^ ' T o''ri e - K e -I at 'f o n b ' :Percy:G(:)etscliius,:Mii.s:;I)oG.. : ■::NEW; YORK : :; G> SCHilRMER ; iBOSTONiTHE BOSTON MUSIC CO. «';;;i; — * — ^ "tU^ " (^^^ same lettersA 7: A. e. f. ff. a. h. Wdiflferent order; DIATOMIC aCALE I c, d, e, f, g, a, 1 2. This Diatonic Scale comprises the tones of the major mode, so designated for reasons given later on. Upon examination it is found that the contiguous intervals of the Diatonic Scale, unlike those of the Natural Scale, are not uniform, but differ as follows : Ex. 4. 1===^^-^^^ ^ whole itep. wh. itap. 1 . wh. it. vh. it, wb. n. 1 ,, » 1 1 1 1 1 1 r 1 1 1 1 1 > •i ) Here the Keynote is reproduced in the next higher Octave, in order to complete the circuit of tones. That is : the distance! between thejrd and 4th tones,* and also between the fth and 8th tones, is only half as great as that between all the other contiguous tones. This has no other importance for us at present than to illustrate the accidental relative location assumed by the seven tones when transferred from their order in the Natural Scale, to that of the Diatonic Scale. At the same time, it is a convenient external guide to the ready mechanical forma. Hon of any diatonic major scale, and should therefore be carefully observed. •These tones are called Scale-steps ( or, frequently, degrees of the scale— L e. Diatonie Kale). THE SCALE. 7 t 13. The diatonic form of the scale is that upon which all practical composition is based. The names given to the seven Scale-steps (numbered from the Keynote upward) , arranged according to their relative importance, arc as follows : First step — Keynote or Tonic ; 5th step (perf. 5th above Tonic) Dominant (dominating tone) ; 4th step (perf. 5th below Tonic) — Subdominant ; 2d step (perf. 5th above Dom.) — Second dominant; 6th step (midway between Ton. and Subdom.) — Sub-mediant; 3rd step (midway between Ton. and Dom.) — Mediant ; 7th step — Leading— TONE. Thus : Ex, 5. C-Major Tonle. Saminut. Toua. BuMom. Donu Sd Dom. HeditnU 8ab«Bild. LtldtB|>tou> ■9 ■ 1*^ 1 i^^^^^=EE| ^==^ -=^ ^ ^;^^-=| ST p. 6tta. 1 4. Of these seven steps, three are very greatly superior to the others, and are therefore called Principal scale-steps. They are, self-evidently, the TONIC and its two perf.-5tli rela^ tives, the DOMINANT and SUBDOMINANT. The 2d, 6th and 3rd steps are called Subordinate. The Leading-tone has specific melodic qualities which characterize and set it apart trom every other step of the scal«<. Lesson I. A. Write out every major scale, first in its Natural and then in its Diatonic form (Exs. 2 and 4 ) ; use no signature, but place the respective accidentalheiore each inflected tone. 33 and 34 may be referred to. B. Write out the 7 steps of every major scale in the order of their importance, viz : Tonic, Dom., Subdom., 2d Dom., Submed., Med., Leading-tone. C. Name, mentally ( in response to teacher's question ) the 3 principal tones of every scale. D. Play the 3 principal tones of every scale on the keyboard in this order : Ton., Subdom., Dom., Tonic. CHAPTER II. Intervals. (Mat. Mus. Comp. §§ 15—20). 1 5. The association of any two tones is called an Interval. Intervals are always counted upward, and along the DIATONIC MAJOR SCALE of the lower tone. The number of the step which is occupied by the upper tone is the INTERVALS. numerical name of the interval. For example : Ex. 6. i i^ -g ST DniMn. fith. -(52- rit. etc. tS>- Si- -»■ -- -S- -S- *i) From ^1 to c^ is an %th or Octave, because, counting upward, along the major scale of C, the next c is the %th step. C-B is a seventh, as * is the seventh step from C, in ascending succession. — *2) Whether within or beyond an Octave, the name of the interval invariably corresponds to the number of the step of the scale occupied by the upper tone (Corap. 6). — *3) The only exception is in the case of the interval next above the 8ve, which in some special cases (see 24) is called a Ninth, instead of a Second. 1 6. AH those intervals which agree with the natural major scale (i. e. where the upper tone corresponds exactly to the scale-step of the lower tone as Tonic), are called Natural or diatonic intervals. Hence, the in- tervals in Ex. 6 are all Natural. They are qualified as Perfect or a.s Major, as follows : The natural (or scale) TINISON, FOTTRTH, FIFTH and OCTAVE are PERFECT. The natural (or scale) SECOND, THIRD, SIXTH and SEVENTH are MAJOR. E-Flat Major. Ex. 7. ^:^= - |7s>-fe- Perfect : 1 t?g- *1) Major. *2) '^E3^ g l=5^=fe-g«^«=t|S=g5=gg=g5^l *i) E-flat—b-flat is a "perfect 5th"; a"5th", because b-flat is the 5th step of the majorscale of E-flat;' and a "perfect" 5th, because B-flat exactly forrifj/ INTERVALS. 5 •i) Not B-natural instead o£ C-fiat I The letter C confirms the interval as a "5th" of some kind or other. The letter B would be some species of fourth.—*!) Not A instead of B-double-flat j the Utter must remain unchanged, as it determines the numerical name of the interval. 1 8. Analogously, any Major interval when extended by an accidental becomes Augmented; when contracted by an accidental, a Major interval becomes One similar contraction of a minor interval, or two contractions of the cor- responding major interval results in the Diminution of the same. Thus : Ex. 9. ■% *\) Thirds.*2) •tn vn an — * ■ Z? Uij. Sth. Angm. 6th. UlBTfitb. " ^^ DimTsth. Hkj. Aupa. Uin. Siis. •i) Not C for B-sharp !—*2) Not D for C-douUe-sharp I Lesson 2. A. Write out the perfect 4th and perfect 5th of the following tones : C, G, F, D, B-flat, A, E-flat, E, A-flat, B, D-flat, F-sharp, G-flat, C-sharp, C-flat, G-sharp, D-sharp.— Write out the major 3rd and major 6th of the same tones. — Write out the major 2d and major 7th of the same tones, in optional order. — Write out the augm. 2d, 3rd, 4th, 5th, 6th, 7th, and 8th of F, B-flat, E-fiat, A-flat, D-flat, C, G, D, A, E, B, G-flat, C-flat, F-sharp, C-sharp, D-sharp.— Write out the minor 7th, 6th, 3rd and 2d of the same tones. — Write out the dim. 8th, 7th, 6th, sth, 4th, 3rd, and 2d, of the same tones, in optional order. B. Name the following given intervals : J?ffl_b ^Tg-pg^g-V-^-^Xg- W-&- ^g:i|^^Tg=H>H-w^4^K 1) *2) *2) i j^ •2) W^ x-s>- ss: §Z_s>_t|^:J#S>-l-^25^j5r :#?=! W— ^"Pzsr *i) The lower tone is to be regarded, in every case, as a Tonic. The number of the upper step, is the name of the interval ; if the upper tone conforms to the scale, the interval is either perfect or major, according to Ex. 7 ; if not, it is augm., minor, or dim., according to Exs. 8 and 9. ^*2) In case the lower tone is an impracticable Tonic, as here, shift the interval todily upward or downward, but without changing the letters ! Thus; lO CHORD-CONSTRUCTION. CHAPTER III. Chord-Construction. CONSONANCE AND DISSONANCE. (Mat. Mus. Comp. §§ 25—26.) 1 9. As has been seen, the most intimate intervals are the Unison, Oc- tave and perfect fifth (paragraph 8.) The other interval relations are quali- fied according to the same rule of proportion, which determines their respective degrees of consonance or euphony with mathematical infallibility leaving nothing to the fallible and unreliable ear but to confirm and accept the result, correcting itself, if needs be, thereby. The next simplest arithmetical proportion is 3 : 4 ; two sets of sound-waves acting upon the organ of hear- ing in these proportions of velocity produce the double sensation of the perfect fourth. This is illustrated in Ex. i , between the upper two tones, c" and «*. The average ear will perceive that this interval is somewhat less agreeable than the perf. 5th, albeit the tones are the same, and therefore the harmonic significations and functions identical. The proportion 4 : 5 gives the major 3rd; 5 : 6 the minor 3rd; consequently the former is the better (most consonant) interval of the two. As the proportion becomes more complicated, the tones are observed to approach each other, and the grade of consonance gradually decreases. Thus : 1:2 2:3 3:4 4:5 5:6 Ex. 10. (atPianof.) 3 ZS3g^ — F~Ly^ — I (Consonances.) ^ ^ \ ^ \ -^ — hg — l-'^g — I p«if. 8. p«if. 6. p«if. i. BlaJ. 8. Uin. S. 20. The next proportion, 8:9, is the major 2d, which is palpably no longer consonant, but dissonant., because the conflict of tone-waves here reaches an extent which is disagreeable. Hence, the minor third is the smallest consonant interval. The proportion 15:16 gives the minor second, which is still more palpably painful. 8:9 15 : 16 Ex. 1 1 (atPianof.) ^^^^j=g55= | (Dissonances.) UkJ. Sd. 2 1 . The Inversion of an interval is obtained by reversing the letters, so that the lower tone becomes the upper. g As this merely in- volves the Octave-relation, it is evident ~^ '^ — from paragraph 6 CHORD-C ONST RUCTION. II that an interval and its inversion are practically identical All consonant intervals remain consonant after inversion, and dissonances remain dissonant. The complete table of Consonances and Dissonances is therefore as follows : Perfect Octaves, and their inversions, perf. Unisons ; Perfect Fifths, and their inversions, perf. Fourths ; *i) Major Thirds, and their inversions. Minor Sixths; ■*i) Minor Thirds, and their inversions, Major Sixths. Major Seconds, and their inversions. Minor Sevenths ; Minor Seconds, and their inversions, Major Sevenths ; and also all Augm. and Dim. intervals, on account of their obliquity to the scale. Consonances Dissonances. 1: *i) Major and Minor 3Tds and 6ths, being no longer /^^f/ intervals, are distinguished as Imperfect Consonances. Chords. (Mat. Mus. Comp. §§ 27 — 37.) 22. Chords are associations of more than two (comp. 15) tones, in exclusively or at least preponderantly consonant interval-relations. Giving first preference to the perfect 5th, as a matter of course, the skeleton of a chord erected upon the tone g (for example) would be, ~ C « This is lore £ \: the proportion 2 : 3 (or 4 : 6, which will prove more £ ? — <^ — conven- ient). The third tone, necessary to develop the "interval" into a complete "chord", must be in consonance with each and both of these tones, therefore the simplest proportion for the three tones together is 4 : 5 : 6, which mathe- matically determines what the ear also unhesitatingly sanctions, viz. the addition of the tone ^-«a^»ra/: ~i_si This is the primary three-tone chord-form and furnishes the %^ —^ — incontestible model of all Primary or Fundamental Chord-structure, nam,ely : any tone as given basis, with its Major third and perfect fifth. 23. Other, externally different, forms can be erected, in which again all the intervals are consonant. Thus : Ex. 12. But these are all readily recognizable as modifications of the original form, obtained solely by means of the Octave-relation, which never alters the harmonic significance, but simply affects a more or less complete Inversion of the chord. 24. No other forms than these can be constructed without marring the consonant condition of the chord; in other words, consonant chords, pr concords, are limited to three tones. Still, the fundamental principle li CHORDS. of chord-structure here revealed may be extended, in order to give the chord a more copious form. Thus, the structure of ascending thirds may be ex- tended to anew tone, [ —y g ~r| but this new tone (in this case_/") must necessarily constitute Fro? — g— — i a dissonant interval (7th) with the fun- damental tone, for which reason chords of four tones will invariably be dissonant chords or Discords. A three-tone chord with one or more duplicated tones, as ( g-g-b-d, g-b-d-d, etc.) evidently does not belong to this species of genuine "4-tone" chords. i .a. ^ -S- zg~ -19- ~a- sr -zr i -i- =i= but the new tone dissonant inter- Still another upper third may be added, thus : (in this case a) gives rise to two additional vals, viz. 7th with b, and 9th with^ (see Ex. 6,"'note *3). 25. Dissonant chords are not only admitted, but even deemed necessary in music, on account of their contrast with consonant harmonies, and the peculiar quality of activity which their dissonances involve. But the fol- lowing limitations are dictated by wisdom : firstly, as Discords are merely ex- tended forms of the Concords, their application should be deferred until the re- lations and progressions of the primary three-tone forms have been thoroughly mastered ; and secondly, the dissonant intervals must be introduced in moderate and judicious proportion to the consonances ; hence, while 4-tone chords may be unexceptionable, those of 5 tones are very rare, and the ad- dition of still more dissonances (as six or seven-tone chords) is obviously out of the question. It is true that dissonances are often multiplied, so that occasionally even all seven letters of the scale are associated simultaneously, — ^f or example, at x, (Mendelssohn, op. 82.) But such dissonant clusters are never "chords." Their demonstration will appear in due time. 26. The concise definition of a chord is then: the combination of THREE (or FOTJE, or FIVE) tones in THIRDS, or in inverted forms reducible to thirds (see 23) . CHORDS »3 2 7. The structure of thirds is the Fundamental chord-form ; in THIS form the lowermost tone is the Root of the chord, from which the latter takes its name, according to the name of the letter or of the scale- step. Thus : chord, be- ^ is the chord of C, or (in C-major) the Tonic cause the Root is C. The other tones (e and g) are called the Third and Fifth of the chord, according to their interval-re- lations with the Root. Two additional tones would be called the Seventh and Ninth. Thus : Ex. 13. i Chord of G. -e>- -*- Book ThM. lUlh. B«T«nUi. Rinth. 28. Three-tone chords are termed Triads ; Four-tone chords are termed Chords of the Seventh ; Five-tone chords are termed Chords of the Ninth. Thus: Ex. 14. g Ohaid of the 7th of ». « Chord of th« 9Ui of D. W --(m •i) •i) Why the ear prefers F-sharp to F-natural in this case vrill shortly be deduced from the simple principles of chord-relation. Relation of Triads within one Key. 29. Any step of the diatonic scale (^excepting the Leading-tone) may be a Root, and develop into a Triad by uniting with its Third and Fifth. And, as already stated, each chord derives its harmonic xwcas from the step of the scale which its Root occupies. For illustration, in C-major : Ex. 15. For convenience, the Triads are also designated by Roman numerals, coinciding with the number of the step on which their Roots stand, and are named accordingly : The One, The Two, The Three, etc. ^ Tonlo •SAtA. Som. Triad. BoeaDm. Triid. 9d.Doia. Trill. Bubmid. Triid. Hid. Triad. f r^§^ T J 1 \%) \ ft \ j-3 e> 1 \e>' I V 1 5? ej 1 ■ «- r -f. S Ex. 16. i P=i EE "Si EF 30. The relative importance of each of the six Triads of a Key corres- ponds exactly to that of the respective scale-step, and depends upon the distance of its Root from the Tonic in perfect fifths ; or, npon its location in the "Natural" scale ("Ss. 2). f4 CHORDS. Assumingi as self-evident, that the Tonic Triad is of first and fundamental significance, the next in importance is the Dominant Triad, then the Sub- dominant Triad, and so on, precisely in the order of Ex. 15. 