example.) 
 
 Exercises 125 — 130 (Major). 
 
 (125) $: T\ S°S\ T .. I D .. \°SZ>\T S \°S&\ T°S \ T. 
 
 I I 3 1 I 3 1 I I I I I 
 
 (126) 3 / 2 : T\ S °S D I T . . °S I D T . . I D . . "S I D* * T\ 
 
 S D °S I J"., I T (o) 
 
chap, i.j Tonic and Dominant Harmonies. 51 
 
 « s I 
 
 (127) 3 / 4 : ri-^i?! r 5°5|z^' 3 °55+.. ] r^ri-s^.. I 
 
 (r p d r r 
 ^° f 1 r (j). 
 
 (i28)7 4 : Z» I "5 Z» I r 5 I •£ Z> I S T ... I °S D j ^ 5 | 
 
 (C r ■ * r'u * * j r c * ' t 
 & l I r(J.). 
 
 (129) E: T \ D..S °S \ &'*T°S\ +S Z> T °S \ T *.*. 
 
 (130) $ : T . . I 5'i I D . . I r Z> I r "S I D +S I Z>« ' I r 
 
 Exercises 131 — 136 (Minor). 
 
 (131) $ : T °S I Z> "T I °Z> "5 I D TV'S T\°D °S\D*^\ ° T - 
 
 (132) 3 / 4 : (j: "2" I D + °S D*"* \°T D T\D+°T °D °S I Z> + .' 
 
 r rcir f c 
 
 n. 
 
 l °£ Z>+ I °T. 
 
 (133) V« : "^ •• -° I 5 •• D* * \"T .. °D °S \ D* * °T. 
 
 c r C 
 
 (134) 3 / 3 : °Z» °5 .. I r .. Z> T I "D °S .. I D °S D* 3 | 
 
 p f t "rr r r r r F r ' r r r 
 
 T °Z> Z>+ IT 5 . . I Z> 4 5 Z? . . I °T. 
 
 I III V I III 
 
 rr r r =• 
 
 (13S) $ : T°5 I T D I 5 7" | °D D+ j °5 Z» + | "5 . . j Z>* 3 | °T 
 
52 Harmony Simplified. [Chap, i, 
 
 (136) a / 4 : °T I °S °T I D* °D I °S . . I £>+ . . I "T D | T °S \ 
 
 C f ' £ T ' U etc. 
 
 The examples which follow now, no longer keep to one key, 
 but by means of a whole-tone step or contra-fifth change which 
 breaks the bounds of the key, modulate in the simplest fashion 
 to that of the plain or contra-fifth clang ; we thus enter a new 
 domain, that of modulation, whose essence lies in the change of 
 functions of harmonies. If, e.g., from the tonic we make a whole- 
 tone step or contra-fifth change, a clang appears to have been passed 
 over, which, as intervening link, is necessary to make the connection 
 of the two clangs following each other intelligible ; and this is 
 revealed by the fact that we expect to hear this particular clang 
 as the continuation of the chord succession. In other words, 
 the whole-tone step and contra-fifth change always appear as the 
 succession of two dominants embracing one tonic, e.g., the harmony 
 succession : 
 
 c+ f* g+ c+ .. n.b. </+ .. g+, 
 3 3 
 
 at N.B. introduces after the tonic c + the harmony d + distant a 
 whole tone from it : our ears immediately accept the succession 
 c + d + as 5 — D, i.e., c + , on account of the d+ which follows, changes 
 its significance into subdominant ; and, therefore, the succession 
 will be correctly noted thus, — 
 
 T \ S D I T ■■ 
 
 = S I D .. I T 
 
 3 
 
 In the following exercises, whenever we come across the sign 
 of equality ( = ) in the indication of functions, a change of sig- 
 nificance from one function to another, i.e., modulation, takes 
 place. 
 
 Kxercises 137 — 140 (modulating). 
 
 im)%\T\DT\'SD\TD\T-i . , , -» 
 
 1 ' I s I 3 = s D T\°S D\ T\ .. .. I 
 
 S D I T S I D °S I T S I D °5 I Z>° ' I T 
 
 (Modulation to the key of the D and back.) 
 
Chap, i.) Tonic and Dominant Harmonies. 
 
 (138) V 4 : °T I •£ ZH* ' I °r 
 
 = "5 1 Z» T 5 J 
 
 53 
 = °Z> 
 
 °S T°S \°T°S .. \°T °S Z)+ I °T (J) 
 
 (Modulation to the key of the *D and back.) 
 
 (i39) H: 7\. I SDTS \D T I =5Z>| 
 
 ff 1 y <=> = DS\DTD i *\T.. \ 
 
 r 
 
 r £ z> . , I rsrsi t s d* * \ t 
 
 3 I "I S I 3 HI I ,51 
 
 I 
 
 (Modulation to the key of the 5 and back.) 
 
 (140)3/,,: "T S T \'S D °T 
 
 hi 11 =°Z> 
 
 "S °£> °S 
 
 = °S D + 
 
 ° r 
 
 °T S T I °S . . I D % 3 I T 
 hi 1 I in I 
 
 (Modulation to the key of the °S and back.) 
 
 In the following exercises the pupil is to determine in this 
 manner the modulations by indicating the changes of function 
 which take place : 
 
 Exercises 141 — 144 (Soprano given). 
 
 a ad d a 3 a d a e g 
 
 a a 
 
 ad a d . . g d a* 
 
 h .. f .. bo bo f bo + / .. c* 
 
54 
 
 Harmony Simplified. 
 
 [Chap. I. 
 
 "bo °io o o °a> "bo "a\> o °eo o °<to o °ea bo* °bo 
 
 Exercises 145 — 148 (Bass given). 
 
 e "a a 
 
 "a a "a 
 
 an do "do .. do eo go do do 4 + * 
 
 °g °c °g °d V * + °g '/ °c °f V 
 
 o s 
 
 g 
 
 148. 
 
 °b .. °e b.."b °a .. I + °e + °b °e + °£ <fc + "5 °« . . °b 
 
chap, it.) Characteristic Dissonances. 55 
 
 CHAPTER II. 
 
 CHARACTERISTIC DISSONANCES PARALLEL-CLANGS LEADING- 
 TONE-CHANGE CLANGS. 
 
 § 7. THE CHARACTERISTIC DISSONANCES (Z> 7 , S vu , S 6 , D vl ). 
 
 We could not, even in our very first exercises, do without the 
 chord of six-four, the natural connecting member between the 
 two dominants, and now we are forced still further to deviate 
 from the current method of teaching harmony (which post- 
 pones the theory of discords till later), by considering the 
 scarcely less indispensable characteristic dissonances which are 
 usually associated with the dominants. Since the dominants 
 are never perfectly consonant, in so far as they are always 
 conceived and judged from the tonic (thus, so to speak, always 
 together with the latter), it cannot be wondered at that they, far 
 oftener than the tonic, appear with additional notes which make 
 their meaning still clearer, and remove all danger of misunder- 
 standing such a succession, e.g., as T + — S + or "T— °D (viz., of 
 conceiving it in the sense of a retrograde plain-fifth step, there- 
 fore of a close in which what was intended as contra-fifth clang 
 would be tonic). These characteristic dissonances are notes in 
 each case borrowed from the other dominant, viz. : 
 
 (a) for the major upper-dominant, the fundamental note 
 of the subdominant (in c-major, g b d\f ' ; in A-minor, 
 eg%b\d). 
 
 (b) for the major subdominant, the fifth of the upper- 
 
 dominant (in c-major, f a c \ d). 
 
 (c) for the minor subdominant, the prime of the minor 
 
 upper-dominant and fifth of the major upper-dominant 
 respectively (in A-minor, b \ d f a; in c-major, 
 d \fakc). 
 
 (d) for the minor upper-dominant, the fundamental note 
 
 (V) of the minor subdominant (in A-minor, d \ e g b). 
 
 The characteristic additional dissonant note at (a) and (c) 
 proves to be a seventh (plain, natural [minor] seventh == 7, VII), 
 at (b) and (d), a sixth (plain, major = 6, VI). 
 
 This method of connecting one dominant with a note of the 
 dominant lying on the other side of the tonic, circumscribes the 
 key in the same manner as does the succession of the two 
 
5 6 Harmony Simplified. [Cb&p. n. 
 
 dominants, the whole-tone step and contra-fifth change, to which, 
 when they occurred from the tonic, we had, for this reason, to 
 ascribe modulating power : 
 
 (a) / [a c e\ g b d and d \_f a c\ e gt b 
 
 S D ^S^ ^Ip 
 
 T 
 
 (b) f a c \e g b~\ d 
 ^S^ '~D~' 
 
 (c) d f a [c e g] b and / an c [e g b] d 
 
 °S °D "°S~" D 
 
 (d) d [ f a c] e g b 
 
 °S C D 
 
 i.e., the combination of elements of two clangs which stand to 
 each other in the relation of two dominants (whole-tone step or 
 contra-fifth change) points to a clang lying between the two, and 
 making their relation intelligible (hence their tonic), just as in the 
 case of the succession of the two clangs. 
 
 In these four new formations we have the first examples of 
 chords of four notes before us, thus the first absolutely dissonant 
 chords (the chord of dominant six-four, which, as we have 
 seen, contains two dissonant notes, the fourth and sixth, is yet 
 subject to the possibility of being confounded with the tonic 
 [T and T respectively], and therefore has to be defined as a 
 
 5 I 
 
 feigning consonance, as a discord under the cloak of consonance) ; 
 the chord of seventh, fifth, and third, or, in short, chord of the 
 seventh of the major upper-dominant (major chord of the seventh) 
 and minor under-dominant (minor chord of the seventh), and the 
 chord of sixth, fifth, and third, or, briefly, chord of the sixth of a 
 major under-dominant and minor upper-dominant, are altogether 
 dissonant, as, besides the complete clang (prime, third, and fifth), 
 they contain a foreign note (the seventh or sixth). The general 
 law for the treatment of dissonant tones (for, as we have hitherto 
 always spoken of prime, third, and fifth as tones, and not intervals, 
 so we shall in future speak of sevenths, sixths, etc., as tones) is : 
 Dissonant tones are not to be doubled ; they may enter by leap, 
 
Chap. II.] 
 
 Characteristic Dissonances. 
 
 57 
 
 but must resolve by step of a second. Naturally this law was valid 
 already for the chord of six-four, in which we had to forbid the 
 doubling of fourth and sixth. The progression by step of a 
 second from the fourth and sixth of this chord is not uncon- 
 ditionally required, because a vicarious (substituting) resolution 
 c'oes not strike us offensively on account of the feigning con- 
 sonant nature of the chord : 
 
 Here at (b) — (d) we have vicarious resolutions in place of the 
 n.illy normal one at (a). 
 
 In the major chord of the seventh this substituting resolution 
 is not possible for the seventh, which, on the contrary, must 
 proceed by step of a second, if the expected harmonic pro- 
 gression follows at all ; and, indeed, the over-seventh regularly 
 proceeds downwards [55 (a)], on account of the striking dissonance 
 of the seventh against the octave, whether the latter be really 
 present next to the seventh [55 (<£)] or be only sounded as an over- 
 tone [natural by-note, 55 (a), (c)] : the notes forming the interval of 
 a second always tend away front each other. The resolution of the 
 dissonance of a second by merging the one note into the other 
 [55 (*0] nas a good effect only in the case of strongly contrasting 
 timbres, and is for the present strictly forbidden to the student. 
 The upward motion of the seventh is permissible only under 
 particular circumstances [e.g., when downward motion would 
 result in third-doubling that is not allowed : 55 (c)]. But naturally 
 where the same harmony is retained, the seventh may change 
 places with another note ; then the rule for progression is simply 
 transferred to another part [in 55 (e) to the bass] : 
 
 S5- 
 
 (0 
 
 (d) [bad] (») 
 
 (/) 
 
 (tr) 
 
 tp^", 
 
 5b 
 
 =j 1- 
 
 ^ 
 
 pllPpPfiPfllfp 
 
 i»= 
 
 J 
 
 3^ 
 
 =e*?= 
 
 ifc 
 
 mm 
 
 Here at (b) the fifth in the chord of the seventh has been 
 omitted; that is quite an ordinary proceeding (as the 5 or I 
 respectively in a chord may in any case be occasionally omitted), 
 
58 
 
 Harmony Simplified. 
 
 [Chap. u. 
 
 and is always to be recommended when we desire to make the 
 bass progression from fundamental note to fundamental note, and 
 to have the subsequent tonic chord complete [with fifth, 55 (g)\ ; 
 otherwise we must forego the fifth on the tonic [55 (/)]. At 55 (c) 
 looking upon the step g c as given for the tenor, and the third 
 required as bass-note for the tonic, the downward motion of the 
 seventh would cause a faulty third-doubling, for the doubling of 
 both prime and third in four-part writing is forbidden as sounding 
 very harsh and dry. Third-doubling sounds well only when the 
 chord is complete ; otherwise, it is preferable to treble the funda- 
 mental ?iote (alto given) : 
 
 56. 
 
 ^ii 
 
 m=\ 
 
 zz- 
 
 -f- 
 
 J. 
 
 r- 
 
 m 
 
 (not): 
 
 (but): 
 
 As the seventh in the progression D 7 — T makes the leading- 
 tone step to the third of the tonic, or, at any rate, has to proceed 
 by step of a second, and, on the other hand, the fundamental 
 note of the tonic is required for the bass in the last, closing 
 chord, the seventh as a bass-note for the penultimate chord is im- 
 possible. [57 ({)]. If the chord of the seventh be not followed by 
 the tonic, but perhaps by the subdominant, there is no necessity 
 for this progression by second ; but it will generally occur sub- 
 sequently [5 7 (a) and (/)] : 
 
 (good) 
 
 (good) 
 
 (wrong) 
 
 This subsequent introduction of an expected resolution, which 
 will often occupy us hereafter (in figuration it is standard, as assuring 
 good progression in the case of frequent leaps), also sufficiently 
 explains why the sixth of the major under-dominant and minor 
 upper-dominant (S h and Z> vl ) and the under-seventh of the 
 minor under-dominant (S vu ) apparently do not require resolution 
 by step of a second. According to our former experience the 
 
Chap. II.) 
 
 Characteristic Dissonances. 
 
 59 
 
 sixth, if sounded with the fifth (no matter whether in the same 
 octave position or not), must either tend towards the seventh 
 [58(a) and (c)] or force the fifth to the fourth [58 (b) and (a*)], as 
 the notes of a second tend away from each other (p. 57) : 
 
 Indeed, such resolution will appear normal, if the following 
 harmony contain the note in question : 
 
 59- 
 
 S 6 D* S 6 T S 6 D z> vl0 T £> VI °S 
 
 But as the contra-fifth clang is generally followed by the plain- 
 fifth clang, the more frequent forms of resolution will be not as at 
 (a) and (c), but (b) and (d), i.e., the dissonant sixth will mostly be 
 sustained and only subsequently proceed by step of a second. 
 But if in the c-major cadence the 6 of the S 6 chord, d, is in the 
 bass and the upper-dominant follows, the d might be sustained 
 [60 (a)], though it need not, but can proceed first to g; the c ex- 
 pected then first appears with the subsequent entry of the tonic 
 [60 (bj\ ; even the chord of six-four may be also inserted [60 (c)\ : 
 
 The resolution of the sixth of the minor upper-dominant, too, 
 may be disguised by means of these intermediate notes [61 (a) — (c)] : 
 
6o 
 
 61. i 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 But the d will mostly be sustained [61 (d) — (/)]. On the other 
 hand, the under-seventh is subject to exactly the same treatment 
 as the over-sixth, and examples 59 (a) — (b) and 60 (a) — (b) are 
 standard for it also, if the I? before the a be simply added : 
 
 62. - 
 
 That the chords of the over-sixth (S 6 ) and under-seventh 
 (5 vn ) readily take just tlie dissonant note for the bass-note we will 
 not conceal ; the reason for this will be quite clear to us later on 
 (dominant of dominant) when we shall have to consider the possibili- 
 ties of chromatic alteration of harmonies (S 6 , as soon as the 1 is 
 raised, becomes D 1 of the D, S vn likewise as soon as the III 
 and V are raised ; but then the 6 and VII respectively have 
 become 1, i.e., natural bass-note). 
 
 The introduction of characteristic dissonances into the domi- 
 nant harmonies completely removes the danger of faulty con- 
 secutive fifths and octaves in the majority of cases, as it gives 
 
Chap. II.] 
 
 Characteristic Dissonances. 
 
 61 
 
 the chords which otherwise have no note in common, two such 
 notes (6 of .S = 5 of £>, 7 of D = 1 of S or V of °S; VI of 
 "D = V of S, VII of 5 = 1 of °Z> or s of Z>+) : 
 
 The exercises which now follow are to be worked out, like the 
 fifth model example, on four staves, corresponding to scores for 
 stringed quartet, with treble clef for the two upper parts (1st and 
 2nd violin), alto clef for the third part (viola), and bass clef for 
 the lowest part (violoncello) ; in these exercises we also keep to 
 the normal compass of the voice as hitherto determined (re- 
 gardless of the compass of the instruments) : 
 
 (Fifth model example.) 
 
 Foremost, as regards the figuring, we must remark that the 
 6 or 7 (or VI or VII) beside the clang sign (T, £>, etc., or clang 
 letter c, g, etc., or the . .) simply requires the chord of the sixth 
 or seventh, whereas placing the numbers above or below the signs 
 indicates particularly the note for the highest or lowest part, as 
 hitherto. 
 
 To learn the meaning of the notes on the stave with the alto 
 clef is easy, if we look upon the missing line for c ' between the 
 treble and bass staves as the middle line, i.e., the five lines reach 
 
 from the / line of the bass stave to 
 stave 
 
 the g line of the treble 
 
 (Alto Clef.) 
 
62 Harmony Simplified. [Chap. n. 
 
 It must throughout be insisted upon that pupils shall not first 
 work out the examples on an ordinary pianoforte double stave 
 
 with & and §| and then write them out in score. They are to 
 
 sketch the work directly in the desired form ; only if this be done, 
 will it be possible to go on working quickly and with certainty 
 from step to step ! 
 
 As the introduction of characteristic dissonances does not 
 imply greater difficulty but rather the reverse, we may venture to 
 take another step forward in the next exercises, and practise the 
 simplest form of figuration or ornamentation, progression of one of 
 the parts in notes of half the value. For the present the resources 
 alone drawn upon are : 
 
 (a) Passing notes, i.e., notes which fill in the melodic gaps 
 between two others entering simultaneously with the other parts, 
 and which stand a (minor or major) second distant from both; 
 thus, e.g., if the plain unfigured movement were to introduce 
 e and g in succession, then / or f% would be a passing note 
 iefg, ef% g). 
 
 (b) Auxiliary notes (only a variety of passing notes), i.e., the 
 insertion of a major or minor upper or under-second, where the 
 unfigured movement would bring the same note twice in suc- 
 cession, e.g., b or bp is the lower, d or dp the upper auxiliary 
 note for c (c b c, c W c, c d c, c d'? c). In cases where neither 
 passing notes nor auxiliary notes can be introduced (where no 
 third has to be filled out, nor note-repetition to be enlivened, in 
 all steps of a fourth, fifth, sixth, or greater interval), 
 
 (c) a second harmony note, i.e., another note of the same 
 harmony, may be inserted as an expedient; in case of need a 
 leap to the octave may be taken, or even the same note may be 
 repeated; e.g., in figuration of the c-major chord a g might be 
 inserted between the e and c '. 
 
 The difficulty in these new exercises lies in the increase in 
 danger of faulty parallel progressions ; for not only may the 
 inserted harmony note effectually produce consecutives which 
 would not exist in unfigured writing, but the accented notes, i.e., 
 those entering simultaneously with the other parts, may form con- 
 secutives which are not removed by the intermediate notes. If, 
 e.g., the soprano in c+ — g + goes from e to d and the bass from 
 e, inserting g, to d, these are consecutive octaves of the worst 
 sort ; but if the bass e goes to c a-nd thence to d, the progression 
 e — d seems to our ears to have been replaced by c — d, i.e., the 
 effect of octaves is not felt : 
 
Chap. II.] 
 
 Characteristic Dissonances. 
 
 63 
 
 Bad. 
 
 Good. 
 
 We now give a mod el- example for these figuration exercises, 
 in which we characterise the inserted notes by numbers ; let the 
 bass be the part to be ornamented : 
 
 "T £> + °T S 
 
 67.- 
 
 (Sixth model example.) N.B. — The closing chord does not need figuration. 
 
 The second chord (D+) receives the seventh characteristic to 
 its significance in the figuration (dp as passing-note from f to 
 dp) ; here we may remark that in figuration not only may the 7 
 be added to the D + without being prescribed, but also, when 
 indicated in the figuring, it enters soon enough, if introduced by 
 the inserted note. Similarly the VII of the minor subdominant 
 and the sixth of the major subdominant and minor-upper- 
 dominant may at any time be introduced in the figuration where 
 not prescribed, and, where they are prescribed, may be missing at 
 first and be added subsequently as figuration notes. If by . . it 
 be required that a harmony with additional dissonant note be 
 repeated, it is not necessary for the latter to be reintroduced, but 
 the dissonant note may be dropped, as happened above (67) in 
 the third bar at the repetition of S vu . 
 
 A part of the following exercises, specially designated, is to 
 be made more interesting by always letting one of the parts 
 (either the bass part or soprano or one of the middle parts) 
 proceed in note-values of double quickness. A particularly 
 easy variety of this exercise is that of extending the figuration 
 to all the parts, so that as far as possible only passing notes, 
 
64 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 supplemented by auxiliary notes, are resorted to, and harmony 
 notes are inserted only in case of need, e.g. : 
 
 68. 
 
 (Seventh model example.) 
 
 S m D °T S vu 
 
 6> 
 
 z» 
 
 The pupil is to work one exercise each with figuration for 
 soprano, alto, tenor, and bass parts, and then (each fifth exercise) 
 with divided figuration. 
 
 Exercises 149 — 160 (for figuration). 
 
 J49) 3 /*: TS 6 jy\ T.... \°S £>..' I T.. 6 I =Z 
 
 1 3 ' I = S 6 D 1 I T 7 t) 
 
 T S . . 6 I Z>< 5 D I T ( ). 
 
 =D> 
 
 (150) a / 4 : T I S 6 D> I T 
 
 I 3 I « s 
 
 = £ D \ .". 3 
 
 Z>' ' l r ( J). 
 
 = Z» 5 I T D I r . .« 
 
Chap, ii.] Characteristic Dissonances. 
 
 65 
 
 (151) 3 / 4 : S 6 iy\T jy T\ D T 
 
 1 3 1 =DS7DT\DT..* 
 
 D T D 1 T°S I D T D I T ( J \ 
 
 (152) *\ % : T \ S*D>\ T.* 
 
 (C r l etc.) =S< 
 
 6 + 
 
 = D S\ J> . + . I TS 6 
 
 I? If I T (J). 
 
 (153) 3 / 4 : T^IZ) ] T \ S ..\D<* T 
 
 <r r ' p n 1 
 
 •• 6 ^-- 7 1 r (j.). 
 
 = 75 
 
 = ^ zm r -s 
 
 6 5. 
 
 (154) $: T\DS 6 \Z>* 3 | r , =5 DT\S^jy\ T( \J). 
 I ' = D S \DT ' "" "' 
 
 (i55) $: "^ I -S v " D \°T°D \ ,. VI 5 vn I Z> . .» | T 
 
 6> s. 
 
 (156) 3 / 4 : 'T£f" , T\D i 3 1 07* vi 
 
 p r 
 
 Z> VI S V 
 
 — S VIl \ 
 
 O^p J~) D7i VII 
 
 rr r "r 
 
 •T'S T \ S va Z>+ I "T ( J ). 
 
 (157) V 4 : T I 5 vn T\S D\'T S vn \ D* . . | 'T .. | -S vn .. 
 
 (^ I * U etc ' Figuration in quavers). 
 
 £» >! I °^(J.). 
 
 (158) 3/, : T I °Z> £ v " Z»+ j T . • vn vH 
 
 .P.,'T#.,T 
 
 T 5 vn 2? j °T S v " .. \ D ., 7. j °T. 
 
66 
 
 Harmony Simplified. 
 
 [Chap. Hi 
 
 (159) B: °T°S D + 
 
 T S vu ZJ'^I T ( J). 
 
 T VII 
 
 1 •• «> 5 
 
 _ S M\l J), 3 
 
 oyi in < 
 
 (160) $-. °r°z>\ °s 
 
 6»S 
 
 VII £)t 3 
 
 r S vn I Z>+ "5 I "T ( ). 
 
 T I =5 vn 
 
 =°2? »S T. . v " 
 
 Note. — Besides the whole-tone step and contra-fifth change, a 
 few more ways of modulation to the keys of the dominant have 
 here been resorted to, and first of all the direct change of meaning 
 of a clang by the addition of the dissonance characteristic to its new 
 significance. Thus in 149, 152 and 153 the + tonic changes to 
 + subdominant on account of the sixth characteristic for sub- 
 dominant significance being added; in 156 the "tonic changes to 
 minor upper-dominant by the addition of VI, in 158 and 159 the 
 minor tonic receives the stamp of minor subdominant by the 
 addition of VII. The returns (retrograde modulations) are carried 
 out in the same way; only in 159 an entirely new expedient is 
 made use of, the chromatic alteration of the tonic third. Rule : 
 the raising of the third of the minor tonic gives the major chord 
 which results upper-dominant significance ; the lowering of the third 
 of the major tonic gives the minor chord which results subdominant 
 significance; in short, the clang resulting from the chromatic 
 alteration of the third receives the significance of the " turn-of- 
 harmony clang" (contra-clang). Even if this rule does not 
 always hold good, it yet forms a valuable hint and support. 
 
 Exercises which are in iambic rhythm (J | J. J* | J), or 
 alternate between the latter and notes of equal value, are to be 
 written note against note in three parts ; the fourth part to be 
 figured then proceeds in notes of the next smaller value (for 
 J I J in quavers, for J» | J in semiquavers) ; the "dotted rhythm" 
 J* I J . is to be opposed by movement in quavers. In these 
 exercises more than one intermediate note will have to be in- 
 serted, without, however, exceeding the limits of the expedients 
 hitherto allowed. 
 
 The following hints will, for the present, be sufficient : 
 
 Part for Figuration : 
 
 m m ,1^^ 
 
Chap, ii.] Characteristic Dissonances. 
 
 Figured Part : 
 
 67 
 
 i.e., the introduction of auxiliary notes on both sides cannot be 
 avoided, and octave leaps will often have to be resorted to. 
 
 Exercises 161 — 172 (not for figuration). 
 
 (The tonal functions are to be added, as hitherto, in working out.) 
 161 — 163 (Highest part given [1st Violin]). 
 
 "a °e d va a °d a + "a 
 
68 
 
 Harmony Simplified. [Chap, il 
 
 164 — 166 (2nd part given [2nd Violin]). 
 
 164. 
 
 m 
 
 m 
 
 t=S* 
 
 o l> Vil > o i™ .. ft Jt ft .. + b.. VII /| 
 
 1 »» 
 
 ft b vu vm I b vn ft 1 ft 
 
 + .. d" e + b 1 e 
 3 
 
 d + a d 6 e* ' a 
 
 III 5 V d c .. 
 
 167 — 169 (3rd part given [Viola]). 
 
 d 6 5 ..' d .. a .. d .. g 6 a + g * » </ 
 
 168. 
 
 07^ VII £»«,*(».. g% 'g% g% "gffy .. 
 
 <■» ..' "Of 5-J'VlIfj °gt 
 
Chap. 11.] 
 
 i6g. 
 
 Parallel Clangs. 
 
 69 
 
 e a b e 
 
 b e 
 
 b e + 
 
 4 3 " 
 
 170 — 172 (Lowest part given ['Cello]). 
 
 "dt dtf °d$ .. + gt yn 7 .. °dt ct 
 
 °J. ^»vn 
 
 7 °gt gt v " + .'• °^» 
 
 § 8. CHORDS OF SEVEN-THREE AND PARALLEL CLANGS. 
 
 If even in the simple consonant clang of three notes we might 
 occasionally omit one note, (for which the 5 in a major chord 
 and I in a minor chord proved best adapted), this will naturally 
 be the case in greater measure, when a fourth (dissonant) note is 
 added to the clang. The omission of the fifth in the chord of 
 the over-seventh we already met with on p. 57, as an ordinary 
 expedient for keeping the closing tonic complete. But the 
 
7o 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 omission of the prime in the chord of the under-seventh is 
 equally permissible : 
 
 70. 
 
 The three remaining notes of the chord of the under-seventh 
 then yield the formation known by the name of the " diminished 
 triad," which formerly caused many scruples and much obscurity 
 in the theory of harmony, because, in blind formalism, it was 
 grouped beside the major and minor chords in a third class, by 
 those who thought it necessary to regard all chords as primary 
 that could be represented as consisting of thirds placed over one 
 another. As we do not at all found the theory of chords on the 
 principle of building up by thirds (c e g does not appear to us 
 like the combination of two thirds of different size, c e and e g, 
 but as the combination of a [major] third c e and [perfect] fifth 
 c g), so b df (S vn without prime) does not appear to us com- 
 parable with c e g and ace, but rather with gb f '(£>' without 5), 
 in as far as both formations arise from the omission of the note 
 most easily dispensable in the chord of the seventh. The chord 
 of under-seventh without prime (I) is only apparently similar to 
 the chord of over-seventh without prime (1), e.g., b df as D 1 in 
 c-major with omission of the principal note. We shall express 
 the omission of the prime by striking through the letter, and 
 shall call the chords of the seventh with omitted prime, chords of 
 seven-three ; then b df is either = g b df (= _g 7 ), thus in c-major 
 and c-minor chord of seven-three on the dominant = IP 1 , or 
 = b df $. (= j£ vl1 ), and in A-minor and A-major chord of seven- 
 three on the "subdominant = $ vn . Although the chord signs 
 correspond entirely, these chords are not of equal value ; for the 
 omission of the prime in the chord of over-seventh means 
 omission of the fundamental note, the note best for doubling, 
 and therefore least easily dispensed with ; therefore, correctly 
 speaking, only comparable with the omission of the V (which is 
 fundamental note) in the chord of under-seventh (omission of 
 /in c vn : d.. dp c) ; both formations, indeed, only occur more 
 frequently in three-part writing without the absence of the 
 fundamental note making itself distinctly felt : 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 7i 
 
 However, the introduction of M> 7 is also possible at times in 
 four-part writing, viz., principally when the doubling of the 5 may 
 be arrived at by steps of a second : 
 
 In the chord of seven-three the fifth is the only note that may 
 be doubled (the third [leading-note] and seventh, as we know, 
 must not be doubled). 
 
 Another formation results from the omission of the fifth in 
 the chords of the sixth ; first, in those hitherto considered, namely, 
 those arising from the addition of the characteristic dissonance to 
 the contra-fifth clangs (S 6 and D vl ) ; in these, by omission of the 
 fifth a clang apparently of the opposite mode arises ; i.e., SI 
 {the stroke through the 5 indicates its omission) apparently yields a 
 minor chord (in c-major f a z d apparently = °a), and D v „ a 
 major chord (in A-minor d e g b apparently = g + ). Thus we 
 become acquainted with a new category, and, indeed, a very 
 important one, of dissonances under the cloak of consonance 
 {feigning consonances). As the feigning clang {"a as /J and g + as 
 b v J) stands to the principal clang in the relation of plain third- 
 change {a is plain third in/ + , g plain third in ° b) or, which is the 
 same thing, in the relation in which tonics of parallel keys stand 
 to each other (F-major and D-minor, E-minor and G-major are so- 
 called parallel keys), we will call it the parallel clang and, in the 
 sign representing the functions of the harmonies, indicate the 
 relation by a / at the side of the S or "D. Thus Sp is the 
 feigning minor chord arising from the omission of the fifth in the 
 chord of the subdominant with over-sixth {S$) ; and, similarly, "Dp 
 the feigning major chord arising from the omission of the fifth in 
 the chord of the dominant with under-sixth [D £'). The parallel 
 clangs open entirely new prospects to us, in so far as they allow 
 of two methods of treatment, viz., either in the sense of the prin- 
 cipal harmonies represented by them or, with augmentation of the 
 feigning, as really consonant harmonies ; i.e., Sp permits [73 («)] 
 of the doubling of the fundamental note of the subdominant (which 
 is third of the feigning harmony), even in parallel motion [73 {b)\ 
 as well as [73 {c)~\ of the doubling of the fundamental note of the 
 parallel clang (which is actually sixth of the subdominant, there- 
 fore really a dissonance), also in parallel motion [73 (d)] ; indeed, 
 also that of the I of the parallel clang, which is the third of the 
 subdominant [73 {e) and (/)] ; and likewise in "Dp it is just as 
 allowable to double the prime (I) of the "D [73 \g) and {h)] as to 
 
7 2 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 double the fundamental note or the fifth of the parallel clang 
 [73 (0 an d (/), the former (!) also in parallel motion, 73 (&)]. Only 
 as regards one point the parallel clangs require great caution : 
 proceeding by leap to the I or 5 of the parallel clang in the bass 
 produces the undesirable effect of six-Jour already known to us, 
 and should therefore be avoided [73 (n) and (0)] : 
 
 73-1 
 
 V" — I — p-"-| — P>-"-r 
 
 Kill) iO v(l) 
 
 i© ' iQ 'l(i'ii) ' !<E) K - a 3Q «I(-0 -K) 
 
 But the possibility thus manifested to us of substituting the 
 parallel clang for a principal clang of the key, is not confined to 
 the contra-fifth clang, but also possible for the others, firstly, for 
 the tonic itself and the plain-fifth clang. These cases have to 
 be explained, indeed, in a different way, since for the tonic there 
 can be no characteristic dissonance (for, on the contrary, the 
 characteristic of the tonic is absolute consonance), and the plain- 
 fifth clang with its own characteristic dissonance (7, VII) cannot 
 produce any feigning consonant formations (as the 7 [VII] is 
 absolutely dissonant not only with the 1 [I], but also with the 3 
 [III]). If, in the first place, we retain the notion of "sub- 
 stitution," we must state its existence in the case of the parallel- 
 clang of the tonic, particularly in the deceptive close, which is best 
 explained as a real close disturbed by a dissonant note and as 
 replacing the tonic by a feigning consonance ; three parts make their 
 regular progression from the plain-fifth clang back to the tonic, 
 and the fourth (in major regularly the bass), instead of the step of 
 a fifth or fourth from fundamental note to fundamental note, 
 makes a step of a second upwards from the fundamental note of 
 the plain-fifth clang to the third of the contra-fifth clang (sixth of 
 the tonic) : 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 73 
 
 M 
 
 (I J 
 
 «\ 
 
 </) 
 
 A 
 
 /t^ 
 
 
 /T\ 
 
 «r— i — 
 A 
 
 ,—g" ! 
 
 i 
 
 , -g- 
 
 ~(4) 
 
 s — n 
 
 \ 
 
 
 
 
 — H — 1 
 
 H 
 
 1\IW 
 
 l(Iil) 
 
 The method of writing at {a), together with the inversions of the 
 three upper parts — at (d) and (e) — is the properly normal four-part 
 form of deceptive close ; but it is not considered necessary for the 
 chord of dominant seventh, or even the dominant chord [cf. (/)] 
 to be complete, i.e., the fifth of the dominant may be omitted 
 [cf. (b), (/),and (g)]. Doubling the third of the parallel clang '(which 
 is fundamental note of the actual harmony — therefore we have only 
 a feigned doubling of the third — ), is positively characteristic in the 
 deceptive close, and the equally possible modes of writing as at (b), 
 (doubling the fundamental note [V] of the parallel clang), or (c), 
 (doubling the I of the parallel clang), remain the exceptions. 
 
 But the parallel clang of the tonic may be introduced not 
 only at the end of a cadence (when it annuls the closing power 
 of the tonic, and thus necessitates a new cadential formation), but 
 also at the beginning of a cadence in the transition from tonic to 
 subdominant. (In both cases, the sixth which takes the place of 
 the tonic fifth must be understood as the third of the subdominant, 
 and has a corresponding effect). The parallel clang appearing 
 after the principal clang, therefore, always indicates the anti- 
 cipation of an element of the harmony which follows logically ; 
 viz. : — 
 
 in T — Tp the newly added note is third of S, 
 in S — Sp „ „ „ „ fifth of D; 
 
 and the relations correspond in the minor key, viz. : — 
 
 in °2'—°Tp the newly added note is third of °D, 
 in *D—°Dp „ „ „ „ fifth (V) of °S. 
 
 And thus, finally, also the parallel clangs of D in major and 
 
74 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 °S in minor may be introduced, and must correspondingly be 
 defined as anticipations of the third .of the closing tonic; i.e., 
 
 in D — Dp the newly added note is third of T, 
 and in °S— °Sp „ „ „ „ third of °T. 
 
 The introduction of the parallel clangs, therefore, signifies a 
 very considerable enrichment of the means of cadential formation 
 and a more detailed subdivision of them. 
 
 In the cadence of the pure major key 
 
 Tp enters between J 1 and S 
 Sp „ „ S „ D 
 
 Dp „ „ D „ T, 
 
 and in the cadence of the pure minor key 
 
 "Tp between "T and °D 
 "Dp „ "D „ °S 
 °Sp „ °S „ "T, 
 
 by which means we gain the two following cadences, likewise to 
 be designated as normal : 
 
 TTp SSp DDp T °T°Tp "D "Dp °S "Sp 
 
 Connecting the parallel clangs with the principal clangs 
 whose accessory harmonies they are, gives rise to no difficulties, 
 as the two clangs have two notes in common ; it is equally 
 possible to retain the doubling of the prime [as happened at 75 (a)], 
 or to double the fundamental note of the parallel clang [as at 
 75 (^)] i tne l att e r is preferable in minor, because the doubling of 
 the prime does not then signify doubling of the fundamental 
 note [76 (a)] : 
 
 The continued fifth-doubling in the principal clangs of the 
 major cadence [76 (i)] would not be happy, though not impossible. 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 75 
 
 The connecting of parallel clangs with one another (Tp — Sp, 
 Dp—Tp, Sp—Dp or °Tp—°Dp, °Sp—°Tp, °Dp—"Sp) corre- 
 sponds entirely with the connecting of the principal clangs 
 of the parallel key, with this difference, that in the former we 
 have good doubling of feigning thirds in place of bad doubling 
 of real thirds in the latter : 
 
 77- 
 
 apparently : j{| jj| apparently: 
 
 The doubling of the leading-note, otherwise so strictly for- 
 bidden, appears permissible here (at N.B.) ; nevertheless, in a 
 succession of several parallel clangs, the method of writing used 
 for the key of the opposite mode is generally to be recommended, 
 and it has a particular charm on account of the abnormal 
 succession of dominants, which in this case appears natural and 
 justified : 
 
 T 
 
 Tp\ 
 
 Sp 
 
 Dp 
 
 (" 
 
 •°T | 
 
 °S 
 
 °D) 
 
 T 
 
 °Tp\ 
 
 'Dp 
 
 °Sp\ 
 
 (- 
 
 -+T\ 
 
 D + 
 
 +S) 
 
 77(«) 
 
 770*) 
 
 A few new harmonic successions result from connecting 
 each parallel clang with the other two principal clangs of the 
 key, viz., in major — 
 
 Tp— S Tp—D Sp—D Sp—T Dp—S Dp—T 
 
 (!) 
 and in minor 
 
76 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 "Tp- 
 
 ■°Z> 
 
 °Tp—°S °Dp—°S "Dp- 
 
 °r°sp- 
 
 -°Z> °Sp—°T 
 
 r i 
 
 (!) (!) (!) 
 
 Here, at 78 (a) — (/) and 79 (a 
 
 (!) (!) (!) 
 
 -(/), the parallel clangs are in- 
 troduced with doubling of their fundamental notes; at 78 (aa) — (ff) 
 and 79 (aa) — (ff) on the other hand with doubling of the primes 
 of the principal clangs, which latter at T&(aa)—(ff) yields a more 
 convenient result on an average than at 79 (aa) — (ff), because the 
 doubling of the minor prime is not doubling of the fundamental 
 note. The harmonic steps new to us which result, are : 
 
 The leading-tone change [78(a) and (aa), 78 (/) and (ff), 
 
 79 (a) and (aa), 79 (/) and (ff)]. 
 The minor-third change [78 (^) and (pi), "]8'(d) and (dd), 
 
 79 (i) and (id), 79 (d) and (dd)]. 
 The whole tone change [78 (c) and (cc), 79 (c) and («■)]. 
 The tritone change [78 (e) and (ee), 79 (e) and («)]. 
 
 As in all these cases it is a matter of connecting a parallel 
 clang with a principal clang, all the steps are naturally made with 
 changing mode (therefore "change"), and indeed throughout with 
 plain changes. 
 
 The conditions for writing these steps singly are the following : 
 
 (a) Leading-tone change (T— Dp, S—Tp;"T—"Sp, ° D—°Tp), 
 i.e., the step from one clang to the change-clang of its plain 
 leading-note (= of the plain third of its plain fifth) connects 
 clangs, which have two notes in common, show a leading-tone 
 step from principal note to principal note, and admit the doubling 
 of both fundamental notes without danger [80 (a) — (i)] : 
 
 &M 
 
Chap. II.) 
 
 Parallel Clangs. 
 
 77 
 
 Exceptional progressions [cf. 80 (c) — (/)] are possible in various 
 ways, and do not imply any forbidden steps. The leading-tone 
 change has a peculiar significance as closing step in place of the 
 retrograde plain-fifth step, Dp—Tox ° Sp—° T instead of D—T 
 and °5 — "T. As the notes in common are too many, the 
 retrograde leading-tone change as close-formation in the major 
 key is generally written so that all the parts proceed by leap (a 
 favourite progression of Schubert's [V£ 81 (a) — (i>)] : 
 
 That this is also possible in an entirely similar manner in the 
 minor key (only with doubling of the feigning fundamental note) 
 we may see at 81 (c). 
 
 (b) The minor-third change (T—Sp, D—Tp; °T—°Dp, 
 °S — ° Tp), the step to the change-clang of the plain minor 
 third, i.e., to the change clang of the plain third of the contra- 
 fifth (! , thus really the progression from the fifth-clang to the 
 third-change clang of a third clang) connects clangs which have 
 no note in common, and therefore give rise to danger of con- 
 secutive fifths and octaves, which may, however, easily be re- 
 moved, but only if we either forego the possible leading-tone 
 step, or double the third in the parallel clang : 
 
 82. 
 
 This step is likewise used with two entirely different meanings, 
 in the first place at the beginning of the cadence, as transition 
 from the tonic to the subdominant which is replaced by its 
 parallel clang, and, secondly (retrograde), at the end of the 
 cadence, substituting the parallel clang for the tonic, as a form of 
 deceptive close; we have discussed the latter at greater length 
 above (pp. 72,73). The equivalent of the ordinary major deceptive 
 close in the region of minor harmonies is therefore as follows 
 (with or without seventh to the ° S) : 
 
7« 
 
 Harmony Simplified. 
 
 J i a — „ — J . ^ — „ 1- 
 
 [Chap. II. 
 
 83- 
 
 Another form of deceptive close peculiar to the mixed minor 
 (with major upper-dominant) we shall meet with later on. 
 
 (c) The whole-tone change (Sp — D and °Dp — °S) connects the 
 parallel clang of the contra-fifth clang with the plain-fifth clang, 
 and has therefore entirely the same significance as the whole-tone 
 step without its risks. This change is highly important for 
 modulation, and we shall have to return to it in considering the 
 chromatic alteration of the third of the plain-fifth clang (Dorian 
 sixth and Mixolydian Seventh. 
 
 (d) The tritone change, in which the distance of the principal 
 notes from each other is an augmented fourth, i.e., the most 
 complicated of all relations in the diatonic scale (/ . . \c . . g] . . b 
 or b . . [e . . a] . . f; that is, relation of the third of the second 
 fifth) gives rise to some difficulties in writing [risk of consecutive 
 octaves and fifths, tritone 84 («)], which can, however, be satis- 
 factorily removed [84 (b) — (</)]. 
 
 84. 
 
 By the introduction of the parallel clangs our further exercises 
 will gain greatly in variety, particularly as we must not lose sight 
 of figuration. The means for modulation likewise appear es- 
 sentially enriched : to the transitions to the upper and under 
 dominant keys of the same mode, hitherto the only ones made, 
 we may now add that to the parallel key, easily made by means 
 of the parallel clangs. If we compare the cadence in the major 
 key extended by the parallel clangs, with that of the minor key 
 confined to the principal clangs, e.g., c-major and A-minor : 
 
 (T— Tp—S—Sp—D—Dp—T) 
 
 ■°e—f + —°a- 
 
 °b — c+ 
 
 °e — °b ■ 
 (°T—°£> 
 
 "a 
 °S 
 
 °e 
 °T) 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 79 
 
 and, conversely, the cadence of the minor key enriched by the 
 parallel clangs with that of the major key confined to the 
 principal clangs (the same keys) : 
 
 (°r— 
 
 "Tp- 
 
 -°D- 
 
 -°Dp- 
 
 -'S- 
 
 -°Sp — 
 
 °T) 
 
 "e — 
 
 c + - 
 
 - °b - 
 
 -g + - 
 
 -°a- 
 
 -r- 
 
 ■ "e 
 
 t* - /+ - g* - c+ 
 {T — S — D — T) 
 
 we are first stiuck by the reversed order of the two dominant 
 parallels as compared with the dominants which have the same 
 sound ; this may be turned to account in effecting a transition 
 from one cadence to the other, e.g. : 
 
 T 
 
 ■°e — °b — °a — "e 
 
 -Tp 
 
 °T — °D—°S—°T 
 
 or, °e — c + — f+— g+- 
 °T—°Tp 
 
 = T — S — D- 
 
 T 
 
 But there is still another possible way of deriving minor 
 from major chords, which we have not considered so far, viz., the 
 (figurative) replacing of a prime by tlie minor contra-second : 
 
 In c-major : +J 1 "* =b \c~] e g, apparently identical with Dp 
 +S U< =e [/] a c, apparently identical with Tp 
 
 In A-minor : °T'" =a c [*] f, apparently identical with °Sp 
 °D* > =eg\_b'] c, apparently identical with "Tp 
 
 These formations arise in the simplest fashion through the 
 plainest figuration of the harmonies by means of passing or 
 auxiliary notes, in the first place in the more complicated form of 
 four-note chords (major-seventh chords), e.g. : 
 
 T 7< S 1< 
 
 In slow movement, in order to remove the extreme dissonance 
 of the major seventh or minor second in the major key, another part 
 
8o 
 
 Harmony Simplified. 
 
 [Chap. II 
 
 will readily move too— viz., that part which had the doubled 
 prime (in minor the doubling of the prime given here [85 (b)] will 
 naturally occur much more rarely than the doubling of the V). 
 In both cases again feigning consonant chords arise, which we 
 may not, however, identify with the parallel clangs. 
 
 NB. 
 
 (ii<) 
 
 
 NB. 
 
 
 
 
 s 
 
 7 -= 
 
 oyi vn> 
 
 °D 
 
 VII> 
 
 
 (IK) 
 
 (=>) 
 
 
 <2>) 
 
 The feigning consonant accessory form of the tonic (T 7< , 
 X wll> or + T n< , "T'") arising from the minor contra-second 
 (major seventh) thus forms a natural connecting link between tonic 
 and contra-fifth clang, a new enriching of the cadence ; also the 
 accessory form of the contra-fifth clang arising similarly (S 7 , 
 Jfi vn> or, which means the same thing, + S n< , °Z? 2> ) does not 
 appear in exactly the same place as the parallel clang of the 
 tonic (between tonic and contra-fifth clang), but rather after the 
 pure form of the contra-fifth clang : 
 
 
 <«>l , 
 
 , 
 
 
 _, 
 
 
 87. ■ 
 
 \m 
 
 =a=s 
 
 
 ^=4= 
 
 -P — ! — H 
 
 
 lb±==i=t= 
 
 
 
 r-—^ 
 
 -x — =!_ H 
 
 Tp S 
 
 Sp D T 
 
 T ?> °Tp "D ;> "Dp °S °T 
 
 We will call these feigning consonances leading-tone substitutes, 
 and adopt the following abbreviated signs for them : ff = + T u< , 
 ¥ = °r s> , * = + -S' n< , and & =°Z> !> . The leading-tone 
 substitutes following directly after the tonic and the contra-fifth 
 clang (even before their parallel clangs) suggest new means for 
 modulation : 
 
Chap. II. 1 
 
 Parallel Clangs. 
 
 81 
 
 Enriched major cadence : (T !?' Tp S !!' *S/> Z> Z>/ T) 
 
 / + 
 
 "« r 
 
 Plain minor cadence 
 
 "e °b "a 
 
 °e 
 'T) 
 
 Enriched minor cadence : ("T *.* "Tp °D ;.* °Z»/ "^ "5/ °T) 
 
 r 
 
 r 
 
 Plain major cadence : 
 
 (T S 
 
 g + c+ 
 
 n t) 
 
 i.e., here again we have two successions which, when inverted, are 
 normal in the cadence of the parallel key, and will by exchange 
 immediately suggest modulation : 
 
 The next exercises, which are intended for figuration, may 
 now make the student acquainted with the tenor clef, and for 
 that purpose they are still to be written as if for string quartet, 
 but with notation of the 'cello part in the tenor clef; only where 
 more than one leger line below would become necessary, the bass 
 clef may be resorted to. The tenor clef is, like the alto clef, a 
 c'-clef ; the line to which it is prefixed (the second from the top) 
 has the tone-significance of once-accented c : 
 
 (Tenor clef.) 
 
82 
 
 Harmony Simplified. 
 
 [Chap II. 
 
 The student should impress the tone-significance of these 
 three notes on his mind, and he will easily become intimate with 
 this clef also. For the rest we will refer him to the eighth model 
 example. The figuration is still to be confined to passing and 
 auxiliary notes and inserted harmony notes, and in each fifth 
 exercise the figuration is to be divided among the four parts. 
 
 T !i < 5 Sp D 1 T Tp Sp D Dp S D T 
 
 90. 
 
 (Eighth model example.) 
 
 Exercises 173 — 184 (for figuration) 
 Tp 
 
 (173) 3 U- t \"<Tp\spn 
 
 (f r etc.) 
 
 Sp Dp\T (J) 
 
 °T °S 
 
 D °T 
 
 = SD 
 
 2> 
 
 T Tp 
 
 (174) E: °T ** ! °D °S 
 
 :+Sp D ..' 
 
 "T r s v " jy 1 °T (J) 
 
 =°.S D .1 
 T Sp 
 
 (i75) 'L--D I TD\ Tp I 
 
 (J T'etol ="T D\"T °D 
 
 S .. I J> *\ T (J .) 
 
 (176) »/ 3 : Sp I D T S 6 I D ..' Tp 
 
 Is I = °t 
 
 = S D 
 °Sp 
 
 <T< II« 
 
 6> 5 
 
 2? Tp I 5 «S/ Dp I 7)> S 6 Z> | r (=>) 
 
 = S T D< 
 
 g! 3 
 
 (177) $=°^. s 
 
 --Sp D 
 
 °t °sp 1 °r (<=>) 
 
 = Sp D\T Sp I 
 
 7> I ^T 7 |.S V " D 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 (178) ■/,: S 6 & 
 
 = S Z?< + 
 
 = °Sp s vu 
 T S 
 
 83 
 D ..» T I 
 
 6 5 
 
 Sp Z>» 3 \Tp Sp D I Z>/ 7> 5 I °,S Z> » I j- (j) 
 
 (179) B: °T 
 
 \ 
 'Sp 
 
 r C 
 
 5 V " T ,S VI1 Z> 
 
 r ■ c r r 
 
 » m m m 
 
 I I I I 
 
 ¥ S vn D °Tp 
 
 t r r u 
 
 r r 
 
 (180) 3/ 8 ; r Z* 
 
 3 S 
 
 (Cj 'I. ctc) 
 
 (Figuration in Semiquavers.) 
 
 = °2> D 1 "T 
 
 °T°S T 
 
 III 
 
 = Sp T £> 7 
 
 °S 
 
 --D S D 
 
 (181) '/,: r D T S T 
 
 3 5 
 
 = Sp 
 
 U 
 
 )=°7p 
 
 S vn D 
 
 D* S D 7 
 = Tp D T 
 
 n~> 
 
 1 r* 
 T S 
 
 7" 
 
 Z>7> 
 
 ■ 5/Z) 
 
 = Z> Tp Sp \ Dp Tp If 
 T 
 
 T S 
 
 (182) %: T D 7 
 
 Tp £\ S I 
 
 I = ".§> £ vn I Z>+ 
 
 = 3? 5/ I Z> 5 
 °Z> '» 
 
 Z>» Z> I T 
 (183) 3 / 4 = "^"Z? "£/ s vn z» r 
 
 III 
 
 °s 
 
 =sp d* s I r 
 
 _ o^ £V1I £, 
 
 = Z?/ 5 6 Z> 7 I 7" .. 
 
 _0 J> £VII 
 
 II> 
 
 (184) °U ■ D I 
 
 r c 
 
 T' etc. 
 
 5 vn r 
 
 I 
 
 T S v " D 
 III 
 
 S vl1 D> 
 
 07 U) 
 
 °T 
 = 2? Z>' 
 
 =°S/ £ VI1 j Z> + "J" (J) 
 
8 4 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 The connecting of parallel clangs and leading-tone substitutes 
 with the contra-clang of the tonic we have hitherto avoided. 
 Since this introduces clangs of the same mode in succession (of 
 which the one, indeed, is always only a feigning consonance), the 
 result is a number of new harmonic steps, viz. : 
 
 Tp°S Sp°S Dp "S °Tp Z>+ "Dp D + "Sp D+ 
 
 («) <*) (<:) (d) « (/) 
 
 I J -J 
 
 9M 
 
 The new steps are : 
 
 (a) The {plain) third-step [9 1 (a) and (</)]," which, in the pro- 
 gression of parts, differs from the leading-tone change 
 only by a chromatic step (a — £?,£"— -g§), 
 
 (b) The {plain) minor-third step [91 {b) and {e)\ differing from 
 
 the third-change only by a chromatic step {a — at>, 
 
 g—g%)- 
 
 (c) The {plain) leading-tone step [91 {c) and (/)], differing from 
 
 the tritone change only by the exchange of a minor 
 
 for a major second. 
 The next exercises introduce also these steps, of which one, 
 viz., the leading-tone step in minor [91 (./)], requires particular 
 notice, because retrograde, in the sense of the progression to the 
 tonic leading-tone substitute from the major upper-dominant, it 
 yields the most important (most frequent) form of deceptive dose in 
 tlie minor key (with or without seventh of the D) : 
 
 92. 
 
 Of 92 {b) we must remark that the distance of alto from tenor 
 amoutits to an octave, which, however, may be approved in this 
 and all such cases, where both couples of parts form thirds. 
 92 {a) — (b) are the proper typical forms of the deceptive close in minor 
 (also with the possible inversions of the three top parts) ; 92 {c) 
 is rare and not so good, because the characteristic progression for 
 the bass to the feigning fundamental note is replaced by that to 
 the fundamental note of the principal clang. 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 «5 
 
 The exercises which follow now are to be written in the/01/r 
 old vocal clefs (soprano, alto, tenor, and bass clefs). In working 
 out, the tonal functions of the harmonies are, as hitherto, 
 to be added by the student. The soprano clef (c-clef on the 
 lowest line) will now be easily learned, after alto and tenor clefs 
 have somewhat accustomed us to the varying position of the 
 C-clef. Its relation to the treble and bass clef is : 
 
 (Soprano clef.) 
 
 The following ninth model example may help to set the student 
 right :— 
 
 = S 6 £>> T .. S 6 6> 
 "T °Sp D °T °S .. VI 3 =S V1 Z>< + » 
 
 94. 
 
 "ft S ft f% ° b S* a d •• z*ft A - ■•' 
 
 (Ninth model example.) 
 
86 Harmony Simplified. [Ch»p. n. 
 
 Exercises 185 — 196 (not to be figured). 
 
 (The clef prefixed indicates at the same time which part is given.) 
 
 do °bb do 7 do 7 go f o o ab 7 + 
 
 °dt gt viI e d% "d% 3 e o ft b o e fy 
 
 ?& 
 
 *=F 
 
 b °gt dt °g% dtf °d% 
 
 e°df+ b °dt °gt + b °gt a b e + °d% b e 
 
 do "aj + 
 
 o-l +7 
 
 g ea 
 
 °c eb ao °c o + an 
 
 °bc+ b + g v VI d c d 7 g b 1. c "ft & 
 
 o VI v " o e vn b 7 °b 
 
 + bo °f o c 7 "a d vu a 7 'a c + "a bo c bo c* 3 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 87 
 
 + ..' to c* g c 1 °e lib 6 o bb 6 c 
 
 6 s 
 
 "ft °c% g da ?. °fy b vl + J o d * » 
 
 t °b + d °b + o 
 
 + ei t f O °d g vn d' d* + eb / ..' 
 
 Pi 
 
 to .. 7 + bo + "a 7 ■£ + to 
 
 193. 
 
 
 
 
 ^^ 
 
 
 i _ 
 
 ffiAqp 
 
 
 -p 1 : 
 
 
 
 
 ^=^=^= 
 
 
 
 
 
 J 1 — U 1 — 
 
 
 
 °f at) + o bo* o + eb + + "d o g "g 
 
 °gt °/t + °/j + + g + + o f% % 
 
 i:t 7 "c% e + d a + . 6 . + + 
 
 g f g °e '•a + + a 1 "a .. + 6 
 
 196. 
 
 °< /+ "b + °a + ..' °« .. </ ..' + °a 
 
88 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 § 9. DORIAN SIXTH, MIXOLYDIAN SEVENTH, NEAPOLITAN SIXTH, 
 PHRYGIAN SECOND, LYDIAN FOURTH. 
 
 The minor subdominant in major and the major upper- 
 dominant in minor disturb the melodic flow of part progression ; 
 the thirds of each introduce the step of the augmented second 
 into the scale : 
 
 NB. 
 
 NB. 
 
 Aversion to this unmelodic step has led composers to bridge 
 over the gap in a like manner in both cases— viz., by chromatic 
 alteration of the third of the plain-fifth clang, so that the latter 
 then stands at the distance only of a whole tone from the third of 
 the contra-clang of the tonic. The simplest and plainest cases of 
 the introduction of the melodic neighbouring notes to the third 
 of the contra-clang are probably those which naturally make their 
 appearance in the figuration, whether they be used as auxiliary 
 notes [97 (a), (c)2 or as passing notes [97 (b), (d) t (e), (/)] : 
 
 (B) in m in w 7b 
 
 m 3 n 3 
 
 97- 
 
 w vin 
 
 /rf= 
 
 W m n 9 l V)3 2|; 
 
 As proved by the J) against the numbers, the interval in 
 question is in all these cases natural, and plain, in reference to the 
 figured harmony.- But these notes, conceived first on purely 
 melodic grounds, may also be harmonised independently in such 
 a manner that they no longer appear in the chord signs as passing 
 or auxiliary notes added to the harmonies of the contra-clang or 
 the tonic, but rather as chromatically altered thirds of the plain- 
 fifth clang [98 («)—(£)]. 
 
Chap. II.] 
 
 98. 
 
 Parallel Clangs. 
 
 if) m (in*) 
 
 89 
 
 to 
 
 T D*> "S T 
 (3>) 
 
 
 T °Dp u< Z>+ 
 
 98 (c) — (d), indeed, may be conceived as mere figuration of the 
 harmony of the contra-clangs, more conveniently in three-part 
 than four-part writing : 
 
 
 ifor^ ^ — !>J— j— - ■ 
 
 \M=^=^ 
 
 =s^eH 
 
 99.- 
 
 tf r r r 5— 
 
 1 1 ' 
 
 ta- -ta. -^ 
 
 =s=rz= i 
 
 
 1. 
 
 
 
 - — -^ 
 
 II III 
 2 1 S vu vm 
 
 °T I> 
 
 The explanation added to 98 {c) and (d) does not necessarily 
 imply that the contra-clang of the tonic ought to follow, for the 
 chords Sp** and °J?p n< may also advance in such a way that 
 their minor contra-second proceeds to the prime [100 (a) — (i)] : 
 
 T Sp" I T °T°Dp n< 1 °T T (S) S T 
 
 T {°D) °D °T 
 
90 Harmony Simplified. [Chap. n. 
 
 Thus we should again have two new leading-tone substitutes 
 before us, but doubly derived ones (leading-tone substitute of the 
 parallel clang of the contra-fifth clang), which, however, seem to 
 point to a nearer path, viz., that struck out at 100 (c) — (d), the 
 insertion of the contra-fifth clang of the contra-fifth clang (second 
 under-dominant in major, second "dominant in minor). This 
 again opens entirely new prospects to us (figuration of a dominant 
 by means of its own dominants), which we shall have to enter 
 further into. 
 
 At first we will confine ourselves to that introduction of the 
 lowered (" Mixolydian ") seventh of the major scale which takes 
 place in order to bridge over to the lowered sixth (the III of 
 the °S), and similarly to the introduction of the raised (" Dorian ") 
 sixth of the minor scale effected in order to gain a melodic transition 
 to the major seventh of the minor scale (3 of the + Z>). In as far 
 as these notes enter as chromatically altered thirds of the plain- 
 fifth clangs, they apparently give the major key a minor upper- 
 dominant and the minor key a major under-dominant : 
 
 (b) t> # jjj^ 
 
 d f a c e g b 
 n.b. ■ — <~~> 
 
 But this conception is not possible in the full sense ; the 
 principal notes of the major tonic and minor upper-dominant on 
 the one hand, and of the minor tonic and major under-dominant 
 on the other, would stand at the distance of a double-fifth step 
 from each other ( c + — (g) — °d ; "e — (a) — d+), i.e., would appear 
 related only in the second degree. The last paragraph showed us 
 what significance the whole-tone changes (such as the harmonic 
 successions c + — °d and V — d + ) would have in tonal harmony, viz., 
 in major, the minor chord is parallel clang of the under-dominant, 
 and the major chord is upper-dominant, and in minor corre- 
 spondingly, the major chord is parallel clang of the minor upper- 
 dominant, and the minor chord is "subdominant ; therefore, the 
 successions °d — c + and °e — d + will easily and readily be under- 
 stood as Sp — D [10 1 (a) — {b)\ i.e., as closing in F-major and 
 G-major respectively, and conversely c + - — "d and d + — "e as closing 
 in d minor and E-minor respectively, in the sense of ° Dp — °5 
 [101 (c) — (d)] ; indeed, even for the inverted successions the same 
 conceptions are not excluded [101 (e) — (/*)] : 
 
 Sp D T Sp D T °Dp °S °I °Dp "S °T 
 
Chap. II.] 
 M 
 
 Parallel Clangs. 
 (/). Or), 
 
 91 
 
 (*) 
 
 4: A J. *d 4 
 
 Ui. 
 
 "S "Dp °T °S "Dp "T 
 
 But in spite of this double possibility of change of meaning 
 and modulation, the introduction of the upper-dominant in major 
 with lowered third and of the under-dominant in minor with 
 raised third without altering the functions is quite possible, only 
 presupposing that the chromatic third of the plain-fifth clang 
 really proceeds in the same part to the third of the contra-clang 
 of the tonic, to which the artificial note is to bridge over. Part 
 progressions in which this is not the case, are, therefore, in the 
 strictest sense not quite logical ; at least they are comparable to 
 poetic licences and tropes, and purposely lead comprehension 
 astray by means of vicarious progressions of the parts, or, as 
 musical ellipses, require leaps in the conception. Every entry 
 of the Dorian sixth without the third of the major upper-dominant 
 following in the same part, therefore, produces that effect which is 
 specifically called " Dorian," because it does not so much take 
 root in our modern clarified harmonic conception, as it reminds 
 us of the time of the harmonic treatment of the old Church modes. 
 
 The four principal Church modes (the four authentic ones) 
 were the scales : 
 
 Dorian: d e f g a b d ^'(with<f as fundamental note of the 
 1 ' closing harmony). 
 
 r 
 
 Phrygian : e f g a b c d' e ( „ e „ 
 
 Lydian : / g a 6 c' d' e' f ( „ / „ 
 
 Mixolydian : g a b 1 : d' e f g' ' ( „ g „ 
 
 » )• 
 „ )■ 
 „ )• 
 
 i.e., the Dorian tonic, so long as b\f or c$ were not introduced 
 (which proved inevitable for the final close), was deprived of 
 plain-fifth clang as well as contra-clang, i.e., of the two most 
 important harmonies : 
 
92 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 The specially characteristic degrees of the four church modes 
 are those printed thick above : 
 
 The sixth degree of the Dorian (Dorian sixth). 
 
 „ second „ „ „ Phrygian (Phrygian second). 
 
 „ fourth „ „ „ Lydian (Lydian fourth). 
 
 „ seventh „ „ ,, Mixolydian (Mixolydian seventh). 
 
 i.e., the major sixth in the minor scale (raised third of the 
 "subdominant), if used unnecessarily, without modulation and 
 without melodic rising to the third of the major upper-dominant, 
 will always produce turns like those peculiar to the Dorian mode 
 of the fifteenth to the seventeenth century ; likewise the minor 
 seventh in the major scale, introduced without modulation and 
 without the third of the "subdominant following in the same 
 part, will reproduce the peculiarities of the Mixolydian : 
 N.B. N.B. 
 
 W|_. | j l_(« 
 
 oj' S ul °D "S vl vn D* + "T S m< °T D 
 
 (T% " " (°T% 
 
 ii n 
 
 N.B. 
 
 T ..% Sp T S D T 
 
 The charm of such turns rests in the momentary upsetting of 
 the tonality, in a certain wavering of conception between the accept- 
 ance of an intended modulation and the retaining of the key, upon 
 which the continuation first decides. This vagueness of key 
 (in the sense of our modern clarified harmonic conception), 
 was in former centuries the involuntary result of seeking for fixed 
 rules for harmonic motion ; nowadays, it is the consequence of 
 the study of old compositions, the wish to be able again to 
 express their veiled sadness and unsatisfied longing ; therefore, in 
 the first place, the result of imitation. But it may, if theoretically 
 understood and generalised, give rise to consciously freer motion 
 within the clearly recognised bounds of modern tonality, by the 
 deliberate treatment of the abnormal for intensifying the expression. 
 For the Dorian sixth retains its soaring tendency and the Mixo- 
 lydian seventh its lowering weight, even though the natural 
 conclusion be drawn from neither. 
 
Chap. II.) 
 
 Parallel Clangs. 
 
 93 
 
 The Lydian fourth and Phrygian second also bring about 
 peculiar variations of the plain harmony proper to the scale ; 
 they both arise from the plain-fifth clang being introduced with 
 its minor contra-second as suspension (or represented by its leading- 
 tone substitute). Thus the following are added to the forms 
 ¥, ,& ¥, &, discussed above : 
 
 &, in c-major : ft \_g] b d and 
 S-, in A-minor : a f [a] t>\f 
 
 The latter chord is known by the name of the chord of the 
 Neapolitan sixth (b'v. is the minor upper-sixth of the fundamental 
 note of the minor under-dominant), because it is said to have 
 been brought into use by the opera composers of the Neapolitan 
 school (Alessandro Scarlatti, etc.). We leave the chord its name, 
 of course, but are clear on this point, that the introduction of the 
 note characteristic of it (the minor second of the minor scale) 
 makes the scale resemble the Phrygian. In the first place, the 
 minor second of the minor scale must needs be conceived as an 
 auxiliary note to the "subdominant prime [103 (a) — (£)], and even 
 when it enters as passing note between tonic third and fifth, it 
 must be regarded as an approach to the fifth and defined as 
 leading-note to the latter [103 (c) — (d)~\ : 
 
 it, therefore, appears less natural when rising, because then there is 
 less reason for it [1 03 (</)]. The Phrygian second (in minor), like the 
 Mixolydian seventh (in major), seems to have a depressing influence; 
 something like the night of the grave, and the odour of decay 
 wafts towards us from both, or at least resignation, renunciation 
 of the enjoyment of existence (on account of their reaching 
 beyond the under-dominant). On the other hand, the Dorian 
 sixth (in minor) and the Lydian fourth (in major) have somewhat 
 of nervous strain, painful longing, yearning. The Lydian fourth 
 is, in the first place, an auxiliary note of the upper-dominant 
 fundamental note and an approach to the tonic fifth : 
 
 104. 
 
 D +1 . i . < 1 D + „< i T* 4< 
 
94 
 
 Harmony Simplified. 
 
 [Chap. II. 
 