3 1 . The Tonic Triad and its two nearest relatives, the Dom. and Sub- dom. Triads, are the Principal chords of the Key (see 14), and represent THE THSEE ESSENTIAL ELEMENTS OF HABMONT, among vsrhich the other three Triads (the Two, the Six, and the Three), called Subordinate chords, are only interspersed for the sake of variety, contrast and embellishment. Ex. 17. C-Major. ^ Principal Triads. Bubordi&ate riladl. ^^^ f s^ I ^ \ r/'g\r3 4 9, ej l /5 ^ 1 \&)-\ -^ \ „ ^ a \ a 16 » 1 \«/— 1 I G \ a " a 1 1 1 t. y 3- 1 ' ^'i I T IV jB^-v n VI m ?*2) •i ) A very fine distinction in the relative importance of the IV and the II will be dis- cussed later on. — *2) To the "Leading-tone Triad" no name or rank can be assigned at present ; see later. From this a significant inference can be drawn in regard to the choice of f-natural instead of f-sharp for the Key of C (Ex. 2, note *i). F-natural can be a Root in that Key; f-sharp cannot. B, which cannot be a Root, is the last tone adopted in C- major. 32. These two classes of chords (Ex. 17 ) will be found, at the piano- forte, to differ in sound. The Principal Triads have a major Third and perfect Fifth, wherefore they are called Major Triads. On the contrary, the Subordinate Triads have a minor Third and perfect Fifth, and are termed Minor Triads. This accidental difference in effect is only oijuing to the ■ situation of the chords iti their Key, and does not in any wise infiuence their fnovements or significance I (Mat. Mus. Comp. §§ 48 — 51.) 33. Another demonstration of the formation of the diatonic major scale may be deduced from the foregoing paragraphs. Assuming 4 : 5 : 6 to be the simplest three-tone proportion, (22) and applying it to the Tonic (say C), the tones c-e-g convene as kernel of that Key. Applying it to the nearest perfect 5th relative of the Keynote (the Dominant, G), the result is g-b-d. Then arises the question, whether it shall be applied to the next relative of the Dom- inant (the iVfo«(/-Dom., D) or to the other relative of the Tonic (the 5'«i-Dom., F) ? The former gives d-F-sHARP-a ; the latter F-NATURAL-a-c. According to this the scale of C may be either C— D—E— F - sharp— G— A — B—C—D— etc, (I— V— -11), II or C— D— E— F-natura^^^S— A— B— C— D— etc., (I— V— IV). I 1 1 IV The question is touched upon in Ex. 2, note *i) which see ; and in Ex. 17, note *i. For the present, preference will be given to F-natural, and the IV, because F-sharp conflicts with the CHORDS. 15 Keynote itself. Hence the formation of the C-scale is adopted as follows (the notation in 0, J and J-notes renders the illustration clear) : ^ -ij °-' I „ J , J -^-r Ex. 18. 34. Still another peculiarity of the scale serves to demonstrate its natural formation, viz ; it consists of two /r^m^/ywOTj/ar series of four tones (the "Tetrachord" of Greek musical theory), each consisting of the spaces whole — ^whole — half, and separated by the interval of a perfect fifth. Thus : Ex. 19. r " 1 JDoin. Tttruhoid. { {Tonio TatrMbord. | j ^S^- at o "^ -zyg- This again confirms the fundamental significance of the perf. fifth-relation ; and affords an- other clue to the preference given to F-natural instead-of F-sharp in C-Major (the tetrachords thus being made alike). Lesson 3. A. Write the major Triad (as I) on every possible tone in the octave, adhering through- out to ^i& fundamental form (27). B^ Write the six Triads of the twelve diatonic scales, in the order of Ex. 17. C. Name, mentally, the I of every Key ; the V of every Key ; the IV; the II; the VI ; the III. D. Find and play these chords at the Pianoforte. (The practice of 4 and 5-tone chords is deferred till later.) CHAPTER IV. Rhythm and Melody. (Mat. Mus. Comp. §§ i— Si 9—13) 35. The images of musical art, unlike the stationary creations of the arts of painting, architecture and sculpture, are progressive ; as in the art of poetry, the impressions in music succeed each other by progressive motion. Therefore, time is absorbed in the expression of a musical thought, and it is the province of Rhythm to define and regulate the divisions and subdivisions of this passage of time. Rule I. The time is divided into absolutely eqjjal units ( Beats, Fractions of Beats, or Measures, as the case may be) ; i. e. the respective units are of exactly equal duration ( like the divisions of a twelve-inch rule.) Rule II. Though the units are alike in duration, they differ in force ; i6 RHYTHM. i. e. some are heavy and others light ( as certain lines on a 12-inch rule differ from others in length or heaviness). 36. The primary units (or beats) are grouped, in conformity to these rules, in uniform Measures, of which there are but two fundamental species ; either a succession of one heavy and one light beat, in regular alternation ; or a succession of one heavy and two light beats, in irregular alternation. The former is called Duple time, or rh3rthm, or measure ; the latter is called Triple rhythm. There are no other species. Duple rhythm: ^ p ' p ^ ' f j * ' ^**=- Ex. 20. Triple rhythm : hni;, Uflil, lun;, llflil. kin?, Uilil, -• etc. h«ftT7, liKH. licbl^ b»T7, Ugbt, llgh^ 3 7. Rule III. The heavy beat (called Accent^ should indicate the beginning of a Measure. If a heavy impression is created by any means at any other point in the measure, the rhythm is "irregular", though not necessarily "wrong". See later. For illustration : Mozart. Handel. Ex. 2 1 , ^^^ Both perfectly regular, because the heaviest (longest) beat or tone stands in every case at the beginning of the measure. Ex. 22. trti-nn-t ^ *i) 3= ii^ •2) i Beethoven. ^J SE?E ^Beethoven. ^ !ftc w ^f ^f •3) *i) Irregular, because the heaviest tone is where a light unit should stand. — *■£) Irreg- ular because of the sf, which transforms a light unit into a dynamically strong one. — •3) Like note *i). 38. Rule IV. The ofttimes necessary subdivision of beats into Frac- tions, and the coalition of beats or parts of beats into notes of greater value, (Ex. 23, note "3), must consequently be so effected that the heavy beats retain the comparatively longer tones ; i. e. subdivisions must take place on RHYTHM. 17 comparatively lighter^ never on comparatively heavier beats, and vice versd. Beethoven Schubert. Brahms. Ex. 23. *i) Regular; 3rd (light) beat subdivided.— *2) Irregular, the heavy beat being so sub- divided that the following (light) unit becomes more weighty. The measure seems to begin with the second eighth-beat.— •3) An unusual example of irreg. rhythm. Without its rhytli- mically definite accompaniment, it sounds like 3-4 time, thus : 39. Rule V. For these reasons, the repetition of a chord from an unaccented beat to an accented one (i. e. over an accent) gives rise to irreg- ular rhythm, and should be avoided. 40. All larger measures than those which comprise but two or three beats, are called compound, and contain as many accents as there are groups. Thus : EX. 24. lore J ^ J J|gJ J J J u^in:jT:jT i\ etc. The u/i^er figure of the Time-signature always indicates whether the measure is simple or compound. In the former case it is 2 or 3 (^' ^» ^» ^' etc.); inthelattercase,4,6,9or 12, /'4, 4, 6, 6, 9, 9. 1.4 8 8 4 4 8 9 16 etc. ) Melody. 4 1 . Any SUCCESSION of single tones is a Melody. Its quality de- pends upon the choice of the tones, and their rhythm or time-values Melody is a manifestation of tone-relations in horizontal or progressive association, whereas "Harmony" associates tones vertically or simultaneously ; the two partly similar processes are only subject to the same natural laws in a limited sense. The principles of Harmony, in the broad sense of Chord-succession, are very distinct; those of Melody far more vague. Harmony is the substratum of all music, and its few sturdy laws fix themselves upon the mind easily, and so firmly, that their fulfilment soon becomes almost mechanical, and indeed is often intuitive ; but Melody is guided by more veiled and subtle conditions, which can hardlybe reduced to a system, but must be left largely to the individual "talent", native sagac- ity, or acquired skill of the composer. Largely — but not altogether: As far as the natural decrees of harmonic combination and succession influence and determine the ruling condi- tions of Melody, the latter can be reduced to apprehensible form, and should be faithfully •bserved until essentially fastened on the mind. 42. Rule I. The general requirements of good Melody are: a. smooth and natural undulation (to the exclusion of awkward interval-sue- i8 MELODY. cessions ) ; b. rhythmic variety ; c. definite and symmetrical delineation (including sufficient Repetitions of the melodic figures, on the same steps, and, better still, on other steps, as Seouences). For illustration : Ex. 25. Beethoven. HeqneuoA of Z. •i) Anexampleofbadmelody, in whicha//the above-named requirements are wanting. •2) A good melody, fulfilling all the given conditions. See Appendix B, i, 2, 4, 8, 9. 43. Rule II. After a wide leap (beyond the interval of a 3rd), the direction of the melody is generally changed. Thus : Ex. 26. ^^^mfyU^^^^^^ 77 •f-^-V"^ good 77 *0 •2) *3) •1) Good, because the tones conform successively to a harmonic structure (the Triad I of C). — *2) Good, on account of the confirmation (and ultimate equibalance) by Sequence in the following measure. — ^*3) Such a change in rhythm frequently cancels this melodic requirement. 44. The seven steps of every scale are divided into two classes : Ac- tive (or leading) tones, which possess a natural inclination to progress, upward or downward, into other tones ; and Inactive ( or central) tones, which have no melodic tendency, but represent the aim of the active tones. The Inactive tones are the ist, 3rd, and 5th scale-steps, i.e. the Tonic or stationary centre of the whole Key, and its two harmonic associates, which naturally share this central quality with it. They are interior tones, within the circle of rest. The Active tones are the 7th, 6th, 4th and 2d steps, or, in other words those exterior steps which lie not within but without the inner circle of harmonic repose, and which therefore strive to gain (or regain) the condition of rest. For illnstration : Ex. 27. i Inactive Steps. Active Steps. 1 -s>- -<9 =- T -ar- 9 =E -^ 45. The DIRECTION of each active step is defined by its proximity to an inactive step, each being attracted most strongly by that inactive tone which lies nearest. Hence the yth step progresses upward to the Tonic ; the 6th step downward to the Dominant ; the 4th step downward to the Mediant ; and the 2d step either upward or downward, to the Tonic or MELODY. Mediant, from both of which it is equally distant. Thus : 19 Ex. 28. ^^ 7 * 6 -*- ■r:r^%- 46. This duality of melodic quality in a Key, — the opposed positiye and negative con- ditions of animation and repose, — underlies all harmonic and melodic life. Like the coil and recoil of the hairspring of a watch, the melodic and harmonic factors swing to and fro be- tween these two groups, with more or less regularity. And need one wonder that their funda- mental tones are respectively Tonic and Dominant, exemplifying the supremacy of the perfect fifth-relation, and further confirming the prevalence of the Dominant, as it is the common- tone, or connecting link, of the two groups ? Exemplified in concrete form : Ex. 29. r\ /^ £1. IM ff. ft. / U I jtf 1 im » a^ ^ « ** (^ 1 K]) g ■■» s % ^ ? ^ § J Iiuet. Iiuot. -S- Tos. Dom. Ton. -'4- -g- -g- Common tone, or AzlB. J r»- &t f T. 1 e^ zs* n fii v \ s 1 1 s ■ FUDdUDAIltalf. 47. Rule III. The natural tendencies of the Active steps should be respected, especially in prominent melodic voices. A multitude of verifications of this important rule will be found in all good melodies. Exceptions will of course also be encountered ; they are due to conditions which will be explained later on. The pupil is urged to scan Lesson 10. See Appendix B, 5, 6. Lesson 4. A. What is the province of Rhythm ? In what respect do its units agree ? In what do they differ .' How many species of Rhythm are there .' Their names ? What is the essential characteristic of each species ? When is a measure rhythmically regular ? Give example. When irregular? Give example. Where is the repetition of a chord objectionable ? What are Compound measures ? How many accents have they ? What is Melody ? B. Write out Ex. 28 in every major Key. C. Write out Ex. 29 in every major Key. £R£CTION OF CHORDS. CHAPTER V. Parts (Voices). Erection of Chords. (Mat. Mus. Comp. §§ 38—45.) 48. All music is based upon Chords, which succeed each other in Harmony, as single Tones succeed each other in Melody. These Chord- successions (Chord-combinations or Chord-progressions) are efTectuated by means of a number of simultaneous melodic farts or Voices, each of which assumes one of the chord-tones, and serves, in conjunction with the rest of the voices, to unite the chords in horizontal order, interval by interval. See Ex. 35. 49. The number of parts or voices generally employed is four. The following example indicates their respective ««»?ej,^their average compass, and their notation : Bass. Ex. 30. -(: :g-U) Tenor ; ~ Alto. i^^ Soprano. Bass and Tenor (Male voices) are written together on the F-staff, and distinguished by turning the stems of their notes respectively down and up ; Alto and Soprano (Female voices) both on the G-sta£E, stems respectively down and up. Ex. 31. Bass and Alto, the lowest of each class, are csileA parallel parts or voices ; Tenor and Soprano likewise. Bass and Soprano are outer voices, Tenor and Alto inner voices. 50. The distribution of the chord-tones among the 4 parts or voices is called erecting the chord. Rule I. The parts must not cross. Rule II. The Alto should never He more than an octave from either of its two neighbors (i. e. Soprano or Tenor) ; but the lower adjacent voices, Bass and Tenor, are not limited by this rule. For illustration : Ex. 31. I of C. ERECTION OF CHORDS. 21 *i) This sign ^ will be used to indicate bad (wrong) examples. Chord 2 is wrong, be- cause the Alto and Tenor are more than an octave apart. In chord 3, Alto and Soprano are too far apart. — ^"2) According to the notation, the Soprano note e lies ie/me the Alto note g: This is forbidden by Rule I. 51. In 4-part harmony, all Triads (3-tone chords) have to be enlarged by duplicating one of their tones (as already seen in 24). BITLE. The best tones to double are the Principal steps of the scale, i. e. tonic, dominant and subdominant, es- pecially when they are roots. Thus, in C-major, the tones c, g ox f: A. Ex. 32. C-Major. I (00) V (gg) IV («) n(fovi(oo)ni(gg) In other words : double the Root of a Principal Triad, and, double the Third of a Subordinate Triad. And, by inference : never double the Fifth of any Triad. 52. Exceptions. It is also possible to double the Root of any Sub' ordinate Triad, because, though a subordinate step of the scale, it is still a Chord-RooT. Ex. 33 a. And it is possible to omit the 5th of a Principal Triad (never that of a Subord. Triad), in which case its Root is tripled. Ex. 33 b. Ex. 33. C-Major. n (dd) Hff) /Vl(aa)ni(ee) IfcS)(cBO») ^ =^-h-g fe ^ V(ggg> IV(fff) Hsto. 53. When the chord is so erected that the three upper parts or voices lie as close together as the chord will permit, the harmony is said to be Close, or compact ; When they are separated by one or more intermediate chord-intervals, the harmony is Optn, or dispirsed. i CLOBI HASUOHT. I T=^- BUItK-WRITIKG. i^ -Z5(- opxH buwoht. 