 But the Lydian fourth and Phrygian second (Neapolitan 
 sixth) have the most striking effect, when followed directly by the 
 third of the contra-clang of the tonic, with which they form the 
 interval of a diminished third (succession of both leading-notes to 
 the tonic fifth) : 
 
 ,(«), (0 , Mi . ! W), 
 
 105. 1 
 
 £■ D T 
 
 6> S 
 
 & °s 
 
 
 IV III 
 
 T 
 
 &s vl< v 
 
 s 
 
 
 About this we must remark that in cases like 105 (a) and (b) 
 (bb in soprano, b^iu tenor) absolutely no effect of false relation is 
 brought about. This must be explained by the interval of the 
 diminished third, as composed of two leading-note steps, claiming 
 precedence over the chromatic progression; this, moreover, is 
 important — bt> (= 2> ) is the artificial note, while b (=5) is the 
 natural one, whose reappearing at any time will, therefore, be 
 easily intelligible. A similar case of " false relation " being quite 
 natural and easily intelligible (for really no effect of false relation 
 is brought about) takes place in the so-called " Phrygian close," 
 at least, in that most frequent and characteristic harmonisation of 
 the descending lower half of the Phrygian scale (a gfe), which 
 gives the closing tone its major chord : 
 
 N.B. 
 
 106.- 
 
 T "Dp °S £>+ 
 
 These last turns are nothing else than half-closes, i.e., cases of 
 resting on the dominant harmony, instead of on the tonic, at the 
 end of larger rhythmical divisions. Nowadays we recognise closes 
 of this kind only for parts of a piece of music, but not for the 
 end of the whole piece ; formerly this was different, and the 
 desire for a complete winding up, with the feeling that all was 
 over and at an end, was not experienced. The strangely vague 
 closes in the Church modes, which, as already mentioned, meant 
 nothing more than ending on a dominant (!), have been handed 
 down to us only as half-closes, deceptive closes, etc., of principal 
 subdivisions, but as such they are certainly of the same efficacy 
 now as ever. 
 
Chap. II.) 
 
 Parallel Clangs. 
 
 95 
 
 Conforming in the main to the terminology generally accepted 
 nowadays, but differing from it in a few points by reason of the 
 results of our own observations, we shall now define the terms 
 close, half-close, deceptive close in the following manner : 
 
 (a) A close is the satisfactory entry of the tonic, allowing 
 
 of cessation without a desire for continuation, at the end 
 of a cadence that takes place at a point possessing 
 rhythmical cadential power in a higher degree (end of 
 period or of section). 
 
 (b) A half-close is the entry on a beat ivith rhythmical 
 
 cadential power in a higher degree of a dominant 
 (fuithout dissonant notes or at least in feigning con- 
 sonant form), necessitating continuation. 
 
 (c) A deceptive close is the entry of the tonic at the end oj 
 
 a cadence on a beat with rhythmical cadential power in 
 
 a higher degree, but with progression of one or more parts 
 
 to foreign notes, which give the tonic a feigning consonant 
 
 form, and therefore lead on to a new cadence. 
 
 This formulation allows of our including a larger number of 
 
 harmonic formations in the separate categories ; for, as regards 
 
 the very first, according to the experience hitherto gained, we 
 
 have a whole series of cadential formulas at our command, viz., 
 
 those from both the dominants with or without characteristic 
 
 dissonances : 
 
 J- o/)(VI) °J~ 
 
 [107 (a), (d), and (/), the closes from the upper dominant, are called 
 authentic ; 107 (b), (c), and (e) — from the under-dominant — plagal closes, 
 designations which we shall drop, because they bring entirely hetero- 
 geneous effects under one heading. ] 
 
 Closes are also possible from the parallel clangs of the 
 dominants [this category leads us naturally to the introduction of 
 the contra-third-clang of the tonic, which is parallel clang of the 
 contra-clang, 108 (e) — (/)]: 
 
9 6 
 
 Harmony Simplified. 
 
 ".§> +r 
 
 To these must still be added the leading-tone substitutes of 
 the dominants [which likewise lead us to two new formations, 
 109 («)-(/)] : 
 
 But, finally, it is possible also to close elliptically (skipping 
 over the expected contra-clang of the tonic) from the chords of 
 the Dorian sixth and Mixolydian seventh to the tonic ; if in 
 major this does not immediately sound right to our ears, yet the 
 minor will show us that it is for want of being accustomed to it, 
 and not for want of tenacity of tonal conception : 
 
 ( Closes. 
 
 Other possible close formations will become intelligible to us 
 as ellipses, only when we shall have become acquainted with the 
 intermediate cadences (in the next chapter). 
 
 The term half-close has usually been confined to the resting on 
 the major upper-dominant [111 (a) — (h)\ ; but, in the absence of 
 sufficient reasons, this restriction is not binding on us. 
 
Chap II.) 
 
 Parallel Clangs. 
 
 97 
 
 in. 
 
 (Half-closes. ) 
 
 "Tp D + °S D+ "Sp D 
 
 This small selection will suffice to show what is usually under- 
 stood by a half-close ; of course, one can actually proceed from 
 any chord of the key to the + dominant and pause there. But it is 
 clear that any dominant, indeed even any parallel clang, and any 
 leading-tone substitute of a dominant may become the bearer 
 of a half-close, only presupposing that it falls on a beat with 
 rhythmical cadenlial power in a higher degree, and is made use of 
 as a point of rest (long note with or without a pause ; indeed, 
 if only no rhythmical change of meaning or feminine ending 
 destroy the effect of half close, it is not even necessary to stop at 
 all). We will now proceed with a few suggestions — again only a 
 selection — as to how a half-close (principal subdivision, close of a 
 part) may be made to one of the other dominants, and we draw 
 special attention to the fact that just this hitherto limited under- 
 standing of the terms, close and half -close, bears a great shai e of the 
 blame, if our modern harmony, compared with that of the flourishing 
 period of the vocal style in the fifteenth and sixteenth centuries 
 under the dominion of the Church modes, appears one-sided, 
 stereotyped, and poor. The suggestion of the possibility of occasional 
 points of rest on the under-dominant and on tlie parallel clangs 
 and leading-tone substitutes of tither dominant, will lead young 
 composers to the understanding of a number of good effects : 
 
 112. 
 (Half-closes. ) 
 
 *J -&• -&>- -<S- -«- -&- -5£ ~ZT 
 
 W 
 
 «*njfr») 
 
 T S Tp S T Sp Dp Sp S Dp 
 
93 
 
 if) 
 
 Harmony Simplified. 
 
 (« 
 
 [Chap. II. 
 cf- IT 3 (/') 
 
 We have already discussed the deceptive close in its simplest 
 forms (pp. 72, 77, 84) ; if we now define it quite generally as a 
 close disturbed by foreign notes, but in feigning consonant form, 
 all closes introduced in 107 — no must be looked upon as decep- 
 tive closes as soon as the tonic does not enter in pure form, but 
 as feigning consonance, thus in the first place as parallel clang 
 or leading-tone substitute : 
 
 "3- 
 
 (Deceptive Closes. )" 
 cf. 107. 
 
 f*Sfe 
 
 ^ (*> 
 
 * M 
 
 M), /* 
 
 1 1 
 
 Uf) 
 
 "-§- 
 
 zztz 
 
 r- 
 
 D 
 
 ~&~ 
 
 IS 
 
 Tp "S °Tp °S Tp D ¥ 
 
 ,„«"), 
 
 W | * ('•) | 
 
 /T\ 
 
 -B=d-=r— H-J— 
 
 /T\ 
 
 fe-*£r— *S— 
 
 1 1 
 
 a 
 
 . 11 -a—i gs n — ^ — 
 
 r 1 
 
 1 1 
 
 
 V ^ n ^ ' 
 
 *z/ 
 
 
 it~i '» irr. 
 
 H 
 
 D "Tp S Tp 
 
 T 
 
 °D "Tp "D -F 
 
 Above (in — 112) we avoided the parallel clang of the contra- 
 clang among the half-closes, for the reason that, in close-formations, 
 it is not looked upon as parallel clang of the contra-clang, but 
 rather as a chromatic transformation of the tonic, viz., as leading- 
 tone substitute 0/ the tonic-variant, i.e., of the tonic of the opposite 
 
 mode .- e.g., a\> + in c-major, not as °Sp, but as T\^, more simply ¥ ■ 
 
 and °g% in A-minor, not as +Dp, but as Tf u<t more simply 3?. 
 In other words, the succession g + — a\> + in c-major [114 (a)] 
 denotes a quick change from c-major to c-minor, making use of the 
 most customary form of deceptive close of the latter '[/)— ff cf. 
 113(A)], and similarly in A-minor °a—°g% [114(0)] is a quick 
 change from A-minor to A-major, making use of cne of the forms 
 of deceptive close of the latter [°S — 3?, cf 113 («*)] ; however, 
 not only the leading-tone substitute, but also the parallel clang of 
 the tonic-variant may be borrowed for deceptive closes, by which 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 99 
 
 means we gain two more new deceptive close-formations, viz., 
 
 for A-minor first e + — V# [=Z>— + Tp, really T\$, cf.114 (f)], and 
 
 for c-major °c—e\>+ \_=.°S—°Tp, really Z'jj, ^ 1 14 {d)~\. But the 
 close to the parallel clang of the tonic-variant is possible not 
 only from the contra-clang, and that to its leading-tone substitute 
 not only from the plain-fifth clang ; we therefore gain a whole 
 series of new possible forms of deceptive close [114 (e) — (ot)] : 
 
 114. 
 (Deceptive Closes. ) 
 
 W, 
 
 w 
 
 5fc 
 
 ^fer 1 
 
 1 
 
 D 
 
 ¥ S v 
 
 ¥ 
 
 Tp Sp °Tp 
 
 Certainly all the deceptive closes from 1 14 (a) — (m) give rise to 
 difficulties in the further retaining of the tonality, and come 
 rather near to a real transition into the fifth-change key (key of 
 the tonic-variant) ; at least they necessitate the use of the chords 
 of the Dorian sixth or Mixolydian seventh for the return over 
 the contra-clang and the quickest possible regaining of the plain- 
 fifth clang or its parallel clang, e.g. : 
 
 (o) to 114 (g). 
 
Harmony Simplified. 
 
 [Chap. II. 
 
 (c) to 114 (a). 
 
 -I 1 
 
 (rf) to 114 (/). 
 
 ¥ Z> 3 > °S 
 
 These last observations have introduced an abundance of new 
 harmonic steps. The introduction of the Mixolydian seventh 
 and Dorian sixth each yield two new feigning consonances (in 
 
 c-major: £> 3> = "d and Jpg = bb + ; in A-minor : S ul< = d+, 
 $"m< = "/#)> whose combination with the principal clangs in- 
 deed only reproduce harmonic successions already discussed 
 (c + — "d and °e—d + = whole-tone change, g+—°d and °a — d + 
 = fifth-change, /+ — "d and °b — d + = minor-third change; 
 °d — °c and d* — e + = whole-tone step); their connection with 
 the parallel clangs also yields no new steps ("d — °e and d + — <r + 
 = whole-tone step, °d — "a and d + — g + = contra-fifth step, "d— °b 
 and d + —f + = minor-th''rd step, a*7 + — °a?and d —°g$ = tritone 
 change). But, on the other hand, the two new harmonies arising 
 from the introduction of the Phrygian second and Lydian fourth, 
 in c-major: °/# (=&-) and d+ (= + £> n<) ; in A-minor: bt> + 
 
 (=&) and °d(= °S n ), supply a few new combinations : 
 
 (a) °c d + (°S— + D n ') and e+— "d (£>+— ° S u< ) are contra- 
 
 whole-tone changes. 
 
 (b) "c—'f% (°S-&), a\>+-d+ (°Sp— +£>"*), e+—b\>-r 
 
 (+£>—S), °g\— °d(+Dp— °S* l> ) are tritone steps. 
 (c)/ + — °/t (S—&) and "b— bi> + (°Z>— S) are chromatic- 
 semitone changes. 
 
 (d) at? + — °/4 (°Sp—&) and °g\ — b$>+ ( + Z>/— S) are 
 
 augmented-sixth changes. 
 To these we must add the connecting of the parallel clang of 
 the tonic-variant with the leading-tone substitute of the plain- 
 fifth clang : h 
 
 (e) e^—'Jl {TQ-&) and "4-*b+ {Z^—S), an 
 
 augmented-second change, a step which is also the result 
 of the connection of the parallel clang of the contra- 
 clang with the parallel clang of the plain-fifth clang 
 (a \>-°b = °Sp—+Dp, and °g%— /+ = +Z>p—°Sp). 
 Finally, the combination of the parallel clang of the contra- 
 clang with the parallel clang of the tonic furnishes the step : 
 
 (f) ab + — °e (°Sp— + Tp) and 
 
 -c+ l+Dp—°Tp) = aug- 
 
 mented-fifth change {double-third change), 
 while the combination of the same with the parallel clang of the 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 subdominant (a7+— "a = °Sp— + Sp, °g$—g + = + Dp—°Dp) repre- 
 sents the chromatic-semitone change already introduced at (c). 
 
 If we still add the leading-tone substitute of the contra-clang 
 (S in major, :©- in minor), this will produce, besides the 
 already mentioned rare steps (in c-major and A-minor : d$ + — "e 
 and "dlff — c+ = augmented-second change, d'Q + — °b and °d$—f + = 
 augmented-sixth change), two more new steps : 
 
 (g) The augmented-third change, S — & (dV + — yjf) and 
 
 &— S (Vjf— b\>+), and 
 
 (h) The chromatic-semitone step: 
 B-—°S"i?d%—°d). 
 
 S—+Z>"< (db+—d+) and 
 
 The parallel clang of the leading-tone substitute of the plain- 
 fifth clang (by the way, the most complicated of our formulas, 
 
 ■•"D'^and °S n ) may be comprehended more simply as plain-fifth 
 clang of the plain-fifth clang, i.e., as dominant of the dominant 
 
 o 
 
 {.&), or "subdominant of the "subdominant (°$); we shall 
 further on become acquainted with many a possibility of intro- 
 ducing the dominants of clangs proper to the scale, but we 
 preserve the special significance of these two, which are the first 
 we meet, by affixing a special sign, viz., the doubled D or "S. 
 The second dominant and the contra-clang stand in intimate 
 relation to each other, as the one harmony may be transformed 
 into the other by chromatic alterations ; if the characteristic 
 dissonance be added, this will prove even more striking 
 
 The contra-whole-tone change, the simplest of the new steps 
 (connecting the contra-clang with the second dominant of the 
 other side : °S — ,© or D + — °$), therefore, requires two chro- 
 matic progressions : 
 
 °S 3 D T & S vu +Z> "^ °S "T D> 
 
 Part progressions which should be avoided are the augmented 
 sixth (a?— /;$, g%— bb ; inverted — as a diminished third — good 
 at any time), and the augmented fourth (ab — d and g\— d; in- 
 verted — as a diminished fifth — good). 
 
 The tritone step (°S— &, °Sp—@, +£>—$, + Z>p—°°g) 
 has, besides the three tritone steps (1 — 1, 3 — 3, 5 — 5, or I — I, 
 
Harmony Simplified. 
 
 [Ctiap. II. 
 
 Ill — III, V — V), also an augmented-second step (5 — 3, or 
 III — V) to be avoided, but is very simple if the possible dimin- 
 ished-third step (1 — 3, III — I) be made : 
 
 »7-i 
 
 
 
 TgT' p 
 
 = 8SC 
 
 ^E^ 
 
 52 
 
 ^= 
 
 I b^< 
 
 jj. 
 
 ^fl^ 
 
 Sgj 
 
 -o S +0"- 11 T "Sp 3 D T Z>+ ".S 3 * 1 T +Z>/ °$ °S D 
 
 The chromatic-semitone change (S — &, °D — °S, "Sp — + Sp, 
 + Dp — °Dp) contains only one possible augmented step, which is, 
 however, obviated if the leading-tone step be made : 
 
 t — l — r 
 
 S+D 11 " 1 T °D S*^ °T°Sp + SpD T + Dp°_Dp°S D 
 
 The aagmented-sixth change (°Sp — &, Dp — £■, & — + Dp, 
 &—°Sp) is simple if the possible step of a diminished third 
 be practicable ; it has the possibility of two augmented seconds 
 (1 — V, I — 5), two augmented fourths (1 — III, 3 — I), an aug- 
 mented fifth (5 — III), and an augmented sixth (1 — I) which arf 
 allowable only in inversion : 
 
 119. 
 
 r~r^ 
 
 "Sp & D T + £p S°S °T S- Up T & "Sp 'T 
 
 The augmented-second change (?\t, — &, /yj'J — §) shows two 
 leading-tone steps and a chromatic step, which are confronted by 
 an augmented-second step (1 — I) and an augmented-fifth step 
 (1-V): 
 
 w._ m. _|_ 
 
Chap. II.] 
 
 Parallel Clangs. 
 
 103 
 
 The double-third change (augmented-fifth change : °Sp — + 7p, 
 
 + D/> — °Tj>) gives occasion for a sustained note (3 III), and has 
 also two chromatic steps, but likewise risk of consecutive fifths 
 (f v) and of steps of an augmented fifth and of an augmented 
 fourth • 
 
 121. 
 
 The augmented-third change, connecting the two most artifi- 
 cial chords (S- — B), gives occasion for making both those 
 diminished third steps simultaneously (2* — 3, III — II<), but, for 
 the rest, an augmented second 5 — V, an augmented fifth 3 — V, 
 and two augmented sixths (1 — V, 5 — I), obstruct the way 
 [122 («)-(*)]• 
 
 122. 
 
 & "$ °S °T 
 
 The chromatic-semitone step [122 (c) — (d)] is not difficult, if 
 use be made of the proper doubling (V of °S, and 5 of Z> + 
 respectively). 
 
 If we now proceed to make the numerous new expedients 
 shown here our own by practical exercises, we choose the simplest 
 forms for this purpose — i.e., write note against note (without 
 figuration; but in order to make a smoother progression to the 
 following chords possible, a change of position by way of figura- 
 tion may occasionally be resorted to). We also forego modu- 
 lation for the present, so as not to lose the power of surveying 
 the whole on account of the abundance of possibilities. The 
 
104 Harmony Simplified. ichap. n. 
 
 exercises following next are therefore to be worked out simply in 
 the four vocal clefs. 
 
 Exercises 197 — 220 (not for figuration). 
 
 (197) % : TD I T&»\ "S..\£>° s \Tp Sp\ @ D 1 ¥ °S I T 
 
 I VII I I 
 
 VII 
 
 (198) 3 / 3 : "T S m< D\ "T "Tp "Dp \ S vl v IP \¥ D $ m * | 
 
 D "T S I D*± J I ¥ D ..» I °T 
 
 (199) 3 /< = T I °S & 1 \¥ Sp B \ D S S \ &* "Tp\ 
 
 s +sp & 1 D Tp °S 2> 1 .'. Z> 6 5 1 r 
 
 VII 6> s 
 
 (200) E: , r , r/ 1 $ m< +z> 2 s \ £* * +rp + np\ 
 
 VII 
 
 $ m< °5 + D n< l I T 
 
 (201) | : r I ,§> Z> I 2? °S I .. a> + Z> ,1< I ..»> "5/ I S vn "Tp \ 
 
 VII 
 
 (202) 6 / e : T| "S °Sp °S"}. 1 +z>/ + rp s m< °s \ s & 
 
 c r c r~ 
 
 Tp S m< I S- D °T 
 
 (203) $: T \ & & \ & @ \ S £> \ Tp S™ I "Tp .. \ 
 
 S 
 
 +z ,n< 1 1 T 
 
 (204) V, : 5 D Tp I .§» .£ S I Z> 5/ & \ 2? S y D< \ 
 
 T'S m\ d ¥ °s\ T ia rrsi.) 
 
 VII o 6> 
 
 (205) B: S m< S m < + D"" 1 I +Df +Tp » "Sp\'S °S D* + | 
 
 0^) o^ oj- yj 
 
 7 iv in 
 
 (206) E : £> 3> MP" 'S'" ' I °^> °7> ^ Z>/> I ,© D S vl< v | 
 
 3» D T (J) 
 
Chap, ii.] Parallel Clangs. 105 
 
 VII 
 
 (207) V 4 : T S- I I D ¥ "Dp \ "g °S °T\ S m< D .. | 
 
 in 7 
 
 VII o 
 
 T S m< T I $ m< D S\"g "S D\"T (J ,) 
 in hi 
 
 (208) E:rZ)'|?+2>|SZ)| 2? "Sp I S +Sp | +Z>" l | 
 
 3 
 
 IV III 
 
 S vi< v 1 J, 
 
 VI 
 
 (209) B: °D "S\ +Dp +Tp I °S'" 1 \ D ¥ \ S m< $ m< \ 
 
 +Dp T I "S "D I "T 
 
 f2io) V«: ^ I S D\ T D*> \°Sp S \ D° !. | °S .. v " | 
 
 r r 3 « c - 
 
 (211) 3 / 4 : °T ..'* °Tp \ D °S I Z> s> ' s I ¥ "Tp °S'* | 
 
 V VI 3 
 
 VII 
 
 .'. D +Dp I +Tp S lu< y n< I D °Sp D\"T 
 
 (212) %: T Tp\"S Dp \Tp S\ Sp \"S D 1. \ "Sp S | 
 
 +5/ 5 I T 
 
 (213) $ : 'T I °Z> 5 vn I "Tp °Sp\°S T \'-D "S \ T T S- \ 
 
 hi hi 
 
 D> °Tp \ s .. vu 1 °r 
 
 (214) 3 l t : -T I °5 1> ' Z> I SP S °D | Sfi $ vn ti[ VI " | 
 
 D+ "D "Sp I "Tp "T S m< I Z>+ +Tp °S'» \ 
 * Z» "5/ I T 
 
 (215) $ : 3? £/ I +D U< * \ ¥ Dp \ Tp &\ D 6 * \ °S n m | 
 
 6 7 
 
 Z>* .. I T 
 
 V VI VII 
 
 (216) 3 / 4 : °^l S m< # m< \ D P \ S S vl D \ +Tp °S \ 
 
 r r : r rr r : r rr 
 
 = > 
 
 7}VI I> I oC2> I /} 1 o'p o cm II I oy 
 
 r r r c r r r c r 
 
106 Harmony Simplified. [Chap. n. 
 
 6 65 VII VIII 
 
 (217) B : +Z> n< ' I 5 .. v " £> 3> S vtl I £>* 3 ¥ °Tp \ S v VI 
 
 in 
 
 3 D I °T 
 
 (218) %:"S\ D $ \ S vn 3 I + -D n< ' I * Z)/ I °^» "5 | 
 
 3 
 
 Tp sp - v " 1 r 
 
 (219) V 4 : °5 I °r S vn °T \°D ¥ &\ S vl °D °T | & °T | 
 
 r r 
 
 VII 
 VII > £VII «II< I +2^n < 1 7 I oy CVI V I oji 
 
 (220) 7,: £ m< I °:T $ UI< D ¥ \ "Dp S v VI °Z> S m< I 
 
 VII ~ " 
 
 D l £ 2)VI £111 < J) I g S Vll o T 
 
 These exercises go as far as is at all possible in the combination 
 of feigning consonant formations that are intelligible as related 
 to one and the same tonic ; if any other formation beyond those 
 displayed here be found intelligible, it will have to be judged and 
 treated according to the same principles. The great majority of 
 the harmonic progressions considered in this paragraph generally 
 induce modulation ; but we again draw attention to the fact that 
 the greatest power of expression in harmony lies not in the 
 frequent (and only too easy) change of tonality, but rather in 
 extending the boundaries of the key ; progressions like b (? + — 6 + 
 
 (S— 3) in A-minor or °f—f% ( = "J? — &) in c-major 
 (without modulation) signify a powerful respiration, as if to 
 burst the fetters of the mortal frame. Naturally the student of 
 composition should be most imperatively warned against the 
 misuse of these strongest means of expression. 
 
 Our view has now become extensive, and the following 
 chapters, which lead us back into the more trodden paths will 
 introduce easier work again. 
 
chap, in.] The Theory of Dissonance. 107 
 
 CHAPTER III. 
 
 THE THEORY OF DISSONANCE. SEQUENCES. INTERMEDIATE 
 CADENCES. 
 
 § 10. COMPLETION OF THE THEORY OF DISSONANCE. 
 
 We have gradually, and as occasion offered, become acquainted 
 with the significance of dissonant formations of all kinds ; it is 
 now time to arrange them according to fixed points of view, and 
 group them clearly, so that other analogous formations, when 
 introduced, will immediately be understood. The most important 
 distinction is that of characteristic dissonances from those only 
 figurative ; the former class we have already become acquainted 
 with, as the most important marks of clangs in their functions as 
 dominants, within the key as well as for modulation (6 added to 
 the+.S, VII to the "S, 7 to the Z>+ VI to the °I>), and of the latter 
 class we have written a great number in our figuration exercises, 
 without, however, giving them special consideration. Now it is a 
 matter of extending the category of characteristic dissonances 
 and of arranging the large number of figurative ones in groups. 
 If we begin with the latter, we shall find that figuration by means 
 of passing and auxiliary notes quite naturally makes us ac- 
 quainted with a lot of dissonant chords, to which, in the usual 
 method of teaching harmony founded on the " figured bass," far 
 too much importance is attached by their being placed on a level 
 with the characteristic dissonances. 
 
 If, in the figuration of the prime or fifth of the major and minor 
 chords by their upper or under seconds, the figured note be 
 doubled, and thus remain present (generally in another octave- 
 position) simultaneously with the foreign note (second or 
 seventh), then chords of four notes will result of a construction 
 partly contradictory to the chords of four notes with which we 
 have hitherto become acquainted : 
 
 (») 7* d) 2 M 6 w 4 w VII> (/) II {g) Vl (/0 IV 
 
 123. 
 
 ^^^^ ^ m^F ^SSSM 
 
 (9) 
 
 (IX) 
 
 H 
 
io8 Harmony Simplified. [Chap. in. 
 
 The figuration of the third yields similar formations : 
 (0 4 (*) 2 M II (*) IV 
 
 If the figurative note (the j<, 2, 6, 4, or VII*, II, VI, IV) 
 proceed immediately by step of a second, i.e., if the 7< coming 
 from the 8 lead to the 6 or back to the octave, if the 2 coming 
 from the 3 go to the 1 or back to the 3, etc., therefore — if the 
 foreign note (entering on an unaccented beat) really prove to be 
 the most natural insertion between two harmonically significant 
 notes, we have before us the most easily intelligible but weakest 
 kind of dissonant formation, and that on the lowest footing as 
 regards effect, so-called 
 
 Passing Dissonances. 
 
 As auxiliary notes, the leading-notes (minor upper and under 
 seconds) of the note to be ornamented are often introduced, even 
 where they are not proper to the scale, by which means the 
 formations of 123 and 124 receive a somewhat different aspect : 
 
 WN.B 7* (*) 2> (c) 6> frf) 4< (e ) VII> (/) II* 
 /rf-^- t ^ - I _ U ■ ■ ! 1 » " > .l«J_. jt^J-iJb 
 
 125. 
 
 VI < w IV» (,-, 4H (i) 2 
 
 11 = 
 
 IV t) 
 
 By this approximation to the ornamented note the more close 
 connection with the latter is very sharply marked* in many cases, 
 however, the effect becomes weak and artificial. 
 
 Many of the chords written down at 123 — T25 have three 
 notes on degrees next to one another (even though in different 
 octave-positions), thus c d e in 123 (b) and (/) and 124 (k) ; 
 
Chap. III.] 
 
 The Theory of Dissonance. 
 
 109 
 
 a 6 c in 123 (A) and 124 (m), whereas all the dissonant chords 
 considered hitherto (S 6 , D VI , S vu , D 1 ) had only two notes on 
 degrees next to each other (*, &, vm, ?)• It is evident that such 
 chords, unless they arise in the fashion already discussed, as it 
 were casually in the figuration, would make themselves very notice- 
 able by their striking dissonance, and they therefore remain 
 alien to plain, unfigured writing, which avoids all that is re- 
 markable ; this style in general prefers feigning consonant clangs, 
 parallel clangs, and leading-tone substitutes. It, therefore, seems 
 quite explicable that successions of consonant harmonies, com- 
 paratively very difficult to understand, should have become quite 
 at home in musical literature much earlier than even the simplest 
 chords of the seventh and of the sixth arising from the addition 
 of the characteristic dissonances to the dominants. In one form 
 of introducing, certainly, not only these last mentioned forma- 
 tions, but also those shown in Examples 123 — 125 were com- 
 mon for centuries, even in the strictest style of writing for several 
 parts, viz., as so-called 
 
 Prepared Dissonances. 
 
 If in the transition from one harmony to another 
 (T — S, S — D, D — T, S — T, etc.), a note foreign to the second 
 be at first sustained and only subsequently proceed by step of a 
 second to a note belonging to the new harmony, a so-called 
 suspension arises (the note belonging to the first clang suspends 
 one of the second for a time). 
 
 We will enumerate the most important cases for the principal 
 harmonies : 
 
 126. 
 
 T S 
 
 T S 
 
 T S 
 
 T S* 
 
 S D< S D' 
 
 S D 
 
 S D 
 
 S D' 
 
Harmony Simplified. 
 
 [Chap. III. 
 
 3 7*8523 52l 
 
 (0 (*) (0 
 
 S Z>»[!] 
 
 To these examples in major the following examples in minor 
 correspond : 
 
 V II I V II III III VII " VIII III VII > vim 
 
 («) (*) W W 
 
 -l-n Vrs=r-\ r-n !^=M- I— n *= 
 
 127. 
 
 Ill 
 
 IX VIII III II I III II 
 
 III V IV III 
 
 w 
 
 
 («) (70 
 
 is) 
 
 (*=^ 
 
 — <&— 
 
 I.", 1 1 — 1| 1,". 1 
 
 — 1- -^-^- ° II 
 
 $=^= 
 
 
 r ■ <* ^ ■ -=- 
 
 -^ 19 = U 
 
 -s«- 
 
 a. 
 
 U -^ ' """ 
 
 1 <s 
 
 fr*— fr- 
 
 v-e*— 
 
 ~-^-l % 1 3 II? 1 " 
 
 "^ n 
 
 !>-< — 1 != 
 
 "- 1 
 
 J p_l l.^—^- 
 
 H-j- ^ U 
 
 °Z> "S 
 
 °Z> 5 V 
 
 °z> .s VI1 
 
 °Z> 
 
 (A 
 
 V 
 ) 
 
 IV 
 
 -, 1 
 
 — ~i— 
 
 V 
 
 .. 1 
 
 III VII » 
 (0 
 
 1 ^-r^ 
 
 VIII V 
 
 II 
 
 - u 
 -e? — 
 
 III 
 
 - 1 
 
 V 
 V) 
 
 — ^ — 
 
 II 
 
 I 
 
 1 
 
 -H 
 
 
 1 ' 
 
 1 
 
 £2. 
 
 
 
 1 
 
 — <&- 
 
 
 1 
 
 V- 
 
 II g? — | 
 
 «— 
 
 
 -H 
 
 -H 
 
 
 
 
 
 z^-=- 
 
 H-F-l- 
 
 — 3- 
 
 
 — t— — 
 
 
 — 
 
 -U 
 
 °Z> °.S 
 
 °5 
 
 III 9* 8 
 
 V 
 
 ('") 
 
 o 1" 
 
 —~l 
 
 1 
 
 (*) 
 
 ~"J 1 
 
 
 
 
 
 
 
 
 — — — 
 
 ■ ^ — 
 
 
 
 
 
 i7 1 ^_ 
 
 ■&• 
 
 
 1 
 I— 
 
 1 gy 
 
 1 — & 1 
 
 Si :g 
 
 1 
 
 
 
 *~l 
 
 
 vl? 4 
 
 °.S Z>'[!] 
 
Chap. III.] 
 
 The Theory of Dissonance. 
 
 i [i 
 
 To these must be added the formations arising from the 
 introduction of the contra-clang of the tonic : 
 
 III 9» 8 3 IX < 8 III 6> s 3 VI « V 
 
 (<») («) W (d) 
 
 128. 
 
 s z>+ 
 
 z>+ °s 
 
 °S +T +T °S 
 
 3 IX<VIII III 9 > 
 
 3 VI<V III 6> s 
 
 CfO (A) 
 
 By the combination of two suspensions possible in the same 
 harmony step, other chord-forms arise, but only some of them are 
 more complicated : 
 
 fa) 
 
 5 2 3 5 a 1 5 2 1 
 
 3 T 8 3 7 < 6 3 7 < 8 
 
 5 4 5 
 323 
 
 ^j^Fi^f^^Tarri 
 
 129. 
 
 Jr 
 
 Jr 
 
 =Ie 
 
 r s" 
 
 D> 
 
 7 4 3 
 398598898 I43 
 
 5 4 3 3 V « 3 7 6 III 9 > 8 
 
 W (/) (•; (*) 
 
 5 Z>' 
 
 Z" 
 
 D> 
 
 D 
 
112 
 
 Harmony Simplified. 
 
 [Chap. III. 
 
 VII 2 3 III VII'VIII III"VII»VIII I 4 3 
 III 6=- 5 V II III V III 9 » 8 
 
 (0 (*) W (««) 
 
 D* 
 
 D+ "S 
 
 Composition in more than four parts, which we shall have tc 
 practise later on, admits a great number of new possible har- 
 monies through suspensions ; good effect, as regards the sound of 
 prepared suspensions, is certain so long as we avoid writing the 
 sustained note simultaneously in the same octave-position as the 
 chord-note which it retards : 
 
 9 
 
 8 
 
 9 
 
 8 
 
 9* 
 
 8 
 
 7* 
 
 8 
 
 4 
 
 5 
 
 7 
 
 6 
 
 2 
 
 3 (J) 
 
 4 
 
 3 W 
 
 5 
 
 4 
 
 n 
 
 v< 
 
 Those dissonances which arise from chromatic alteration of a 
 chord-note (so-called altered chords), belong as a rule to the class 
 of passing dissonances, i.e., a chromatically altered (raised or 
 lowered) note may be inserted as a figurative element, when, in 
 unfigured writing, there would be a step of a major second. Such 
 chromatic passages are generally quite easily intelligible, as 
 inserting a leading-note to the following chord-note, e.g. ; 
 
Chap. III.] 
 
 The Theory op jJissonance. 
 
 113 
 
 
 s 
 
 5* 
 
 3 V 
 
 v< 
 
 VII 1 1< 5 
 
 131- 
 
 tJ -«- 
 
 
 J_^ J s, 
 
 1 
 1 — ' — n — " 
 
 
 -H? — U — «-= — r-f — H 
 
 
 
 
 
 
 • f J — 1- - ! = i: fl 
 
 z» 
 
 But our ears often refuse to understand formations like 
 1", I*, 3*, III*, because the interval of the augmented third 
 arising from them (1 * — 3, 1 — 3*, III — I*, etc.) sounds toe 
 much like the fourth, and may under circumstances lead to a 
 wrong conception of the harmony : 
 
 (a) (bad) (/■) (good) (c) (good) (rf) ? 
 
 (Naturally the 3* of the T and D, the 1 * of the T and S, the 5 > 
 of the S, in major, and likewise the III* of the "T'and °S, the 
 I* ofthe°y and °Z>, and the V* of the °D in minor, have no 
 claim to be admitted, as they coincide enharmonically with an 
 easily intelligible note proper to the scale ; moreover, it should be 
 remembered, that in chromatic passages it is only a question 
 of gaining a ltading-tone step to the next note.) In cases like 
 132 (a) and («'), it would be preferable to write and conceive the 
 figurative note as an auxiliary note (/$ auxiliary note to g), 
 although it does not return, but, on the contrary, is chromatically 
 altered in the next chord (quitted auxiliary note) : 
 
 133 
 
ri4 
 
 Harmony Simplified. 
 
 [Chap. Ill 
 
 Perhaps many would prefer to write also bfy (4b or VII*) 
 instead of a% in 132 (6) and (c). One would also rather see the 
 S> of the + T and the V* of the °T and °S written as auxiliary 
 notes to 5b and Vb [134 (a) — (/)], whereas the 5> of the D and 
 V* of the ".Sare quite intelligible [134 (g) — (AJ] : 
 
 <«) 5* (») 4* 
 
 In general, it must be confessed that chromatic raising is 
 altogether much more familiar to us than chromatic lowering, for 
 which the practice of the present day may in part be responsible. 
 
 But now both the " passing dissonances," arising from diatonic 
 progression by second through intermediate degrees, and "altered 
 chords," arising chromatically, come in a line with "prepared 
 dissonances," and indeed outdo the latter in harshness and power 
 of dissonance, as soon as they are moved to the accented beat in 
 the bar ; in this manner we obtain the third and most important 
 category of dissonant formations, 
 
 Unprepared Dissonances. 
 
 All the dissonant formations introduced as prepared dissonances 
 above (126 — 130), may also enter freely, without preparation of the 
 dissonance, and with more or less good effect ; this third category 
 therefore includes all dissonant formations. Certainly we should 
 be very wrong in assuming that any dissonance might with im- 
 punity enter unprepared ; on the contrary, it will under any cir- 
 cumstances be well to bear in mind, that any such free entry 
 is always more or less the result of substitution or ellipse. The 
 following examples throughout confront the unprepared dissonance 
 with the prepared, that entering by step of a second on the 
 accented beat, with the passing note on the unaccented beat, as 
 
Chap. III.] 
 
 The Theory of Dissonance. 
 
 "5 
 
 with the more original and more perfect form [cf. (a) with {ad), (b) 
 with (M), etc.]. 
 
 (*' 4 (/>'■) 4 
 
 The following examples are throughout to be compared with 
 the prepared dissonances at 126, of which the progressions given 
 here are only vicarious forms : 
 
 to 2 (« 2 [*1 M 7* 00 7' 
 
 ■=*' gj_ ■ ■_ ! . , , 1 u — , , ■ - n — I- 
 
 I 
 
 : .g).gszgzfligl^^; 
 
 ■j= 
 
 136- 1 
 
 tr—r 
 
 =F 
 
 J- 
 
 I 
 
 I 
 
 I 
 
 mm 
 
 m^mm 
 
 *=E 
 
 <*) 4 to 4 
 
ri6 
 
 Harmony Simplified. 
 
 [Chap. Ill 
 
 The examples in minor (Example 127) by means of vicarious 
 progressions yield the following unprepared dissonances : 
 
 W VII » w VII >[3] 
 
 The bracketed $ or j? in 136 and 137 changes the whole-tone 
 suspensions into leading-tone suspensions, and marks the melodic 
 relation of the note in question to that following in the same 
 part even more unequivocally ; but, on the other hand, disposes 
 of the theory that this combination results from mere vicarious 
 progression (with change of position of the chord), or, at least, 
 demands in addition the assumption of a chromatic passage 
 after the kind at 135, e.g. : 
 
 136 (S) for : 
 
 13M 
 
 The transformation of the examples from 131 onwards into 
 
Chap. III.) 
 
 The Theory of Dissonance. 
 
 117 
 
 unprepared dissonances will now scarcely be necessary; besides, 
 they all yield leading-note suspensions as it is. But now we may 
 say in general that, before any chord-note, unprepared who/e-tone or 
 semitone suspensions from above or below are possible, but that they 
 are by no means of equal value. Leading-note suspensions from 
 below are at all times easily intelligible, those from above, on the 
 
 contrary, only when they are proper to the scale, or at least introduce 
 
 
 nearly related harmonies (III of °S in major, III of °^ in minor). 
 But we most emphatically warn all against the misuse of suspensions 
 foreign to the scale. Too much pepper and salt spoil a dish. 
 
 The enlightenment we have now acquired as regards the 
 theory of dissonance we shall first turn to advantage in diversi- 
 fying our figuration exercises. The following group of exercises 
 is to be worked out in such a manner that every example, as far 
 as possible, introduces prepared dissonances o?i the accented beats, 
 and, as in Exercises 149 and those following, one example each 
 with figuration of the soprano, of the alto, of the tenor, and of 
 the bass, and every fifth with distribution of the figuration among 
 all four parts. The following remains to be noticed as regards 
 the execution of these exercises : 
 
 (a) For the preparation of the dissonance a chord-note entering 
 on the preceding unaccented beat will serve (prime, third or fifth 
 of a real harmony or of a feigning consonance [!], or also the 
 seventh of the + D or "S or sixth of the + S and °Z>). 
 
 (b) The dissonance has to proceed by step of a second ; only the 
 VII of the °S and the 6 of the .S may first proceed to the funda- 
 mental note of the + /?, and let the progression by second follow 
 subsequently. 
 
 (c) When the part to be figured gives no opportunity for the 
 introduction of a prepared dissonance on the accented beat, the 
 syncopation is to be carried through, by tying a note common to 
 both harmonies ; in such cases the syncopated part is absolved 
 from the necessity of proceeding by step of a second, and, if 
 possible, it will proceed to a chord-note which yields a prepared 
 dissonance for the next accented beat. 
 
 (d) In figuration for bars of three beats, or where the 
 figuration is to introduce three or even more notes to each chord 
 of the other three parts, only the note immediately preceding the 
 accented beat is to be tied, so that the syncopation is only partial, 
 as may be seen from the following commencements : 
 
 139- 
 
 I 
 
 («)(*|cD™ 
 
 .. s 6 
 
 9 J m 
 
 .. D 
 
 T 
 
 1 
 
 — ^Rll — ' 
 
 
 ** 1 
 
 
 1 ftF^ 
 
 ' j-* 
 
 \ 
 
 J—ii 
 
 
 
 . & ■ 
 
 ^i 
 
 J J 
 
 \ 
 
 ^"'P ^ : p 
 
 
 
 ~t — \~f==. 
 
n8 
 
 Harmony Simplified. 
 
 [Chap. III. 
 
 (*)(.*! j. )r .. d 
 
 lr &i-^ — J-. J» I 
 
 The following (tenth) model example may serve to render the 
 application of these rules intelligible ; we will take the alto part 
 for figuration : 
 
 T B> T S c Dp Tp Sp 
 
 At NB., as the note falling on the accented beat is consonant, 
 a chord-note follows, at bars 3 and 4 the same one, at bar 6 
 another, in bar 8 the seventh, and at NB.t chromatic alteration of 
 the third takes the place of simple repetition (°S instead of S + ). 
 
 Exercises 221 — 236 (for syncopated figuration). 
 
 (221) B '■ T I J 1 " Tp \ S Sp\& 1. \T Tp\°S D \ Dp Tp \ 
 
 S" D I T 
 
chap, iti.j The Theory of Dissonance. 119 
 
 VII 
 
 (222) $ : S v " I D+ S v " I D+ °T I S m " D \ °T °D \ "Sp $ vu | 
 
 D**?. I ¥ °S\°T 
 (223) : 3 / t : T\ S 6 D \ T S \ Sp Dp \ Tp °S \ D* 1. \ 
 
 T f etc. 
 
 2? °5 1 d s 1 r 
 
 (224) 3 /. : °r 5 vn \ D ¥ \ °S °D \ °D/> S \ D °D \ °S T \ 
 
 I I I etc. ' 3 ' 
 
 5VII £>+ J o T 
 
 (225) %'. r\n n \ 2 S \ D sp \ s> d \Tp t \ 
 
 U I etc. 
 
 Sp =S I Z> + I T 
 
 (226) 7. : "T I 5 VU Z> I °T °D I °5/> ^ vn I D "D I .. 2 » °S I 
 
 L» ! t etc. 
 
 Z> ^ I °5 Z> I T 
 '227) V 4 : £ -O I ^ .. I Dp T I Sp D \ T °S\ D Dp \ Tp D \ T 
 
 r r Tetc. 
 
 (228) 3 / 4 : "^ I - °S I °Z^ T I S vn D I T °Dp \ °Tp °T \ 
 
 f (^ etc. 
 
 °S .. v " | Z>« + I "T 
 
 (229) B: r I S 6 T S 6 D I T °S D Dp \ Tp Sp D* + \ 
 
 Tp S T (Figuration : / | . s J J J > | J") 
 
 (230) E : T .. C .S I T S v " D "T \ "D °T S v, \ .. | 
 
 Z> 7 ^ S VI1 D 1 I T 
 
 (231) 3 / 2 : T S ?. \ D Dp T \ Tp D ..' \ T Sp D \ T Tp Sp \ 
 
 D Tp S\ Sp D<- 1. I T (Figuration :}JJ .M^J) 
 
 (232) 3 / 2 : °T I °S Z> 7 I ¥ "Tp \ "S "Dp \ "Sp +D \ °T | 
 
 $ T \°S D \'T 
 
Harmony Simplified. 
 
 fChap. in. 
 
 (233) $: T I S- +S I D Sp I +£>"< 1 I ¥ Tp \'S Dp, 
 
 (234) $ : T S yn I Z» ¥ \ D °Sp \ Tp °S \ D °T \ S T\ 
 
 in in 1 
 
 Z> 7 I °:T 
 
 2> 1 I 
 
 (235) %:"T \°Sp °S*~ I .'. D I ¥ °S \ D "Tp \ S™ M I 
 
 Z?/ D> I T ( JJ) 
 
 (236) : B : °T | 5" 1 * Z> | F °Z> | °S S vu \°D D+\ +Dp +Tp | 
 
 °5 5 vn I "Tp °Sp I T 
 
 § 1 1. SEQUENCES. 
 
 The method of teaching harmony founded on thorough-bass 
 was for a long time at fault, owing to the similarity of the figuring, 
 counting from the bass, in putting on the same level chord- 
 formations which, according to their harmonic sense (their 
 " function "), were of widely different value, and thus in 
 assuming, for each degree of the scale, not only a triad, but a 
 chord of the seventh, and at the time of the worst formalism 
 (about 1800 a.d.) even a chord of the eleventh, and of the 
 thirteenth : 
 
 (<z) Major. 
 
 T Sp Dp S D Tp Hf 
 
 m (*) 
 
 (£) Minor. 
 
 "T $*" °Tp °S °D "Sp "Dp 
 
 T 1 " S 6 D 6 S" D 1 T 6 D* 
 
 (d) Minor. 
 
 7*VI CVII ^pVIIa. OVI jytl JiVllt* CH 
 
Chap. III.] 
 
 Sequences. 
 
 121 
 
 To these we must first add those formations resulting from 
 the introduction of the raised sixth and seventh degrees of the 
 minor key (taken from the ascending melodic minor scale) : 
 
 (jy ) 
 
 £>+ T vl % Uf 
 
 VI 
 
 (S.T..) 
 
 V VII 6=» VI 1x0 
 
 r vi« ^iii* Bi £m<= D , T vn t\ UP* [$ mS ] 
 
 and also those formed by the lowering of the seventh as a bridge 
 to the third of the °S in major : 
 
 H3 . $^ T-^ *% *$ *?i >g__| 
 
 It is evident that such formalism can have no object, as we 
 should never see an end of it ; we merely need to remember 
 the Lydian fourth in major and the Phrygian second in minor, 
 or even the chromatic leading-notes of the former paragraphs. 
 But the representation we have hitherto given now dispenses us 
 completely from the necessity of devoting particular attention 
 to these " accessory triads " of all sorts and even accessory 
 chords of the seventh and of the ninth, etc. The nucleus of all 
 harmonic motion, in our estimation, is formed by the three 
 principal pillars of the cadence : 
 
 tonic, subdominant, and dominant, 
 
 around which all the rest adheres as bywork, thus in the first 
 place the characteristic dissonances (S 6 , If, S vu ; D vl , S vn , &>), 
 then the feigning consonant, vicarious, accessory forms of the 
 principal harmonies (parallel clangs and leading-tone substitutes), 
 
Harmony Simplified. 
 
 [Chap. III. 
 
 furthermore the chords of the Dorian sixth and Mixolydian 
 seventh, which are also feigning consonances rendered necessary 
 on melodic grounds, and finally the absolutely dissonant for- 
 mations (those proper to the scale and those with notes foreign 
 to the scale) arising variously by means of passing notes, auxiliary 
 notes, anticipations, and suspensions. 
 
 Only in so-called sequences these incidental— as it were, casual 
 — formations enter with the appearance of equal rights beside the 
 characteristic dissonances; this led theorists astray quite long 
 enough, until Fr. J. Fe'tis opened their eyes for them. Sequences 
 are, as Fetis was the first to recognise and express, not really 
 harmonic, but melodic formations — i.e., their ruling principle is not 
 the logical progression of their harmonies, but the proceeding by 
 degrees through the scale. Briefly, a sequence is the i?nitation 
 several times of a motive, proceeding upwards or downwards 
 through the scale of the key. If we formulate the definition thus, 
 it sufficiently expresses that even passages for one part like the 
 following are sequences : — 
 
 144. 
 
 (<0 1 2 
 
 1 1 
 
 3 ld) 1 2 3 
 
 The single imitation of a motive does not form a sequence ; 
 the name sequence rather implies that that manner of progression 
 of the motive is to be adhered to, which would stipulate at least 
 two repetitions of the motive. 
 
 Any sequence in a part to be harmonised will more or less cer- 
 tainly give occasion for the other parts to proceed sequentially ; but 
 it is only when they do so proceed that we call part-writing 
 a sequence. Now as regards the harmonies, the sequence 
 (harmonic progression) thus formed is the imitation, proceeding by 
 step through the notes of the scale, of a succession of harmonies ; the 
 model of the harmonic progression must consist of a succession 
 of harmonies which has logical sense in itself — that which follows 
 in the imitation is accepted as the result of a sort of necessity 
 of nature ; and only when the sequence is relinquished, do the 
 tonal functions resume their efficacy. This, indeed, goes so far 
 that within the sequence even the doubling of leading-notes and of 
 
Chap. 111.] 
 
 Sequences. 
 
 123 
 
 dissonances may be unhesitatingly introduced, which outside of it 
 (and also in the initial motive) would be altogether faulty. 
 
 We will sketch a few beginnings of sequences in explanation 
 of the above : 
 
 5 D Dp 
 
 «4M 
 
 T D Sp 
 
 NB . °T °S "Dp 
 
 Tp Dp M> 7 
 
 c rp°sp y 
 
 S 6 D 7 T 7 ' 
 
 D' T S 7 ' 
 
 S 7 *Dl 
 
 UP D s Tp 
 
 T S 6 Sp 
 
 D 6 Dp S 7 " 
 
 Here we find all those "accessory chords of the seventh," 
 etc., enter with rigid necessity into the chain, but without their 
 tonal significance exerting the least influence on the progression, 
 only so to speak as a mechanical impress of the harmonic suc- 
 cession at the beginning of the sequence. 
 
 But, naturally, motives for sequences may be longer than 
 those we have hitherto given ; any figuration of the motives of 
 145 (a) — (/) may be strictly imitated, e.g. : 
 
I2 4 
 
 Harmony Simplified 
 
 [Chap. III. 
 
 Sequences apparently imitating at the interval of a third and not 
 by degrees, as — 
 
 Tfi 
 
 D 
 
 
 
 
 r 5 
 
 
 
 
 
 T. 
 
 ' 
 
 ,'w. ■ ' i 
 
 l' 'i J-. 
 
 H7- - 
 
 # 
 
 i 
 i 
 
 i 
 
 4 
 
 iS — 
 
 1 
 
 -&- " r ' ? — t- 
 
 1 -s>-'"^-e- "^" 
 
 
 
 
 
 
 
 = r = 
 
 1 i 11 ! 1 ' — 
 
 i 1 H 
 
 are yet founded on progression through the scale, as a glance at 
 the three lower parts at 147 (a) and at the bass of 147 (b) will show, 
 they are the only uniform harmonisations of the scale possible 
 without consecutive octaves and fifths (one would almost feel 
 inclined to call the scale itself a sequence !). 
 
 Beautiful effects are obtained when the extent of the sequence 
 motive does not coincide with the species of bar, and so the har- 
 monies which correspond with one another come at points of 
 different rhythmical value, e.g. : 
 
Sequences 
 
 125 
 
 As the tonal functions are suspended during the imitations of 
 the sequence motive, there can be no object in indicating them ; 
 we therefore only give indications for the harmonies of the motive, 
 and just intimate at the first imitation, whether the sequence 
 rises or falls ; but, for the rest, abbreviate the indications by 
 means of brackets (as many brackets as imitations), as was the 
 case already at 145 (a) — (/) (the figures added below may therefore 
 be omitted as being understood). 
 
 The following exercises devoted to initiating into the writing 
 of sequences are again easy, and give us an opportunity at the 
 same time of making a first attempt at five-part writing. This 
 will require no new rules. Naturally we need fear exceeding the 
 maximum distance of the parts from one another favourable to 
 euphony still less than in four-part writing, as we shall have to 
 find room for five parts within the same total compass (which we 
 shall retain throughout the book) ; but, on the other hand, we 
 must remark that the two lower parts may quite well occasionally 
 be distant a whole octave from the three upper parts, or the three 
 lower from the two upper, without a sense of isolation arising. 
 Doubling of thirds and fifths will occur more frequently in five- 
 part than in four-part writing, but is still limited by the same 
 restrictions (doubling of thirds by parallel motion is permissible 
 only in parallel clangs and leading-tone substitutes ; thirds which 
 form leading-tones with notes of the tonic, may never be 
 doubled). The following (eleventh) model example may serve to 
 guide the student. The highest part is to be written in the 
 treble clef : 
 
 9 
 
 SS' 
 
 D T S 
 
 Sp D T D 
 
 149- 
 
 (Eleventh model example.) 
 
126 
 
 Harmony Simplified. 
 
 [Chap. III. 
 
 T °S T °S § .. Z» 3 1 
 
 Exercises 237 — 248 (in five parts). 
 
 (237) $ : T [ IP T I S 6 D> I S S^ I 
 D S I °S D \ T 
 
 (238) V 2 : T I 05 vii d \ ¥ T V1 S lu " I Z> S 11 "" B 6 ' 
 
 6»S 
 
 5"!-=^ VII VIII 1^+^111-= J)+\0 T £. .. |£)4 3 7|» r 
 
 I 1 r- 
 
 « 5 
 
 (239) »/ 4 : Z I S« 2? .'. I ip S< ~ I 27 T | | | 
 
 ^T Z>' A I Z "S d 1 z 
 
 (240) $ : °T S v " I Z> T I S .. I Z> T I ^ I ""= .. I Z>»- I 
 
 V V III III V 
 
 6»s 
 
 ^ m -= I Z>' 3 I "■§> £ vn I D 
 
 (241) V, : °Sp S I I Z>« 7. Tp \ Sp Tp Sp \ D T S\ 
 
 3 3 
 
 1 1 . 1 1 1 — ■ — 1 « 
 
 MP 
 
 I 5 Z>' + I T 
 
 (242) %: T \ S" Mf \ I Tp \°S D' \± T \ D Sp \ \ 
 
 ~~ ' Z' I T 
 
ihap. in.] Intermediate Cadences. 127 
 
 1 1 — ; — 1 1 ; 1 
 
 (243) $ : ^ vn D> I °T "D I °Sp °S I I I °T 
 
 °S D I "T 
 
 (244) s/«: 7> 5/ Z> I 7 1 £ Z> I f D~Tt> I n r I "" *" I 
 
 Sp D \T 
 
 ~i r 
 
 v IV III v v iv in v 
 
 (245) 3/ 2 : °t\ ,. vll ~ S vu D I "TS m ,v v nI I "Dp D ul IV v »' | 
 
 r r r r 
 
 ' j ' 2*=" ' I T S vu .. I D**S WU D>\..\ °T 
 
 x 1 v v 
 
 1 1 (— 1 
 
 7 
 
 (246) V, : T\ S Sp D\DpTp S v " | Z> 2 '=- f V I ^ ^ I ^ 7 I 
 
 7-= 
 I 1 8 7 < 7^ 
 
 5"= I .1 ;.- 5 I D\ % \ T 
 
 1 
 
 (247) E: T S 6 \ Dl , Tp | | 5/5|rr5 f i)| 
 
 1 _ 4 3 V 1 3 
 
 n Dp 1 1 t> s 6 z? 1 r 
 
 (248) B : T \. S a ** I ^ .. I I zT 
 
 7« 3 3 2 
 
 I Z" 
 
 § 12. INTERMEDIATE CADENCES. 
 
 More gifted pupils will very likely often have felt the avoid- 
 ance of familiar chromatic alterations in our exercises hitherto, as 
 a rather unnatural restraint ; at least, many, of the turns to be 
 developed in the following may by experience often have entered 
 their minds, while we, with the single exception of a few har- 
 
 # o 
 
 monies anything but commonplace (S-, &, S UI< , Z> 3> , lj), ", °@, 
 
 o 
 
 °$), kept strictly to harmonies proper to the scale. The result 
 will, however, justify our procedure. Our aim was to develop the 
 
128 
 
 Harmony Simplified. 
 
 [Chap. III. 
 
 feeling of tonality to the utmost extent, and to teach the student 
 to still understand, in their relation to the ruling tonic, harmonies 
 apparently very remote from it ; this paragraph only seemingly takes 
 a step in the opposite direction, by introducing the harmonic turns 
 which are generally called transitions, in contradistinction to real 
 modulation, the actual change of tonality. Under any circum- 
 stances a rational method of teaching harmony must always strive 
 to obtain an ever wider field for unity of conception. So, in the 
 end, actual modulation must be compared to a harmony step from 
 the tonic to some nearly related chord, i.e., new tonics reached by 
 modulation must always be comprehended similarly as harmonies 
 within the key — they have tonal functions in an extended sense. 
 In transitions we express this very definitely by leaving unchanged 
 tlie indication of the functions of the tonics reached. We now make, 
 to express it briefly, cadences to the several harmonies hitherto 
 characterised according to their position in the key {real and feigning 
 consonances) ; these harmonies, then, are to be considered as tonics, 
 ivithout, however, their tonal functions being altered. 
 
 Let us return to the simplest forms of cadence, the connection 
 of the tonic with its dominants of the same mode : 
 
 T—S—D—T and °T—°D—°S—°T. 
 
 These acquire quite a different aspect, if by addition of a note 
 foreign to the scale (7I3 or Vllfl of the tonic), or by chromatic 
 alteration of a chord-note, we change each harmony to the 
 dominant of the next : 
 
 T 7.t] 5 .'-= D 
 
 °T vlI ti °D l " °S. 
 (S vl1 ) ($ vn ) 
 
 Here the indication of the alteration of tonal harmonies (by 
 7b, VII t|, l^ P) still seems the more convenient and easily 
 intelligible (that which, in reading, renders most easy the trans- 
 lation of the chord signs into conceptions of harmonies). But 
 when more than one chord is to be referred to a following chord 
 as tonic (for the time being), the indication of harmonies as 
 dominants of the following harmony will not only be more con- 
 venient, but also more correct (corresponding to the real course 
 of thought). We express such relation by placing the chords in 
 question in rounded brackets (as we did by way of supplement at 
 150 in the lower row). 
 
 Rule : Chord signs in brackets are not to be understood as 
 
Chap. III.] 
 
 Intermediate Cadences. 
 
 129 
 
 relating to the principal key, but as circumscribing the chord 
 immediately following the bracket, as tonic, e.g. : 
 
 "T (S vu D) °D {S vu D) S 
 
 This new expedient leads to a number of new turns, for 
 similar intermediate cadences may be made not only to the 
 principal harmonies, but also to all the parallel clangs and 
 leading-tone substitutes : 
 
 T (S wa D>) ¥(S vn iy)Tp(°S D)Sp (S Z) 7 ) Z)(S VU Z>') 
 
 O, .1 1 , J . 1 , ! 
 
 5gE2 
 
 Efc 
 
 ±=c 
 
 rr r 
 
 ^ 
 
 4= 
 
 Sr 
 
 ■T 
 
 & £ J- 
 
 2&L 1= 3L. 
 
 VJ. hj. t^ b-J- 
 
 i f=r3& 
 
 T (°S £') °S {S 6 D) °Sp S- @" 
 
 A 1 . 1 — 1- 
 
 D T °T {°S £>+) °S (S+ D) °Sp S vu D °T 
 
 At times such cadential formation with the dominants may 
 result from a harmony intelligible v\ ithin the key, without return- 
 ing to it ; then an arrow pointing backwards under the bracketed 
 harmony succession, shows that the preceding chord is its tonic : 
 
130 
 
 Harmony Simplified. 
 
 [Chap. Ill 
 
 
 ^ M 
 
 i 
 
 1 
 
 
 
 
 1 
 
 
 b£— °— 
 
 
 
 
 -j <-j — h 
 
 153- 
 
 ' |S " S " &. 
 
 i 
 
 JBL. 
 
 1 t 
 
 1 
 d 
 
 i 
 
 1 
 1 
 
 i 
 
 - r 
 
 
 
 ~ r ~ 
 
 
 
 
 
 -r— " 
 
 B^r-fe ^ 
 
 ^^^^^ 1 
 
 °r F (5 z>) °>s z>+ °y 
 
 In such cases, in place of the chord circumscribed by the 
 intermediate cadence, and positively expected to follow, another 
 comes in. But if, by chance, this chord do not even precede the 
 intermediate cadence, and the harmony to which the cadence 
 leads be skipped, then we indicate the chord expected in angular 
 brackets after the rounded ones : 
 
 «5<M 
 
 T S 6 £>' T (S m Z>')[Tp]S 7 * D* ' T 
 (*> i ! 
 
 "T (S V11 D)["D] & °S D "T 
 
 Rule : The harmony indicated within the angular brackets is 
 the merely imagined tonic of the preceding intermediate cadence 
 indicated in the rounded brackets, and is itself not introduced at 
 all, but skipped over. 
 
 So as to be able to read quickly the chord signs enriched by 
 these new expedients, and to have present at once to the mind 
 the required harmonic successions, the student must, as soon as 
 he comes across rounded brackets, look directly to the chord 
 
Chap, in.] Intermedia te Cadences. i 3 1 
 
 following them, and understand the bracketed indications of 
 functions as referring to that chord as tonic. 
 
 The exercises which follow now are to be worked out for four 
 wind instruments, viz., for oboe, clarinet, horn, and bassoon. Of 
 these the notation for the oboe is in the treble clef, for the 
 bassoon in the bass clef ; but the clarinet and horn are so-called 
 transposing instruments, and the manner of writing for them is 
 quite different. So as to be clear, once for all, about transposing 
 instruments, it should be noticed that the fundamental note of the 
 key whose name they bear is written as c, e.g., written note c on an 
 J< horn means the note f ; on an A clarinet, note d; on a B\> 
 trumpet, note 6?, etc. ; all the other notes should be read as 
 interval signs, written in their relation to c, but to be understood 
 in their relation to the fundamental note of the instrument, e.g., the 
 note /J is to be read as an augmented fourth, and on an A horn 
 would signify the augmented fourth from a, therefore d\, on a B\> 
 clarinet the augmented fourth from bfy, therefore e, on an E 
 trumpet the augmented fourth from e, therefore a\. But, further, 
 the student must know whether an instrument transposes upwards 
 or downwards. The clarinets and horns, with which we are firstly 
 concerned here, transpose downwards. In the following exercises 
 we shall make use of the clarinets only in C, B?, and A, cus- 
 tomarily used in the symphonic orchestra ; C clarinets do not 
 transpose {c retains the significance of c'), Bfy clarinets transpose 
 a whole tone, and A clarinets a minor third lower. The C 
 clarinet is to be used only in exercises in the key of c-major, the B? 
 clarinet in all exercises with key-signature in flats, the A clarinet 
 for all keys with sharps, and also for K-minor. Horns (natural 
 horns) we assume as existing in every tuning of the twelve semi- 
 tones : B, B\f {At), A, A\f (G$), G, F$ (G\>), F, E, Ev (D%), D, 
 Db (C|), C, and also in low B, B% and A, the latter transposing 
 another octave lower. The part for horn is written in the treble 
 clef and without any key-signature (according with the usage of 
 composers of symphonies), and each |j or j needed is placed 
 before its particular note ; in the case of the clarinet, the number 
 of flats or sharps in the signature of the natural key of the 
 instrument (Bt? clarinet : B^-major = 2^, A clarinet : A-major 
 = 3$ ) is to be subtracted from those in the key-signature of the 
 exercise, e.g. : 
 
 Key of the exercise AP-major =■ 4U 
 Tuned in b? -major = 2I? 
 
 Remainder (for key-signature) = 2b 
 
 Key of the exercise G$-minor = 5$ 
 Tuned in A-major = 3 J 
 
 Remainder (for key-signature) = 2J 
 
132 
 
 Harmony Simplified. 
 
 [Chap. III. 
 
 If the key of the exercise have fewer flats or sharps than the 
 natural key of the instrument, then the excess is represented by 
 the opposite signature (\f for $, and \ for \>) : 
 
 Tuning of the instrument B?-major = 2I? 
 Key of the piece D-minor = 1? 
 
 Key-signature — 1$ 
 
 Tuning of the instrument A-major = 3$ 
 Key of the piece A-minor = ojf 
 
 Key-signature = 3b 
 
 Retaining the normal compass for voices, with the clarinet for 
 the alto part and the horn for the tenor part, the pupil may be 
 sure that he is not expecting impossible things of the instruments; 
 more detailed explanations of the nature of the instruments are 
 therefore not needed here (on this point cf. the author's 
 " Catechism of Musical Instruments "). Our principal aim now 
 is to prepare the pupil gradually and thoroughly in the practice 
 of reading from score, and with the introduction of transposing 
 instruments an important step forward has been taken. 
 
 The following (twelfth) model example is calculated to illus 
 trate the above clearly : 
 
 "T S vu D 7 °T {S vu Z>;.)[°Z>] °Tp {S vu 2?;.) °5 
 
 I I 
 
 Oboe. 
 
 (Twelfth model example.) 
 
 D m If "T {S s I 7 ) 5 .. 
 
 ry t 07 
 
 ■"s> 4 •• ■* 
 
Chap, i ii. j Intermediate Cadences. 133 
 
 Exercises 249 — 263 (for Oboe, Clarinet, and Bassoon). 
 
 (249) %: T {$? \ D 1) \ Sp ® \ D I I (S vn D) \ [S/>] g S | 
 
 265 
 
 & D \ T 
 
 (250) % : °T "D I T m \ &\D l.\ ¥ °S \ D (2?') | [°S] "Sp 
 
 M 9 ' I D\" I I "T 
 
 (251) jf ; y 1 s vn z>| °7> $»» I \„ D> I ff (2>) |°5.. VII | 
 
 3 
 
 D °T\ .. D 1 \ "T 
 
 I vn if 
 
 (252) $: 1$ S vu \ B> "T \ °S (S vn I Z>) .. I £ v " VI " I 
 
 z> ^ 1 5 ni "= z> 1 °r 
 
 (253) $: "^ 
 
 5 VI1 Z> 
 
 "T" °5 I Z7 (Z») I Z> (.S vn I 
 
 D 1 ) °5 I Z»J* + I °T 
 
 (254) $ : T I 7.tJ °S I D (°S\Z> /.) | [Tp] S (Z») \ S- V~- 
 
 D". 
 
 T 6 =- s 
 1 ■- I 1 
 
 (255) V. : M" D I (/^) 5/ D I r Sffi « 1 D* & ?. 1 2? .■- 1 1 
 
 3 7 3 *t 
 
 Tp Sp Dp \ T ?:t\ S \ £>l S 6 £> \ T 
 
 (256) B: 5nr „, | Z>< & f (S v " Z*) | [»5J S I 
 
 $»=- in * z^=- + 1 °r 
 
 IV III 
 VI« V 
 
 (257) B: £f£ S™ I Z> F 
 
 ^ Jk\ 
 
 = D\ ..1 T I S D> \ T 
 
 .. Z> I °T 
 
 (258) V. : S 6 Z? ..' I T Tp 
 
 sp °s s 1 z>jj 2 * I 1 T 
 
 D\ + .». I (Z») 7> .. 
 
 ./?/ 
 
134 Harmony Simplified. [Chap. hi. 
 
 (259) E : T {B>) I Tp (Z») I Sp {D>) I D -.' | T ..'tj \ S »* \ 
 Z>J ?. \ T 
 
 (260) V 4 : D I T "5/ I "J 2 * 1 I Z> ..' I ¥ (Z> 7 ) | .. 
 
 • 15= 3 
 
 1 1 
 
 Z** + I T 
 
 (261) $: °r , 2> I 5™ Z> I °T 
 
 =°Tp $ vu I D 6 * .'. I T 
 
 £5 
 
 I =°Tp D 
 -.F LP \ T 
 
 
 (262) $: T 6 s 1 5'" 6 
 
 = S V1 I .. v " (Z*) I D ..I, 
 
 3> 
 
 =S VU I Z>+ 1 
 
 =^ in< zH 
 
 = Z>/ Sp I Z* + I T 
 
 oT 1 
 
 (263) $: r ..»« 1 5 
 
 Z* ..»« I Tp (IP) 1 5 r 1 
 
 c« 1 — rp 5, : t 
 
 =iS vi vn I D I 
 
 Exercises 264 — 280 (for 2 Trumpets and 2 Tenor Trombones). 
 
 For trumpets the notation is the same as for horns (without 
 key-signature) ; but they sound an octave higher. Trumpets 
 exist in all tunings from high e? to low a. Tenor trombones do 
 'not transpose, and are written in the tenor clef with the usual 
 key-signature. These exercises are therefore to be arranged like 
 the following (thirteenth) model example (with a stave for each 
 couple of instruments with similar notation) : 
 
 8 7-= 
 
 T (IP) °S D> Tp W) Sp @>~ Z>« *~ (&>*) 
 
 K6. 
 
 2 ED Trumpets. 
 
 2 Tenor Tromtxmes. 
 
 ,^_„ 1 ,_, — |. 
 
 f V 'r^f^ft 
 
 (Thirteenth model example.) 
 