1 r- PABT- WK IT I NQ. | -i ^=^^ ^^=^=^ Close harmony is most frequently used in instrumental music, and may be employed by the pupil in the majority of his sight-exercises at the pianoforte. Open harmony is the superior kind, and chiefly used in vocal music; it will be almost exclusively employed in all the leritten exercises of this book. 22 ERECTION OF CHORDS. 54. The paramount importance of the uppermost voice (the Soprano) as that upon which the leading of the Melody proper devolves, renders it necessary to distinguish its various grades of effect and influence, according to the interval of the Chord which is assigned to it. For this purpose the term "Position" has been adopted, and is applied as follows : "Position of the Root" or "Octave," signifies that the i?oo/ (or its Oc- tave, which is the same thing) lies in the Soprano ; "Position of the Third"=the Third of the chord va. the Soprano; "Position of the Fifth"=the Fifth of the chord in Soprano. For illustration : Ex, 34, FoBitlon of the Boot or Sta. Vat. of tho Sid. BOPRAHO-T^OOT. ■^- '^1 ^- ^jgrm^ J- ^- T ^ P«. of the 5th. Ch. of D. Cb. of B-flkt. Oh. of E. ^ ±f^ J. ^ Oh. of A.flkt. Lesson 5. A. Erect (in writing) the I of every Major Key in as many forms as possible, first in the Pes. of the Root, then Pos. of the 3rd, and then Pes. of the 5th (Ex. 34), but always with the Root in Bass (fundamental form). Observe the rules of duplication aS»^ oiSdssion illustrated in Ex. 32 A, and Ex. 33 B ; and avoid the errors noted in Ex. 31, chords 2, 3 and 5. — B. Erect the VI of every Major Key in its 3 Positions successively (but Root in Bass), observing 60th rules of duplication (Ex. 32 B ; Ex. 33 A).— Find and play these erections at the Pianoforte (without notes). CHAPTER VI. Rules of Part-Writing. (Mat. Mus. Comp. §§ 46—47.) 55. In leading the parts or voices through a series of chords, the fol- lowing rules must be strictly observed (by the beginner) : BULE I. The parts, each and all, should progress as evenly (horizontally) as possible. Wide skips should be avoided, and diatonic movement (i. e. along the scale) preferred. A tone which is common to two successive chords is gen- erally retained in the same part. For example : RULES OF PART-WRITING, 23 Ex. 35. N. B. Each "measure" is an example by itself, without any con- nection with the next! *i) This is an aggravated example of objectionable voice-progression ; Soprano, Alto and Tenor all make a wide leap, instead of progressing more evenly as in the following measure. — *2) Here the common tone g remains where it was (in Tenor); the following measure, though admissible, is not quite as good. — *3) The skip in the Soprano {g — t) is justified by the extreme smoothness of the other voices. This rule of SMOOTH 70ICE-FB06BESSI0N is the most essential and general law of harmonic succession. 56. Rule II. (Double rule.) Saccessive perfect fifths, and successive octaves [or unisons] in any pair of parts, in parallel direction, are prohibited. Successive perfect 5ths sound badly, in the majority of cases. Successive 8ves are forbidden in ^ar^-writing, because they reduce the number of tone -lines (voices) and create a blundering impression. For illustration : It is not without significance, that almost all of the above erroneous progressions are chiefly due to the violation of other simple conditions, — especially those of Rule I. In measure i, Tenor and Bass progress parallel from one perf. 5th to another; but at the same time the Tenor makes an unnecessary leap. — Measure 2: Bass and Alto run in parallel perf. 5ths ; at the same time the u in Alto is a false duplication of the 5th of the Triad (51). — Measure 4: Soprano and Bass progress parallel from one octave (c — c) to another {d—d); at the same time, the Tenor makes an unnecessary leap. — Measure 5: Tenor and Soprano run in parallel octaves; at the same time the Fifth (0) of the second chord is omit- ted. — Last measure: consecutive unisons in Bass and Tenor. — n. b. It must be remembered that successive Sths and 8ves are wrong in any two parts, but only when they follow each other in the same pairl In Ex. 37, meas. i, the perf. 5th in Ttnor and Alto (g— d) doe» not make "parallels" with the next perf. -t'l in Bass and Tenor (c— g). 24 RULES OF PART-WRITING. 57i As these erroneous parallels are often provoked by leading the voices all in the same direction (upward or downward) , it is wise to carry the uffer farts in contrary direction to the Bass, when convenient. 58. Rule III- Allow the leading-tone to ascend to the tonic, if practi- cable, in whichever part it lies. And respect the natural downward tendency of the sixth and fourth STEPS, especially in Soprano. (Compare 47). Thus: 7th step 6th step. 4th step. ??*2) ??*2) ?»3) Ex. 37 C-Major. I *i) When the 4th step is doubled, as here, it is liable to ascend m one of the parts (see also the Tenor in the last measure). The correct progression however (downward) is given to the most prominent or most melodious voice. (In this case the Soprano descends, correctly ! in the following measure its ascent is dubious ; in a middle voice it is usually immaterial). — *2) Compare measure 6. — ^*3) An unnecessary skip in Soprano. 59. A GENERAL EXCEPTION to all these rules of Fart-writing is applicable (and often almost obligatory) in case a chord is simply REPEATED, instead of being exchanged for a new chord. Hence, even wide skips are not objectionable j the natural tendency of active tones is not urgent ; and reiterations of the satne 5thor 8ve are unobjection- able, during the Repetition of a Chord. Lesson 6. (n. b. In all of the following studies the Soprano-part alone may be added to the Bass, throughout, before filling in the Alto and Tenor. 1 Connect (in writing) the I with the V in C-mdJor, in as many ways as possible — ^but always with Root in Bass — according to the foregoing rules. See model, below. — Connect the I with the IV in the Keys of G, E, and B-major. — Connect the V with the I in F, B-flat and G-flat major (with especial vigilance in regard to the first clause of Rule III, — 58). — Connect the IV withtha I in D. A-flat ^i»4 E-major (observing the second clause of Rule III). — Find and RULES OF PART-WRITING. 25 play these chord-successions at the Pianoforte in close harmony (53)1 i. e. the three upper parts in the right hand, and the Bass alone in the left. Model. Ex. 38. C:I-IV B-flat:V-I •i) The choice of Triads determines the Bass-progression ; here c — f, because I — IV of C. The Soprano talces first the Root or 8ve (c) byway of systematizing the exercise ; its pro- gression is a repetition c — c, as no other tone of the zd chord (f,a,c,) lies as near as this. The same is true of the Alto (e—f) and the Tenor moves with similar ease and smoothness from g to a. — ^"2) Soprano starts here from the Third (-a//^/8ves with Bass. — *2) See Ex. 43, note *2) . On the second beat, the Tenor, in holding its c quietly, casually doubles the Fifth (c in Sopr.). This is justifiable. See 55, last clause. THE THREE PRINCIPAL TRIADS. 29 69. The other Prin. Triad (the V) should not be used before this Ca- dence formula (thus : V-IV-V-I) because the V will not readily precede the IV. See 64, Rule III. It would sound thus : Ex. 4-5. at pianof. ^ J m i r p ^s J i J £ i r p lot: I 1^1 ^^ i P J. P The irregularity is justified to a certain extent by turning back imme- diately into the V (thus : V-IV-V) so that the IV appears to be but an in- terpolated chord. The last two measures, above, are very objectionable, because c, as fifth of the IV, does not sound enough like the Tonic of C to satisfy the progfression of the Leading-tone in the Soprano. This must be tested by ear. YO. Adopting the formula of Ex. 42 (I-V-I), any of the three Prin. Triads may be preposed. Thus : V- (I-V-I) ; IV- (I-V-I) ; or I- (I-V-I) : Ex. 46. i M ^ jij ^yf\- ^. r ■zsH g TTT "r~r i J: ^ 1 ^ r -I- *i) TSH or) I f^ r i r •f f^ *i) This only differs from the preceding measure in substituting a. half-note in Alto and Bass for the two quarter-notes. Such diversity of Skyt.':m is very desirable I But observe 38, Rule IV. 7 1 . Adopting the formula of Ex. 43 ( V-V-I) , any of the 3 Prin. Triads may be preposed. Thus : I- (V-V-I) ; IV- (V-V-I) ; or V- (V-V-I) . These are left to the pupil, who will also pursue this system of retrograde experi- ments one or two chords farther. It has already become evident that the possibilities multiply at every new chord, and that they must ultimately be- come innumerable. Lesson 7. A. Write out the chords given in 71, in the manner of Exs. 44 and 46. (See Ex. 41, note •l)_Write out the Cadence-formulae IV-V-T; I-V-f; IV-V-V-fJ IV-I-V-f; I-I-V-Tj andV- V-V-t in the Keys of G, F, A, E-flat, B and D-flat respectively (i. e. one in each Key), in 3-4 time, according to the foregoing examples. — B. Take the formulae of Ex. 44, xa& place one more Prin. Triad before them, at the keyboard. 3^ PRINCIPAL TRIADS. CHAPTER VIII. Principal Triads. Continued. T2. The next experiments will be made in progressive order (comp. 65), at the beginning of the Phrase. As stated in 61, the independent Phrase begins with the I.' As this can progress either into the V or IV (64, Rule I), or into a repetition of itself, it follows that the choice of the second chord in the Phrase is optional. Thus (in 3-4 time) : Ex. 47. d. *2) e. *3) (I) T (I) IT *l) Of the 3 initial progressions liere given (a, b, c), l-v is the best, for reasons implied by 30, last clause. Hence, the majority of Phrases begin in this manner. — *2) All the pre- ceding measures may also be shifted to these beats, in case the Phrase is to begin on a light beat (Ex. 40, a and b). — *3) This apparent violation of 64, Rule IV, (repetition of a chord over, or into, an accent) is always permitted at the beginning of a Phrase. 73. The addition of further chords is effected as before, and is subject only to the rules of 64. Thus, the formula I-V (Ex. 47 a, the I accented) may be extended to 3 or 4 Triads as follows : I-V-I ; I-V— V ; (I-V-IV-$-) ; i_V-I I IV; I-V-I I V; I-V-V | I; (I-V-FlT^) ; and so on. 74. The formula t-IV (Ex. 47 b) may be extended to I-IV-I ; I-IV-~ V; I- IV-IV; I- IV-I | V ; (I-IV-I | IV?) *i) ; I-IV-V|I; (I-IV-^ I IV ■^) ; (I-IV-V I V0) ; I-IV-IV | V; I-IV-IV | I; and so on. *i) Doubtful, because the Dominant is too long absent. Comp. Ex. 47, note *i). The paramount importance of this chord must not be forgotten. 75. The formulae I | V and I | IV (Ex. 47 d, the I unaccented) maybe extended to l\'^-\\ I | V-V; I | V-I-IV | ; I | V-I-V | ; I | V-I-I | ; PRINCIPAL TRIADS. 31 r I V-V-V I ; I I V-V-I; (I | V-'V-IV"| ^) ; (I |'V-IV-V| ? see Ex. 45) ; I I IV-I-V; I | IV-V-V; I | IV-IV-V; I | IV-V-I; and so on. A few of these are exhibited below, in different melodic forms : Ex. 48. A-Major. ■MiM^-^^ Se rrffr-rf I T I IV I IT I tA *i) This -wide skip (£-sharp— d) is justified by chord-repetition. See 59 ; and 43. Lesson 8. A. Write out, as before, all the initial-formulae given in 73, in G-major. — B. Write out the formulae given in 74, in B-flat major. — C. Write out the formulae of 75, in £-major. — D. Find and play these formulae at the Pianof. in close harmony (53), in diSerent Keys. CHAPTER IX. Principal Triads. Continued. 76. It only remains, now, to apply the larger formulae of Lessons 7 arid 8 to the phrase-skeletons given in Ex. 40, and determine the harmony for the beats still vacant, as before, in order to complete the Phrase. For illustration : beginning with I-V-I | IV — , and closing with — IV-I-V | 1, the intermediate harmony might be : Ex. 49. C-Major. i i,l 'S: -A -A. "TTT- 1^ 3a PRINCIPAL TRIADS. Or, with rhythmic modifications (whereby the number of chords may vary) : Ex. so. i a. *i) -m ^ ^ m M i. •2) i J.. M n f u AA m m J. i ^ *i) The succession of chords is here identical with Ex. 49 b ; only the rhythmic form is modified. — ^•2) This example illustrates that it is not necessary for each beat to be clothed io«A4<7j<5>arafef^<»»-rf, but that one chord may answer for two or more successive beats, in mute repetition. It is the uneven rhythmic conditions thus produced to which 38, Rule IVi refers. T7. This harmonic process is applied to Phrases in Duple-time (2-4, 4-4) in precisely the same manner, only excepting that the altered rhythmic relation of the beats affects the location of Repetitions (39, Rule V). Thus: I-V I I, or I-IV | V, but not I-V | V, nor I-IV | IVj etc., etc. For example : Ex. 5 1 . C-Major.*^ i 2r im ^ . n. ]r \ i^^ ^ i f^ rv) V G-Major.. *i) Here there is a chord-repetition from the 2d beat to the 3rd in Duple-time, i. e. over into an accent (the 3rd beat being heavy, Ex. 24, No. i). This would be as irregular as Ex. 22, note •3), were it not that the chord commenced upon the 1st (or heaviest) beat. Hence the repe- tition, taken as a whole, does not run into or past a comparatively heavier beat I — *2 ) The Lead- ing'tone (f-sharp) in Alto must ascend,e^m. at the cost of the tone d. See Ex.43, note *')• Lesson 9. A. Write a number of complete 4-measure phrases, in different major keys, in 5 time, imitating the style of Exs. 49 and 50. B. Construct phrases in other major keys, in \, \ and | time. Use chord-repetiUiw freely, and avoid too uniform rhythm. HARMOmZING OF MELODIES. 33 CHAPTER X, Harmonizing of Melodies. 78. As stated in 41 (which review), Harmony or Chord-succession is the substratum of all music ; it is the source from which all melody is derived (be it with or without direct and conscious intent) . Hence, the system adopted in the above Exercises, of constructing Phrases upon the basis of Primary Chord -SUCCESSION, is obviously the most natural and correct one. Never- theless, the process is often reversed, not only in framing exercises for the pupils' guidance, but especially in the actual practice of Composition (when the observance of harmonic conditions has become, so to speak, automatic). T9. In working out a Phrase _/>-o»« the Melody (as Soprano) downward (i. e. in harmonizing a given Melody), the following facts must be recalled: The melody will not contain (at present) any other tones than the p steps of its Key. Of these, the 1st, 3rd and 5tli scale-steps belong to the I of the Key ; the 5th, 7th and 2d scale-steps belong to the V ; and the 4th, 6th and 1st scale-steps belong to the IV. Thus : Ex. 52, C-Major. E^ ^^ 8tap 9. 8t«p,8. Stop 4. StapS. sup 0. Stop 7. -g- SeealsoEx. 18. 80. The Tonic and Dominant tones (steps i and 5) each belong, as is seen, to two different Prin. Triads^ while each of the other steps repre- sents but one. The choice between the two chords, at these points, will be dictated by the Rules of 64, and other familiar established principles. For example, applying Ex. 52 to the following given melody: Ex. 53. C-Major. Steps : i a= iS Chords . I ■ V I I IV I I T T IV •l) »2) •3) *4) I IV ▼ V I IV •s) *l ) Of these two chords, the I must be chosen (61 ).— *2) The choice falls upon the I ; the V could hardly progress into the IV of the next beat (64, Rule III. But see Ex. 45).