Chap, in.] Intermediate Cadences. 
 
 Tp S 6 $1% D\ S S- D\ 3 Dp T 
 
 '35 
 
 i.e., the trumpets are always to be taken in the tuning corre- 
 sponding to the key of the exercise. The notation for the trom- 
 bones does not vary, as they are not transposing instruments. For 
 these school-exercises the trumpets in low a and BJ7 are preferable 
 to those in high a and bI?, as they necessitate fewer leger-lines. 
 
 (264) 
 
 "T .. I °Z> ^ vn 
 
 v=» 
 
 .#»* D I "T 
 
 D I °T (£>') l °S .. I T °S L 
 
 (265) $: S 0* I D ¥ I S wu VUI I D (JP") \°S °T \ 
 
 .. VII tl D 1 I S V1 LP I °T 
 I m-= 3 I 
 
 (266) $ : T Tp I 5 Sp I D J I Tp (D>) | .. (Z») | Sp S v " | 
 
 D\ ..■' \ T 
 
 (267) $: 7Vt| I S ..■>* I (£ vn VI " I D „')| 7> (5 VI1 I Z> .'.) I 
 
 Z# #'» I Z^ + I T 
 
 (268) $ : 5 6 * I Lf * I (Z>) [7>] 5 I § (2?) | ".§> &~ | 
 
 ^9- r 1 +£>"" 1 I r « - I t 
 
 D J I ¥ S I 
 
 (269) $: T "5/ I Z*» VI1 
 
 __o C VII 
 
 Z>J + 1 7* 
 
 (270) $: T I .9™ |'| Z)+ ^ I °4/> ZJ I °5 Z» I T 5 | 
 
 (271) $ : °T Tp I (Z> Dp j S) °S | Z> (Z>) | °7)> (Z>) | >S v " | 
 
 Z>r ± I °r 
 
136 Harmony Simplified. [Chap. m. 
 
 (272) »/.: $*» D {&*■) \Tp S (p) I .. "Sp B\X.\E^^\T 
 
 (2 73) % ■ T I (5"" 2?) I [2>] S (S 6 1 2?) 5 1 (S™ 2?) I 5/ S™ | 
 
 m\\T 
 
 VII I 
 
 (274) $: ^ 2? I S 111 " +&p I ^'"- 2? I "Sp ..'- I (.S 6 2>) I 
 
 [°7>] (S V11 2?) I [°5] 5 vn 2> I °T 
 
 (275) $: r .S I D Tp I (5™ D)\D..\ (7' VI, B 2?) | 3? 5 | 
 
 &\D\T 
 
 D\. 
 
 Tp 
 
 =Dp D I Tp 
 
 =2?" 
 
 (276)$: T\ Sp(D)\ -vn 
 
 T $>■"" \ Dl \\ T 
 
 (277) $: r« », |S -s VI1 I (^> ,) I [?>] (5 V " 2?') I 
 
 (278) »/,: (#- 2?) [7>] 5 I (2> 7.) [2?] T | (Z? 7.) S | 
 
 $'- 2" ^ 
 
 (279) Hi: & "I (#•*) Tp I (S v " 2>) I D (#$, I 2?) [7>] 5| 
 
 (2?) S I #i; D I 7- 
 
 7 
 
 (280) %:*T\ (S #'» I Z>) [°Z>] .S v " I 2> (5 vn \ D)°S\ 
 
 'T (S v " I 2>) [°2>/] 29'=* I 5 V " 2> 7 | 'T 
 
 Exercises 281 — 289 (for 2 Valve Trumpets in high b|? and 
 2 Valve Horns in f). 
 
 Here all the instruments transpose. Valve trumpets in high 
 b? are written without key-signature, in so-called cornet-notation, an 
 octave higher than the trumpets in the preceding exercises, other- 
 wise most of the notes would continually lie under the stave. 
 The following (fourteenth) model example may render this clear : 
 
Chap. III.] 
 
 Intermedia te Cadences. 
 
 137 
 
 (Fourteenth model example.) 
 
 D .. °T D 1 °T °S Z>1' 
 
 o y 
 
 I=--5H 3 
 
 (281) $: D 0* I D (5 V1 I D ,) I 3 (Z") I g (&) I °Sp .. I 
 
 3 
 
 < 8 
 
 '2» 1 
 
 (282) 0: (Z>) I "S'' 1 I D (,S V " I Z> ..') I [•£] #£ , I 
 
 S vl (B>) I T/) (£ v ") I Dl„ 5 7. 1 -t 
 < in 55; 3 
 
 (283) $: C T\ $""{J®>~ I D) .. I '."tt Z>' I 5? D + \°T 
 
 (284) : T I ^|» Z>^ I £ VI ^ I Z> (Z» 9:> ) I + 2> (Z») 
 
 •^ S\m,ZD\>T 
 
 (285) $ : Z»" C T I 5 V " S I --^S v '' 
 
 =°Sp \ S vl D\*Tp {D)\ .. J v 7 
 
 d> ¥ 1 5 VI1 iy 1 °r 
 
 (286) $ : °T ("£ I Z?) [°7>] Z> I T (°S/ \°S £>) \ [°5] "5/ .'. 
 
 S $'» I ZJJ* I I T 
 
 (287) £: T Tp I +Z> ni I "S (£ IX< \ D) TP \ (Z? j.) 
 
 j>] sp S' 1 » z» 1 z 
 
138 Harmony Simplified. [Chap. m. 
 
 (288) $: °T I S- $>~ I D (S™ I D ..') I [°S] +£/> S™ I 
 
 i> (Z> VI1 I D>) [°.S] 5 I .. D I T 
 
 (289) &: T '& \ 3 Z? \ 2} & \ & _(Z») I 2?/ (Z») 
 
 < 
 
 Exercises 290 — 300 (for 2 Oboes, 2 Clarinets, 2 Bassoons, 
 
 and 2 Horns), 
 to be written on four staves, the two clarinets in unison with 
 the oboes, the two horns in unison with the bassoons, as in 
 the fifteenth model example. 
 
 (Fifteenth model example.) 
 
 (Z>> j d rp°sp- vu Ly t ik?~n> t 
 
 H-rmS 1- 
 
 (290) $ : T °Sp\_{D) [Tp]T\$ £ | (£ £>) \ [Tp] T °Sp 
 
 1 _CO 3 
 
 (D) \_Tp\iy\T 
 
Chap. III.] 
 
 (291) $: °T 
 
 Intermediate Cadences. 
 
 139 
 
 S y " D I ¥ (Z>) I 5 
 
 ' I = J ^ I D I- I 
 
 ="5 .7" Lfi* + I T 
 
 (292) $: Sg I i S I Z>/ (.#»"■) I 2J» 5 I /^ s r I 5J3 J I 
 
 VII I 5 s. 
 
 ™c III 
 
 (293) &: 7* »* I 5 #»* I Z? ..I, I 2? (If) I 5 (Z>) 1 sp $tz I 
 
 ^ I .'. I t 
 
 G> 
 I 
 
 (294) %'■ T V* \\ .. \ S ** \* .. \ $> * \ ' D \ f 
 
 (295) ft: 3 A= T W T I S 6 D (D) \ Sp & D \ (D> \" ») | 
 
 [5/] 5J \*D>\T (JD>) &\® D Dp\T 
 
 (296) >/ 4 : r v "t; D I °r (5 V " Z?) I ['S] (S m * D ?.) I ['S] » 
 
 D ?. \_(S™ J? I) I \_Tf\ °T W>\ I I I S'V l v v I 
 
 3 c\a III 
 
 (297) t- TP\ (-&>') ■■ \ & T \ S^ T\ M IJ> \{D) Tp\ 
 
 °S°Sj> I T 
 
 (298) $ : T "Sp I #'=* D I ^ Z> I (D) Tp \ °S "Sp | 3 D \ 
 
 * 4 '< I 3 
 (299) »/.: r (S l,l « Z>) I Z? (5"" Z») I °S (» Z?) I |\S] +5/ 
 
 z?/ (#•») 1 2j> y/si $» z»j + 1 o sp °s ..™ 1 r 
 
 (300) »/, : °^/ I "# °^> "J I ^ T (/?') I » (5 Z>) I .. "J #'=»| 
 •T °S $»* ! Z^» s ' I °T 
 
140 Harmony Simplified. [Chap. in. 
 
 The sign eg occurring in a few of these examples between 
 two numbers, indicates an enharmonic tie; e.g., in 290, if we assume 
 D-major to be the key of the exercise, then 5? (the prime of the 
 parallel clang of the minor under-dominant) is to be sustained as 
 0$ (third of the dominant of the tonic parallel). 
 
 All these examples, as indeed all those merely indicating the 
 functions of harmonies, should be worked out in a number of 
 different keys. As no part is given, and also but little of the bass 
 part is indicated, it is possible for each working to turn out 
 different. The great value of this kind of exercise arises from 
 its leaving complete free play for melodic progression. The aspiring 
 student will not be satisfied with a merely correct connecting 
 of each two chords which follow each other, but will soon learn 
 to look for the melody lines of the exercise as a whole, at least in 
 the soprano and bass. 
 
CHAPTER IV. 
 
 THE CHANGE OF TONAL FUNCTIONS (MODULATION). 
 
 § 13. CHANGE OF MEANING OF THE SIMPLEST HARMONY STEPS. 
 CHARACTERISTIC FIGURATION. 
 
 In our exercises hitherto we did not, indeed, entirely avoid modu- 
 lation, but only resorted to a very few means of transition, and 
 those only occasionally and without particularly discussing them, 
 merely for the sake of giving animation and variety to the ex- 
 amples; our principal aim was directed towards strengthening 
 the feeling of tonality and extending to the utmost the circle of 
 harmonic formations intelligible in their relation to one and the 
 same tonic. Our formulas for the tonal functions gradually 
 became more complicated, but became simpler again with the 
 introduction of intermediate cadences. We, indeed, succeeded in 
 characterising every chord not only as a transformation of another 
 major or minor chord, but also as a more or less equivalent 
 representative of some tonic, dominant, or subdominant. 
 
 We now set ourselves the opposite task, that of finding out in 
 which direction harmony steps which, according to the obser-" 
 vations made in the previous chapters, are intelligible without 
 denial of the tonality, are calculated to incite modulation. In so 
 doing we shall soon perceive that the very simplest succession of 
 harmonies may help to bring about modulation, if we call to our 
 aid either characteristic dissonances or characteristic figuration- 
 notes, or again rhythmical expedients. 
 
 Even in our first explanations we could not but acknowledge 
 the fact that the contra-fifth step in its outer form coincides en- 
 tirely with the retrograde plain-fifth step, and likewise the plain- 
 fifth step with the retrograde contra-fifth step : 
 
 (T — S) in c-major : c + —/ + = contra-fifth step; 
 
 in F-major: c + —f + , plain-fifth close (D — T) 
 (T — D) in c-major : c + — g + = plain-fifth step ; 
 
 in G-major : c + — g + , contra-fifth close (S — T) 
 (°T—°D) in A-minor : °e — °b = contra-fifth step ; 
 
 in E-minor : °e — °b, plain-fifth close (°S — °T) 
 ( T— S S) in A-minor : °e— "a = plain-fifth step ; 
 
 in D-minor : °e — "a, contra-fifth close (°T—°Z)). 
 
142 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 The step to the contra-clang of the tonic also coincides with 
 the close from the contra-clang to the tonic in another key : 
 
 (T + — °S) in c-major : c + — V = turn of harmony ; 
 
 inF-minor: c + — V, turn-of-harmony close (Z>+ — °T) 
 (°T — Z> + ) inA-minor: "e — e+ = turn of harmony; 
 
 in E-major: °e — e + , turn-of-harmony close (°5 — T + ) 
 
 It is, therefore, evident that we only require to add the 6 to the 
 T to prompt its change of meaning to S, or the VII to make °S 
 of the °T, or 7t] to stamp the T as D ; similarly the sudden entry 
 of 4< in the figuration of the major tonic will give the latter 
 under-dominant significance, the merely passing 7^ will prepare 
 its change of meaning to dominant, and the minor tonic, with 
 a IV >, becomes minor upper-dominant, with a VII t], under- 
 dominant. 
 
 The types of figuration, true to the scale, for the principal 
 harmonies are : 
 
 NB. 
 
 vii: vi" 
 
 {d) J- descending 
 
 (i)°D NB. 
 
 vni] viq 
 
 The figuration in scale form of the contra-clang of the tonic, 
 as we know, necessitates besides the third, foreign to the scale, the 
 introduction of the Mixolydian seventh or Dorian sixth : 
 
 ( s ) "S in major. 
 
 IX- 
 
 160. 
 
 lit) III 
 
 (VI* Vlltj) 
 
Chap, iv.) The Change of Tonal Functions. 
 
 (/,) D + in minor. 
 
 143 
 
 A 3 
 
 (6* 7B) [9"\ 
 
 but what is striking in the natural figuration of these harmonies, 
 does not lie in the sixth and seventh being greater or less, but 
 rather in the plain second and third contradicting the scale of the 
 key (for which reason the second or ninth, where not proceeding 
 to or coming from the third, is, as a rule, taken minor [<}>, IX", 
 as auxiliary note to the octave, or 2>, II*, as auxiliary note to 
 the prime]). 
 
 The parallel clangs and leading-tone substitutes, when the aim 
 is to give expression to their meaning as strictly as possible in 
 figuration, should be ornamented as far as possible with the notes 
 of the scale of the key : 
 
 („) Tp or ? 
 
 161 
 
 [cf. 159 (d)\ (VII-Vlfl) cf. 159 (f)\ Vllfl Vlfi 
 ( r ) Dp or ¥ (,/) °^ in major. 
 
 IV* (VII- V1H) \cj. 1 59 Ml 4" 
 
 [</ '5° («)] 
 
 (,) S- in major. 
 
 (ft D in major. 
 
 [cf. 159 (*) and 161 (d)] 
 U )°Tp or S- w °Dp 
 
 IV- 
 ['/ 159 («)] 
 
 [(/■ iS9 («)] 
 (0 °Sp or ¥ 
 
 k/'59W] n 
 
 (i) i£ in minor. 
 
 {cf 159 (*)] 
 
 [cf. 159 (*), 161 (</), (*),(*)] 
 
144 Harmony Simplified. [Chap, iv 
 
 (/) +Dp in minor. („,) D in minor. 
 
 IV* IV* 
 
 \cf. 159 (*)] ['/ iS9 (3), 161 (A (0, (0, (*) 
 
 but in this manner no forms at all result which would deviate 
 from those at 159 and 160; the fact, however, that the parallel- 
 clangs coincide also in their figuration with the principal clangs of 
 the parallel key, is a welcome help in modulation, as it, at least, 
 does not prevent change of meaning. The most important 
 results of this examination into the scale figuration of the most 
 essential chords are : 
 
 (a) The prominent role which falls to the augmented fourth 
 
 (4< in the + S, IV* in the /?; but also [in major] 4< 
 in the °Sp and S- and IV in the Dp and &, and [in 
 minor] IV* in the +Dp, & and 4< in the "Sp and S-). 
 It should be noticed that the 4< is introduced only into har- 
 monies with + under- dominant significance, the IV', only into 
 harmonies with ° upper-dominant significance ; for in "Sp and 
 § in major, the heightening of the under-dominant significance 
 is unmistakable, and similarly in + Dp and & in minor, the 
 heightening of the upper-dominant significance. 
 
 (b) The significance of the natural seventh (7I}, Vlltj), 
 
 which always gives the major chord upper-dominant 
 significance, and the minor chord under-dominant sig- 
 nificance (in major 7 to the D, VII to the °S and the 
 + Sp ; in minor, VII to the °S, 7 to the + Z> and the 
 'Dp). 
 It will be sufficient to keep these two points well in mind ; in 
 so doing we shall in many cases choose a path different from that 
 followed by the all-levelling custom of the day, which carries out 
 all figuration more or less in the sense of tonic significance by 
 introducing the plain fourth in place of the augmented and 
 adopting the leading-note to the prime (octave), e.g., 159 (6) and 
 161 (i) with£|? instead of b, 159 (c) and 161 (h) with /J instead of f, 
 159 (e) and 161 (c) with /J instead of/, 159 (/) and 161 (a) with c\ 
 instead of c, etc. The (three-part) new exercises in figuration 
 asked for later on [ex. 304(/)] will give the student an oppor- 
 tunity of turning these observations to the right use. 
 
 As regards the assistance of rhythm in the change of meaning 
 of clangs, we will at present only remark that chords falling on 
 accented beats receive increased attention, whereas to those 
 entering on unaccented beats we readily ascribe only transitional 
 importance; i.e., for example, we should look upon a chord 
 entering on an unaccented beat between two harmonies of the 
 same sound which are related to it, and are placed upon accented 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 145 
 
 beats, as a kind of ornamentation of them (in the sense of the 
 intermediate cadences of the preceding chapter), as harmonic 
 figuration. So long, therefore, as the accented beats retain the same 
 harmony, no actual harmonic motion takes place. In the following 
 example : 
 
 TD\TD\TD\T.. 
 
 3 
 
 D T 
 
 D T | D 
 
 the G-major chord in the second half is just as much ornamented 
 by the c-major chord as in the first half the c-major chord is by 
 the G-major chord ; in other words, we should figure this more 
 correctly thus : 
 
 T (Z> | T D | T D) | T .. 
 
 = S | T (S | T S) | T 
 
 a conception whose correctness is immediately proved if we 
 add the characteristic dissonances (D 1 instead of D, S 6 instead 
 of S): 
 
 D 1 jy (l)S 6 S 6 S 6 
 
 (II) 
 
 iy d 
 
 1 — U — r-i — ' ' 
 
 /TS 
 
 -H 
 
 pf — — ^ 
 
 •J 1 
 
 C** =-» 
 
 O 
 
 II 
 
 A f i A t i 
 
 
 v' 1 — 
 
 fT^Vv 
 
 
 
 The continuation as at II differs from that at I only in that 
 the upper-dominant (d 7 ) instead of the under-dominant is taken as 
 figuration for the new tonic. The possibility of changing the 
 meaning of the very simplest harmony steps is thus proved 
 (c — g transformed from T- — D into .S — T, without the aid of notes 
 foreign to the scale) ; but it should be noticed that the incitement 
 to modulation does not lie in the step itself, but outside of it. 
 We may, by making use of the same expedient (transferring the 
 dominant to the accented beat and the tonic to the unaccented), 
 similarly give changed meaning to the following steps : 
 
146 Harmony Simplified. [Chap. iv. 
 
 T S 
 
 changed 
 
 into D 
 
 1 T 
 
 °T°S 
 
 jj 
 
 „ °D 
 
 1 °7 1 
 
 °T°D 
 
 jj 
 
 » °s 
 
 1 Q T 
 
 + T°S 
 
 jj 
 
 „ + D 
 
 \ Q 7 1 
 
 "T £>+ „ 
 
 „ °s 
 
 \+T 
 
 for which every pupil will easily construct examples. But after 
 this it will be quite intelligible that a plain-fifth step or a turn of 
 harmony must be all the more likely to lead out of the key, 
 when made from a dominant in the direction opposite to the 
 tonic; the successions D(D).., S(S) ..,°S(°S) .., "D (°Z>) . . , are 
 perfectly familiar to us from § 12 as passing treatments of a 
 dominant as tonic (intermediate cadences). They become real 
 modulations if the harmony settles on the new tonic, i.e., if a 
 period closes with it, or indeed a new one starts in the key 
 reached. Rule : Any harmonic step going beyond a dominant (i.e., 
 resorting to the dominant, foreign to the scale, of a dominant) is 
 sufficient itnpulsefor a modulation to the dominant in question, but 
 to overcome the resistance offered by our feeling of tonality, in 
 the first place the assistance of rhythmical relations is needed (the 
 elements of which have been explained above, and further details 
 have yet to follow). 
 
 § 14. MODULATING POWER OF HARMONY STEPS. 
 
 If even proceeding by step beyond a dominant may incite 
 modulation, then naturally proceeding by leap beyond it must be 
 all the more calculated to render the dominant the central point, 
 to make a tonic of it. Every whole-tone step, because it corresponds 
 to the transition from one dominant to that on the other side 
 (S—D, D—S, °&—°S, °S—°£>), has power to modulate to the 
 clang skipped. The extended tonal system of harmony, as we 
 have developed it in the preceding chapters, presents an entire 
 series of whole-tone steps, whose latent modulating power may at 
 any time become active, by mere resort to characteristic dis- 
 sonances or expedients in figuration, or simply by proper use 
 of rhythm (the varying accent of time-beats). As whole-tone 
 steps, besides the connecting of the two dominants, we find the 
 successions : 
 
 (A) in Major 
 
 : (a) Sp-Dp, 
 
 in c 
 
 -major 
 
 : "a — °b, skipping °e (Tp). 
 
 
 (b) ¥-Sp, 
 
 5) 
 
 11 
 
 °b-°a, „ 
 
 °e (T P ). 
 
 
 (c) T— &, 
 
 >! 
 
 >> 
 
 c + —d+, „ 
 
 g + (£>)■ 
 
 
 (D) T—g, 
 
 >> 
 
 )> 
 
 c + —h + , „ 
 
 f + (5). 
 
 
 (e) Tp—D*~, 
 
 JJ 
 
 ?) 
 
 °e—% „ 
 
 "« (■*)• 
 
 
 (f) Tp—B; 
 
 >1 
 
 u 
 
 °<-°/t> » 
 
 °* {Dp)- 
 
 
 (g) W—'S, 
 
 It 
 
 jj 
 
 °d— °c, „ 
 
 "g i'T). 
 
 
 (h) A'—'Sp, 
 
 :> 
 
 jj 
 
 b?+—a?+, „ 
 
 et>+ (°Tp). 
 
 
 (1) '2p-», 
 
 )» 
 
 jj 
 
 eP+—dp+, „ 
 
 a? + CSp). 
 
Chap. IV.J 
 
 The Change of Tonal Functions. 
 
 '47 
 
 (Here we put aside the harmonies that may be introduced 
 in intermediate cadences, because they form very pronounced 
 dominant steps to new tonics, and therefore require no more 
 explanation.) 
 
 (B) in Minor : (a) "Dp—Sp, in A-minor : g+— ■/+, skipping c+(°T/>). 
 
 <*)¥- 
 
 "Dp, „ 
 
 „ f + - 
 
 -g+, 
 
 j} 
 
 f+(»7» 
 
 (c) "T— 
 
 °S, „ 
 
 "«- 
 
 -% 
 
 )i 
 
 °a (°S). 
 
 (pyr- 
 
 (*.)°Tp- 
 (F)°Tp- 
 (g) S m " 
 
 — ° II 
 
 — «S i> 
 
 —D + „ 
 
 » °e- 
 „ c+- 
 
 -n 
 
 -d + , 
 
 >> 
 
 °b (°Z>). 
 g+ i?D P ) 
 
 /+ {°sp 
 
 a+(+T). 
 
 (i)+Tp 
 
 - + -Dp „ 
 
 
 
 
 °c\{+Tp). 
 
 °gu + m 
 
 Surprising effects (in the best sense) are obtained, when the 
 composer introduces one and the same succession of harmonies 
 under similar conditions (i.e., at corresponding places in the 
 thematical construction), proceeding from it at one time without 
 change of tonality, and another time making use of the modulat- 
 ing power of the step (compare with each other the examples 
 with single and double letter indications) : 
 
 163. 
 
 , A. <*) («*) (3) 
 
 1 r w I s ' 1 < w r- w 1 s ' 
 
 ^ 
 
 = mJi^ m 
 
 T Sp Dp T T Sp 
 
 °S °D °T 
 
 £ Sp D 
 
 ¥ T JJ D T T M 
 
 ~>D°S Z>+ [°T] =D .. T 
 
 T M Sp D 
 
 or .S^ 2 * ' 
 
 ■5/j r 
 
 ^^ 3 > 7'«=-5 
 
Tp Z> 3 
 
 -S D 6 ** 
 
 Tp +D n " x T Tp & 
 
 = '£>"S Z»+ 
 
 l-O-^l 1 J n ( «>l 1 J „,. , 
 
 •| W - ' 1 
 
 
 ^-^J.^ -d A U _ 
 
 J- A J. 
 
 i 
 i 
 
 \t^-, , _!)^J.^ r . , y ■ « ■ 
 
 ^-i — =i 1 — ' 
 
 ¥3 
 
 = °D°S B 6 ' 
 
 T °S" "' 2? 
 
 , . B - w 
 
 1 I ! 
 
 (a») , i 1 | W ^, 1 
 
 
 — * — ** — W~ 
 
 11 -» » * ' 1 "-^1 1 1 ' 1 g [ " 
 
 J- J 
 
 I * * * f- ■ h .'i i* * r - ^ h 
 
 
 |_J_J 1 1 
 
 I- 1 — i — i — i ¥*-> — i — L — i — i — II 
 
 °T °Dp °Sp C S Z»+ °T"Dp "Sp °T ;.'"£>p °S Z>+ 
 
 , m 
 
 <s. 
 
 _ I | 
 
 , Wj _ j , 
 
 i. i («). |, 
 
 •' 1 n 
 
 <j£=j=fr= 
 
 f1~*" 
 
 
 
 ll.g S^ ^ ?^ -y— 
 
 ^^ 
 
 J/i i 
 
 (| 
 
 I 
 
 ■ it ^ ^ — 
 
 -T'-i ,JL ' i i 
 
 » il * jB — 
 
 i=l — m=n 
 
 V 
 
 
 
 
 i '1 
 
 U f—B 
 
 -SD I T =°D°ST D" °T 
 
Chap, iv.] The Change of Tonal Functions. 
 
 149 
 
 Like the whole-tone step, also the contra-fifth change, lying 
 tonally between the plain-fifth clang and the contra-clang, cir- 
 cumscribes a tonic (T or °T). This step, which occurs but 
 once between harmonies of the same key, may therefore be 
 
Harmony Simplified. 
 
 [Chap. IV 
 
 employed very effectively for modulations ; and, as it is very 
 easily intelligible, there is nothing to hinder its being made from 
 any harmony of the key. The typical forms are °S — Z> + and 
 D+ — °S ; the following progressions are the result of imitation : 
 
 (i) in Major : 
 Sp=°S—D+, in c-major 
 
 "a- 
 
 - + ithe d t S onfch<^)-- + - 
 
 Tp=°S—D+ 
 Dp=°S—D + 
 £)^—°S—D+ „ 
 
 T=D—°S 
 
 S=£>—°S 
 
 etc. 
 
 (2) in Minor : 
 °T =°S—D, in A-minor : 
 
 °e— b+ 
 
 °b—fi+ 
 
 °d—a+ 
 
 °D=°S—D 
 
 )) 
 
 'b-. fi+ 
 
 °g=°S—£ 
 
 )) 
 
 °d—a + 
 
 °Tp=D—°S 
 
 J» 
 
 c+—°f 
 
 °Dp=D—°S 
 
 J) 
 
 g+—°C 
 
 S™~=D—°S 
 
 )) 
 
 d+—'g 
 
 etc. 
 
 
 
 °b (Dp) or «+. 
 °f* (&) or b+. 
 "a (Sp) or d+(@). 
 f+ (S) or °c(°S). 
 
 b?+(g)or°f(°§). 
 g+(Dj or "d (J?~) 
 
 , °b (°Z>) or«+ (Z>+). 
 
 , yi?& or b+ (+B). 
 
 , a(°S) or d+ {S'"~). 
 f* (°Sp) or v. 
 ^(°7?)or£«. 
 
 , -+ (°Z>/) or V (-J?). 
 
 The difference of mode of the two dominants produces the 
 double possibility of turning to a new T or + T; but the former 
 or latter will have to be preferred, i.e., it will be expected with 
 greater probability, according as it is or is not a clang of the tonal 
 harmony. Of course there is no meaning in accumulating unexpected 
 turns one on top of the other ; the saying of a harmonist, to whom 
 a prize was awarded, that any chord might follow any other chord, 
 may be true for two chords considered in isolation ; but the 
 third chord is, as we shall see, anything but free, and the choice 
 can waver only within a small circle, according to the ambiguity 
 of the combination started from. 
 
 We now come to the ftfth-chdnge~--wir\cit we- came across 
 tonally as the changing of the contra-fifth clang into the contra- 
 clang of the tonic T—S—°S—T; °T—°D-D + —°T, i e., the 
 
 opposition of the contra-fifth clang is more marked than that of 
 the contra-clang, in proceeding to which a kind of retrograde step 
 is taken, in as far as we return from the contra-fifth of the tonic 
 to its prime, e.g., c + —f + — V — c + ; °e — °b — e + — °e. It should be 
 
 noticed that here the minor chord arising from the lowering of the 
 third of the major chord (f 3 '= °c) becomes "sub-dominant, and the 
 major chord arising from the raising of the - third of the minor 
 
chap, iv.] The Chance of Tonal Functions. 151 
 
 chord, + dominant ; to this the most frequent and important 
 modulating significance of this step entirely corresponds, no 
 matter from what clangs it occurs, i.e., in general terms : the 
 alteration of a major chord into a minor chord (by lowering the 3) 
 gives the latter the significance of a "S; the alteration of a minor 
 chord into a major chord (by raising the III) gives the latter the 
 significance of a + Z>. Thus from the clangs of the tonal harmony 
 we again obtain an abundance of new turns, most of which we 
 have already considered among the intermediate cadences, and 
 which we shall therefore only briefly indicate : 
 
 A. (Major) : 
 
 
 
 
 
 
 
 
 T— }?~=°S, in 
 
 c-maj< 
 
 )r : 
 
 e+—'g 
 
 leads 
 
 to g+ (D). 
 
 
 D—*-='S, „ 
 
 
 >> 
 
 
 g+-°d 
 
 >> 
 
 „ "a (Sp) or 
 
 dm- 
 
 sp-"r=z>, „ 
 
 
 J) 
 
 
 °a—d+ 
 
 >t 
 
 ., g + (-D)- 
 
 
 Tp—vr=D, „ 
 
 
 )> 
 
 
 °e—a+ 
 
 >> 
 
 „ "a (Sp) or 
 
 dm)- 
 
 dp-™t=d, „ 
 
 
 >J 
 
 
 °6—e+ 
 
 a 
 
 » °< {Tp). 
 
 
 B. (Minor) : 
 
 
 
 
 
 
 
 
 -T— I . I . I "=Z», in a 
 
 -minor 
 
 ■: °e—a + 
 
 u 
 
 „ "a ('S). 
 
 
 
 °S— ul "=D, 
 
 1) 
 
 
 )> 
 
 °a—d+ 
 
 ,) 
 
 „ g+ {'Dp) or 
 
 °d (°$). 
 
 °Dp—?*=°S, 
 
 »! 
 
 
 »» 
 
 g+-°d 
 
 j) 
 
 » °« C-S) 
 
 
 
 °Tp—?.*=°S, 
 
 1} 
 
 
 >! 
 
 c + -g 
 
 >t 
 
 „ g + (°Dp) or 
 
 °d ("$). 
 
 °Sp—?.'=°S, 
 
 >» 
 
 
 »> 
 
 f+—°c 
 
 ii 
 
 „ c+ (°Tp). 
 
 
 But since the fifth-change is tonally intelligible also in the 
 sense of D— 1> in major and °S — I . u< in minor, the above rule is 
 not without exceptions ; on the contrary the major chord arising 
 chromatically may also proceed as chord of the Dorian sixth (S ,u< ), 
 and the similarly formed minor chord, as chord of the Mixolydian 
 seventh (D 3> ); thus the following progressions arise : 
 
 A. (Major) : 
 T—}y=D^, in c-major=c + — °g, leads over °fto°c(°S) or/+( + 5). 
 
 s-?-=&~, „ =/ + -v, „ „ ■# „ °A°i) „ #+(*). 
 
 „ «+ „ °e(Tp) „ «+. 
 „ 5+ „"b(Dp)„ e+. 
 
 „ 5+ „ °b(°D)„ e+(D+). 
 
 „fpMm, * + ( + £). 
 
 „ V „c+(°Tp)„°g. 
 .. °/ „/ + (°^)„ V. 
 
 Sp— l }}"=S" 1 *, 
 
 )> 
 
 
 =°«-a? + „ 
 
 7>- ,, . I -=5 I,I -=, 
 
 H 
 
 
 =<V— a+ „ 
 
 Dp— 1 }}"=S m " 
 
 j n 
 
 
 =°5-* + „ 
 
 B. (Minor) : 
 
 
 
 
 yi IIK^ CI1I«= 
 
 in A-minor— V — a + „ 
 
 °Z>_'««= =£'"*, 
 
 
 » 
 
 =°3-« + „ 
 
 °£>p—?~=D", 
 
 
 7J 
 
 =g+-°d „ 
 
 °Tp—?r=D^, 
 
 
 >> 
 
 =c+—°g » 
 
 °Sp—?.'=D^, 
 
 
 1) 
 
 =f + -°c „ 
 
152 Harmony Simplified. [Chap. iv. 
 
 Another different interpretation of the fifth-change, more im- 
 portant than these, which are but seldom successfully carried 
 out, is that based on the change of the second upper-dominant back 
 into the parallel clang of the under-dominant in major ; I say the 
 change back, as the second upper-dominant in reality arises 
 chromatically from the parallel clang of the under-dominant 
 (j5/> m< = &• conversely therefore ^ 3> = Sp). By this means 
 the rule that the minor chord arising chromatically becomes 
 "sub-dominant, receives the new addition, "or parallel clang 
 of a major sub-dominant," and a few new modulations are 
 added to those developed above on p. 151 : 
 
 T— ?.'—Sp, in c-major : c + —°g, leads over /+ to bk-+(g) 
 
 similarly in A-minor : °Tp — ?."=S/>. 
 D — ?."=Sp, in c-major : g+- — °d, leads over c+ to f + (S) 
 
 similarly in A-minor : °Dp — ?."=Sp. 
 S—?.~eS)=Sp, in c-major :/+— V, leads over ib + to e2 + (°Tp) 
 
 similarly in A-minor : °Sp— ?r~= Sp, etc. 
 
 The examination into the inversion of the relation (in minor 
 
 "Dp^—'M, returning °§ m< =°Dp), we leave to the pupil (e.g., 
 °T—lll< =°Dp—°S—°r, from A-minor to B-minor). 
 
 § 15. MODULATIONS BY MEANS OF CHORDS OF SEVEN-THREE 
 AND OF MINOR NINE-THREE. 
 