— *3) May be either I or V, because the following beat (see *4), will be the I. — ^•4) The IV fa not possible, as it would give rise to successive 5ths (Sopr. and Bass) with the following V*— *S) The IV is canceled by 62. 34 HARMONIZING OF MELODIES. 8 1 , The Chords (and Bass-part) will therefore stand as follows : IIIIVTITIITV- Bx. 54. « r ^ m lij ^ TT •1) •2) i^ T IT T I f¥f etc •i) Ex.47, note *3).—*z) The Vmight be regarded as preferable here,on thegrounds of 74,note»i). — *3) Ex.45. 82- Another illustration, in Duple-time J Steps :i 7 1 Ex. 55. D-Major. j r'WTfrJ rii Tfi g^ 3 1 s 7 1 Chords : (it) (it) (i) •i) *2) *3) (IT) •4) (IT) (I) (IT) •2)«3) •!) The Triads in parenthe- sis are can- celed. •i) Mustbethel(6i).— *2) The IV cannot follow the V.—*3) The I cannot be repeated from the 2d beat into the accented 3rd beat..iv*4) The IV cannot follow the V, nor be re- peated from this beat i^to the next. Lesson 10. A. Play Ex. 55 at the Pianoforte, in complete close harmony. B. Harmonize the following major Melodies (in 2, 4 and 8-measure Phrase-form), according to the above direc- tions : — 2. *4) m 3. '" i i ¥^ ^ -P— P- 1 F m- $ !^^ j ^Tir- '^r r-iFriT¥~r w «fTr-A i SeI^ 3t=t •0 HARMONIZING OF MELODIES. 35 i rF^ if=nf^ =P=#- •2) 8. ^ ^iijj^g i girii^i^sg a ES ^^ mi ^ 11^ •3) *i) This fraction of a beat (a) is more likely to be the IV, like the preceding fraction t^, than to change the harmony to the I. Hence the slur. — *2) When the Leading-tone de- scends, as here, to the 5th step, the latter must also be harmonized with the V, and not with the I; because nothing but chord-repetition will justify the melodic licence (59). — ^*3) In this chord (IV) it will be found necessary to double ^.contrary to the general rule (51)1 on ac- count of the wide skip which follows, in the Soprano, — "4 ) Turn all stems upward. To THIS Lesson, add Appendix C, No. i. CHAPTER XI. The Minor Mode. (Mat. Mus. Comp. §§ 82—89.) 83. The line of research and argument in Chapter I, leading up to para< graph 1 1 (which see), distinctly proves that, of the two Modes recognized and employed in modern music, that one known as "Major" (because its Prin. Triads have a major Third, 32) is the Natural one. 84. Theother, i. e. the "Minor"mode, is consequently to be regarded as an Unnatural or Artificial mode, and is accounted for as an arbitrary modification of the natural major mode (from a simple and justifiable motive, as will be seen). 85' This modification affects the two Mediants, i. e. The third and sixth steps of the major scale, which are lowered (by an accidental) so ai to transform the correspond- ing major intervals into minor intervals. Vo other steps are changed! 36 THE MINOR MODE. Thus: C Major (Ex. 3.) C Minor. Ex. 56. i ^ ,ra g ^ ifaa-s-'^s^ ^^v»- -^"^^^ ra34Sg78 la 34s ^Tan%&4kZ^ 86. The scale thus obtained is called the Harmonic minor mode; it is the only theoretically accurate minor scale, and is the same in both ascending and descending succession. Still other modifications, subsequently rendered necessary by melodic considerations (to be explained in due season), are basedupon this Harmonic minor /woa?e, which must therefore be firstthorough- ly mastered. 8 T. It appears then, that a minor scale is derivedy'/'o/w the major m.ode of the SAME Keynote. (C minor from C major; A minor from A major, etc.) And the lowering of the 3rd and 6th steps results from transforming the Prin. chords I and IV from major into minor Triads (see 32) . Thus : C Minor Scale : C Minor Chords : -19- /-e-\ L-S'-li-S- Ex. 67. g^^=bF-g-=^^^^ ;(i) ^,g)^^ Compare Ex. 18. I IV -V»I ) •i) The same principle of transformation, (which contracts the major yd to a minor yd, thus drawing it nearer to the verge of Dissonance and enlivening the harmony with a slight unction, more welcome, and also more active, than pure Consonance — see 19, 20, and Ex. 10.)— .> would be applied to the other Prin. Triad, the V, also, if it were practicable. But as it would infringe upon the Leading-tone, it is not feasible in the Harmonic mode. Hence: 88. The Leading;.tone of the Harmonic minor mode remains the same as in major (85), and therefore the DOMINANT TBIAD IS ALIKE IN BOTH MODES. 89. The Signature of each minor mode is borrowed from that major mode whose Keynote corresponds to the Mediant (3rd step) of the minor, because that is the scale which it most essentially resembles. For this rea- son the latter is called the Relative major key. {Do not confound this with the Original major I See 87.) Thus the Relative of c minor is E flat therefore its signature is 3 flats, one of which however must subsequently be canceled in the farts ^ viz., that one which interferes with the major : ^ BIB. liSl. JK Leading-tone of the minor scale. For illustration : THE MINOR MODE. 37 Ex. 58. C MiNOK. ^^ 3= E Minor. . 81c of G. Tf. jv^'' 15= f a » le fii-^ 1*: ] etc. *i) •i) The relation between a minor scale and its Signature is furthermore illustrated, and partly accounted for, by the history of the Minor mode, whose origin is traced to the "Hypo- dorian" (or "Aeolian") mode of ancient Greek theory. This was one of the seven octave-scales which were deduced from the fundamental tone-system (corresponding to any of our modern major scales — , say the white keys of the Pianoforte) by beginning and ending with each of the seven letters of the octave, respectively. The "Hypodorian" ran along the white keys (for ex- ample) /r '^ whereby the half-steps were located between the 2ii and yd, and ^h and dtk tones. This scale, not adopted by St. Ambrose, but later on by Gregory as "Tonus II (Plagius Proti)," and still later by Glarean as "Modus Aeolius", developed in course of time into the descend- ing melodic minor mode of modern theory. The above example (A to a) is obviously based upon the succession of the scale of C major, to whose tones it exactly corresponds, but beginning and ending with the (nth step instead of with the ist ; for which reason it was called the Rela- tive minor of C va^yx, and borrowed (or retained) the Signature of C major. In the same manner, C minor ( or C- Aeolian) began and ended with the 6th step of £-flat maior, and retained the Signature of the latter. Why, as stated above, one of these flats must however be can- celed, in submission to the Leading-tone of the Harmonic scale, will now be understood. 90. The treatment of the Prin. Triads in minor is in every respect the same as in major, only excepting the following restriction: The harmonic minor scale contains the unnatural melodic progression of an augmented second^ between its 6th and 7th steps (in C minor, a flat — b natural ; in E mi- n— — I nor, c — d sharp, etc.) . This succession must be avoided, in both directions, in all the voices. See 42, Rule la ; 58, Rule III ; Appendix B, 6. Thus : i . C Minor. ^ ^^^^^^i= "^Sgi 99- -gr^ i^i^^'^gglfe-^ •f- 3 s 4 5 e 7 8 8 7 ^Tsri Lesson 1 1 . A. Write out all the major scales (excepting D flat and G fiat) and place their own minors below them, using no signatures, but accidentals, as follows : C MAJOR. ^^^^^ C MiNOK. etc. (over) 38 THE MINOR MODE. (The minors of c sharp, g sharp and d sharp may be taken from the majors of c sharp, g sharp, d sharp ; or, if these prove too complicated, they may be transposed from the scales of B flat, A flat and E flat). — B. Harmonize the following melodies, as in Lesson lo ; watch THE 6th and 7TH SCALE-STEPS I be Careful that each moves in the proper direction, and that neither of them is doubled ; do not neglect the accidental before each Leading-tone : i I. »i) 2. "2) M^JEES E5 2!^ w ^ i 3 E^ ^U^^ i *?: ^ *-• ^ •3) ^m s 'tiiC J^ JJ - 'g-gl- ■z^ ^^ •4) l'»\|j | JJ7q7"PF^ ^m^ T *i ) This melody is in A minor, as the last tone proves. It is therefore harmonized as if it were in A major. — •2) D minor ; treated as if it were D major. — *3) Lesson 10, note *i).- — *4) Here there is no alternative but the chords V — IV. To THIS Lesson, add Appendix C, No. 2. CHAPTER XII. Subordinate Triads in IMajor. (Mat. Mus. Comp. §§90 — 108.) 9 1 . The Triads upon the subordinate scale-steps (the II, VI, and III — see 3 1 ), are not to be regarded and employed as new and independent chords, but as the Parallels of the three Principal Triads, in the place of which they are respectively used, chiefly for the sake of variety. 92. The relations are as follows: The VI is the Parallel of the I (Tonic Element) ; The II is the Parallel of the IV (Subdom. Element) ; and The III is the Parallel of the V (Dominant Element). SUBORDINATE TRIADS. 39 In other words, the VI is the Subordinate representative of the Tonic ele- ment ; the II is the Subord. representative of the Subdom. element ; and the III the Subord. representative of the Dominant. For illustration : Principal : Subordinate : Parallel-relations : m Ex. 69. w -Sr t ^ iii=i *2) E«^ *l) Compare Ex. 17. By placing tlie IV here, ielaw (and before) the I, the relation between the two bodies of Triads is more accurately illustrated. — *2) It will be observed that the Par- allel chords represent Relative Major and Minor Keys. — ^*3) These chords are not parenthe- sized because of any doubt as to the relation, but because the III is so very limited in its use that it can hardly claim consideration in this connection. The II. 93. Of the Subord. Triads the strongest is the IT, which, coming next to the V, in perf. 5th-succession (see 30), has as good a claim to the rank of a Prin. Triad as the IV — possibly a better. This is touched upon in Ex. 17, note *i) (which see), and will be more fully elucidated in due time. The best Interval of every Subordinate Triad is its Third. Place the Third in Soprano whenever practicable, and double the Third in pref- erence to the Root. 94. The II often takes the place of the IV, before the Perfect Cadence. Compare Ex. 41 . For illustration : Ex. 60. C-Major. •l) Double either / (the Third) or d (the Root, as in the first measure). See Ex. 33 a. — ♦z) Comp. Ex. 43, note •! ). — *3) This wide leap to the Leading-tone, in Soprano, is allowed iii descending i^KC'aa1iOTi\.y.—*li) Comp. Ex. 41, note *4). Here the irregular progression, from the 6th step upward to the 7th, is less objectionable than in the former case, because the chords are related. But it should be avoided, if convenient— *s) Wrong ; see Ex. 42, note *2). 95. Aside from this (its best progression) the II may connect as fol- lows with other Triads : Ex. 61. ?? •2)A "S) •*) •5)?? •5)?? ¥> SUBORDINATE TRIADS. •i) This Foreign Progression II — I is very ungraceful and should be avoided. — *2) The progression of the II into its own Parallel the IV is forbidden. No Subordinate Triad can precede its own Principal chord. — ^•3) IV — II, on the contrary, is an excellent progression, of the nature of Tl Repetition (the chords being Parallels) and entitled to many (if not all) of the licences of chord-repetition (59). — ^*4) I — II is not as objectionable as the reverse (note •i), because the Tonic Triad can progress in all directions. — ^*s) V — II is objectionable, on the grounds of 64, Rule III. But it is better than V — IV, as the chords V —II are related. See Appendix A, Section i. The VI. 96. The VI is the counterpart of the I, and is employed exclusively as inferior representative of the Tonic harmony. Like the I, the VI can progress into every other chord (64, Rule I), only excepting into the I itself, which, being its own Prin. Triad, it cannot precede (VI — I -^-jcomp. Ex. 61, note *2) Hence, the VI may precede the perfect Cadence ; thus : I *3.)'| Ex. 62. C-Major. •i) Double either a (the Root) or c (the Third — as in the first measure). See Ex. 33 a. •z) Permissible. Comp. Ex. 41, note *4), and Ex. 60, note *4). — ^*3) An unnecessary leap in Soprano ; and inexcusable, because a Foreign chord-progression. Q 7, The full table of connections of the VI is as follows : Ex. 63. 3- fisiS -9-^- ^ »1) ^^^^ »2) m VI IT Tl *i) Excellent, like Ex. 61, note *3), which see.— *2) Thisdoesnot contradict 64, Rule III, because the VI is a Tonic chord, as well as the I. See Appendix A, Section 1, Lesson 12. Write out the following chord-successions in the usual manner, without regard to rhythn (uniform quarter-notes or half-notes), in a number of different major keys : IV-II-V-I||VI-II-V-I|1I-II-V-I||IV-II-VI-V-I||I-II-VI-II-V-I|| i_v-ii-v-vi II i-vi-i v-v-v-i II i-v-vi-vi-v-i II i-i v-ii-i-vi-i V- v-i a N.B. A part of the Lesson must be done at the Pianoforte (close harmony) at sight SUBORDINATE TRIADS. 41 CHAPTER XIII. Subordinate Triads. Melodies. 98. In applying the Subord. Triads to the harmonization of melodies, the following facts must be recalled : that the VI can take the place of the I ( 96 ) and therefore harmonizes the 1st step of the scale (more rarely the 3d step, and never the 5th) ; that the II can take the place of the IV, har- monizing the 4th step, (rarely the 6th step and never the ist) ; and that the II may also be used as independent harmonic factor (93), harmonizing its own step — the 2d — (just as the I does the ist step, the IV the 4th step, and the V the 5th step) . Thus : Ex. 64. g ^g^I a. ' ■Mr 6. b. Stop 4. Btqi*. 'or VI I \V1 r»«/ Bot TI •0 step 1. Step S, ^^^ 'orH \llnr« ' fegS I or II *i) Rare, because the Fifth of the chord would be in Soprano, — always the weakest Po- sition. 99. Applying these rules to Melody 9 of Lesson 10, the following sub- stitutions may be made (observe parentheses) : step. Ex. 65. &Major, (^■frirh-J W Step. 4 -frrr VI J . «) *l) Not the VI. ^ T^ .^ J. r ^ y^s •i) ^ (IV) VI (I) •l) Notthell.— »2) 1 00. Furthermore, with special reference to the 2d scale-step : 1 Ex. 66. _ -V V „ V (U7I) II V (T^T) •2) 42 SUBORDINATE TRIADS. *i ) Whether the 2d step is to be harmonized with the V, or II (Ex. 64, c) depends largely upon the tuxt Melody-tone. This d might be either V or II, as the VI follows. — ^*2) This d cannot be a V, because the latter could not be repeated over the bar-line. — *3) The following tone (e) must be harmonized with the I ; therefore choice falls upon the V for d, as II — I is objectionable (Ex. 61, note *i). — ^"4) Must be the V, as the II cannot be repeated from the preceding (light) beat. The III. 101. As already stated (Ex. 59, note *3), the III is very circum- scribed in its uses, — owing to its remoteness from its Tonic-centre (in perf. 5ths ; see 30; and Ex. 17). It is almost exclusively limited to harmon- izing the Leading TONE,w^e« the latter descends diatonically (into the 6th step). For illustration : Ex. 67. C-Major. a. 1*1) ^ 5b^ n b. very rare : J. F^ ^ i i i ir M VI III IV •l) This apparent violation of 47 and 58, is justified by (as it is owing to) the descending diatonic scale, in which each tone (the Leading-tone included) is impelled downward by the momentum of the preceding tone. If approached from a lower tone, in ascending' direction, the Leading-tone must ascend ; comp. Ex. 43, note *l). — The same is inversely true of the as- cending diatonic scale, in which the ^h and 6th steps are impelled upward. N.B. N.B. N.B. „ » g >^ \e3 g ^. IE -s>—'S>- -—zr- The 6th and 7th steps are harmonized with the IV and V respectively, only excepting when they progress thus improperly (6 into 7, or 7 into 6), in which case the Parallel Triad is to be used. Lesson 1 3. Melodies, to be harmonized with all six Triads ; and with reference to the following sum- marized table : See Appendix A: Steps : C-Major. 5pg Exceptions : 6 7 7 W-- Triads : " IV I IV j- fl, ^» g i ^^ I n m SUBORDINATE TRIADS. 43 First re-harmonize, with the material of this Chapter, Lesson lo, Nos. I, 2, 3, 7. I. i a « — 1»- 2. *i) ^3^ •1) »i) f^ s JsS ^^ 3- . *2) =P=Ffe la :t=± £ i fci Pfcfi: ^ ♦^=P= •4) fe »s) »4) *3) •s) f w ^ ^:m=m\\^'\' \ r fm =t±t i *3) 6. "Ein' feste Burg." Walther. m s T7. 4 ry -!g-ig (S^ »-^^ :^ i I I ig — SEE ?= ?^ •i ) Each of these long notes may be harmonized with one chord, or with two (J — notes), at option.— *2) At each of the repeated xia\£s in this melody the chord must be changed, (ac- cording to 64, Rule IV).— •a) Ex. 67 a.^*4) Ex. 60, note *4) ; or Ex. 62, note *2). •S ) Harmonize d with the III ( Ex. 67 b.) To This Lesson, add Appendix C, No. 3. CHAPTER XIV. Subordinate Triads in IVJinor. The Period. (Mat. Mus. Comp. §§ 109— in j 112— 114.) 1 02. The notation of the II, VI and III in minor must conform to the Harmonic minor scale. Thus : Ex. 68. C-MlNOR. i^^ rh;=^g-^ i^ :te ■mz II TI 44 THE PERIOD. a) The II, having a diminished Fifth, is a Diminished Triad . It occurs very rarely in its _futfdamenial form (Root in Bass). 6) The III, having an augmented Fifth, is an Augmented Triad. It is even less frequent in minor than in major. c) The VI is a MAjor Triad, and of equal importance in both modes. 1 03. The II and III, owing to their dissonant Fifth, are Discords. Therefore, only the VI can be used in minor at present. See 90, which also applies to the VI. The Period. 1 04. The Period-form consists of two Phrases, of equal length, and similar in Time, Key and general harmonic character. 105. The first of the two is called the Antecedent Phrase. It begins with the I, (beat, and Soprano-Position optional, as usual) , and closes upon an accented beat of the 2d, 4th or 8th measure, not with the Perfect Cadence^ but with a so-called Semi-cadence. (Compare 61 and 62). 1 06. The Semi-cadence is usually made upon the V, (preceded by the IV, II, VI or I) ; but it may be any other Triad — excepting the III — ; even the I, with Third or Fifth (i. e. not the Root) in Soprano. And it must be a chord of comparatively longer duration than the adjacent chords, in order to interrupt the rhythm, and thus distinctly mark the end of its Phrase. For illustration ( — a two- measure "Antecedent") : Ex. 69. , ,r, 1 j 'W^- -}-*| P S -»^ ^ ^U 'm i^TF ri Prffl ■W *3) fe :St± Pff •2) *i) Or the VI, by taking a in Bass. — *z) This Semi-cadence on the Tonic is often called "Imperfect", because it is only prevented from being "Perfect" by not having the /^ooi in So- prano. — ^*3) The Cadence on the VI (V — VI) is called "Deceptive," because V— I Is tx- pecttd. THE PERIOD. +5 107. The second of the two Phrases is called the Conseqjjknt. It should begin on the same beat as the Antecedent, (with any convenient chord) , and must close with the Perfect Cadence, on the same accent as the Antecedent, which it must exactly equal in length. The Antecedent sketched in Ex. 69 might be complemented as follows : Ex. 70. Antecedent. V Consequent. 3=1= g •§-*■ — ■ * J — rrt- rr t I- -J •2) •3)1 ' I I I i '- ' — f r « u P *4) IT f ±ii5 ^ Tin •2) f *4) *i) Comp. these 4 measures Tfith the 4-measuTe Melodies of Lessons 10, 11 and I3,and observe the distinction between the Phrase (as uninterrupted chord-series), and the Period (or Double-Wri&€). Not the number of measures, but the presence or absence of a Semicadence defines the Form. — *2) Semicadence. — *3) The Melody of this Consequent Phrase runs parallel with that of the Antecedent. This is favorable, but by no means obligatory. See 42 c. *4) Perfect Cadence. Lesson 14. A. Write out the following series of chords, in 4-part open Harmony as usual, formulated in Phrases of 4 measures : I-V-VI-IV-V-I-V-I in the following forms ; the rhythm, location of barlines, and Repetitions being optional : 1. C minor, 2-4 Time, beginning on heavy beat ; 2. A minor, 3-4 Time, beginning on light beat ; 3. F sharp minor, 4-4 Time, beginning on heavy beat. Directions: i. Fix the barlines. These may be drawn between any of the given chords, almost unlimited option being possible. But care must be taken to preserve the sum of four measures, and to locate the Cadence properly. — 2. Determine the number of Melody- tones for each measure; this will decide the number of chord-repetitions which may be neces» sary, and the rhythm. — 3. Write out the Bass ; then the Soprano ; and then finish. See Appendix B. B. Re-harmonize the following melodies, introducing the VI at least once in each melody:— Lesson 11, Nos. 3, 4, 6 ; Appendix C, No. 2, a, d, e. C. Write a number of original four-measure phrases, in different minor keys, and different kinds of time, as in Lesson 9, — using only the three principal triads, and an occasional VL See par. 103. 46 CHOitD-INVERSION. CHAPTER XV. Chord-Inversion. 1 08. The fundamental forms hitherto employed (with the Root in Bass) are naturally very strong and ponderous, but also to a certain degree ungrace- ful and unwieldy. Therefore it is not only admissible, but often eminently desirable, to modify the form of a Triad hy placing either its THIBD or its FIFTH IN THE BASS, instead of the Boot, thus effecting the HTVEESION of the chord. (23). I 09. This alteration of the lowermost part fulfils the same purpose as the distinction of "Position" in the uppermost part (54), and affords the Sass similar opportunities for smooth and graceful melodic progression (instead of the almost constant succession of wide leaps which were unavoid- able in the rugged Basses of the foregoing Lessons and Examples). See Preface, I. 1 1 O. When the Bass thus assumes the Third of the Triad, the latter stands in the First Inversion. For illustration: Ex. 7 1 . Chord of C. i ^ lii ^^ Chord of C. -4=4= Chord of G. r T -^ROOT.- T -igTl ofD: ofF T i r Fund. form. First Inv. Fund. form.First Inv. First Inv. 111. The first Inversion of a Triad is designated "Chord of the Sixth," because the shape of the Triad (as regards its component intervals from the Bass-tone upward) has changed from "Root — 3rd — ^5th,"to "Bass- tone — 3rd — 6th": Triad (c-e-g). First Inversion (e-g-c). -M g '-^i^ °-fe CHORD-INVERSION. 47 The figure 6, when attached to any Bassnote, will therefore serve to indicate that the itt in- version of the chord is required; or, in other words, that the Bassnote in question is not the Root (as hitherto) but the Third of the chord ; — the Root must therefore be sought a yd hlaw the given Basstone : =3= _ ST SI Chord of C. Chord of A. Chords of the Sixth. 112. Rule I. In a chord of the 6th, the Soprano usually takes the Root — or, if more convenient, the Fifth of the chord. But rarely the Third, which should not appear simultaneously in both Soprano and Bass. Ex. 72 a. Rule II. Double, as usual, any of the Prin. tones of the scale ( Tonic, Dom. or Subdom.) . But observe that all rules of duplication are of second- ary importance, when they conflict with other rules, — especially that of ffood melodic progression. Ex. 72 b. Rule III. In an Inversion, no Intervals should be omitted. Rule IV. Change the Basstone at each accent, and change the chord also if possible. a. Chord c-e-g. b. chord c-e-g. *4) d-f-a. *5) g-b-d. *6) I tr-i r:^^ — n tiv:=rr r- r/p-t— n-zn/r- Mi/n r Ex. 72. C-Major, •i) In C major, c-e-g is the Tonic chord, or I. With e (the Third) in Bass, it is fhe ist Inversion ; this is indicated by Ij (spoken : One-one), and figured 6 . — *2) The II (d-f-a) with/ in Bass ; hence Hi (Two-one).— •s) The V (g-b-d) with * in Bass, hence Vi (Five- one). — ^*4) Doubtful, because e is doubled. — *^ These three duplications are all admissible. — *S) Doubled Leading-tone, — always wrong. 1 13. The Ist Inversioni of the I, T, IV and n are excellent, and should be freely used. But the Ist Inv. of the Subordinate VI and III must he shunned. 114. The substitution of the Third for the Root, in the Bass voice, 48 CHORD-INVERSION. lightens and beautifies a Triad, and also materially facilitates its connection with other chords. The movements of Chords of the 6th, therefore, while subject tn g-eneral to the same rules of progression as their respective Triads, are far less constrained. See ii8. (Mat. Mus. Comp. §§ ii8 — 139>) 115. Applying the principle of ist Inversion to the following Chord- series, I I V-I I IV-II I V-V I I II the results would be : *l) "2) "S) Ex. 73. C-Major. •i) The V (g-b-d), with the Third in Bass and Fifth in Soprano.— »2) IV (f-a-c), Third in Bass, Root in Soprano. — ^*3) V^ — Root in Sopr. — ^*4) I^ — Root in Sopr. — •$) IIj — Root in Sopr. — ^^6) *6) Neither of these two Cadences \i perfect, as they both involve an Inuer- Furthermore (Bass alone) : •2) •3) *4) ^ Ex. 74. Bass. rBra 12^ a. %1 f=-* s jrt^ii ^^ TS^' m ■ •4) ^^. i^ ^ 1 E -Bl- :*^ 1*3) r ~i — ^r k r ff ^ i , -i f=^ s ^- ±: •1) es *5) *i ) See 1 22 a. The Sequence must either be abandoned, or else altered, whenever it strikes the Leading-tone Triad. — *2) This is the combination of a Triad and a 6th on the same Bass ^ tone. It is figured 5 6 or 6 5, as the case may be, and is very frequent and good. The Soprano generally takes the differentiating tones (5 and 6) while the other parts remain unchanged. See note *4). — *3) See 122 b and c. — *4) Here the combination 6 5 (note *2) is made on a single beat. The slur indicates that they are to be treated accordingly, and not as inde, pendent melody tones. — ^•s) Inexact Sequence ; see 122 d- Lesson 16. A. Harmonize the following Melodies, with Triads and chords of the 6th ; with constant reference to the table in Lesson 13. — See 112, Rule IV; and Ex. 75, note*i ). First re-harmonize, with the material of this chapter, Lesson 10, Nos. 1, 2, 3, 5, 6; Lesson II, Nos. 2, 6; Lesson 13, Nos. 1, 3, 6. i l^^^ =t *2) i s =i=P»: Efca! 3E3E^ ^ *2) ^ ^ ^ •3) 15: •2) »4)- |cfc*:^^»=F?=^ ^ -•— ^ iSE »s) «it «4)_ ^g^^^ S[ ■f t r *. U M ;t±=F ^E£ I Ii IV *6) I IViIIi 7t — 1 — "Ttpt — ■ r^~ f ~r~ tfp— I*- -j — i — ' — S==5— — - ia-L^--:^:=t=^-^3t-=^ = z:zJ=: ^ sm CHORDS OF THE SIXTH. 8. 'r) 53 ^ E^^ i s g l g l I tHJg? iS rrrujJ ^ a=a IV V *5) -«»-V •l) In regard to the irregular Rhythm, see Ex. 78, note *4). — *2) The II in its Triad- form is not commendable in minor (see 102a), but in \X.& first Inversion (IIi) it is treated in minor precisely as in major. Therefore it may be used here, notwithstanding 103. — *3) May be the VIj. — *4) Successive 6ths (119). — *5) These brackets indicate Sequences ; see note •6). — •6) The chords for the initial figure are given. As the Sequence lies one step higher (in this case) the chords I-Ij-IV become II-IIj^-V, and so on. Each Sequence is calculated in this manner. — •/ ) A new Bass-tone for each repeated note, throughout. B> Extend the following measures in exact Sequences, at the Pianoforte : i 5^ 4- 2: ^ m- ^_y Wi^^ u ± J- r'- m 8 f I 'e « ^ ° 4 times. 4 times. 4 times. To This Lesson, add Appendix C, No. 4. e 4 times. CHAPTER XVII. Chords of the Six-Four. 1 23. When the Bass assumes the Fifth of the Triad, the latter stands in the Second Inversion. Comp. no. — For example: Chord of F. Ch. of D.Ch. of A. Ex. eo. etc. Fund. Triad, ist Inv. 2d Inv. 2d Inv ad Inversion. 54 CHORDS OF THE SIX-FOUR. \ 24. The 2d Inversion of a Triad is designated "Chord of the Six-four" because the shape has changed from "Root-3rd-5th,"to "Bass- tone-4th-6th" : Triad (c-e-g) ; istlnv. (e-g-c); 2D luv. (g-e-c). i 'Sssast.- 3E -©FWie ^=- The figures 6-4, when attached to any Basstone, will therefore serve to indicate i that the Second Inversion is required,!, e. that the Bassnote in question is not the Root, nor the Third, (as hitherto), but the Fifth of the Chord. The Root must therefore be sought a tfh below the given Bassnote : a % -C\' ■^ II ^ 1. &< ^ w _^o_~ » » e> 1 II Compare iii. Chord of C. Chord of A. Chord of F. The Tonic-6-4-chord. 1 25. The 2d Inversion is the weakest (though not the least useful) form of a chord, and is therefore subject to many restrictions. A 2d In- version is never employed to represent or substitute its own fundamental chord, but only for the purpose of harmonic embellishment. The best six- four chord is the 2d Inv. of the Tonic Triad, i. e. the I, (I, in 2d Inv. or »' One-two" ; comp. Ex. 72, note *i). 1 26. The Tonic-6-4-chord may be connected (preceding or following) : a) With the Triad on the same Basstone, viz. the V. This may occur anywhere in the course of a Phrase or Period, but it is of peculiar importance at the Semi-cadence, and at the Perfect cadence. For illustration (both major and minor) : Ex. 8 1 . C-Major AND Minor. •1) J=^=i =p3^ ^m m -J.. *2) ^g f ^ t I i i SUt CHORDS OF THE SIX-FOUR. 55 Pkmod.. A •3) *4) i J SZ ^=^ J» Y ^2 V »5) *i) This la does not produce a Tonic impression, but merely that of a casual embellish- ment of the Dominant. — '2) The figures 5-3 denote the Triad. In this connection the in- terval 6 (wherever it chance to be) should progress into the 5 ; and the interval 4 into 3. — *3) Semi-cadence ; the 1 3 always stands accented at this place, and also when it precedes the Perf. Cadence. — •4) Perf. Cadence. — *5) Such a repetition of the Bassnote over the barline (in analogy to 39) is objectionable. N. B. Each accent must be founded upon A new Basstone. See 112, Rule IV. The rhythmic location V | Ig or I^ | V is not allowed 1 1 2 T. The Ig is furthermore connected, before or after : b) With any other form of the same chord, as Repetition. Thus : (major and minor) : I I, Ij I Ij I, I ^ -J— ,^ -i Ex. 82. C-Major AND Minor, i ^ r J 111 a?^^^ ^33 I Ii la V In con- -jg ;='— = junction ' ' with J J I Ex. 81 : :^ i^-i- T S i ^^ ^ f t I f ^ •1) v~». fej f j=5 f= u % 1° I i i m etc. 6 e 4 *l) This illustrates an important exception to 39 (which see) ; viz. a chord may be re- feated mer the accent, when it changes to the second Inversion (more rarely, to the fikst). 112, Rule IV. 128. The Ig may also be connected, before or after : e) With the Triad or chord of the 6th upon the next higher or next lower Basitone ; i. e. in Diatonic progreasion. 56 For illustration : CHORDS OF THE SIX-FOUR. *1). yj J,J „ J , JJ j , J„j i , J 1, J J , J ]J LrJ-i Ex. 83. C-Major AND Minor. f-rrr pf rt I i ggS^:g rt pot: t t I I « I I |8| |°|« .11. •i) Vl-Ia. An exception to Ex. 63, measure 4; justified by Inversion. —"a) These parallel 5ths are very tempting and imminent. More than ordinary caution must be exercised in all connections of I-II or II-I in Major. — ^*3) Six-four chords cannot appear in succession; they afford each other no support. — Comp. 119. 1 29. These three connections of the Tonic -6-4- chord constitute the basis upon which the movements of all 2d Inversions are regulated. Hence the following deductions are applicable to 2d Inversions in general : Rule I. Six-four chords can neither enter nor progress with a skif in the Bass-voice, excepting when a Repetition (Ex. 82, and paragr. 