 Continuing with chromatic alterations, we find quite similar 
 changes of meaning of harmonies, first by raising the major 
 prime and lowering the minor prime, e.g. : 
 
 c + — }." =c\ e g ; °e — }."=a c e\t 
 
 The chord arising in both these cases is dissonant, and is a 
 chord of seven-three, which may proceed either in the sense of 
 major (IP 1 ) or of minor ($ vu ). This formation occurs tonally as 
 Sp— }* = $ vn or "Dp—}* = &, and in both cases it is only 
 the mode that changes and not the tonal function (alteration of 
 the contra-fifth clang into the contra-clang, thus fifth-change) ; 
 also the change of the chord of the Neapolitan sixth back into 
 the minor sub-dominant chord of seven-three (S- — $ vn ), and 
 the change of the chord of the Lydian fourth back into the 
 major dominant chord of seven-three (& — JP") outwardly yield 
 the same formation, e.g. : 
 
 in c maior i ^ b * (="/*> ~A { d {=g> ) . 
 in c major \ f a7 fa ( ==rf j r f )_y a y d § ( =e vii) , 
 
 . (d f bt (=£t>+)— d f b% (=ft VI1 ) 
 mA-mmorj^, ^ jj_^ /| $ \=e>/ 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 153 
 
 and here, too, the function remains the same (yjf and g 7 with 
 dominant significance, bfy + and & vn with sub-dominant signi- 
 ficance). 
 
 But now any feigning consonance in tonal harmony may, with 
 unerring effect, be changed, by similar chromatic alteration of the 
 prime, into a chord consisting of two ?ninor thirds, and the latter 
 may proceed equally well in major sense or in minor ; 
 
 A. (Major) : 
 
 T— 
 
 S— 
 
 D — 
 
 m- 
 
 °Sp- 
 Tp- 
 Sp- 
 
 <-( J 
 
 < f^ 7 
 
 -\£vi. 
 
 <_/^ 7 
 
 ~\s vu 
 <(M» 
 
 ~\s vu 
 
 <_/^ 7 
 ~{s yu 
 
 >_/^ 7 
 
 —\$ vu 
 
 up — .. — ix v " 
 
 NB. 'S-^={f m 
 
 v — .. — j^vii 
 
 B. (Minor) : 
 
 ov , i> ($ vu in A-minor 
 
 T ~~ -{if 
 
 on I> J •/> 11 
 
 D ~ -{& 
 
 .f$ vu „ 
 U' 
 
 j$ vn „ 
 U> 7 
 
 C <?VH 
 
 $ 7 in c-major : c + — ^ 7 leads to °a (^>) or aT + (.©), 
 :^ + -b v " „ f%{@p,&) or b+, 
 
 :f+—e v " 
 : ^+-e' 
 
 : ^ + — fe 7 
 : ^ + -4 V " 
 : d? + — F 
 
 -h? 7 
 
 _„vu 
 
 'b {Dp) or e+. 
 V (7J») or «+. 
 
 >, °4 orft + - 
 „ "b (Dp) or e + . 
 
 .- *#■ 
 „ Jl> + (#). 
 „^ + (2?)orV(^,^ 3> ). 
 „ ^ +(.£)• 
 „^ + (Z))orV(ir/) I 2?'»). 
 „ ^ (°7». 
 „ f + (r, thus tonally) 
 or "g (°T). 
 
 "S- 
 
 o 
 
 °S- 
 
 "b—z 1 
 
 M 
 
 f + (S) or °c(>S). 
 
 "b—d vn 
 
 1) 
 
 °a (Sp) or d+(3). 
 
 "c—A'O 7 
 
 11 
 
 g\> + - 
 
 "c—a? vn 
 
 n 
 
 e]>+(°Tp). 
 
 '1%-z 1 , 
 
 n 
 
 c + (T, thus tonally). 
 
 °/#-* vn 
 
 11 
 
 H (Tp). 
 
 : °,-^" 
 
 11 
 
 °d(°g) or g+ ('Dp). 
 
 : °e—F 
 
 11 
 
 b\>+ (»). 
 
 : °£— d v " 
 
 1! 
 
 °a (°S). 
 
 : "b—z 7 
 
 '1 
 
 r i°sp). 
 
 : °a—z vn 
 
 II 
 
 e+ (°Tp). 
 
 : °a—h\> 7 
 
 II 
 
 ei>+. 
 
 : °d—P' n 
 
 II 
 
 /+ (°Sp) or V. 
 
 : °d—e)> 7 
 
 II 
 
 ab + - 
 
 II 
 
 
 S 7 
 
 -P 
 -b vn 
 
 °a( 6')orfl' + (6' ,u *, 
 °<»(^)or^+(5 m< ) 
 
154 Harmony Simplified. [Chap. iv. 
 
 »/,, i<- P v "in A-minor : g + —f$ vu leads to°4 (+2}»). 
 ^ " XL 1 „ : £■+— & „ °e (T, thus tonally) 
 
 orfl + (+r). 
 .c* i«_J* VI1 „ :/ + -e v " „ °£(°Z?) or «+ {D+). 
 
 P '• ~(f 7 „ :/ + -^ „ ^ + CZ?/)orV(^) 
 
 NB ^ .<_^ VB .- :^ + -^ v " „ °4- 
 
 ■ ~W „ :^ + -^ 7 „ Vf(+7». 
 
 «_i< (^ V " .» :&>+— jt v " „ °< (r, thus tonally). 
 
 " -L0» „ :#+-*' „ ,+ (°7}>). 
 
 Like the chords of seven-three (IP" and ^ vn ), also the chords 
 
 9> IX < 
 
 0/ minor nine-three (IP 7 , or briefly ^* and 4? VI1 or S lx< ), are char- 
 acteristic and particularly effective forms of the dominants ; any 
 chord of minor nine-three may, like any chord of seven-three, 
 proceed either in the major sense or the minor, but either way 
 will lead to the same tonic : 
 
 [ ff 9> ie M/ 9> ) 
 b d f dp = < ■? lx< ' .' ' j. IX < > of c-minor or c-major. 
 
 Chords of minor nine-three arise in the first place from raising 
 the prime of a chord of the over-seventh or lowering the prime 
 of a chord of the under-seventh : 
 
 A. (Major) : 
 
 in c-major: g 7 - 
 
 ' „ ■■ r- 
 
 — ea ,x< \ both lead to eb + 
 
 m i<_ ( ^ 9> in c-major: ^'—je 5 * ) both lead to °e (Tp) 
 •■ -}£ix< ^ . gl _ ^ix< | orfl+ 
 
 cvu i>_iS lx< >, : c yn — e^ ,x< Iboth lead to e 
 
 ° ■■-\Mfi > „ : c vu — br* | (°Tp) or °fr. 
 
 B. (Minor) : 
 cvu i»_ / ^ IX< in A-minor : a 111 — z lx< ) both lead toc+(Tp) 
 * "~\ -0" „ : «™-$* ) or'g. 
 
 m i<_i^ 9> .» = « 7 — £ P' {both lead to Yfc 
 
 V - ~ \ S*< „ : *-£$*« / (+7J») or/#+. 
 
 Moreover, chords of minor nine-three may be formed at any 
 time quite simply by altering the prime of the clang and simul- 
 taneously adding the natural seventh, e.g. : 
 
 c e g — cflf e g b? or a c e — /Jf ace? 
 
 But by adding the natural seventh in this manner (T — .}< and 
 
 T— y "§) one of the two possible ways of progression which, as 
 we saw above, were open to us by alteration of the prime, falls 
 
chap, iv] The Change of Tonal Functions. 155 
 
 away ; i.e., whereas c% e g is intelligible either as ft or h vn , and may 
 therefore either proceed to D-minor (D-major) or B-minor (B-major), 
 after the addition of the bfy only the road to D-minor (D-major) 
 remains open, since the chord tends that way both in major and 
 minor sense. The pupil should now find out which of the paths 
 opened on pp. 153-4 fall away when the seventh is added with the 
 chromatic alteration of the prime (instead of .'.*, read everywhere 
 
 A i> 
 
 - 1 *, instead of. 1 .', everywhere .. vn t|). 
 
 The nine-three chords acquire fresh importance from the 
 possibility of enharmonic change of meaning of single notes, 
 which we have already turned to advantage here and there in our 
 exercises. We will, in the first place, establish the relation of the 
 notes in major and minor sense without enharmonic change of 
 meaning, then, e.g., in b dfap as g 9 * or £ IX< : 
 
 J? 
 
 i.e., a change of meaning of the g> to the III, of the 7 to the V, 
 of the 5 to the VII, of the 3 to the IX* would yield no new 
 nine-three chord, but the same in the minor sense. On the other 
 hand, every shifting of the numerical indications yields a different 
 chord, e.g. ; 
 
 a? 9=-= V a\> 
 / 7 =VII/ 
 
 a? 
 
 9* 
 
 = 
 
 7 a? 
 
 / 
 
 7 
 
 = 
 
 5 / 
 
 d 
 
 5 
 
 = 
 
 3 d 
 
 b 
 
 3 
 
 CO 
 
 9*c\> 
 
 \ 
 
 ^n * s = ix- d r ,x '> ° r ais °i a 5 =3 d r^- 
 
 l«3 SIIhM {b 3 s 9 »c\>) 
 
 But since the function of the nine-three chord always remains 
 the same (JP 9> or £ lx< do not actually mean two different things, 
 but are different expressions for the same thing), a modulation by 
 means of enharmonic alteration of one or more of its notes, 
 cannot otherwise be determined with certainty than by indica- 
 tion of the change of meaning of one of these notes. Taking 
 bdfa?=Jp 9> and # IX< in c-major (c-minor) as starting-point, 
 we shall find in 
 
 (3 CO 9>) (IX < 2g I") (3 CO III) (IX< "CO o>) 
 
 &■»= lp» or £ ,x< = £ IX< or £■» = £ IX< or ^ IX< = !/.■» 
 
 that it changes uniformly to d/a\> cfy, the dominant nine-three 
 chord of E?-major or Eb-minor, etc. It becomes evident from 
 this trial that there is scarcely any object in writing the formula 
 Jp 9> or # IX< twice or of placing M> 9> next to # IX< (unless one had 
 in mind a bass-progression which would be bad for j? 9> , but good 
 for # IX< , e.g., for b dfdp the step in the bass from/to c, which 
 could only be approved of for # IX< , as f would be fundamental 
 
156 Harmony Simplified. ichap iv. 
 
 note [V], for IP 9> on the other hand bad, as /would be seventh 
 [7]) ; it will therefore be sufficient to indicate the change of 
 meaning over the one formula $»" or $ lx< , but naturally avoiding 
 the change from major into minor numbers, and vice versd. Then 
 the result of changes of meaning of b dfd$ as M> 9> or °4? IX< in 
 c-major or c-minor, indicated in a form easily surveyed, is : 
 
 (3 ^O 9>) 3 9* 
 
 (ia) ty» from (g) b dfa? into (£?) d f cfy c\> (=M>° > of E^-major 
 
 or E|?-minor). 
 
 (IX < !££ Ill) IX < III 
 
 (b) S lx< from b df cfy {c) into d f a!) cV ('!>) (=£ IX< of 
 
 E|?-major or EP-minor). 
 
 (9> CO 3) 9 3 
 
 (2A) W from (g) b dfaV into («) g% b d /(=&>* of A-major 
 
 or A-minor). 
 
 (Ill JJ5 IX <) III IX < 
 
 (b) $ IX< from b d f a\> {c) into g\ b d f (a) {=$<** of 
 
 A-major or A-minor). 
 
 (3A) "J** from (g) b d f a} into (<:#) 4 g$ b d (=#" of 
 
 FJf-major or F^-minor). 
 
 (or aa) *Jp& from (g) b d f a\f into (ct) e%g% b d (=Jp» of 
 
 Fp-major or F$-minor) 
 
 (V 15 IX<) v ix< 
 
 (b) £ ix< from b df a? (<r) into e$g$b d (/#) (=£ IX< of 
 
 fJ -major or F$-minor). 
 
 (Ill S?[ VII) III VII 
 
 (or bb) $ ,x< from b d J a} (e) into e% gl b d (/#) (=$ lx * of 
 
 F$-major or Ff-minor). 
 
 Other changes of meaning would not really lead to other 
 progressions, but only to differently written ones, e.g., 5 jg 3 to 
 £#'" (d~^_c % ) and 5 ^ 9* to Ah 9 * (d^iebp), which have already 
 been introduced above in a simpler manner. 
 
 A similar enharmonic change of meaning may be effected 
 with chords of seven-three, not, however, resulting in chords 
 of seven-three, but in imperfect chords of nine-three (without 
 fifth, s or *) ; e.g., b d f may change meaning to c^ df, b J. c\, 
 cV ep\> /, b c x e% by means of the clang signs : 
 
 (3 CO 9 =■•) (7 5d 3) (5 go 0=» ) (5 Ks 3* ) 
 
 My=H)\r, JP>=JZ>y, M>'=M~, ^>'=MT 
 
 also in the minor sense : 
 
 (Vii «? in) mi eg ix-=) rv co mi (V S ix-=> 
 
 S v " = S lx r, £ V " = .£ 1X ', ^ VlI =^ ,x "=, ^ V1I = ^ IX ', 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 i57 
 
 For the easier and more convenient management of the clang 
 signs for these complicated formations, it should not be over- 
 looked that the sign jo always requires the enharmonically altered 
 notation of the note, and that this altered notation in changes of 
 meaning to 3, VII and IX* generally introduces notes with Jf or 
 x , whereas in changes of meaning to III, 7 and 9* it generally 
 introduces notes with fc or bfe, and not the reverse. 
 
 We most decidedly caution against the misuse of enharmonic 
 changes of meaning ; for, excepting where they enter as passing 
 illusions (with subsequent retracting), they positively mislead the 
 ear, and are devices founded merely on the limited power of 
 logical comprehension. On the other hand by opportunely 
 turning ambiguity to advantage, effects of the most surprising 
 beauty can be attained, like mystical views of remote domains of 
 the tone-world, inaccessible by ordinary paths. It remains to be 
 specially remarked that such ambiguous enharmonic harmonies 
 may at times be figured in a sense different from that determined 
 by the context, e.g. : 
 
 9» io=- 9> 9=- io» 9=> 
 
 Here, as it were, the intensity of the feeling of tonality mocks 
 at the most forcible means of modulation. 
 
 Chords of seven-three and nine-three, where not proper to the 
 key, resulted in the first instance from chromatic alteration in 
 connection with that of the fifth-change, but involving an even 
 more marked sense of dominant harmony than was the case with 
 the latter. We now again return within the range of tonal har- 
 mony, so as to fathom the degree of modulating power possessed 
 by harmonic successions which can indeed be understood tonally, 
 but need not ; in so doing we shall again follow the order in 
 which the harmony steps occurred during the gradual extension 
 of our range of observation. 
 
 § l6 MODULATIONS BY MEANS OF THE THIRD-CHANGE CLANGS. 
 
 The third-change may, similarly to the fifth-step and turn of 
 harmony, be made use of for a simple exchange of keys ; first 
 for really passing from the principal key to that of the tonic 
 parallel, if the aid of rhythmical expedients be also accepted. But 
 also any third-change from a dominant, to a certain extent 
 undoubtedly suggests modulation to the key of the tonic parallel * : 
 
 • The following short examples are all to be worked out in several keys, or, at 
 least, to be played at the piano. 
 
'5« 
 
 Harmony Simplified. 
 
 [Ch.,p. IV 
 
 (a) from T to Tp : T D \ T .. 
 
 =°Tp 
 
 (b) from D to Dp : T \ D Dp 
 
 °T D | °f. 
 
 ay 1 
 
 (c) from S to Sp: T\ S Sp I 
 
 —"S °r. 
 
 (d) from °r to °Tp: °T D \°T . 
 
 Tp\ T D | T. 
 
 (e) from °Z> to "Dp : "T "D \ "Dp 
 
 =D T. 
 
 (f) from °S to °^:T| °S "Sp 
 
 T. 
 
 Naturally if the modulation is to be regarded as definitely 
 made, another close will be needed to establish the new key. 
 
 The leading- tone change, minor- third change, whole -tone 
 change, and tritone change, being transitions to principal clangs 
 of the parallel key, and being readily comprehended in the sense 
 of that key, have similar modulating power, which one often 
 enough experiences in minor as endangering the retention of the 
 tonality (e.g., in sequences in which we only too readily pass over 
 to the conception in the major sense). 
 
 Possible modulations by means of leading-tone changes are : 
 
 (A) 
 
 y IK 
 
 =°D™- l 
 
 (b) T\ S !!" 
 
 O •T I 2> I 
 
 (c) 
 
 o r n 
 
 (d) °T I °D 
 
 s z»+ i c r. 
 
 °S Z>+ I T. 
 D | T. 
 
 S D \ T. 
 
 The minor-third change may effect modulations in the following 
 manner : 
 
 (a) T 
 
 Sp 
 
 = Tp\'S D+ | °T. 
 
 (b) T D 
 
 Tp 
 
 —"Dp I "T "S | °T. 
 
 (c) "T °Dp I 
 = Tp D I T. 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 159 
 
 (d) °T °S 
 
 
 
 = Sp 
 
 T S\ T. 
 
 The whole-tone chatige similarly : 
 
 (a) T | D Sp\ 
 
 =°Dp °S | °T. 
 
 (b) °T 1 °S "Dp 1 
 
 = Sp D \ T. 
 
 Likewise the tritone change : 
 
 (a) r | 5 Dp 
 
 
 = ¥ "D 
 
 y 1 
 
 (b) °T \°D °Sp \ 
 
 = 3? 
 
 s 
 
 T. 
 
 But all these steps may equally well lead into other keys than 
 the parallel key, by either starting from a different point, or 
 changing meaning in another sense : 
 
 1. Modulations by means of leading-tone changes : 
 (a) T I S !!"= > 
 
 -T !!"* j S D I T (e.g., c-major— F-major). 
 
 (B) T I D 
 
 =T 
 
 (c) T I "S" 
 
 =T 
 
 S D I T (e.g., c-major — G-major). 
 
 S D I T (e.g., c-major — D^-major.) 
 
 (d) T I °Sp !!"= I 
 
 =T l }."\ S Z> \ T (e.g., c-major— Al?-major). 
 
 (e) T\ S 
 
 =°D !S 
 
 (f) t !!" 
 
 o ya> I 
 
 °S D I °T (e.g., c-major — D-minor). 
 
 °S D I °T (e.g., c-major — E-minor). 
 
 (g) T I °S m l I 
 
 =0 .p* l \ °S D \°T (e.g., c-major — F-minor). 
 
 (H) T\ Sp .=> 
 
 (1) T I Dp 
 
 T (e.g., c-major — F-major). 
 T (e.g., c-major — G-major). 
 
 (k) "T \"S T I 
 
 =°T . a .=" I °S D I °T (e.g., A-minor — d minor). 
 
i6o 
 
 (l) "T I °D .."■ 
 
 O *T* 2> 
 
 (m) T I °Z> 
 
 =+.S II< > 
 
 (n) a T 
 
 Harmony Simplified. iChap. iv. 
 
 °S D \°T (e.g., A-minor — E-minor). 
 jy+ | +2* {f.g. t A-minor — G-major). 
 
 S D \ T (e.g., A-minor — F-major, etc.). 
 
 2. Modulations by means of minor-third changes : 
 (a) T\ S 
 
 =r sp d 
 
 T (e.g., c-major — F-major). 
 
 (b) T\ D Tp 
 
 =T Sp D J T {e.g., c-major — G-major). 
 
 (c) T | Dp 3 \ 
 
 = S D \ T (e.g., c-major — G-major). 
 
 (d) T I & Tp 111 ' 
 
 = Tp D 
 
 (e) T\Dp 3 
 
 = Tp D 
 
 T (e.g., c-major — D-major). 
 T (e.g., c-major — G-major). 
 
 (F) T | ?r- S I 
 
 = S D \ T (e.g., c-major — Ep-major). 
 
 (g) °T I °D S m " ; 
 
 = & D \ T (e.g., A-minor — G-major). 
 
 (h) °T I °@ T m - 
 = S D 
 
 T (e.g., A-minor — D-major). 
 
 (i) "T \°S °Tp \ 
 
 =S'" D J T (e.g., A-minor — F-major). 
 
 (k) "T I Sp °§ 
 
 =°Tp °S 
 
 (l) °T I "Dp °T 
 ="Tp °S 
 
 °T (e.g., A-minor — D-minor). 
 
 °T (e.g., A-minor — E-minoi) 
 
 3. Modulations by means of whole-tone changes : 
 
 (a) T I Tp 0| 
 
 =Sp D I T (e.g., c-major — G-major). 
 
 (b) T I Dp Tp nv - j 
 
 =Sp D j T (e.g., c-major — D-major). 
 
 (c) T I °S g \ 
 
 =Sp D I T (e.g., c-major — E[7-major). 
 
chap, iv.] The Change of Tonal Functions. 161 
 
 (d) T I & Dp™' 
 
 =Sp D 
 (e) T I & Dp m 
 
 D 
 
 (f) T 1 n*>- T 
 =Sp D 
 
 (g) °T I °Tp °g 
 
 =°Dp °S 
 
 (h) "T I °^ c 7/>* 
 
 (1) T I Z>+ °S> 
 
 =°Dp °S 
 
 (k) °r I $ °,§> 3! - 
 
 (l) "T I S °.§>3» 
 
 =^„ °S 
 
 (m) T I 5'"-= T 
 
 T 1 {e.g., c-major — A-niajor). 
 °T (e.g., c-major — A-minor). 
 T (e.g., c-major — F-major). 
 
 °T {e.g., A-minor — D-minor). 
 T {e.g., A-minor — G minor). 
 
 T {e.g., A-minor — FJf-minor). 
 T {e.g., A-minor — c-minor). 
 T {e.g., A-minor — c-mnjor). 
 T {e.g., A-minor — E-minor). 
 
 4. Modulations by means of tritone changes : 
 T {e.g., c-major — G-major). 
 
 (a) T & 
 =S Dp 
 
 (b) T I & 
 
 = ¥ \ °D °S I T {e.g., c-major— E-minor). 
 
 (c) T I Tp $ 
 
 =+T' : * S T {e.g., c-major — F-major). 
 
 (d) T\S °T \ 
 
 =S Dp I T {e.g., c-major — A?-major). 
 
 (e) "T S- I 
 
 —°D °Sp 1 °T {e.g., A-minor — D-minor). 
 
 (f) °T £ 
 
 = ¥ S D I T {e.g., A-minor — F-major). 
 
 (g) "T \°Tp "S I 
 
 = ¥ °D\ °T{e.g, A-minor — E-minor). 
 
 (h) 'T I & T" 
 
 =°Z> "Sp 
 
 "T {e.g., A-minor — cj-minor). 
 
1 62 Harmony Simplified. (Chap. iv. 
 
 § 17. MODULATIONS BY MEANS OF BOLDER HARMONIC PRO- 
 GRESSIONS. 
 
 Nicety of feeling as regards the nature of modulation will be 
 specially formed by means of such turns as are intelligible within 
 the key and abstain as far as possible from notes foreign to the 
 scale. The harmonic progressions now to be discussed with 
 regard to their modulating power introduce foreign notes more 
 and more, so that the paralysing of their modulating tendency is 
 scarcely possible. In tonal harmony the steps in question result 
 from the connecting of the contra-clang of the tonic with the 
 parallel clangs, i.e., clangs which are all only indirectly intelligible 
 (for even the contra-clang of the tonic is that undeniably in a 
 certain sense : its third has the effect of a chromatic note and 
 may not be doubled). 
 
 1. Modulation by means of leading-tone steps. Analogous to 
 the tonal form of the step (?Sp — D + and Dp — °S in major and 
 minor) every leading-tone step as representing both dominants, 
 has the effect of pressing directly towards the tonic skipped, 
 and, therefore, if proceeding from other harmonies, it induces 
 modulation : 
 
 (a) Tp °°§ I 
 
 =Dp °S I T [°T~\ (e.g., c-major — F-major or F-minor). 
 
 (b) & T 
 
 =Dp °S 
 
 (c) T\ S Dp m 
 
 (d) T\g Tp 1 
 
 =°Sp Z>+ 
 
 (e) T I ^ T 
 
 =°Sp D 
 
 T (e.g., c-major — G-major). 
 Sp D+ \°T (e.g., c-major — A-minor). 
 °T(e.g., c-major — D-minor). 
 T [°7"] (e.g., c-major — F-major or F-minor). 
 
 (f) "Tp Si I 
 
 =°Sp D + I °T \_T~\ (e.g., A-minor — E-minor or E-major). 
 
 (g) ^ T m<: \ 
 
 =°Sp Z> + I °T (e.g., A-minor — D-minor). 
 
 (h) T I "D "Sp*- I 
 
 =Dp °S I T (e.g., A-minor — c-major). 
 
 (1) T I °°M "Tp^ I 
 
 = + Dp °S I T + (e.g., A-minor — G-major). 
 
 (K) "T I & °T\ 
 
 =Dp °S I °T (e.g., A-minor — E-minor). 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 163 
 
 But the rdle of the leading-tone steps is not as yet at an end. 
 After the experiences we have had (p. 1 1 6) as regards the figuration 
 of harmonies by leading-notes (auxiliary notes), there will be no 
 cause for wonder that finally in place of all three notes of the 
 harmony, their respective upper and under seconds may enter ; 
 by this means so-called auxiliary Jiarmonies arise, which in the 
 first place have no modulating power and are understood only as 
 figuration. As they are feigning consonances, they share with all 
 feigning consonances the peculiarity that they may be treated as 
 real harmonies (with doubling of the feigning fundamental note) ; 
 if one of the leading-notes be a note of the key otherwise capable 
 of being doubled, nothing stands in the way of its being doubled 
 here also. For C-major and A-minor we obtain the auxiliary 
 harmonies : 
 
 6* 
 
 7 < 
 
 II* 
 
 II* 
 
 4 
 
 4 < 
 
 IV 
 
 IV* 
 
 2> 
 
 2< 
 
 VI * 
 
 VII* 
 
 II* 
 
 II* 
 
 11-= 
 
 II* 
 
 IV 
 
 IV* 
 
 IV 
 
 IV s 
 
 VI* 
 
 VII* 
 
 VI* 
 
 VII 
 
 with some of which we have already become acquainted under 
 other names [(a) as S; (c) as °Sp in major, (g) as &, (i) as + Z>> 
 
r&4 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 (in minor)]. It is more convenient to write the auxiliary har- 
 monies in three parts than in four ; in four-part writing it will 
 be preferable to call to aid an auxiliary note in the opposite 
 direction : 
 
 But it is remarkable that the contra-leading-tone steps do not 
 so unconditionally tend towards a tonic skipped as other far- 
 reaching steps (pp. 52, 146, etc.), but rather lead us to expect a 
 fifth-step or turn of harmonies in the same direction : 
 
 / 
 
 r-9 1 — fa — 1 ik 1 1, g" J& nftg i 
 
 1 ' . 
 
 1 „ -g hhg- T hgg-]] 
 
 
 
 
 
 167.- 
 
 t) r . b. ^ fefp «f?l 
 
 -P: S> Sf r 
 
 *" i i 1 T u 
 
 > .. V T- 1- 
 
 
 ■ w — = 1 H 1 1 
 
 
 — H H 
 
 c+— dt>+— g'o + "e—°d%—"ai c + —a+—ft+ "e—"eb—"h 
 
 Probably the effect produced is due to a confusion of the 
 leading-tone step with the chromatic-semitone step ; assuming 
 the latter [167 (c) — {d)~\ in place of the former, the progression 
 corresponds entirely to our experiences ; the succession f+ — ffi — 
 /jf* may then be expressed as (S) [&] D T, or also S- £} D, and 
 is intelligible. 
 
 2. Modulation by means of third-steps. The only third-steps in 
 tonal harmony (not taking intermediate cadences into considera- 
 tion) are Tp— °S and S— + S in major, °Tp—£> + and &—°D in 
 minor. But in another sense the third-steps require greater 
 attention. Namely if — considered purelj harmonically without 
 having regard to scales — the plain-fifth clang is nothing more 
 than the nearest related partial note of the tonic clang, detached, 
 so to speak, and rendered independent as representative of its 
 own clang, the idea suggests itself of rendering the third-note 
 independent in the same fashion, separating it from the clang of 
 the tonic and confronting it with the latter as the bearer of its 
 own clang ; then a kind of dominant significance will attach to 
 the third-clang of the major tonic, similar to that of the plain- 
 fifth clang, and the contra-third clang may also lay claim to a kind 
 of under-dominant significance, while in minor, here as every- 
 where, the relations will turn out exactlv reversed. The under- 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 i65 
 
 dominant effect of a^ + in C-major we have hitherto defined as 
 "Sp, the upper-dominant effect of °g# in A-minor as + Dp, e + in 
 C-major we first became acquainted with as (D) Tp and "c in 
 A-minor as (°S) "Tp. But tfiere can be no doubt that the third- 
 clang is capable of closing directly to the tonic, without the sense of 
 an elision being felt ; e + — c + does not close as if "e had been 
 skipped, "c — °e not as if c + had been skipped, nor does a\l + — c + 
 need the mediation of V, or °g§ — "e that of e + . The formulas 
 are: 
 
 (Z>) Tp T {°S)°Tp "T °S V 
 
 T & 
 
 Their cadential effect and direct harmonic intelligibility will 
 be all the clearer and more certain, the more massive and pon- 
 derous the tone-complex is by which it is sounded, i.e., the less 
 the progression of the several parts strikes the ear. But herein 
 also lies the reason why the third-step can never have equal rights 
 with the fifth-step. Harmony is certainly the fountain-head from 
 which all music flows, but the diatonic scale is the primeval bed, 
 the banks of which the stream may at times overflow, but into 
 which it is always forced again. The scale recognises chromatic 
 progression only as passing through an intermediate degree, never 
 as a cadential member of a melodic formation ; the chromatically 
 altered note always appears like an approach from the preceding 
 note to that next following. But all third-steps contain a 
 chromatic step ; if intended as a close, the part which has to 
 execute the chromatic step seems disagreeably wanting in motive 
 for its progression. In 168 (a) — (d) the g\ — g, dfr — a, efy — e, c$—c 
 as cadential steps are not quite logical. Since the second note 
 of the step belongs to the clang of the tonic, the first is, properly 
 speaking, tending away from it, and so our indication of the 
 third-clangs hitherto as dominants of the third-change clangs or 
 as third-change clangs of the dominants, is, for melodic reasons, 
 certainly justified. The g$ in 168 (a) should by right proceed to 
 a before going to g, similarly the a? in 168 (b) first to g and then 
 
i66 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 to a, the eV in 168 (c ) first to ^ and then to c, the c Jf in i68(y) first 
 to <f and then to ^ [(/: 168 (e)— (h)~\. 
 
 It is possible to obtain real cadential significance for the 
 third-steps, if the possibility of confounding chromatic steps with 
 leading-tone steps be taken into account (which we have already 
 verified in the opposite sense, p. 164), but at the cost of the clang- 
 unity, in place of which the feigningly consonant dissonance 
 enters : 
 
 
 w 
 
 
 «„ 
 
 
 M 
 
 
 (rf) 
 
 
 
 169.- 
 
 
 <3 
 
 
 
 11 JO 
 
 B 
 
 •i; 8 ^— 
 
 ^ 
 
 
 ft): i-j — 
 
 
 
 
 Hhc — 
 
 b ^ = l 
 
 = 
 
 
 =H 
 
 
 
 
 ' <sj 
 
 ""' 
 
 
 
 
 * — 
 
 
 Z?/ 
 
 °5/> a - 
 
 D-' 
 
 y 
 
 But the feigningly consonant nature of this formation allows of 
 the doubling of the feigning fundamental note, so that in reality 
 the effect of a third-step arises. 
 
 Though we can prove the cadential power of third-steps only 
 conditionally, yet, on the other hand, their modulating power is 
 all the more beyond doubt, and it acts- in the sense of the 
 intermediate relation disclosed at 168. If now we make third- 
 steps from other clangs of the tonal harmony, we obtain the 
 modulations : 
 
 (a) T Dp™-* I 
 
 ="Tp D I °T(e.g, c-major — A-minor). 
 
 (b) 5 Tp m " 
 =°Tp D 
 
 (c) 5 * 
 =T °Sp °S 
 
 (d) d (D) \_np-] 
 
 =°Tp D 
 
 (e) D °Tp 
 =T°Sp °S 
 
 T {e.g., c-major — D-minor). 
 + T[°T] (e.g., c-major— F-major [F-minor]). 
 
 T (e.g., c-major — E-minor). 
 °7 , [7 ,+ ] (e.g., c-major — G-minor[G-major] 
 
 (f) S S+ I 
 
 =°Tp D \ °T (e.g., c-major — Bi?-minor). 
 
 (g) Dp T*» 
 =Tp "S 
 
 T (e.g., c-major — G-major). 
 
 (h) & D^ I 
 
 =Tp "S I T 1 ^^] (e.g., c-major— D-major [D-minor]). 
 
chap, iv.] The Change of Tonal Functions. 
 
 167 
 
 (1) °Sp T 
 =°Tp D 
 
 °T '{e.g., c-major — F-minor). 
 
 (k) °T -Sp 3 " I 
 
 —Tp °S I T (e.g., A-minor— c-major). 
 
 (l) "D °Tp* a 
 =Tp °S 
 
 (m) "D & 
 =°T Dp D 
 
 ( N ) °s (°s) [•#] 
 
 =Tp °S 
 
 T (e.g., A-minor— G-major). 
 T + [°T] (e.g., A-minor— E-maj or [E-minorJ). 
 T (e.g., A-minor — F-major). 
 
 (o) °S + Tp I 
 
 =°T Dp D\ + T [T] e.g., A-minor— D-major [D-minor]). 
 
 (p) & °D I 
 
 =+Tp °S I + T (e.g., A-minor— B-major). 
 
 (Q) °Sp T m ' 
 =°Tp D+ 
 
 (r) S- S m " 
 =°Tp D + 
 
 (s) + Dp "T 
 = + Tp °S 
 
 T (e.g., A-minor — D-minor). 
 "T (e.g., A-minor — G-minor). 
 + T (e.g., A-minor — E-major). 
 
 .But the third-steps open up to us another quite new path, 
 and the result will entirely satisfy us as to the apparent slighting 
 of the third-clangs compared with the fifth-clangs ; for, in point 
 of fact, the third-clangs could not lay claim to perfectly equal 
 rights, for the simple reason that their relation to the tonic is 
 more distant than that of the fifth-clangs. The third (cf. Intro- 
 duction, p. 3) is the fifth note in the series of naturally related 
 notes (in major and in minor sense) ; the fifth, on the other hand, 
 is the third note of the series. How, then, if we could prove 
 that from the clang of the 5 th partial note over that of the 3rd a 
 forcible close to the principal clang would be made, i.e., that the 
 fifth-clang after the third-clang leads back to the principal clang ? 
 If, in the first place, we build up harmonies of the same mode, 
 the following successions result : 
 
 (a) Major. 
 