59). That is, the Bass is either stationary, or is limited to diatonic (step-wise) progres- sion. Rule II. Six-four chords must be connected with Triads or 6ths; not with other 6-4 chords. Rule III. A chord may be repeated over an accent -when it becomes a 2d Inversion. Rule IV. In six-four chords the Basstone (the chord-Fifth) is almost invariably doubled. See also 112, Rule 3. (Mat. Mus. Comp. §§ 141 — 149). 1 30. One exception to Rule I is applicable to the Tomc-6-^-chord only, in the major mode : viz., a skip in Bass from the II to tha I,, when the latter is accented. Thus : Bx. 84. n-i,. i J ^S2- l s i=i i J s § U f= I s CHORDS OF THE SIX-FOUR. 57 Lesson 17. A. Write out the following chord-progressions in at least four Major keys, in 4-part •pen Harmony: V-Ig-V ; I-Ia-Ii; IV | ^g-V ; Vl-Ia-Ii; IVi-Ia-VI; Hi | la-V; II | I2-V. B. Play all the above chords (excepting the last one) at sight, in the corresponding Minor keys. C. Construct an 8-measnre Period with the following series , in A-flat major, (4-4 Time) — , inserting the la at each *; (attention is again directed to 112, Rule I) : I I • V IVj I •IIi« V I Ii "I IV I *VS I I* Ii VI I V • IV III I *V**V I I H D* Construct 4-measure Phrases in G minor, A minor, F-sharp minor, and B-ilat minor, (3-4 Time), with the following chords: I | V-I-V | I-I-I | IV-I-V | I|| substituting Ig for I at option. E. Construct 4-measure Phrases in F and D major (4-4 Time) with the following chords : I I IVi-I-IIi-I-V I VI-IV-I-V I VI-I-I-I I I-V-I II substituting la for I wh«re desirable tr necessary. CHAPTER XVIII. Other Six-four Chords. Melodies. (Mat. Mus. Comp. §§ 151 — 160.) 131. As stated in 1 29,the other Six-four chords are regulated by the same principles of progression as the I^. But they are still weaker than the latter, and therefore more limited in their employment. The most effective andfrequent (to a certain extent "stereotype") connections are those here given : a. In connection with the Triad of the same Basstone : Ex. S5 C-Major. i i»i) ^=rf7 IhelV, a ^ J^ -#if^- i iiJ- '%' IIS §li Vr VI*2) ^ The IX, M J I S ^ ■4-* Mj -*-4 « The VI, m a^ -fTf ^2 1 I gfgav III ^ •i) In this connection the 6-4 chord is only an unaccented embellishment of the Triad represented by the j/'a/(C«o?'j'5ajJ/'<»«if; thus, the IV3 embellishes the I (like the Ig embellishes the V in Ex.81).— *2) The II3 embellishes the VI.— *3) This chord-cluster, in C major (with f>natural), is palpably intolerable. "Vim Dominant 6-4 chord is nearly, if not quite, the weakest of all. 58 OTHER SIX-FOUR CHORDS. 6. As Refetition : ■±3L Ex. 86. C-Major ■ ' The IV, rt-f-r- a. — F''^ a. T ^ — Tf Ho. VI J=J: ? y 88 8§ iriVj n Hg vivij Ttt J-J- 33E ^ ^^ I el Vf\ ^ '^ "^ f |g sag •i ) In conjunction with the preceding connection, Ex. 85. Comp. Ex. 82. c. In diatonic connection (with adjacent Basstones) , in the capacity of Passing Chords : I •!) •2) *3) IV»i) Ex. 87. C-Major, i »2) 1 J I •3) •1) fe J-J-)- h=^ •3) ^ I I I i i J VI, s i i I r i_j- ---#-^4 ^ !:>:«£• a 4 •5) ^ 1^ •3) »3) J I- J -i — ^ -^-^ trr rr °'i i-i^ -:;i 1=L m, 4- i ' j - ■=rff^ ro^' ^ytn^ OiaER SIX-FOUR CHORDS. 59 •l) Here the Six-four chord is a Passing chord {icoenX^A or unaccented) between a Triad and its ist Inversion (in the first measures, I — I^ with intermediate 6-4 chord).— •z) Here the 6-4 chord passes from one 6th to another 6th, in the same direction. Compare 119. *3) The 6-4 chord passes diatonically downward from a Triad; this connection is generally made, as here, within a single beat. — ^*4) The following four measures are a repetition and extension of the illustrations in the preceding chapter, and are introduced here only by way of analogy — .•5) These connections of the II2 are of doubtful quality. 1 32. It is not necessary to memorize all of these formulae, but merely the few simple principles from which they arise. The relative quality, or ad- missibility, of the various examples is very easily determined by testing the melodic conditions involved (with reference chiefly to 47 and 58) ; or — by EAR ! The latter test may safely be left, now, to the student who has mas tered the foregoing chapters. See Appendix A, Section 3. 1 33. The illustrations in Exs. 85, 86 and 87 refer to the major mode. But they are also applicable to minor, excepting where the II or III appears, and where the 6th and "/th steps of the scale are melodically connected (in any voice) ; see 90. 1 34. In general, the rhythmic location of a Six-four chord, on a light or a heavy beat, is entirely optional ; but there are cases where the distinction is necessary, viz., in the connections of Ex. 81 and Ex. 85 (the 6-4 chord pre- ceded by the sam.e Bass-tone) the 6-4 chord must be unaccented ; (see Ex. 81, note *5) ; in the connections of Ex. 84 the 6-4 chord must be accented. 135. When a Six-four chord occupies an accented beat, it evinces a strong inclination to progfress into the Triad of the same Basstone. Thus : J:^yTTV-'J^||J|-L ltt J| ] J I i i lJjj Ex. 88. -^w i J. # -«;V-Discords should be the First and best, class (in analogy with 30) ; but it must be considered, that the Tonic would inevitably forfeit its inde- pendence and the attribute of repose peculiarly essential to it as "Tonic," the instant it became alloyed with a dissonance. Hence the Tonic harmony is exclusively consonant, and for that reason the First-class Discords must be sought beyond the Tonic, namely, upon the Dominant. (When another 3d is added to the Tonic Triad, above or below, it ceases to be a Tonic-harmony and becomes a Third-class Discord I) — *2) The 3d and 4th Discord- classes are extremely rare, and scarcely maintain any appreciable connection with their Key. CHAPTER XIX. The Chord of the Dominant-Seventh. 1 40. The Chord of the Seventh upon the Dominant is ob- tained, then, by adding one higher 3d to the Dominant Triad. Its form and general treatment are identical in Major and Minor. In keeping with 64, Rule III, its harmonic inclination tends toward the Tonic harmonies, namely : the I itself, the I3, and the VI (see 96) chiefly in Triad-form. The Resolution of the Dom.-7th into the I is called Normal; that into the VI, Deceptive (comp. Ex. 69, note *3). In performing the Normal Reso- lution, the Fifth of the Dom.—yth is often omitted, and the Root doubled. For illustration : Normal Resolution V-I. Ex, C-Major AND Minor. K. 9 1 . I VIator ) { 1*4), ^3; cr'3; -g — Bg- *i) V *8) ■^ *2) ft rt fr -f i-^ -r-t-t J-f-^^ j I - -»■ i ■*■ ft DOMINANT-SEVENTH. 63 Deceptive Res. V-VI. *i) Marked thus: V: and called "Five-seven."— *2) The Fifth is omitted.— *3) The 7th, which may lie in any part, is here in Alto ; it descends to e according to 138, Rule I.— *4) If the wide skip in Tenor (measure 2) is to be avoided, the Fifth of one or the other of the chords must be omitted.— *s) It is a question whether the Leading-tone (* in Alto) can progress downward thus ; if not, one of the Fifths must be sacrificed.— *6) 138, Rule II ; therefore the Res. of the V into the 1st Inversion of the I is not practicable.— •;) Into the zd Inv. of the I, however, the V may resolve. Comp. 126 a, which may also read"V." — •8) These examples are all eqtially applicable to Major AND HiNOR; '\.K.the chord-yth de- scends either a WHOLE-STEP or a HALF-STEP I 141. The manner in which the Seventh of the Dominant is introduced is a'linost entirely optional. The following modes are however distinguished : Strict : diat. from above ; diat. from below ; prepared. Free : (with skips). Ex. 92. C-Major. *i) J U^A ^P Jr-. frn J- J a I ' IV I J *l) Here parallel 5ths occur, between Alto and Tenor ; they are perfectly admissible be- cause one of the 5ths (b-f) is not perfect. 56, Rule II, only forbids successive perfect sths I *2) N. B ! Comp. Ex. 41, note •4). — ^*3) A skip of 7 tones, as here in Soprano, can only be justified during a Repetition. See Appendix B, 8. Lesson 19. 7 7 A. Write out the V in every Major and Minor Key, with Its two Resolutions (V-I 7 and V-VI), in ordinary 4-part harmony. — B. Find and play these chords at the pianoforte in close harmony, without notes. — C. Write out the following Cadence formulae,ya a number of different Keys (Major or Minor), Time and Rhythm optional : I-V-V I III; IV-Ia-V I III; II-VI-V | I|l; III-IV-V | HI; VI-IIi-V 1 I|l; V-VI-IVi-V | 1]). H DOMINANT SEVENTH. CHAPTER XX. Dominant-Seventh, and its Inversions. (Mat. Mus. Comp. §§ 175—178). 1 42. The principle of Inversion is applied to 4-tone chords as well as to Triads, and is effected in the same manner, viz., by placing the Third, Fifth or Seventh in the Bass-part, instead of the Root. Review 108, 109 and no. 1 43. The effect of Inversion upon chords of the Seventh is as follow^s : a) When the Bass assumes the Third, the chord stands in First Inversion (as usual) ; the Root and Seventh lie above the Basstone in the intervals of a 6th and a 5th, wherefore the desigfnation "Chord of the Six-five" is adopted. (Comp. in). 6) When the Bass has the Fifth, the chord stands in Second Inversion ; the Root and Seventh lie respectively a 4th and 3d above the Basstone, giv- ing rise to the designation "Chord of the Four-three." (Comp. 124). c) When the Bass has the Seventh, the chord stands in Third Inversion ; the Root lies above the Basstone in the interval of a 2d, hence the designation "Chord of the Second." For illustration : Fund. Chord j (g-b-d-f); ist Inv. (b-d-f- 2D Inv. (d-f-g-b); 3D iNV. (f-g-b-d). Ex. 93. -«a- i »!) Sm ZSnr I *2) 2 «. *3) *i) The complete figuring (including the note d also) 'would be, 6 ; but it is only neces- sary to indicate the Hoot and Seventh, as these define both the name and quality of the chord. These two tones (in this case f-g) are contiguous, and therefore easily distinguishable. In the ist Inv. they are at the top, in the 2d Inv. in the middle, and in the 3d Inv. at the bottom of the chord-form; thus: -g«g- ZS!»Z *2) Full figuring 4 J review note *!). *3) Full figuring 4. review note *i). Observe the distinction between the fundamental chord and the 3d Inversion ; in the former, the 7th stands above, and in the latter below, the original Triad ? DOM IN ANT-SEVENTH. 65 1 4'4-. These various forms of the Dom. -seventh are extremely impor- tant in Harmony, and though differing apparently but very little in effect, they actually possess, respectively, very marked individual characteristics, which are of great significance to the discriminating composer, (so much so, that certain Masters are noted for their preference for, or peculiar treatment of, one or the other form of Inversion). Rule I. The chord-seventh resolves as before, diatonically dovantuard. Rule II. In the Inversions no Interval should be emitted. Rule III. The Inversions of the V are limited almost exclusively to the 7 Normal Resolution (into I or I^) ; i. e. only V itself can pass into VI. Ex. 84. C-Major / AND Minor. J I istlnv. (Vi)»i) 2d Inv. (Va). 3dInv.(V,). i VI i I I Ii •i) Vi — spoken "Five-seven-one." — *i) An awkward skip from the Leading-tone (in Bass).— *3) The Deceptive Resolution of the \st Inversion of the V, into the VI, is pos- sible in Major only, but not frequent. The parallel 5ths which must result, (in this case they are in Alto and Bass) are not inadmissible, because one of them (b-f) is not n '^ m ii-i -,nf^ ^ff ! * -^= P=^ E£? \^ i •2) 2- "a) l"^~r[f~r ^~F p^^g^=^^ -«- *i) ^^ •3) ! h I I =J6c: IzT-e- ^^FFt a) ffli 1^=^ ^•"^ *i) #^^^ ^ ?=*: jM-x|| p^^»--* ^ i i* Pf rn^+^^ ^ FF?=W^ft«^ Si ?=s= 3t ^E *^?±^ i^ ^^ ^^F^ ^ i ^ «!^ •i ) Slurs usually indicate that the tones belong to the same chord. The choice (and num- ber ) of changes in chord/orw are optional.— "2 ) Here the 4th step (e-flat) is to be harmon- ized with the V, although it does ttot descend diatonieally into the 3d step ( as conditioned in 146, Secondly ). The reasons are obvious. — ^"3 ) A different Basstone for each repetition of the Soprano note. — ^"4 ) Pianoforte style. Change lower voices at each slur. To This Lesson, add Appendix C, No. 6. Lesson 24. Construct 4-measure Phrases with the following chords, in puple and\Triple Time alter- nately, and in at least 4 alternate major and minor Keys ; the Rhythm, the hord-form, and the Inversions { Bass ) of every K optional, as usual. See directions, Lesson 14 A ; Preface, If I-V-V-V-I-V-I-IV-IIi-V-V-V-V-I. DOMINANT-SEVENTH. 71 CHAPTER XXIII. Dom. -Seventh. Other Licences. (Mat. Mus. Comp. §§ 182—185). 1 48. Besides the above Licences, naturally attendant upon chord-repe- tition, there are two others of a more irregular nature, viz., the stationary seventh, and the ascending resolution. 1 49. The chord-seventh may be held (stationary) in the same part, while the V progresses into either Subdominant chord (IV or II). The , . 77 harmonic progressions V-IV, and V-II, are exceptions to 64, Rule III ; compare Ex. 45, and Ex. 61, note •5) ; but they are rendered feasible by the connecting-link which the stationary Seventh affords. Being "irregular" however, they require subsequent justification by an immediate (or early) return to the Dominant harmony. (See again the context of Ex. 45). Rule. The chord-seventh, during this change of harmony, must remain undisturbed in the same voice, and must not be doubled. For example : •0 ^^ Ex. 99. J. 1 EEE^ ^=:i •l) =rr=^ -4- i J -i,.U- J i 1 t- ^-IVj-^ I s e 4 fi ? n *. ^=^ •2) •2) ^=£^ ' 8 ! J J J J4 * =£ ^ J i i f=QT=f J i J r J i I I I T nj-\ IV IV I •3) •4) 7 7 *i) After the irregular progression V-IV, the V returns. — *2) The irregular progression is followed by a Tonic chord (I or VI) ; but the V soon after reappears. — *3) The f in Bass disturbs the stationary 7th, and is very objectionable. Comp. 138, Rule II.— *4) Contrary to the Rule. 1 50. The chord-seventh may ascend (and resolve) diatonically, •J2 DOMINANT-SEVENTH. when the Bass- fart accompanies it in parallel thirds. For illustration t •i) Ex. lOO. *^rF t ^ ^ r T ^Ei r 7 r •i) See Ex. 95, note "i). ^ kl Lesson 25. A. Write out the following chords (open 4-part harmony, as usual) in alternate major T 7 and minor Keys, using uniform quarter-notes or half-notes: — V-IVj-Vi-V | I; Vi-IVa-Va-Ii; Vi-IIg-V; V3-IV-VB-V1 1 1; Va-II-Vij V-IVi-Ia-Vs-Ii; Vi-V-IIa- VI; I-Vs-Vg-IVa-I. B. And harmonize the following Melodies : I Z^ -&- -9- -&- -&- -S- i»qcs: sa m^ *i) *2) •2) i tSr- ^^^ =F^^«= =#t: =i=p: % E^?e *t I *3) •4) •5) *i) Tenor; add other 3 parts. — *z) Tonic 6-4-chord; see 126, second clause. — ^•3) Ac- cording to Ex. 99.— *4) Three Basstones.— *5) According to Ex. 100. To This Lesson, add Appendix C, No. 7. CHAPTER XXIV. The Incomplete Dom. -Seventh. (Mat. Mus. Comp. §§ 186—189). 151. The term '■'■ Incomplete' is employed by the Author to signify the omission of the Root of a chord. 152. The chord of the Doin.-S«yenth is very frequently used thus, without its Boot, as TBIAS UPON THE LEASIKG-TOITE. INCOMPLETE DOMINANT-SEVENTH. 73 (See Ex. 17, note *2). Thus: Ex. 101. C-Major AND Minor. i C ompl . V ; Inversions ; 7 7 Incomplete V(Vo)»i) - g^-g ^"- t *i) The o denotes the Incomplete form. 1 53. The strongest proofs that the Leading-tone Triad is simply an Incomplete Dominant- Seventh consist in the facts, that it contains the most essentially characteristic feature of all Dom. harmonies, viz. the Leading-tone ; and that its harmonic movements coincide in every respect with 7 Ihose of the Complete 7. 