 (6) Minor. 
 
 I70. 
 
 (Major.) 
 
 (Minor.) 
 
i68 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 Here the chromatic note (g'fl, ait) no longer causes any dis- 
 turbance, because, though its diverging tendency is felt, it is 
 cancelled by the forcible logic of the progression. 
 
 But not only does the return from the third-clang over the 
 fifth-clang to the principal clang, by means of clangs corresponding 
 in mode to the series in question, appear normal and logical, but 
 we find also a series of clangs of the same mode, whose principal 
 notes present in succession a clang of the opposite mode, likewise 
 forming a return : 
 
 (a) Major. 
 
 (3) Minor. 
 
 171. 
 
 (Minor.) 
 
 (Major.) 
 
 though, perhaps, the ear will slightly object to 171 (b), in con- 
 sequence of its not being accustomed to the progression. 
 
 But third-clangs are also readily followed by a fifth-step 
 in the same direction, which is, no doubt, explained by th« 
 leading-tone step formed as total result ; the latter, which by itself 
 is not easily intelligible, will then rightly be divided into a third- 
 step and a fifth- step. 
 
 172.- 
 
 w 
 
 (« 
 
 \ u 
 
 w 
 
 * W) 
 
 m 
 
 J bJ , .b . 
 
 fe 
 
 ^^ 
 
 =fc=: 
 
 z$=t; 
 
 Ig gP 
 
 T "Sp T{D)[Tp] 
 
 =D T =S T 
 
 'T (°S)[°Tp] 
 
 T Dp 
 =°S< 
 
 But we must here beware of delusions ; whether the third 
 clang be the expected sequel of the two first, or the second 
 be a natural connecting member between the two others, I should 
 not like to decide ; anyway, the latter conception of the case has 
 long been familiar to us in intermediate cadences. Certainly it is 
 very instructive and strengthens comprehension to bring a large 
 number of chords under one common point of view ; in this case, 
 therefore, to understand only the third clang as the principal point 
 of the progression, and to attach further conclusions to it : then 
 we should again have reached the leading-tone step with its 
 tendency to another fifth-step forward. So as not to lose the 
 thread in the labyrinth of possibilities shown here, it will be 
 necessary to remain conscious of the solid foundation, the strictly 
 
Chap, iv.] The Change of Tonal Functions. 169 
 
 tonal logic, according to which, in the first place, all lowered 
 notes tend to proceed downwards and all raised ones upwards, a 
 law against which, e.g., examples 172 (a) — (d) only seemingly offend. 
 Every leading-tone progression denotes a return, every chi-omatic 
 progression an onward impulse ; if these two sentences be applied 
 to the examples, the result will be found entirely satisfactory. 
 
 3. Modulation by means of minor-third steps. We may sum up 
 the remaining steps briefly, since the impelling forces of modu- 
 lation have gradually been disclosed to us, and only a few new 
 applications of the same points of view remain to be considered. 
 The last investigation cleared the way for understanding minor- 
 third steps as possible only in regard to a third, principal clang. 
 The steps c + — a + and c + — e2 + must be referred to the clangs 
 f + , °e and aX + , °g respectively, and similarly "e — Vjf and °e — °g to 
 a+ > °£$ an d c + , °b respectively, i.e., the following ways of pro- 
 ceeding from minor-third steps appear quite logical : 
 
 e + — a+ — e + ; a+—c+—/ + ; 
 
 c+ — e'p +— aV+ ; ek+— c+ — g+ ; 
 "e — Yjf— "g% ; Vjf— 'e — 'a; 
 °e — °g—"c; °g — °e — °b. 
 
 These progressions occur, to be sure, in tonal harmony : 
 
 In C-Major : In A-Minor : 
 
 °c — "a — °« <+ — g + — c+ 
 
 °S —+Sp—Tp Z>+— "Dp —°Tp 
 
 but there they have not the sense of real closes (returns) to the 
 last clang, but rather that of deceptive closes ; but if their actual 
 cadential power be beyond doubt, we cannot do otherwise than 
 make room for the third-clangs and minor-third clangs within 
 tonality, besides fifth-clangs and their parallel clangs ; but we 
 shall not require new signs for them, particularly as on account of 
 the chromatic steps their direct power of making a cadence to 
 the tonic appeared "problematical. We need only recognise the 
 harmonic successions : 
 
 In Major : In Minor: 
 
 T— "Sp — +S—T °T— +Z>p — Z>+— "T 
 
 T—(D)\_Tp~\— D—T °T— (°S) [°2>] — °5 — °T 
 
 T— °Tp — £>— T "T— +Tp —°S—°T 
 
 T—(Z))[Sp']— S—T "T— {°S) [°£>p~] — °Z>— °T 
 
 as independent cadences, i.e., not to be compared to intermediate 
 cadences ; they are, however, not bilateral, but one-sided cadences, 
 as in their case only one side of the relationship is doubly repre- 
 sented. Under the same category come the leading-tone steps 
 
170 Harmony Simplified. [Chap, iv. 
 
 with insertion of an intermediate harmony, both proceeding and 
 returning : 
 
 In Major : 
 
 (a) T-'Sp ~ 
 
 (b) 'T -{D)\Tp\-(D){Dp\- D 
 
 In Minor : 
 
 ( c ) °T— +Dp — & — °D 
 
 (d) °T—'S\?Tp\—°S$Sp\ — °S — °T 
 
 y. - . 
 
 in which the inserted clang is always as closely connected to the 
 next as possible (cf. the lower brackets). The simplest forms 
 of one-sided cadences are T— +S— °S— T, °T—°D—D+—°T, 
 T—Sp—S—T, T—Tp—S—T, °T—°Sp—°S—°T, T—Dp— 
 D — T, °T—°Dp—°D—''T, etc., which are logical, because they 
 proceed from tonic to dominant by means of notes in common, 
 or similarly return from dominant to tonic. Anyway, such 
 cadential formations are, so to speak, only half ones, and should 
 not be regarded as principal bases of harmonic motion, but rather 
 as accessory forms. 
 
 § 18. MODULATION BY MEANS OF THE MOST FAR-REACHING 
 HARMONY STEPS. 
 
 The tritone-siep may be found between the chord of the 
 Neapolitan sixth (&) and the major upper-dominant, as well 
 as between the chord of the Lydian fourth (&) and the minor 
 under-dominant ; it is one of the most interesting substitutions 
 for the whole-tone step, and forcibly circumscribes a tonic (which 
 may be either + T or °T). If it proceeds from any other harmony, 
 it produces a change of key : 
 
 A. In Major : 
 
 (a) °sp — m \ 
 
 =S- — D \ T [_°T] (e.g., c-major — G-major [G-minor]). 
 
 (b) .S— I 
 
 =5 — D \ T \?T] [e.g., c-major — E-major [E-minor]). 
 
 (c) T — ! 
 
 =S- — D \ T [°T] (e.g., c-major — B-major [B-minor]). 
 
 (d) D — 
 
 =& — D , T [°T (e.g., c-major — Fjf-major [pfl-minor]). 
 
Chap, iv.] The Change of Tonal Functions. 
 
 171 
 
 'e) Dp —"$ 
 =& — °S 
 
 T [T] {e.g., c-major — r-major [F-minor]). 
 
 W Tp - I 
 
 =£* — "S \T [°T] (e.g., c-major — BJMnajor [B^-minor]). 
 
 „ B. In Minor : 
 
 (G) +Dp — °§ ! 
 
 = & — °S \°T [ + T\ (e.g., A-minor— D-minor [D-major]). 
 
 (h) °Z> — 
 
 = & — °S °T [ + T] (e.g., A-minor— F-minor [F-major]). 
 
 (1) °T — I 
 
 = & — °s| °T[+T] (e.g., A-minor— B>-minor [B?-major]). 
 
 (K) °S — I 
 
 =& — °S I "/"[+7 1 ] (e.g., A-minor— E?-minor [Efr-major]). 
 
 (L) °Sp — 3 I 
 
 = § — D\ °T\^T~\ (e.g., A-minor — E-minor [E-major]). 
 
 (m) "Tp — I 
 
 = •§ — £>\ °7 7 [+Z'] (e.g., A-minor — B-minor [B-major]) 
 
 (n) 'Dp — 
 
 = iS — D °T[+T](e.g., A-minor— FJJ-minor [F#-major]). 
 
 The contra-whole-tone change is represented tonally as the 
 transition from the minor under-dominant to the second upper- 
 dominant (°S — ]j)j), and may naturally as such modulate to the 
 key of the dominant : 
 
 (a) "S —& 
 =?°§—D 
 
 (b) Sp — 
 =°k —D 
 
 (c) Tp - 
 =°^ — D 
 
 ( D ) t*>— 
 
 =°°$ —D 
 (e) Dv— 
 = °S — D 
 
 A. In Major: 
 T (e.g., c-major — G-major). 
 
 °T [ + T] (e.g., c-major — E-minor [E-major]). 
 
 "T [ + T] (e.g., c-major — B-minor [B-major]). 
 
 + T["T] (e.g., c-major — D-major [D-minor]). 
 
 >T[+T] (e.g., c major — A-minor [A-major]). 
 
172 
 
 Harmony Simplified. 
 B. In Minor : 
 
 fChap. IV. 
 
 (F) D+ — °, 
 
 (G) 'Dp — 
 
 °T (e.g., A-minor — D-minor). 
 
 y^Z 1 ] (e.g., A-minor — F-major [F-minor]), 
 
 (h) °Tp - I 
 
 ==© — °S I T\?T~\ (e.g., A-minor — Bb-major [B^-minor]). 
 
 (1) r m< — 
 
 =-© — "S °T[+T] (e.g., A-minor — G-minor [G-major]). 
 
 (k) S 1U< — I 
 
 =-© — °S\ + T [°T~\ (e.g., A-minor — c-major [c-minor]). 
 
 This step is particularly easy to write, if both harmonies are 
 introduced with sevenths, in which case two tied notes and two 
 chromatic steps are possible : 
 
 173- 
 
 D> g* 
 
 The chromatic-semitone change will be most easily intelligible 
 as the progression °Sp — + Sp (in c-major = afe + — °a) or of + Dp — 
 °Dp (in A-minor = °gt — g + ), or again as the transformation of 
 "■5^ into ^y,', 1 , (in A-minor =/ + — °ft) or of Dp into M^ %> (in 
 c-major = b — bb + ). Where it proceeds from other harmonies, 
 the progression will correspond : 
 
 A. In Major. 
 (a) T I S —& 
 
 ="Sp-S^< D 
 
 ( B ) T I S— D» 
 
 T (e.g., c-major — A-minor). 
 °T [e.g., c-major — F-minor). 
 
 (c) T \ S — & I 
 
 =°Sp — + Sp D I + T (e.g., c-major — A-major). 
 
 (d) T I &—D*> 
 
 —°Sp — + Sp D + T (e.g., c-major — F-major). 
 
 (e) T I §f* 
 
 —°Sp I Sm< D I °T (e.g., c-major— E-minor). 
 
Chap. IV.) 
 
 The Change of Tonal Functions. 
 
 '73 
 
 (f) T I ®« 
 
 =°Sp I + Sp D | +T (e.g., c-major— E-major). 
 
 (g) T | D- 
 
 =°Sp—$\lU D "T (e.g., c-major— B-minor). 
 
 B. In Minor : 
 
 (a) T| "£> — & • 
 
 = + Dp—°Dp °S j °T (e.g., A-minor— c-minor). 
 
 (b) 'T \ *£> — $■ 
 
 = Dp—M>\^S 
 
 (c) "T | & —S 1 "" 
 
 = + &p—°Dp °S 
 
 + T (e.g., A-minor — c-major). 
 
 "T (e.g., A-minor — E-minor). 
 
 (d) "T I &— S m ~ I 
 
 = Dp — ^, °S I + T (e.g., A-minor — E-major. 
 
 (e) *T 
 =+Dp 
 
 (f) "T 
 =+Dp 
 
 -#5-, °S | T + (e.g., A-minor — F-major). 
 
 "Dp °S | "T (e.g., A-minor — F-minor). 
 
 (g) °T \ °S — 
 
 = Dp—Jp> i9 . S 
 
 + T (e.g., A-minor — Bit-major). 
 
 The student should also work out a number of possible modu- 
 lating applications of the augmented-second change, double-third 
 change, augmented-sixth change, and augmented-third change, 
 analogous to the models given above ; this will be an excellent 
 practice for his powers of conception, and will cause him to return 
 with pleasure to simpler forms. 
 
 § 19. INDEPENDENT CREATION OF MUSICAL SENTENCES, 
 PERIOD FORMATION. 
 
 The student who has earnestly and assiduously endeavoured to 
 fathom the laws of harmonic logic, will no longer need the pre- 
 scription of definite harmonic successions in his work. As we 
 have accustomed him from the first to dispense with a given part 
 (which for the thorough-bass student is always set), and by means 
 of the continuous indication of the tonal functions made him 
 more and more familiar with the innermost nature of harmony, 
 he will for a long time have felt the strict directions for the 
 connecting of harmonies irksome, and perhaps already have tried 
 on his own account to form intelligible sentences. Every gifted 
 pupil will try to soar beyond his school-work ; and we will now 
 not only give him full freedom to do so, but directly set him the 
 task of showing vhether he has learnt to think musically. We 
 
174 Harmony Simplified. [Chap. iv. 
 
 shall still need to give him a few explanations as regards the 
 nature of musical rhythm. If his sentences are to turn out satis- 
 factory, not only harmonically but musically in general, he must 
 first learn how the laws of symmetrical construction, hitherto only 
 scantily suggested, may be specialised, on what foundation they 
 rest, and of what exceptions they admit. 
 
 Music is the art of symmetry in succession ; just as in archi- 
 tecture the eye seeks out the parts of a form which are 
 symmetrical with one another, so in music the ear desires to 
 perceive parts symmetrical with one another in succession, and 
 from them with the help of memory to build up and understand 
 the whole work of art. To comprehend music by listening is, 
 therefore, more difficult than to take in a structure by looking at 
 it ; the latter remains in its place and leaves the mind time 
 for the gradual penetration into details, after first grasping the 
 principal outlines — -in music the opposite way is absolutely 
 prescribed : whoever does not comprehend the smallest sym- 
 metries can never penetrate so far as to understand the whole. 
 Besides, the work of art in sounds hurries past so rapidly and 
 irrecoverably that there is but one comfort, viz., listening to it 
 again, so that it may perhaps be understood at a second or third 
 hearing, if this was not possible at the first. 
 
 The blocks out of which music is built are the bars, but not 
 in the sense that what is contained between two bar-lines would 
 correspond to the smallest independent ideas (motives) ; the 
 comparison between music and architecture holds to a greater 
 extent than is at first apparent, for in structural art also, single 
 blocks do not correspond to motives ; rather — covered with 
 sculptures or in fret-work — only when firmly joined together do 
 they yield motives which are partly worked on one stone and 
 partly on the next. 
 
 A bar in the first place consists of two time-beats, i.e., divisions 
 of time of medium duration practically corresponding to the 
 speed of the pulse, which for human beings serves as the most 
 natural subdivision of the course of time ; these time-units are 
 perceived by the ear through change of the tone-substance, or by 
 interruption of the sound (rests). The two beats of the bar form 
 the first small symmetry ; the second, so-called accented, beat 
 closing the symmetry is, as such, rendered prominent by lingering 
 on it — but as a rule very slightly — (accent), and besides, the 
 connection of the two beats is made clear by the increase from 
 the unaccented beat to the accented— crescendo. The accented 
 beat may be twice as long as the unaccented, and this fact gives 
 rise to triple measure. The accented beat, then, may be followed 
 by a silent one (rest), or the accented note be sustained during 
 an extra beat, or finally, it may be followed by another note. 
 Thus, in the first place, the primitive beginnings of all musical 
 form take root in these subdivisions of time : 
 
chap. iv. i The Change of Tonal Functions. 175 
 
 .1 The 
 
 Change 
 
 ' 0.F 
 
 Tonal 
 
 Functions. 
 
 
 
 
 J 
 
 U 
 
 I 
 
 J ' 
 
 2 
 
 J 
 u 
 1 
 
 a 
 
 ! * J 
 
 u 
 
 I 
 
 J etc. 
 
 a 
 
 
 
 
 Or: 
 
 J 
 
 
 
 J r 
 
 
 1 
 • 
 
 
 J 
 
 r 
 
 J 
 
 J 
 
 » 
 
 etc. 
 
 Or: 
 
 1 
 m 
 O 
 
 
 1 
 
 
 1 
 • 
 
 J 
 
 
 J 
 
 
 J 
 
 
 etc. 
 
 Or finally : 
 
 1 
 m 
 O 
 
 
 J J 
 
 
 1 
 
 u 
 
 1 
 
 m 
 
 J 
 
 • 
 
 
 J 
 
 J 
 
 etc. 
 
 In notation the bar-line has, for about three hundred years, 
 been placed before the accented beat ; it does not, therefore, 
 actually divide off bars, but marks their points of stress : 
 
 4-- •— l— • m— I— J , ' I J eta 
 
 3 J I J ' J I J ' J I J 
 
 4 
 
 etc 
 
 Not the beat before the bar-line (the up-beat), but the beat after 
 the bar-line is called the first beat (the point-of-stress note). The 
 unaccented beat following the accented one in triple measure is, 
 in the first place, to be regarded as a prolongation of it as a sign 
 of its accent, but it may introduce new tone-substance, first, in a 
 sense of belonging to the accented beat (thus, e.g., in the synco- 
 pation of the third and first crotchets followed on the second 
 crotchet by the resolution of the dissonance, p. 117). But finally 
 this second beat may even be detached from the first, and be 
 referred to the next accented one : 
 
 NB. 
 3-J-J-J— J J l-J-1- 
 
 by which means a much more restless formation, rather foreign to 
 the original form of triple measure (J|J), arises (with double 
 up-beat). 
 
 But now bars combine in symmetries in the same manner as 
 time-beats, i.e., the first (unaccented bar) is answered by a second 
 (more accented) ; then, also, these tivo-bar groups are confronted 
 with one another and form half-periods of four bars, two of which 
 (the fote-section [protasis] and after-section [apodosis]) make up 
 the largest normal form, the sentence ox period of eight bars : 
 
 Bar. 
 
 * jTj ■ j 1 j " j I J ' J l J '"J 1 J'JIJ"JIJ'J1J 
 
 * (2) (4) (8) 
 
 Two-bar group. 
 
 After-section. 
 Period. 
 
176 Harmony Simplifiev. [Chap. iv. 
 
 Or : I J I J ' J I J " J I J ' J IJ '" J I J ' J I J " J I J ' J I J 
 
 (2) (4) (8) 
 
 Of the same import as these rhythmical formations we have 
 those in (J» (*/,), a / 8 , %, and 3 / 2 measure, only differing in the 
 
 manner of writing (for which, naturally, there are important 
 aesthetic reasons). If every two such bars be contracted into one 
 great bar («/„ 3 / 4 , C|0 [VJ> % 7s, 7*)- then the bar-line belongs 
 to the point-of-stress note of the more accented of the two 
 bars, e %. : 
 
 e-J~-J— J-J-J- 
 
 (2) 
 
 Unfortunately, composers often do not proceed quite correctly 
 in this matter, and place the bar-lines to the points of stress of the 
 1 st, 3rd, 5th, and 7th bars, so that then all cadential effects are 
 removed to the middle of the bars, and consequently the bar-line 
 does not fulfil its task. Conversely, also, composers often write 
 bars too small, which, according to the tempo, contain only one 
 time-beat. If we look upon the limits of the fluctuation of the 
 rate of the pulse as normal for those of time-beats (between 
 60 and 120 M.M.), then we must count every two bars as one 
 in notations like the following : 
 
 j. =100. 
 
 3-.N-J JU-J-^fc-U—H^-UUL etc. 
 
 (2) 
 
 g-JJ-J— J— i— J ' J U-^LUUL 
 
 4 
 
 (2) 
 
 etc. 
 
 Therefore, particularly in measures of three beats, it is im- 
 portant to see clearly, whether the time-beats given in the no- 
 tation are really time-beats, or, on the other hand, whether the 
 whole bar-values correspond to beats, or, finally, whether the long 
 and short values have the effect of time-beats of differing length 
 (so, e.g., in 3 / 4 J = 150, it is very convenient, and therefore 
 correct, to look upon the values J \J J \J continuously as 
 time-beats). 
 
 The same principle which is the reason for a slight lingering 
 on the accented beat of the bar, and which gives rise to the bar 
 of three beats (the ancient Greeks even recognised the ratio 2 : 3 
 for the duration of the two beats), i.e., the principle of clearly 
 distinguishing the single symmetries by marking the accented beats, 
 stipulates the familiar pauses on the points of stress vf the two-bar 
 
chap, iv.i The Change of Tonal Functions. 177 
 
 groups, or at least on those of the half-periods, which we find so 
 frequently in folk-songs, chorales, etc. : 
 
 * J I J ' J I J "J I J ' J I 2 '"J I J ' J I J "J I J 'J I J 
 
 V (2) (4) (8) 
 
 In more developed art this simple means of subdivision is 
 occasionally replaced by an idealised one, namely, that of the 
 prolongation of the accented beat for the duration of three beats, 
 which gives rise to three-bar rhythm : 
 
 % J I J ' J I JJJ " J I J ' J laQjT'J I J ' J| 
 
 , ' (2) ' -. ' (4) ' -v ' (6) 
 
 -ra. 3 Bars. 3 Bars. 
 
 J I J '"J I J ' J I J ! J :|| 
 
 (8) 
 
 3 Bars. 3 Ba- 
 
 Here we may remark that the long accented beat does not 
 necessarily entail a complete cessation of all sound-motion ; 
 especially the after-section, which, as answer to the first four bars, 
 has more the character of unity, favours a continuous motion. 
 But altogether three-bar rhythm may abandon its original sense 
 in the same way as triple measure. 
 
 This, then, is the normal eight-bar construction (we retain this 
 name even for the actual twelve-bar period of continuous three- 
 bar rhythm, still using the numbers 2, 4, and 8 for the principal 
 points of rest — the concluding values of the several symmetries). 
 
 As regards the relation of rhythmical form to harmony, a few 
 remarks have already been made (that dissonances on the un- 
 accented beat, entering and proceeding by step of a second 
 [passing-notes], are not striking ; that dissonances falling on the 
 accented beat are best prepared by tying; that cadential effects 
 [perfect close, half close, deceptive close] are possible only on 
 time-values which conclude greater symmetries ; that harmonies, 
 coming on unaccented beats, between repeated ones coming on 
 the accented beats, have the effect of figuration). We may now 
 say generally that accented beats are really the bearers of harmony 
 effects, and that, the more accented a beat is, the more decidedly will 
 a harmony effect be expected of it. This may be explained thus : 
 every point of stress of a symmetry represents a unit of higher order ; 
 i.e., beyond the motion in plain time-beats, we are conscious of 
 the units of bars, and of bar-groups, and finally of half-periods 
 or even periods : 
 
 ,. Motionin crotchets: jlj' JTj "jTj ' jTj B, jTj ' JTJ "JLJ ' JTj 
 (2) (4) (6) (8) 
 
 Z. Motion in minims : I «l \ a \ a I e) \ a I a I m I at 
 (2) (*) (6) (8) 
 
*1& Harmony Simplified. [Chap. iv. 
 
 3. Motion in semibreves : I <=> • \ o \ \ o \ \ a 
 
 (2) ( 4) ' (6) ' (8) 
 
 4. Motion in breves : I —- : I =a 
 
 (4) (8) 
 
 A glance at a modern orchestral score in many parts, proves 
 the correctness of this explanation (e.g., look at the first move- 
 ment of Beethoven's c-minor Symphony, with its harmonies for 
 the wind, entering at the 4th and 8th bars, and each time being 
 sustained through four bars ; this same movement also contains 
 sufficient examples of motion in semibreves and minims, besides 
 figurative motion in quavers not hitherto discussed). The above 
 scheme also shows clearly that the first bar is to be understood as 
 a higher kind of up-beat to the second, and similarly the second 
 to the fourth, and the fourth to the eighth. 
 
 The simplest deviation fro;i the eight-bar period, set up as 
 norm, is the omission of the unaccented beat, the up-beat to the first 
 bar at the beginning. Then, as it were, motion in minims enters in 
 place of motion in crotchets, and the latter comes in subsequently : 
 
 * m • » 9 1 » <~'tr 
 
 O. S> I => I 22 c "~ 
 
 I (2) I 
 
 Similarly, also, the unaccented bar may be entirely missing 
 at the beginning, so that the first value represented belongs to 
 motion in semibreves : 
 
 11 il 1 m 
 - 1 -* m -\- M =r- etc. 
 
 w 
 
 but, nevertheless, the second bar-motive may be introduced 
 complete (with up-beat) in crotchet motion : 
 
 Beginning, thus, with accented beats (without up-beat to the first 
 bar, without first bar, without first bar-group — indeed, without fore- 
 section [commencing ex airupto]) does not stipulate any sort of 
 irregularities as regards the further course of the work, i.e., all the 
 following periods may be complete. But in conformity to the 
 laws of artistic modelling, the peculiarity of a theme cause 1 by 
 its commencing on an accented beat, will often be retained by it 
 in the course of elaboration, i.e., imitations of it will again be 
 incomplete at the beginning ; but this will by no means stipulate 
 gaps in the following symmetrical construction ; on the contrary, 
 
Chap, iv] The Change of Tonal Functions. 179 
 
 extensions of the endings generally arise, i.e., the scheme is filled 
 up by appendages to the cadential values, e.g. : 
 
 2 J " J I J ' J I JJJ IJ " J I J ' J I JJJ 1 
 
 (4) (5) (6) (8) (9) (2) 
 
 J " J I J ' J I .MJ etc. 
 (4) 
 
 Here the fore-section begins with the accented beat of the 
 second bar, and the after-section with the accented beat of the 
 sixth bar, and the following period enters similarly again ; the 
 eight-bar construction is, however, retained consistently. Extended 
 endings need by no means consist of sustained notes, and may even 
 proceed in crotchet motion or even smaller (figurative) species ; 
 but they must be intelligible as appendages to the close {appended 
 motives). 
 
 But it is also possible to interrupt the strict symmetry by 
 commencing with accented bars, and dropping the missing un- 
 accented bars altogether, e.g. : 
 
 2 J "J I J' J I J '"J I J "J I y J I J I J" J I etc. 
 
 Here the first and fifth bars are constantly omitted. 
 
 Conversely appendages to cadential values are possible at any 
 time, without the new members having to commence incompletely 
 on that account : 
 
 1 11 1 1 I 111 1 1 1 1 1 1 1 
 (8) (8a) 
 
 Here, at the end of the fore-section and after-section, the last 
 two-bar group is repeated (which is equally possible with the same 
 or similar tone-substance as with different) ; likewise after every 
 second bar the accented bar may be repeated [(2), (2a); (4), (4a); (6), 
 (6a)], or at the end of the whole period the after-section may be 
 repeated. It is also possible at the end of the period first to 
 repeat the whole after-section, then the last two-bar group, and 
 finally only the eighth bar. 
 
 Peculiar disturbances of symmetry arise from the contraction 
 of endings with new beginnings, particularly from the coinciding 
 of the cadential bar with the beginning bar of a new period 
 (8 = 1 ) ; but contractions of smaller form-members are also 
 
i8o 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 possible (4 = s, indeed even 2 = 3, and 6 = 7); also in such a 
 manner that repetitions of cadential members overlap {e.g., the 
 repetition of the after-section with 8 = 5). It will be sufficient 
 for the harmony student to practise the more important forms ; 
 first of all, entirely regular constructions, then three-bar forma- 
 tions, then those with elision of the unaccented beginning bars 
 of half-periods, then close-repetitions, and finally formations con- 
 verting the eighth bar into first or second. It will be wiser for 
 the present merely to study bolder overlappings in the works of 
 the great masters, without as yet attempting to practise them. 
 
 Exercises 301 — 305 (free Invention of Harmonic Periods). 
 
 (301) Formation of regular eight-bar periods in % B, */ t 
 (J I j)i an d Vs (J • I J •) measures, which, in the fore-section, 
 remain in the principal key, and, in the after-section, modulate 
 (for each modulation a new example in a different key is to be 
 written) : 
 
 A. (Major) : (a) to the upper dominant by means of T 6 ~ S 6 . 
 
 (b) „ „ „ SU=ry. 
 
 V.W II II II ■* ~ »J' 
 
 (d) „ parallel key by means of Sp="S. 
 
 (e) „ „ „ Sp m < = S 1 "*. 
 
 (f) „ „ „ D=°Dp. 
 
 (g) „ parallel of the dominant by means of Tp= °S. 
 
 (H) ,, „ ,, ,, o = d-. 
 
 0) ,, „ „ „ Sp v< M>^ s> . 
 
 (k) ,, under-doniinant by means of ^= S. 
 W >, „ „ D» = Sp. 
 
 (m) „ „ „ Dll = S vn . 
 
 B. (Minor) : (a) to the parallel key by means of S vl = S 6 . 
 
 (b) „ „ „ S ,n <=g. 
 
 (c) „ „ „ r vu ^=§,% 
 
 (d) „ minor upper-dominant by means of T vu h 
 
 [ = 5 vn . 
 
 VII 
 
 ( E ) » 11 >i SnK^iy. 
 
 W „ „ „ n-iy?. 
 
 o 
 
 (g) „ minor under-dominant by means of "§= °S. 
 (h) „ „ „ S™-T y '% 
 
 (1) ,, ,. „ Tp=°Dp. 
 
 (k) ,, parallel of the minor under-dominant by 
 
 [means of S-=S. 
 'l) „ parallel of the minor under-dominant by 
 
 [means of °S= Sp 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 181 
 
 (302) Formation of regular eight-bar periods which can be 
 added to those of 301, and which, having emphasised the 
 new key by one or more cadences in the fore-section, modulate 
 back to the original key. The return modulations are to be 
 effected at : 
 
 A. (Major) : (a) by means of T 7 $ =B>. 
 
 B. (Minor) 
 
 to 
 
 11 
 
 >> 
 
 £>1>=S 6 . 
 
 (c) 
 
 It 
 
 )» 
 
 Sp=Tp "S D.. 
 
 (D) 
 
 11 
 
 n 
 
 s vl =s 6 . 
 
 to 
 
 J) 
 
 )» 
 
 T™=&% 
 
 to 
 
 )) 
 
 »j 
 
 s I> =y\ 
 
 (G) 
 
 11 
 
 )) 
 
 T J V > < ={&») Sp. 
 
 (H) 
 
 )' 
 
 j» 
 
 °T S=Dp S 
 
 (0 
 
 >» 
 
 )) 
 
 /.»> = £?;. 
 
 (K) 
 
 ») 
 
 »» 
 
 T 1< =J/^. 
 
 to 
 
 If 
 
 )» 
 
 £>" = {£>) Sp. 
 
 (M) 
 
 )> 
 
 3J 
 
 T^=°S. 
 
 (A) 
 
 >» 
 
 >» 
 
 T"={M> 7 ) °S. 
 
 to 
 
 )) 
 
 11 
 
 si:=»>. 
 
 (c) 
 
 J> 
 
 11 
 
 &b=r vl % 
 
 (D) 
 
 t» 
 
 )> 
 
 t 1u< =d. 
 
 (E) 
 
 11 
 
 )J 
 
 T i> = yu (o S y 
 
 to 
 
 it 
 
 J) 
 
 £>\ > > =S vn . 
 
 (G) 
 
 n 
 
 J) 
 
 (H) 
 
 j) 
 
 )J 
 
 ym< CHI 
 
 (I) 
 
 i) 
 
 11 
 
 °Sp=&. 
 
 00 
 
 »» 
 
 11 
 
 s=s. 
 
 to 
 
 »> 
 
 11 
 
 Tp .. vn =S v ". 
 
 These exercises may at first be executed in four parts, note 
 against note, but not stiffly written in notes of the same duration, 
 but, on the contrary, in order to incite the imagination, pregnant 
 with rhythmical motives like the following sixteenth model 
 example [cf. 301 (a) — (h) and 302 (a)— (h)] ; the omission of the 
 up-beat or of the first unaccented bar may already be allowed 
 in these exercises (without shortening the form) : 
 
 Schenando. ( J . |J . ) 
 
 
 
 ^ cres. 
 
 
 | 1>—N | ■■ e 
 
 
 
 * -%- ~$- -m- - 
 
 
 
 p- 8 
 
 
 -% — | 
 
 . r - | j> nQ 
 
 \ ^-fc^Ji-E- 
 
 _i — ^ 1 _ ^ , 
 
 ) 
 
 7f1 +-'-* 
 
 ' *• ( 
 
 — »— — » — « — 
 
|82 
 
 Harmony Simplified. 
 
 [Chap. IV 
 
 (303) Formation of periods in three-bar rhythm, 
 
 (1) by means of the insertion of an unaccented bar 
 after the 2nd, 4th, 6th, and 8th bars (cf. above, p. 177); 
 
 (2) by means of the elision of the 1st and 5th bars (order 
 of the bars ||: accented — unaccented — accented :(|) ; 
 
 (3) by means of the insertion of a close-repetition after 
 the 2nd, 4th, 6th, and 8th bars. 
 
 Take for the order of modulation of these periods : 
 
 A. In Major : 
 
 (a) to the second upper-dominant by means of T 6 t< =Zf. 
 
 (b) „ „ „ I?=S 6 . 
 
 Z>»=°S. 
 
 parallel of the dominant by means of 7p vnl Q = S vu . 
 i) >> o = *3-. 
 
 VIK 
 
 (O 
 
 (D) 
 (E) 
 
 (F) 
 (G) 
 
 °s- i i l i=r^'. 
 
 B. In Minor : 
 
 (a) to the second "upper-dominant (or second + upper-dominant) 
 
 [by means of °Tp = S-. 
 
 (b) „ „ „ D™^S™. 
 
 (c) „ „ „ T"J<=$ 1X< . 
 
 (d) „ dominant of the parallel by means of T VI = S 6 . 
 
Chap. iv.] The Change op Tonal Functions. 183 
 
 (e) to the dominant of the parallel by means of S '" * = D. 
 
 (f) „ „ „ D V »>=S'<. 
 (G) „ „ „ D\^ = l$>. 
 
 (304) Formation of four-bar half-periods leading back, so that 
 the periods in 303 may be repeated after them ; but the latter 
 are, in this case, to be divested of modulation in their second half, 
 and to close in the principal key (as in the seventeenth model 
 example). These exercises are to be written in three instead of 
 four parts, and in three separate exercises a free figuration is to 
 be carried through, first in the highest, second in the middle, and 
 third in the lowest part ; then, two exercises are to be written 
 with distribution of the figuration between the three parts. 
 Special rules for three-part writing are not needed. In addition 
 to the means of figuration made use of hitherto, the occasional 
 introduction of unprepared dissonant notes on accented beats 
 may be employed (accented auxiliary notes, suspensions), as also 
 leaping to foreign notes on the unaccented beat, which proceed 
 by step of a second to chord-notes falling on accented beats 
 ( [feigning] passing notes by leap). The seventeenth model 
 example points out these notes by asterisks. 
 
 The returns to the principal key in these intermediate half- 
 periods, which, as stated, are to consist of four bars, and not three, 
 are to be effected by the following changes of meaning, which 
 may take place at once (as a rule these intermediate half-periods, 
 which may grow into full eight-bar intermediate periods, remain 
 for some time on the dominant of the principal key, causing the 
 re-entrance of the latter to be expected with heightened suspense 
 [Mixolydian]) : 
 
 A. (a) by means of 7' 7 fi = Z' 7 to the key of the dominant, whose 
 
 tonic is again turned into dominant by adding 7^. 
 
 (b) by means of D 3> to the key of the dominant, and then 
 
 by means of D\> =S 6 to the principal key. 
 
 (c) by means of S 7 § = D 1 directly to the principal key. 
 
 VI 
 
 (d) by means of T m< =D 1 to the parallel key, and from 
 
 there by means of °S= Sp to the principal key. 
 i> 
 
 (e) by means of T VI = S V " to the parallel of the under-domi- 
 
 nant, from there by means of ° T= Sp to the principal key. 
 
 (f) by means of °S** Tp directly to the principal key. 
 
 (g) by means of §= .S directly to the principal key. 
 
 B. (a) by means of T'>=S VU (or TH=$ yu ) directly to the 
 
 principal key. 
 
 (b) by means of D\* to the "dominant, from there by means 
 
 of T u " «=Z> to the principal key. 
 
 
 
 (c) by means of °$-=°*S to the "dominant, and from there 
 
 o 
 
 again by ,§— S to the principal key. 
 
1 84 
 
 Harmony Simplified. 
 
 rChap. IV. 
 
 (d) by means of Z 7 t{= S v " directly to the principal key. 
 
 (e) by means of Sp=°S to the "dominant, from there by 
 
 means of D\\ to the principal key. 
 
 (f) by means of T'\\ = B 7 to the parallel key, then by Sp 
 
 = °S to the principal key. 
 
 (g) by means of S=>S to the parallel key, then by means 
 
 of S 7 «=S yn> to the principal key. 
 
 (Cf. 303, 2 B d, with mixed figuration.) S ul< = D 
 
 
 
 
 
 * 
 
 
 -C^Ipjv,. 
 
 cres. 
 
 * 
 
 
 
 r*s n 
 
 1 Jj J I 
 
 ~i— 
 
 
 174.- 
 
 «-* 1 
 
 p 
 
 
 1 r— 
 
 ^t 
 
 L= r 
 
 ■ 
 
 
 
 m- 
 
 r 
 
 
 .* — 
 
 — 
 
 
 ' -" ^f'i ■' — 
 
 
 
 r. 1 j— 
 
 — r — 
 
 -T— a- 1 
 
 (Seventeenth model example.) (4) 
 
 («) 
 
 (4) (6) (8) 
 
 In this example, partly on account of the short kind of bar, 
 the dividing off of the half-periods is rather intrusive ; this im- 
 mediately becomes more tolerable if to the fourth and eighth 
 bars confirmation be appended (to be inserted in 174) : 
 
 '7H 
 
 (4a) (8a) (8a) 
 
 (3°S). Formation of eight-bar periods with insertion of closer 
 confirmations : 
 
 (1) by repeating every accented bar (2nd, 4th, 6th, 8th) ; 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 "«5 
 
 (2) by repeating the accented groups of half-periods (1 — 4, 
 
 3a— 4a, 5—8, 7a— 8a) ; 
 
 (3) by repeating the whole after-section (1 — 8, 5a — 8a). 
 These periods, extended by insertions, should include modu- 
 lation and return ; the examples in major should modulate in the 
 fore-section to the dominant, parallel of the dominant, second 
 dominant, or dominant of the parallel, making use at pleasure of 
 the expedients shown, and in the after-section restore the principal 
 key; the minor examples may make modulations to the parallel 
 key, ° dominant, second ° dominant, or parallel of the ° dominant, 
 and in the after-section return to the principal key. The exercises 
 will gain in interest (because forming small finished compositions), 
 if a second period be appended to the first, either in the form 
 here asked for, or in the three-bar rhythm of Exercise 303, for 
 major in the key of the under-dominant, "under-dominant, or 
 under-third, for minor, in the ° under-dominant or parallel of the 
 under-dominant ; it should join on without modulation and be 
 repeated ; but the repetition is not to come to an independent 
 close, but to make the return modulation, and, in place of the 
 cadential eighth bar, let the beginning of the repetition of the first 
 period enter (8= 1), as in the following eighteenth model example. 
 These pieces may also be thought out and written down for piano. 
 Directions as regards figuration, etc., we shall dispense with 
 entirely, and leave free play for invention, also with respect to the 
 number of parts, which may be increased or lessened at pleasure : 
 
 Tempo di Minuetio. 
 
 176. 
 
i36 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 i ill ill -f ■ |" I 
 
 2?.C. alFine. 
 
 To promote skill in the management of parts, and as another 
 preliminary exercise in reading score, a few attemps at six-part 
 writing are to follow, for which the exercises in former chapters 
 may be used. Six-part writing is more unwieldy than four- or 
 five-part ; it necessitates still more doubling than the latter, and 
 cannot entirely avoid crossing of parts. But the doubling of real 
 thirds by parallel motion is still forbidden, as also the doubling of 
 dissonances (excepting simultaneous passing notes in two parts). 
 Six-part writing is more conveniently read and worked out as 
 3 + 3 parts, or in case of need 4 (upper) + 2 parts. These 
 exercises should be worked out on six staves, so as to attain 
 
 quickness in reading score, and the mezzo-soprano clef 83=== and 
 the high bass clef (baritone clef) g:= are to be added to those 
 
 hitherto practised. The following nineteenth model example is 
 the working-out in six parts of Exercise 198 : 
 
 VII 
 
 °T S m< D °T °Tp "Dp S V1 v I? ¥ D $ nl< 
 
 -*= — <s — , *-. = — , — &—. 1-^ — ip 8 -p. 
 
 177- 
 
 lE frr' V r 
 
 5SE 
 
 7T.-H <S>— 
 
 m 
 
 eIe 
 
 m 
 
 (Nineteenth model example,) 
 
Chap. IV.] 
 
 The Change of Tonal junctions. 
 
 187 
 
 § 20. PEDAL-POINT AND MODULATING SEQUENCE. 
 
 We must still mention two formations, one of which adds to 
 the complication of note combinations to the utmost extent, and 
 the other puts the feeling of tonality to the strongest test by 
 means of modulations heaped on one another. We do not class 
 the two together without reason ; for their combination is not 
 only possible, but first shows the full force and real significance 
 of each. Neither of them is entirely strange to us now. Simpler 
 pedal-point formations have occurred repeatedly in our exercises 
 when a harmony was figured with foreign notes (e.g., Exercise 
 
 8 7< 7fl 
 6 6> 5H 
 
 258 : D* 3 ); sequences are familiar to us, at least tonally, 
 from § n, and intermediate cadences have already introduced us 
 nearly up to the modulating sequence. The whole circuit of 
 harmony is rounded off by the insertion of these key-stones. 
 
 The pedal-point has developed historically from the chord of 
 six-Jour by means of increased figuration and gradually more 
 extended ornamentation of the suspended fourth or sixth, or of 
 both, over the sustained dominant fundamental chord at the last 
 close of the period. The primitive forms of pedal-points are 
 
 8 1 
 therefore Z> 4 \ D 6 s , J> *, D* — \ £>' — \ etc.; also the shake 
 on the third or fifth of the dominant formerly almost indispensable 
 for closes, comes under this category (6 — 5 or 4 — 3 in rapid 
 alternations), and if the turn be added at the end or the slide up 
 to it at the beginning, or if both shakes oe combined, the relation 
 to the pedal-point becomes all the more striking. The small 
 cadenzas formerly (up to Haydn's time) interpolated as a matter 
 of course at the stereotyped pauses on the chord of six-four at 
 the close of sonata or concerto movements, with their wide scope 
 
1 88 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 (e.g., D. G. Turk advised those who did not know how to im- 
 provise a proper cadenza to be satisfied with making a shake), 
 illustrate most clearly the history of the origin of the pedal-point. 
 The extent of a pedal-point varies a great deal according as 
 it just fills out the last bars of a symmetrical construction, or 
 comes to a standstill at the 6th bar (by which it will generally be 
 introduced), stipulating the repetition several times of the group 
 5 — 6, or again entirely breaks through the symmetry, and inde- 
 pendently forms whole periods, or even series of periods, by 
 itself. But the two bars 6 — 7 of a regular eight-bar period will 
 be sufficient to prove the value of this peculiar effect, e.g. (in 
 five parts) : 
 
 The chords indicated with * are among the most complicated 
 that can occur (with from 3 to 4 dissonances of a second) ; our 
 figuring, which allows of separating the sustained bass-note (to 
 which the name pedal-point, in the narrower sense, belongs), and 
 indicating the chords resulting above it in the manner hitherto 
 employed without the pedal-note, lessens the horrors of such 
 formations to such a degree as tallies with the effort required of 
 the ear in comprehending them. The first example did not even 
 need a rounded bracket, but could be indicated throughout in 
 relation to the principal tonic. The following one goes a step 
 further, and inserts a few intermediate dominants : 
 
 '79-{ 
 
 °S &'(D>> : ~) Sp(D) Tp^J^"D T(S vn fSMfi"T 
 
 Both examples close with short pedal-points on the funda- 
 mental note of the tonic. 
 
 The combination with the modulating sequence increases to 
 
Chap. IV.] 
 
 The Change of Tonal Functions. 
 
 189 
 
 the utmost the call for power of tonal perception, which in the 
 pedal-point finds, as it were, a tangible embodiment. The nature 
 of the modulating sequence differs from that of the tonal 
 sequence, in that not only a melodic formula, but also a harmonic 
 one is imitated in it, i.e., that a succession of functions is repeated 
 in other keys ; if, in so doing, the mode of the tonics were never 
 altered, and the size of the intervals in progression strictly re- 
 tained, the sequence would soon reach the end of notation, i.e., 
 the limits of representation, and could only be continued by 
 means of enharmonic alteration : 
 
 Progressions of this sort, which are familiar to all singing 
 masters as a form of accompaniment for exercises in messa di voce 
 on notes rising or falling by degrees, are naturally of extremely 
 doubtful artistic value. On the other hand, the formations related 
 to them, which only retain the formulas of functions, but vary 
 the size of intervals in progression and the mode of tonics 
 reached with regard to the principal key (half tonal sequences), arc 
 of far greater importance, e.g. ; 
 
 S If T (°S D 7 ) Sp (°S D 1 ) Dp (S D 7 ) S (S D 1 ) D 
 
 The result is naturally nothing more than a tonal sequence to 
 the several harmonies of which intermediate cadences are made. 
 
 There is nothing to hinder such a formation from being 
 supported by a pedal-note ; indeed, with a little caution, it is 
 possible to build up a strictly modulating sequence at some length 
 over a pedal-note : 
 
190 
 
 Harmony Simplified. 
 
 [Chap. IV. 
 
 182. 
 
 Q 1 ; 
 
 
 
 
 
 
 j—^j- 
 
 1" , - 1- 
 
 — -j-^i 
 
 
 -^2=r- 
 
 
 -»-5— 
 
 
 
 
 
 -»$*- 
 
 
 
 gp 
 
 ^= 
 
 p4- 
 
 -W- 
 
 — 1 
 
 — ,& — 
 
 1 
 
 Z3t= f 
 
 . 1 bJ 
 
 1 
 
 r 21 - 
 
 ^1 
 
 **- 
 
 kJ 
 
 Si. 
 
 V 
 
 ^~T< 
 
 — g> 
 ) - 
 
 
 i — e>— 
 
 1 
 
 s- 
 
 ^ 
 
 
 e?- 
 
 
 
 m 
 
 6 
 
 Z>' 
 
 ] 
 
 (/?0 
 
 s 
 
 (/?') 
 
 © (£> 7 ) 
 
 °7>" 
 
 = 3 
 
 I : 
 
 7 1 
 
 Tio 
 
 These detailed explanations will suffice to enable the student 
 to analyse the most elaborate pedal-points, such as the celebrated 
 one on D in the third movement of Brahms' German Requiem. 
 To teach him, however, how to practise anything so ambitious 
 does not come within the scope of a book like the present one. 
 
igi 
 
 EXPLANATION OF THE TERMINOLOGY AND THE 
 CHORD SIGNS IN ALPHABETICAL ORDER. 
 
 (All explanations are also given in the text). 
 
 Clang is the harmonic unit resulting from the combination of 
 a principal tone with its fifth and third on the same side. As 
 the fifth and third may be taken either from the overtone series 
 or the undertone series, we have two clangs, the over-clang 
 (major-chord) and the under-clang (minor-chord), e.g., c with its 
 over-fifth, g, and over-third, e, gives the c over-clang or C major 
 chord, c e g ; e with its under-fifth, a, and under-third, c, gives the 
 e under-clang or A minor chord, ace. 
 
 Contra-, as addition to the indication of an interval, means 
 that it is conceived in a direction opposite to the clang mode, e.g., 
 a is the contra-fifth (V) of the E major chord. 
 
 Contra- clang (turn of harmony) of any chord is the clang of 
 opposite mode formed from its prime; e.g.,/ a^ c (= V) is the 
 contra-clang of c e g ( = c + ). 
 
 Crossing out a number means omission of a harmony tone 
 corresponding to the number (which, therefore, can only be 
 J > 3> or S> or I> IHj or V) ; e.g., B% means Dominant with the 
 sixth and without the fifth ; but the omission of the prime is 
 indicated by crossing out the clang sign (&, J[P, $ IX "% etc.). 
 Also in the indication of the leading-tone substitutes (&, S-, etc.) 
 the omission of the Prime is understood. 
 
 Dominant (abbreviated D) is the clang lying a fifth higher 
 than the Tonic; + Z> = major over-dominant, i.e., Dominant being 
 a major chord (usually simply D), °D = minor over-dominant, 
 i.e., Dominant being a minor chord. 
 
 Harmony steps. The terminology of harmony steps starts 
 from the indication of the interval of the principal tones (primes), 
 which is qualified, according to the clang started from, as either 
 plain or opposite (contra-) ; sequences of clangs of equal mode 
 are called "steps," sequences of clangs of opposite mode, 
 " changes." Suppose, e.g., the interval of the principal tones to 
 be the fifth c g ; if we start from c + , g is the plain fifth (in the 
 major sense) ; if from °g, c is the plain fifth (in the minor sense). 
 If we start from V, g is contra-fifth, if from g + , c is contra-fifth. 
 Therefore c* — g + and "g — °c are plain-fifth steps, + g — + ^and °c — °^, 
 contra-fifth steps ; c + — °g and °g — c + , plain-fifth changes, °c — g + 
 and g+ — V contra-fifth changes. We call plain, in major, all 
 
192 Harmony Simplified. 
 
 intervals resulting from ascending fifth- and third-steps; in minor, 
 all intervals resulting from descending fifth- and third-steps. 
 The whole-tone is to be conceived as double fifth-step {e.g., c d = 
 c — g — d), the leading-tone, as combination of a fifth-step and a 
 third-step in the same direction (e.g., c b = c — g—b); the tritone- 
 step, as a combination of two fifth-steps with a third-step 
 {e.g., cf\ = c — g — d—f$) ; the minor-third is to be considered 
 as major-sixth, i.e., as connection of the fifth-tone and the third- 
 tone, e.g., e g as [C] — g — e', or as [b"~\ — e' — g; this interval is to be 
 regarded as plain when it proceeds from the fifth-clang {e.g., for 
 C g e', from g + ) to the third (in the case mentioned, therefore, in the 
 direction of the ascending harmonic natural scale) ; a simple and 
 easily surveyed rule is this : an interval is plain when it ascends 
 from a major chord, towards the side of the J tones, or descends, 
 from a minor chord, towards the side of the P tones. We call 
 plain, therefore, the third-steps c + — e + , and "c — °afy, the minor- 
 third steps c + — a + , and °c — Vj?, the chromatic steps c + — £$ + , and 
 °e — °e'7, the double-third changes f + — °g$, and "e — °aP, etc. All 
 harmony steps can also be understood as being made backwards 
 (retrograde); the retrograde plain steps, then, externally present 
 the same appearance as the advancing contra-steps, and the 
 reverse ; while the plain and contra-changes cannot interchange 
 their roles (i.e., a retrograde plain-fifth change still appears as a 
 plain-fifth change, not as a contra-fifth change); the contra- 
 changes are always the most complicated of the successions of 
 clangs whose principal tones form the same interval. 
 
 Intervals (second, third, etc.), and the numbers designating 
 them (2, 3, etc.) are considered only rarely and exceptionally in 
 this book as well as in all other writings of the author, as the 
 simultaneous sounding of two notes. They, rather, serve, as a 
 rule, only to indicate and characterise single notes in their position 
 relative to the prime of an over- or under-clang. Therefore, 
 augmented, diminished, and similarly complicated intervals are 
 mentioned only on the occasion of giving instruction as to the 
 management of the single parts (avoiding intervals difficult to 
 sing) ; generally the expression " third " means the third-tone of a 
 clang (therefore, only one, not two notes), " sixth," similarly, the 
 note which lies at the distance of a whole-tone from the fifth. 
 
 Leading-tone substitute is the chord of opposite clang mode 
 arising from replacing the prime of a clang by its minor contra- 
 second (second of the side opposite to the clang principle). We 
 indicate the major chord substituted in this way for minor chords 
 by a =» through the clang sign, thus : ¥, &■, &, the minor chords 
 similarly substituted for major chords by a -= through the clang 
 sign, thus : ff, &, & ¥, therefore, in a minor is a c [e]f ( =/ + ), &, 
 in c major, ff [g] b d ( = °f%), etc. Inasmuch as the =■ through 
 a clang sign sufficiently indicates the leading-note from above to 
 the prime of a minor chord — which leading-note, when substituted 
 
Explanation of the Terminology. 193 
 
 for the prime, changes the minor chord into a major chord — the ° 
 can be dispensed with. 
 
 Letters (small) indicate the primes of clangs ; for instance, 
 f + = c over-clang (c major chord), "e = e under-clang (minor 
 chord under e, therefore a minor chord) ; where the clang sign 
 ( + , °) is wanting, the + is to be considered as omitted (a major 
 chord prescribed), unless italic numbers indicate the minor mode 
 (see Numbers). 
 
 Letters, capital (T, D, S) indicate the functions of clangs, as 
 Tonic, Dominant, and Subdominant. 
 
 Natural are those plain (q.v.) intervals which are component 
 parts of the clang; therefore the 1 (8), 3, 5 of the over-clang 
 (major chord) and the I (VIII), III, V of the under-clang 
 (minor chord) ; also the minor seventh (7, VII), for instance, in 
 the c major chord, H7, in the At> major chord, gX, in °c (= f minor 
 chord), d, etc. In cases where a natural interval is to be in- 
 dicated explicitly as such (for instance, where a chromatically 
 different form of it preceded or was to be expected), a 1} may be 
 added to the number, which, however, has no altering signifi- 
 cance, but only indicates the same interval that would be pre- 
 scribed by the number without the addition ; for instance, T vn % 
 = minor tonic with natural (i.e., minor) under-seventh, in a minor, 
 f\ a c e. 
 
 Numbers (i — 9, I — IX) indicate tones according to their dis- 
 tance (interval) from the prime of an over- or under-clang ; all 
 Arabic numbers indicate intervals counted upwards, all Roman, in- 
 tervals counted downwards ; they indicate, at the same time, the 
 clang mode, so that also in minor the ° is omitted whenever num- 
 bers are used along with the clang sign. In particular 1, 3, 5 (I, III, 
 V) indicate the essential parts of the clang (prime, [major] third, 
 [perfect] fifth); 2 (II), the major second; 4 (IV), the perfect 
 fourth ; 6 (VI), the major sixth ; 7 (VII), the minor (!) seventh ; 
 8 (VIII), the perfect octave ; 9 (IX), the major ninth. Altera- 
 tions of these values, which are the properly normal, are indicated 
 by «= (= raising a semitone) and > (= lowering a semitone). 
 The position of a number under the clang sign or the repetition 
 points (..) replacing it, indicates that the tone prescribed by the 
 number is to be given to the bass part (3, n,, <)); the position 
 over the letter or the points (],\, '.'?) indicates that it is to be 
 given to the highest part. Numbers after the letters or points 
 (if, e vn , . . VI ) prescribe only the addition of the indicated tone to 
 the harmony, without defining its position. It is a proof of the 
 simplicity of our method of chord signs that tones which would 
 require double raising (^) or double lowering (*), never occur, 
 and cannot even be comprehended. 
 
 Parallel clang (abbreviated/) of a Tonic, Dominant, or Sub- 
 dominant is that clang which stands to it in the relation of the 
 Tonic of the parallel key to the Tonic of the principal key. For 
 
194 Harmony Simplified. 
 
 instance, c major and a minor, g major and e minor, are parallel 
 keys, therefore g + is the parallel clang of °b (e minor), c + the 
 parallel clang of °e (a minor), and conversely °e and °b are parallel 
 clangs of c + and g + . The clang mode of the Tonic, Dominant, 
 and Subdominant is indicated also in the compositions Tp, Sp, 
 Dp, in the manner explained above (major by a + or without 
 any addition, minor always by a °), and the mode of the parallel 
 clang is always the opposite. For instance, in Tp the Tonic is a 
 major chord (because there is no ° to the T), the parallel clang, 
 therefore, a minor chord, in "Sp, the subdominant a minor chord, 
 its parallel clang, therefore, a major chord. Any numbers re- 
 lating to the management of the parts always follow the mode 
 
 of the parallel clang, for instance Sp, because the third of the 
 
 in 
 parallel clang of the major Subdominant is a minor third (III). 
 
 Plain is applied to an interval, when it is conceived from the 
 principal tone of a clang in the sense of its mode ; therefore, from 
 a major chord the upward intervals are plain, from a minor chord, 
 the downward (from c + , a is plain sixth = 6, from °e, g is plain 
 sixth = VI) ; intervals conceived in the opposite direction receive 
 the addition of contra- to their name ; for instance, b is the minor 
 contra-second (II <) of the c major chord. Cf. Harmony steps. 
 
 Second upper-domixant is the Dominant of the Dominant 
 
 o 
 
 (S, °M) > second under-dominant is the Subdominant of the Sub- 
 dominant (.f, °M). 
 
 Signs : 
 < (with a number) means " raised a semitone;" >, "lowered a 
 
 semitone." 
 = meaning " converted to," always indicates a change of the 
 tonal functions, that is to say, a modulation ; for instance, 
 T 6 = S 6 , means " Tonic with sixth " converted to " Subdomi- 
 nant with sixth." 3^9, 
 «E means " enharmonically changed to;" for instance, MP* con- 
 verts, in a minor, g\ b ///into b dfa% by means of changing 
 the 3 g$ into the 9 > a% which is enharmonically identical 
 with it ; the chord sign, therefore, indicates a modulation 
 into c major or c minor to whose Z^ 9> the chord in its new 
 writing corresponds. 
 ( ), the round brackets, emancipate the indications of tonal func- 
 tions from the Tonic of the principal key; the Dominants, 
 etc., indicated in such brackets have their meaning by refer- 
 ence to the chord following immediately after the brackets, 
 whether it be a principal clang (D, S, °S, D+) or a feigning 
 consonance {Tp, °Dp, S-, &, S m< , etc.); for instance, 
 (D 1 ) "Sp = Dominant seventh of the following minor Sub- 
 dominant parallel (in c major : e? g bb d?). There are cases 
 where the chord to be conceived as Tonic of the functions in 
 
Explanation of the Terminology. 195 
 
 ( ) does not follow at all ; if, in such a case, it precedes, 
 the reference of the bracketed indications to it can be shown 
 by an arrow pointing backward, for instance 5 (S) ; if it 
 
 neither precedes, nor follows, it is indicated, after the round 
 brackets, in square brackets [ ] (see the following). 
 [ ], the square brackets, indicate a harmony as the conceived tonic 
 of functions indicated in round brackets immediately before 
 it. The chord indicated in square brackets, then, is omitted, 
 skipped, in its place another one, that is not expected, 
 follows. 
 . . means the repetition of the preceding harmony ; after brackets 
 ( ) it means repetition of the chord preceding the brackets. 
 After complicated signs with dissonances, it means only the 
 continuation of the principal harmony, not of the dissonances, 
 for instance, in D\ f-, the continuation of the Dominant har- 
 mony, but with the J proceeding to *. D* .., however (with- 
 out numbers or + with the ), would indicate the continua- 
 tion of the chord of six-four. 
 Subdominant (abbreviated S) is the clang lying a fifth lower 
 than the Tonic ; + S = major Subdominant (Subdominant being a 
 major chord), usually simply S ; °S = minor Subdominant (Sub- 
 dominant being a minor chord). 
 
 Tonic (abbreviated T) is the clang from which the key is 
 named, therefore, in c major, the c major chord (c + ), in a minor, 
 the a minor chord (°e) ; the Tonic of the minor key is indicated 
 by °T, the major Tonic, in contradistinction (see Variant) to it, 
 by T + , but usually simply by T. 
 
 Variant is the Tonic of opposite mode, in c major the c minor 
 chord, in a minor the A major chord. It is indicated by °T and 
 T + respectively. 
 
196 
 
 ALPHABETICAL INDEX. 
 
 {The numbers indicate the pages.) 
 
 Accented bar, 175 
 
 Accented beats as bearers of harmonic effects, 177 
 
 After-section, 175 
 
 Altered chords, 112 
 
 Alto clef, 61 
 
 Ambiguity of harmony steps utilised, 147, seq. 
 
 Appended motives, 179 
 
 Arrow pointing back (< ), 129 
 
 Augmented fourth in figuration, 142 
 Augmented second bridged over, 88, seq. 
 Augmented-second change, 100-102 
 Augmented-sixth change, 100-102 
 Augmented steps in part progression, 37, 46, 47 
 Augmented-third change, 101-103 
 Authentic cadence, 95 
 
 Bass part, 14 ; must not proceed by leap to or from 5 (I)> T 9 ! may thus pro- 
 ceed to S in the connection -S 1 — Z>, 36 
 Bassoon, 131. 
 
 Beginnings on the accented beat, 178 
 Bilateral cadence, 29 
 Borrowed deceptive closes, 98-99 
 Brackets, round (), 128; square [] after the round ones (ellipsis), 130 
 
 Cadence, 94, 95, seq. 
 
 Calligraphic rules, 12 
 
 C(antus) f (irmus), 25 
 
 Chain of fifths, 10 
 
 Characteristic dissonances, 55 ; as means of modu'ation, 66 
 
 Characteristic figuration tones, 142 
 
 Chord of nine-three, 1 54, seq. 
 
 Chord of six-four, 22 ; minor, 24 j its effect to be avoided even with the 
 
 parallel clangs, 72 
 Chord of seven- three, 69 
 Chromatic alteration of chord tones, 112 
 Chromatic part progressions, 49 
 Chromatic progression means advance, 169 
 Chromatic-semitone change, 100-102 ; modulating, 172 
 Chiomatic-semitone step, 101-103 
 
Alphabetical Index. 197 
 
 Church modes, 91 
 
 Clang, 7 
 
 Clarinet, 1 31 
 
 Close, 94, etc. 
 
 Common tones are kept in the same part, 18 
 
 Confirmation of cadence, 179 
 
 Consecutive octaves, 17, 34, 62 ; fifths, 18, 34 
 
 Consonance, 7 
 
 Contra-clang, 48 ; figuration of its third, 88 
 
 Contra-fifth change, 47 
 
 Contra-fifth step, 28 
 
 Contra-second, minor, 93 
 
 Contra-whole-tone change, 100, 101 ; modulating, 171 
 
 Z3% 55 ; Z?vi, 55 
 
 Deceptive close, 94, 98, requires a feigning consonance, 71, 73. 
 
 Diminished steps not always good, 46 
 
 Diminished-third step, 94 
 
 Dissonances, characteristic, 55, 107 ; figurative, 107 ; passing, 108 ; prepared, 
 
 109; unprepared, 114 
 Dissonances in the cloak of consonance, 22, 56 
 Dissonant tones may enter without preparation, but must proceed by step of 
 
 a second, 56 
 Dissonant tones must not be doubled, 24 
 Dissonant tones (not intervals), 56 
 Distances, normal, of parts in plain four-part writing, 14 
 Dorian sixth, 88 ; proceeding elliptically, 96 
 Double-third change, 100-103 
 Doubling of chord tones, 12, 20, 71, 125, 168 
 
 Eight-bar rhythm as foundation of musical form, 177 
 
 Elliptical progression of Dorian sixth and mixolydian seventh, 96 
 
 Enharmonic figuration of J/fl" etc., 157 
 
 False relation, 49 ; correct after the Neapolitan sixth, 94 
 
 Faulty part progressions, 17, 20, 38, 49, 57 
 
 Feigning consonances, 22, 56, 71, 79, 80 
 
 Feminine ending, 1 79 
 
 Fifth, when in the bass, must be doubled, 15 ; may be omitted, 12 j may not 
 
 be doubled it the resolution of a chord of six-four, 22 
 Figuration, 62 ; divided, 63 
 Five-part writing, 125 
 Fore-section, 175 
 Four clefs, 85 
 Functions, 9 
 
 Fundamental note, 13-15 ; best for doubling, 12 
 Fundamental scale, 1 
 
 Half-close, 94 ; its conception widened, 97 
 Harmonic relations of tones, 2 
 
198 Harmony Simplified. 
 
 Harmonics, 2 
 Horn, 131 
 
 Intermediate cadences, 127 
 Intermediate section, 183 
 Interrupted cadence (deceptive close), 72 
 Interval, 2 
 
 Leading-note must not be douhled, 20 ; may be doubled, 75, 122 
 
 Leading-tone change, 75 ; modulating, 159 
 
 Leading-tone progression means return, 169 
 
 Leading-tone progressions (semitones) in the connection of chords, 18, 35 
 
 Leading-tone s-teps, 84 ; modulating, 162 
 
 Leading-tone substitute, 79 
 
 Leading-tone suspensions, unprepared, 116 
 
 Leaping of parts when the same harmony is repeated ( . . ), 22 
 
 Lowering the major third yields °S, 66, 150 ; = "D, 151 
 
 Lydian fourth, 91 
 
 Major and minor interchanged (in the borrowed deceptive close), 44 
 
 Major, character of, 16 
 
 Major close in minor, 45 
 
 Major deceptive close (D — T/>), 72 
 
 Major fifth (5) may be omitted, 23 
 
 Major seventh (7) proceeds downwards, 57 
 
 Mathematical definitions of intervals, 2 
 
 Melodic connection of chords, 1 8 
 
 Melody, I 
 
 Middle parts, 21 
 
 Minor and major interchanged (in the deceptive cadence), 98 
 
 Minor, character of, 16, 29, 44 
 
 Minor chord of six-four (£$*), 46; {S'$, 24 
 
 Minor deceptive close, 77 
 
 Minor prime may be doubled, 20 ; may be omitted, 12 
 
 Minor-third change, 75 ; modulating, 160 
 
 Minor-third step, 84 ; modulating, 169 
 
 Minor upper-dominant, 29 
 
 Mixolydian seventh, 88 ; proceeding elliptically, 96 
 
 Modulating sequence, 189 
 
 Modulation, 9, 52, 66 141, seq. 
 
 Natural seventh in figuration, 142 
 Neapolitan sixth, 93 
 
 Oboe, 131 
 
 Octave, 2-3 
 
 Octaves by leap in contrary motion, 18 
 
 Omission of chord tonts, 12 
 
 One-sided cadences, 169 
 
 Over-clang, 10 
 
 Overtones, 2 
 
Alphabetical Index. 199 
 
 Parallel clangs, 71 
 
 Passing notes, 62 
 
 Pedal-point, 34 
 
 Period, 175 
 
 Phrygian second, 88 
 
 Plagal cadence, 95 
 
 Plain-fifth step, 16 
 
 Preparation of dissonances, 117 
 
 Prime (centre of tone relations), 2 
 
 Prolongation of final notes, 177 
 
 Raising the minor third yields +Z>, 66, 150; = S ln * , 151 
 
 Related tones, 2 
 
 Relations of tones, 5 
 
 Rhythmical relations determining the quality of harmony steps, 47 
 
 S», i-vn, ss 
 
 Score, 38 
 
 Second has a diverging tendency, 57 
 
 Second, progressions of, 18 
 
 Section, 175 
 
 Sequences, 120; modulating, 189 
 
 Seventh, 7 in the penultimate chord should not be in the bass, 58 ; VI1 in 
 
 S vn in the bass, 60 
 Sign of equation (:=) indicating modulation, 52 
 Six-part writing, 186 
 Sixth in S 6 in the bass, 59,60 
 Skipped clangs are expected, 146, siq. 
 Soprano clef, 85 
 String-quartet score, 61 
 
 Suspensions, 22 ; foreign to the key, 115-117 
 Symmetrical construction of periods, 173 
 
 Tenor clef, 8 1 
 
 Tenor written an octave higher, 50 
 
 Third must not be omitted, 13 ; must not be doubled, 13, 20 ; particularly 
 when the fundamental note also is doubled, 16 ; may be doubled in the 
 parallel clangs, 71, 75 ; is regularly doubled in the deceptive close, 73 
 
 Third-step, 84 ; modulating, 164 ; cadential, 165 
 
 Thorough-bass system, 120 
 
 Three-pulse bar arises from prolongation of the accented beat, 174 
 
 Tonic equivalent to absolute consonance, 72 
 
 Transitions, 128 
 
 Transposing instruments, 131, 134, 136 
 
 Tritone, 37 ; in the same harmony, 47 
 
 Tritone change, 75<; modulating, 161 
 
 Tritone step, 100, 101 ; modulating, 170 
 
 Trombone, 134 
 
 Trumpet, IU 
 
 Turn of harmony, 44 
 
200 Harmony Simplified. 
 
 Turning after leaps, 18-19 
 Twelfth, 3 
 Two-bar group, 175 
 
 Under-clang, 10 
 
 Unprepared dissonances explained as ellipses, 114 
 
 Valve horns and trumpets, 136 
 Vicarious part-progression, 57 
 
 Whole-tone change, 76; modulating, 159 
 Whole-tone step, 34 ; modulating, 146 
 
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