7 1 54. The Vo is a Diminished Triad (because its Fifth is diminished) ; therefore, like the II of the minor mode, it is very seldom used in the Triad-form (see 102 a). The best form of all Diminished Triads is the Ist Inversion (chord of the 6th). The 2d Inversion is also available, but inferior to the ist. 7 155. Rule I. The Vo is alike in Major and Minor, both in form and 7 general treatment. Its progressions correspond to those of the V itself. Rule II. Any Interval may be doubled, excepting the Leading-tone. Rule III. The dissonance (dim. 5th), generally descends, but may also ascend. For illustration : e e 6 a 4 ,44, •1) Triad-form; rare. — *2) ist Inversion. — ^»3) The dim. 5th (f) is doubled; (/is a Principal tone of the scale ; comp. 51, Rule) ; one ascends and the other descends.— *4) Comp. Ex. 60, note *4). — *5) Comp. Ex. 67. — *6) The 2d Inversion; treated like any other 6-4 chord. — *^) A succession of 6-4-chords, contrary to 1 29, Rule II. This is al- ways permitted when one of the 6-4 chords is a Discord, as here. — *8) Also applicable to Minor, excepting where the 6th and 7th steps are melodically connected, — as in measures 4; S. 6, 7- 74 INCOMPLETE DOMINANT-SEVENTH. 156. This chord (Vq of C) will be found to coincide exactly with the II of the Relative Minor scale, thus : i -== * g i J=i !'' Stationary Dissonance: •4) •1) When the 9th progresses thus into the 7th, the latter, in descending, resolves them both. In the next measure the 9th leaps downward into the Leading-tone ; comp. Ex. 98 note *5). — *2) The 6th step (a) as Dom.-Ninth, should not progress upward (into b), for obvious reasons. — ^*3) In such rapid succession this may be justifiable. — *4) A Dom. chord ; g comp. Ex. 99, note *i). The next measure, V-IV-I, is however also possible. — ^*5) These transitions into II or VI are doubtful. Additional illustrations : Grieg. Schumann. Ex. 1 06, 78 DOMINANT-NINTH. Lesson 28. B A. Write out the V and Vq in every major Key. B. Harmonize the following Major Melodiec, with reference to this summarized table (comp. Lesson 21) : Steps : C-Major. ^J .3 -^ '■^—•s- .O- N. Bl -N.BI S=Sji^ -gT^'g- ^5=^: ■^-tgr •to< XT •*<>• TT " Yo IV in-" (O Vn T IT^* 7 •"• .<.. 'o v-V, i ^ *i) t=^ i= s^ -^r^=^^ssmu m w ttt:^=±=y ^ I i^^p^^^ s -» — » - ^ tiS rat tf %* i> r? - fg rg fa m ^ ■7 ^W-r ^ — ^^ \ r r -^ \ — \ 4^_i_4M — ^— f--s^_J ^-W-^ -^ =-z^l i ^ f^^ -•-r^ Eg ^fe I 5 *i ) Two Basstones. — Also re-harmonize Lesson 22, No. 2. CHAPTER XXVI. Dominant-Ninth in Minor. 1 63. The ninth of the Dominant, being the 6iA step of the scale, un- dergoes modification in the Minor mode (85), so that the chord of the Z7(7x».- DOMINANT-NINTH IN MINOR. 79 ninth, unlike all other Dominant chords, differs externally in Major and Minor (Comp. 88, 140, 155 Rule I). Thus: )^. iiE Maj. V. Min. V. 1 64. The transformation of the 9th from a major to a minor interval does not alter, but rather confirms, its obligations, and facilitates its treatment in certain respects. The Rules given in 161, and in 162 (which carefully review) are also valid for the Minor Dom.-Ninth, with one exception, viz., THE NINTH OF THE MINOR CHORD may Ue in EITHER MIDDLE VOICE, quite as well as in the Soprano. But it is very rarely placed in the Bass; and, as usual, is never less than a gthfrom the Root (in the Complete chord). For illustration: Ex. 107. C-MlNOR. Complete V. (Compare Ex. 104 a). J I I ■ ■ , , ■ J J S3 IS i t — r E J i PF ^ Ji ^ W A V V •i) The 3d Inv. of the Cefw/Zrff Dom.-Ninth (i. e. 7thinBaas). As extraordinary as this chord looks (and sounds), it is nevertheless perfectly correct. — *2) The ist Inv. of the Compl. V. See note *i). These unusual forms are somewhat more easily obtained in Minor than in Major. — *3) Stationary dissonances. Here a 6-4 chord is exceptionally introduced withaleap in Bass (Comp. 129, Rule I ; and 130). 8o DIMINISHED-SEVENTH. The Chord of the Diminished-Seventh. (Mat. Mus. Comp. 165. i 203—205). The Incomplete Bom -Jfinth, or the chord of the Seventh upon the Leading-tone in the Minor Mode, is a CHOBD OF THE DIMINISHED-SEVENTH. (So-called because it is the only legitimate chord which contains the pe- culiar interval of a dim. 7th) . It is one of the most frequent and important forms of the Dom. harmony, distinguished alike for its fascinating effect and its almost incredible flexibility. (See Ex. 129, note *i). 1 66. The treatment of the chord of the Dim. 7th coincides with that of the Compl. V. The 9th (i. e. the 7th from the Leading-tone) may lie in any voice, either above or below the Leading-tone (but it should never- theless be avoided in the Bass voice, as much as possible) ; and it resolves diatonically downward. For illustration : «. IDS.) Ex, C-MlNOR. Diminished 7th (Vo) ^ T-T" E b-i p [ ^P-^ r' I ' A tez -r -^1 r-^ ^F=F= IVa 1 i LU=J=i: •3) EfcJt ■ ^^ f ^ i i i^ f r Ji EE ?^ VIx ' N. B. a e 3 4, 7 V *i) The false melodic progression from the 6th step to the 7th, in Minor (see 90), is here iustified by Repetition. — *2) Even in Minor, where one of the 5ths is imperfect, these paral- lels are deprecated. Comp. Ex. 104, note "g). — *3) The f in Bass is actually the 7th of the chord, wherefore its best progression is diatonically downward. But comp. Ex. loz, measure 6 (alto), and 155, Rule III. — ^*4) The original 9th in Bass is objectionable, because it gives the weakest chord-form. It is best in Repetitions. DIMINISHED-SEVENTH. 8i Additional illustration, for Analysis : Adagio. Ex. I09 V ^ ^ la I9V I„ V -T^ ^ I, la VI, Lesson 29. 9 A. Write out the V complete in every Minor Key.— B. Write out the chord of the Dim. 7th, and its Inversions, in every minor l^arC. Find and play these chords at the Piano- forte, without notes. Re-harmonize Lesson ii, Nos 4, 5, 6; 16, Nos. 4, 7; 18, Nos. 4, 7; 21, No. 4; 22, No. 4. 9 B, Harmonize the following Minor Melodies, using the V (occasionally Complete but chiefly Incomplete ) at each * : i ^=C5 Mg^jJiE^ ^ trt :t=t i • ^ ±ji: itr a ^— .'g— .g- -+- *i) ^^^-fff- 3 fil (2- iE :»^ fl< zb- i 3- •2) •2) ^ :Jt5 w- t«*: ^^ j/jjina ^ ^ ^ fie p=ti: 82 DIMINISHED-SEVENTH. ^ m mp= ^■ika ^^-^^j*^ •3) -^ i •i) Two Bassnotes. — *2) Lower voices J. — ^•3) Lower voices J "1 "1 , and the same i the next measure. CHAPTER XXVII. Unfigured Basses. I 6 T. In adding the three upper parts to an Unfigured Bass, the same general rules must be observed as in adding three lower voices to a given Mel- ody. The two processes, though inverse, are nearly identical. The follow- ing table (which compare carefully with that given in Lesson 28) will there- fore suffice : Ex. 1 1 0. C-Major AND Minor. (nwi.) •o (nj IV "1 S5 Si -^ ud fi?- dte -g-«°» O -^ u Steps : T \> o V ) (i) 1 68. Besides which, however, the following generalities must be recalled and borne in mind : — The Bassnote is not as likely to be the (^oxA-Fifth, as it is to be the Root, Third 7 or Seventh. — The Leading-tone is not likely to be a "Root apparent" (see 154), as Vq. And in Minor, neither the 2d nor 3d steps are likely to be Roots. In all Minor Basses, use the Incomplete Dom.-Ninth (chord of the Dim. 7th ) very freely. Lesson 3 1 . Add Soprano ( and then Alto and Tenor ) to the following Basses ; See Appendix B, and Preface, I : '•*3) •4) '^ •1) _ «i) ;gg- g» ( g 2- UNFIGURED BASSES. 83 3- *S) §& |±±±: f^'j | Jj^jlVll l !!X^^J%%l J. •!) •!) •!) »<^J | J Jf i f rnr,if i J-Lnrri"r.^ ^ •i) •i) ^^ *i) m jjji'^ ji j J * f ^=*— # •ij Two melody notes. — *2) One Melody-note to each slur. — *3) Stems down. *4) Basses I, 2 and 5 in mtnor also.— *5) All minor Basses in two ways. Lesson 32. 1- *l) *l) *I) ,^2. -•- , •3) •4) ^^ m& Qf^ =^ * * s* %^^^ ^ (6) «^- lT^fp ^ g feg^Q=^ ji^ggp :^ i ^ ¥r F^- (t) (I) (?)(2) ^V.^rJJ | irTf]UTI[^ 6. •2) S^ i^ i"i ^^s ^:^[[; l »:J^IJJi:^i l frF jj i^^> ip^i7iiQ^ p ^ w ? CZTTT *i} Three Melody notes.— ^2) Close Harmony. Strict attention te tie tlurs; oat lielodj' note to each. •3 ) Also in miner. — '4 ) In two ways. 8+ DIMINISHED-SEVENTH. CHAPTER XXVIII. Chord of the Diminished-Seventh, Continued. 169. In working out the next lesson, the student will put the broadest possible construction upon the term "Dom.", and determine at his own dis- 7 7 9 9 cretion the form (V, V, Vq, V, or V„) and the Inversion (Bassnote) of each Dom. -chord, giving preference, however, to the Chord of the Dim.-Seventh. The Rhythm (arrangement and repetition of the given chords in the meas- ure and beat) is also quite optional. The following example will serve as a model : Given the chords Solution : I I Dom. I I-IV I la-Dom. | I || D minor (or major), Duple Time. S=^ Ex. 111. E minor, Triple Time. i ^ J^-^ ^t s: i ^=^ i p^ -j-j— ^ i^E J-i-^ i etc. ^ r=f-- f „ ^ IT V ^ ^ ^ r *i) Minor only. In major the Tenor might take a or ;. Lesson 33. A. Construct two Phrases (at le^t) in different ilf2»<;r keys (alternating between Duple and Triple Time) with each of the following chord-series (filling out the measures with Repk- TITIONS); follow closely the directions given in Lesson 14 A, and see Preface, I : SECOND-CLASS DISCORDS. 85 (4 *"«* i) I-I>on».-I I Dom.-VI-Dom. | I-Dom.-I-IIi | Dom.-I y ($ and I) I-IV I Doin.-IV-Dom. | I-II-Dom. | I || (5 and I) I I Dom. | I-IIj | la-Dom. | I 1| B. Construct two (or more) Periods, in Minor, with the following chords, using the Dim. Seventh at each *; everything else optional : (I and I) I-*-I I "-IV-V | I-*-I | V | «-IV-* | • «-I 1 II1-I3-V 1 1 || CHAPTER XXIX. Second-Class Discords. (Mat. Mus. Comp. §§ 206 — 211). 1 TO. The fundamental tone of the 2d Discord-class must be sought one perfect 5th higher than the Dominant, or two perfect 5ths above the Tonic; it is therefore the Second step of the Scale. Review Ex. 90, and context. The 2d class comprises the same number and forms of chords as the Dominant class, viz., the chord of the Seventh, Complete and Incom- plete ; and the chord of the Ninth, Complete and Incomplete (to which may be added, the consonant 3-tone chord, or Triad). Thus: Ex. 1 1 2. C-Major. i 2d~Dom. Concord. Discords. •2) lYz -»- 3E -W- •i)i OOB^. U InoonpL or IV *3) =i= S riV •1) "Two-SEVEN."— *2) The II without its Root proves to be the Subdominant Triad, the IV 1 See next paragraph. — *3) Called "Four-seven." 171. It is now necessary to revert to Ex. 17, note *\, and 93, (which see), and elucidate the apparent contradictions which are presented by the Subdominant or Second-class body of chords. About the Discords of this Class there is no uncertainty, but the Concords (II and IV) as has been seen, do not, in practice, preserve their actual theoretical co-relations with full emphasis. From the above Example it is now theoretically apparent that the Triad II is the Principal representative of the "Subdominant" harmony, while the IV is only an Incomplete 7 form of the II. This confirms the theory that no chord-Root can be accepted upon any pep feet 5th BELOW the Keynote. Practically considered, preference is likely to be given to the IV, because of its sM^fnat proximity to the Tonic. The degree of prominence which eithe' of these two equally-poised chords assumes, depends upon the accidental emphasis given to 86 SECOND-CLASS DISCORDS. the tones d or/ respectively. The following table illustrates this (in C major), and demon* strates the coincidence of the Sub.-Dominant with the 2d-class chords, in the tones f-a-c : Third rank — Second-Dom. (7th) d-F-A-c. Sth Second rank — Dominant g-b-d. 5th 5^- First rank — Tonic C-E-G. 5th (Third rank ?) — Subdominant F-A-C. One incontestable and significant deduction for the student is, that the Subdtminant or Second-Dom. Chords bear the same relation to the Dominant harmonies, that the Dom. does to the Tonic. Therefore the term "zd-Dominant" is peculiarly indicative, and preferable to "Sub- dominant." 1 72. The distinctive external characteristic of fundamental zd-class chords is their Minor Third — , in C major the tone f instead of f-sharp : This interval distinguishes them from the Dominant or ist-class chords, whose Major Third, being the Leading-tone, is their most significant feature. 173. The chord of the 7th upon the Second step and its Inversions, (to which this Lesson will be limited), resolve most naturally into the preced- ing chord-class, viz., Into the Dominant Chords, whereby the chord-seventh de- scends diatonically. as usual. Thus: Ex. 1 1 3. C-Major AND Minor. m *i) (5) ^ /^)-g- ^ ft K fta fi. =4: ±S J-4- ■X.J T-J J J J 11 1 (J)i- •3) - / - - i - -f-t ^ fc m -i — ^ 7 7 Vo V SECOND-CLASS DISCORDS. 87 •l) A-natural in major, aaAa-flat in minor.— •2) These first five measures illustrate the Resolution of the II into each of the Jive Dom. chord-forms.— *i) The 2d Inv. of the II is much the best in Minor. Otherwise no distinction whatever is made between the two modes. 7 1 74. The II and its Inversions, like the Dom. -Discords, are also en- titled to the Licences of Repetition (comp. 147), and those involving the stationary Seventh (comp. 149). Por the progressions with cto^oTiar^ Seventh (into the Tonio chords I or VI) the 2d-class Discords all evince great preference. For illustration : Ex. 1 14. C-Major AND Minor. \ n ^ ^ ^ Jri f iij iU *4) «— t: ■ -^ i J i : T7T •3) 2 r-T :^:: 3 a I *i) A curious example of parallel 5ths (perfect) in both pairs of upper and lower parts. They axe justified by chord Repetition! — *2) It is not unusual for the 7th of the II7 to leap (fozvmi/art/thus to the Dominant. Comp. 150, and consider that here it is the Tonic itself. •3) Comp. Ex. 84. — ^•4) Wrong, like Ex. 99, note *3), which see. 1 75. The Introduction of the dissonances in 2d-class chords demands closer attention and more restriction than in Dominant-chords. Review Ex. 7 92, and Ex. 95, and limit the Seventh of the II to strict Introduction, as much as possible. Thus : Repetition of chord : Ex. 1 1 5. GMajor AND Minor. % % . I VI n •l) Ex. 83, note •2). 1 76. Especially unique is the Introduction of these chords after Dom- inant HARMONIES, thus : V-II, V-II, etc. This is merely another version of 149 (which review), and involves the following Rules: a) The 7th (or 9th) of the Dom. remains ttationary. 88 SECOND-CLASS DISCORDS. b) After the 2d-claBs chord, a Dom.-chord 7nust return, in some form or other. For illustration : Ex. 1 16. C-Major. 7 T 7 7 V fl V i 2 § V, *i) These first 2 measures are applicable to major and minor. But the others demand modification, as usual, wherever the 6th and 7th steps are melodically connected. — *2) Two stationary 7ths in succession are objectionable. Further illustration : Presto. Ex. 1 17. F# Min. I i i I ^^ ^3=^=^=^ 7 ^x Mendelssoh n. Op. 38 . Lesson 34. Write out the following 8 groups of chords in 8 different Keys (major and minor alternately), 7 without regard to Rhythm; the 5th of the H itself may be omitted; all Inversions not spec!' fied are optional • be careful to resolve all the Sevenths I I_II_^_VI; VI-Hi-Va-Ii; I^-IIi-Ia-V; I-II2-V0-I1; I-ili-VIa-il-Yo-I; I-IVa-II,- T T 'J 1 9 1 777770 7 «• Vi-I; I-Va-IT-V,-Il3-Vo-Vs-Ii; I-V-IIa-V-Va-IIi-Vo-Ii-II-Ii. SECOND-CLASS DISCORDS. 89 Lesson 35. Re-harmonize Lesson ii, Nos. 3, 5; 13, No. 3; 18, No. 4; 21, No. 2; 27, No. 4; 28, No. i. 7 Harmonize the following melodies, introducing some {optional) form of the II at each »: I. f^rp^=3=^ B^ K^'-W- 3t:± ^ :Up: =i=^ ^^ F— ^ ±=ai ^ f^p^ffl =^ ^ CHAPTER XXX. other 2d-CIass Discords. Discords of the 3d and 4th Class. ITT. The chord of the Ninth upon the 2d Scale-step is extremely rare in its Cotnplete form, but available and important without its Root, as Chord 7 OF THE Seventh on the 4TH Step (IV). Its treatment corresponds in 7 every essential particular to that of the II, excepting that it is more rigorous. ■Licences of Introduction or Resolution are almost entirely precluded , Review 173, 174 and 176, with reference to the following illustrations: Regular Resolution. N. B! Ex. 1 1 8. C-Major AND Minor. i *3) ZISZ W- Ssi— ee- 8 = 7 i J7 JL n IV iVj rsTa IV3 ^ nL^r I I ^^ ■f-«r- *I) TTT 3=t==t i~Jj i *2) / ■•-Tr« 4 i^ ^ Stationary Dissonance. Dom.-IntroducHon. ^^- f=f ^ i I rrr J i J ^^j- J ^ ^ ^^^ 7 IVi f^. iV„ ■? — h—v 9° THIRD-CLASS DISCORDS. •i) The IV cannot resolve into the TVtin/V without danger of these parallel 5ths. There- fore the chord usually resolves into the Dom.-SeventA or Ninth. — *z) The Inversions of the 7 IV are seldom employed. — ^"3) In minor, e and a become e-flat and a-flat. 1 78. Of the 3D AND 4TH-CLASS Discords (see Ex. 90), the most 7 important is the chord of the Seventh on the 6th step (VI). Its connections are as follows : fi^fi ^^ hJJ^ *i) Principally in Major; but also in Minor, where the melodic connection of the 6th and 7th steps can be avoided. — *2) 3d-class chords resolve "regularly" into those of the 2d-class (II, II, etc). — ^*3) Analogous to 176. — ^•4) An "irregular" (but very common) resolution, into Dom.-^oxAs. 1 T9. All the rest of these remote Discords are least objectionable, be- cause most comprehensible, when used in Seojience-relations with better chords. Review carefully 120, 121 and 122, with their examples. The possibilities here are far more numerous than in the former lessons (among Concords), because the sum of chord-forms and Inversions is much greater. (But observe 122 f ). All questions of quality or admissibility must be left exclusively to the ear. See 132. A few random examples will suffice : Ex. 120. C-Major. ^ ^ m M ? 7 7 niTi 7 7 n V f & ^ -ffl- 7 7 I IV f= ^ -J- f- m r r F=P ^S rr f U ^ 7 V 7 VI SEQUENCES. 9> i i=j=i j.j jj^ j^ii ±^fc^ ^ P J ^^ i i. J. a*s ^ =p=i= ^^ o n o m VI 7 n / i L^ j=^ 7 9 VI Vo i i fl ^FT=:3= w p r i J — i- .; iiJ-U i^ ?^^ ^^^ f^ p^ Further illustration : Presto. P Ex. 121. AT THE »i_^.. . - Piano- < ^^^''^- ^ FORTB. ^^ il^ I >^- ^^^fe i Schumann. Op. 20. ^^ Ei ^3 ^^a ^ ^ s ^ ^s j=^ &- ^I- *i) When the tempo is so rapid, successive beats, of similar harmonic import, ilenJ ; therefore these chords are defined by grouping iatA beats (represented by each Bass-figure) together. — *2) The figure in ^-notes continues throughout, as in the first and last measures. The pupil is to play it in its correct farm I 92 SEQUENCES. 1 80. One extraordinary chord of the 4th Discord-class claims special mention, viz., the Triad upon the 3D Step, in the Minor Mode. It is an Augmented Triad (102 b), and is treated thus : Ex. 122. C-MlNOR. 1^ T *■ t ■ ' ••■ ^ iv-%'i (Mat. Mus. Comp. §§ 212 — 219; 220; 221). Lesson 36. A. Continue the Sequences in Ex. 120 a, b, d, e, f, g, a few measures farther, in exact re- percussion. — Bi Harmonize the following Melodies : t «# I. •!) ^ 2. *l) ^= ^^ l^. ¥^-0- -ft — •' =ltt i ^ ^ ^ :»^ !^ * I 3- *i) H=^ ^4^ J-^-4^ ^ 4^— N ^=^=^^^y^ -•— z;^ fcttst 7 I IIV m V VI •2) fe^^'J^J^^a&rffiEa a p VI IVi f^ 7 7 •i) At each • a 2d-class Discord (II or IV). — *2) The brackets indicate Sequences. Also re-hannonize Lesson 22, No. 2. DIVISION THREE. KEY -RELATIONS AND ASSOCIATIONS (MODULATION). CHAPTER XXXI, The System of Keys and Modes. (Mat. Mus. Comp. §§ 262 — 269]. 181. The harmonic principle according to which the tones of a Key or Scale are singled out from the innumerable range of musical sounds was demonstrated in 9 and 10, which review. The number of tones thus associ- ated to form a harmonious group or family was confined to seven, in order to exclude any contradictory element. But when the tones are singled out (con- formably with the same principle of tone-relation) as independent Key-notes, there is theoretically (and actually) no limit to the number, because a pro- gressive series of absolutely perfect Jths is infinite, never returning to corroborate the initial tone. Practically, however, a limit is] assumed at that point in the series where the assonance with the first tone is so nearly comflete, that the necessary adjustment is effected almost or quite impercep- tibly, viz., at the i2th tone. Thus (beginning, for example, with the tone G-flat, and ascending in perfect 5ths) : G-flat-D-flat-A-flat-E-flat-B-flat-F-natural-C-G-D-A-E-B-F-sharp 1 a 3 4 6 6789 10 11 la The last (izth) tone impresses the ear so nearly like the first one, that the' ACTUAL difference in pitch can easily be ignored, in favor of a complete or closed circuit of tones. 182. The above tones constitute the Keynotes or Tonics of the 1 2 Majoi Keys (or 13, if both extremes are included) of our modern Tone-system. The following circular arrangement displays their relative locations, their Signatures, and (upon the concentric inner circle) their Relative Minor Modes, in a clear and accurate manner. The Major Keys are indicated by Capitals, the Minor Keys by small letters : . -^ ■' OS) 94 SYSTEM OF KEYS AND MODES. Ex. 123. C •i ) The distance from point to point is a perfect 5th, or Harmonic Degree, along each line- Major and Minor. The difference between the size of the upper and lower arc serves to il- lustrate the actual difference between G-flat and F-sharp (E-flat and D-sharp), but is inten" tionally exaggerated. 183. The degree of ^ey-relationship being determined, like all other tone-relations, by the interval of the perfect 5th (see 8 and 30), it is obvious that the degree of relation of one Key to any other is simply a question of distance along the lines of the above chart. For example, the Keys of G and F are nearest related to C, whereas D is two degrees, E-flat three degrees, F-sharp six degrees removed from C. This corroborates the natural assumption that those Keys must be most closely related which have the least number of differentiating tones : The comparison of the C and G scales exhibits only one single differentiating tone (F-sharp); all the rest of the tones are common to both of these Keys. This last assump- tion is the hypothesis upon which the location of the Minor modes depends, in the above chart, and the determination of the Relative (review 89) Minor Mode in general. Thus, the Key of a minor, being the "Aeolian" of C major, and agreeing in one of its melodic forms exactly with the scale of C, is placed opposite C major as its most intimate attendant. See Ex. 58, note *i). 184. Each Key is seen to be surrounded or attended by five proximate Keys, called its Next-related or Attendant Keys. For example: From C Major., (natural scale), I . The Relative Key, a Minor (natural scale) ; MODULATION. 95 2. The Dominant Key, G Major (i sharp scale) ; 3. The Relative of the Dominant Key, e Minor (i sharp scale) ; 4. The Subdominant Key, F" Major (i flat scale) ; 5. The Relative of the Subdom. Key, d Minor (i flat scale). They are most readily determined BY Signature, because the comparison of Signatures instantly reveals the degree of similarity, or difference, between any two Keys. The Next-re- lated Keys, consequently, are indicated by next-related Signatures, i. e. such as do not differ by more than one accidental. All the rest of the 24 major and minor Keys are more or \e,%& foreign to the Key of C. The so-called Remotely-related Keys will be defined later. Modulation. (Mat. Mus. Comp. §§ 270—277). 185. Modulation is the act oi progressing from one Key or Mode into another, or of exchanging one Key for another. The exchange is effected by the substitution or transformation of one or more of the members of the original group into agreement with the cluster of tone-relations constituting the desired Key. 186. The PROCESS OF Modulation, while subject in general to the foregoing rules of part-writing, is furthermore regulated by the following special rules : •» EULE I. Modulations are limited ordinarily to the five next- related Keys. A transition which extends ^ej)/o«fl? /i4c next Signature is called "Extra- neous," and is always subject to special conditions. RULE II. The desired Key is most easily and regularly reached through one of its Dominant ilst-olass) chords 770 9 (V, V, Vo, V or Vo in any form). Rule III. The Key may also be attacked at any Second-class chord 7 7 (II, II, IV, IV) in any form. But of the remaining class, i. e. the Tonic chords, only one single representative is valid as legitimate modulatory chord, namely, the Tonic Six-four chord, on an accented beat. EULE IV. It is always best to close the original Key upon one of its Tonic chords ( I or VI in the usual forms). It is also possible to abandon a Key at some other, non-Tonic, chord, but often awkward, and always conditional. Hence the following fundamental modulatory formula (which will be the pupil's sole guide for a while) : Abandon the first Key at one of its Tonic chords, and enter the desired Key through its Dominant class — , more rarely through its Second class, or through the accented I,. 96 MODULATION. Illustration of these Rules : Ex. 124. FromC to G.*5) Rule II and Rule IV. *z) ^^ 4 •i) Pf JJ ? i ^ Ff J^ ^ r-ff ii iii «^ IjGV I G^a OlaGVo Rule III. »3) i tfi iit^g Mi M a tzfcii i ij.il i I li 1;^?= i Ji r f I I . Eztizb iS3 3= FS^ p^-- ^ OVIGV i ±? OIiGVo u oil an Vi •4) i4=i ^-^ *— ^ i=^i itztt f ' wi e r r rr ij-i -w iJi I m^^^ 01 an V •i ) The modulatory transition is eflfected by the connection of the two chords under the I '; the first one is the Ii of the original Key (C), which brings the latter to a su£S- ciently marked c/ose, leaving no impediment to the "change of Key," or "modulatory digres- sion"; the second of the two chords ushers in the desired Key (G), through the Leading-tone agency of its Dominant chord. — *2) It is evident that the rhythmical location of the modu- latory chords (on heavy or light beats)is of comparatively little moment. — ^*3) The new Key (G) is entered through one of its Second-class chords (the II); this resolves into the I)omitiant,3.ndi therefore merely serves to protract the modulatory process. — *^) G is entered through its n-V II Dl-eVoll El-fit V II g«I-E V II bH-GbVo ll C I-Bbla-VII bl-fSIa-Vll *^V Resolve the last chord of each group into its I. — CHAPTER XXXII. Next-Related Modulations. Continued. 188. A modulation is distinguished as Complete, when the prospec- tive Key becomes the final aim of the digression, and is confirmed as such by a complete Perfect Cadence in the new Scale. Such transitions are nat- Hrally made upon a somewhat broader plan than "trao'iient" modulations (189), and must absorb at least a whole Phrase or Period. 98 NEXT-RELATED MODULATIONS. Lesson 38. Harmonize the following Melodies, introducing the modulatory transition at the * : 1. • 2. fc* ^ X '^^^ ^m -ft-—»- ^ ■•■■li- ^S=ts AtofS ^ 3- f to A^. ^JE^^ ■d — » :ttt •i) Eb-Bb. gBfe^^ftN=F=^y^f#f^ i m f rFF ^ri b-e. ^^ ft^ ^ ^ F¥^ ^ft=:3 ^ 3^ E-A. g-d- i^3 5^3 E^ «=^=^ i ^^^^:^=^ -lt^r-*-li •0 *i) Either a Dom. chord, or a zd-class chord (of new Key), at option. Lesson 39. Harmonize the following Melodies, as in Lesson 38; each in at least two different ways : I. • i^ t^ < g . •- -»- sz ■ e > . m it^ Gt7-bt>. «i) i fci ^ ^ U J J L,. l| Vf!f^=^ ^ *2) B-ctt. jt g - fi i- g«-F*- ■^^^ '3) bb-Gb. •3) ^ 7 7 •i) 2d-class chord of new Key.— "z) These two a's may be either Ij-IV or IV-Ia of the new Key.— *3) Dominant or 2d-class of new Key, at option. NEXT-RELATED MODULATIONS. 99 189. CHAPTER XXXIII. Next-Related Modulations. Continued. A Modulation is distinguished as Transient, when the new Key occurs in the course of a Phrase or Period, and is followed either by the original Key again, or by some other next-related Key. Transient mod- ulations are frequently very brief, only extending through a few beats, some- times only including two chords, but not less than two ! Because : 190. A modulation is never consummated until the new Dominant chord has been resolved into {and confirmed by) Us Tonic harmony; no Key can be unmistakably represented by less than these two chords^ V-I (or Y-VI), in some form or other. (Comp. Ex. 128, notes •z) and *3); Ex. 147, note *3) ; and Ex. 150). The modulatory process remains the same as in Complete transitions. For illustration : Haydn. . 126.\ ( Allegro, i D Maj. i» tt e $ 5: ^ ^ m I m DI bVn eV„ 4^ H ^-#- 1- ^ 191. Transient modulations very often assume the form of Sequences, whereby, as usual, certain irregfularities are tolerated (121). For example : Presto.^ Ex. 127. ^m E Maj. -9- ^ ^ B 7 EI oSV„ I V J^ ^ ^ ^^M^ ^ ^=^ TLi^^o I = n 7 V Mendelssohn. Op. 7. *i) The meaning of c-natural is explained in 194, No. I. lOO NEXT-RELATED MODULATIONS. Lesson 40. Hannonize the following Melodies, introducing Transient Modulations as indicated (at each * ) : i O ^ - Jmsgj ^^^^^m * • ^rtf? feL^ ^^^ii=^^^^ * • ^ l^>^^Mri j±dd:-rHgg-^ FmOj^ ^ ytyt-ju J j*iJ-iLj^j^^ i gdjf^l4j^ ^^ ^ ; r7>^#i^ |y%g r'PJiB^Ji^jji Jjtif^jTy ii tJ ^ f44 Lesson 41. Harmonize the following unfigured Basses, with Transient Modulations at each * : •l)»l) 2, *I) • « =r^ »l) *1) *2) •l) B^ff=E • « « • « * 3t±; S ^==8^ *i) -Hr-^J l Pr ilJ.II NEXT-RELATED MODULATIONS. lOI •2) ^y^^JB^M^+^^ t ^^ ^g g #J-_* A ^^ « « • I ^^3 p - • ^1 •i) Two Melody-notes. — *2) One Melody-note to each slur. Close harmony. CHAPTER XXXIV. Altered Chords in Major. (Mat. Mus. Comp. §§ 241—248). 192. Altered chords are such as contain one or more tont^ foreign to the Scale in which they appear. They represent the most fugitive grade of Key-association, or, more strictly, are only incipient modulations, not con- summated by regular resolution into the Key to -which they legitimately be- long according to their notation. From which it is to be inferred that an Altered chord is distinguished from the Legitimate chords by the manner in •which it PROGRESSES. Viz. : 193. An Altered chord is always followed by some chord which un- mistakably characterizes and confirms the ■prevailing Key, L e. usually by the I, sometimes by a Dom.-Siscord ; rarely by any other chord. For illustration : c Minor. Ex. 128. e min. i^ C Major. G Maj. C Maj. I^^ w =l*r •l) ♦TS- *2) ^ S^ M ^P 7i 7 V *3) ^ 7 n C Maj. b min. C Maj. ^eP Bgga f^^^ ^ :S^gSz. 1 u 7 n 7 T ^^ ■sr VI 7 Y I02 ALTERED CHORDS. *i) This is the legitimate Incompl. Dom.-Ninth (ch. of the Dim. Seventh) of C Minoi (see 165, and Ex. 108); and is confirmed as C minor chord by its resolution into the I of C minor (c-E-FLAT-g). 2) Here the very same chord progresses into the I of C Major (0- E-NATURAL-g) thus identifying itself as a C major chord, with the casually altered a-flat, (6th step lowered). — ^*3) This chord appears to be the Dom.-seventh of G major and is confirmed as such, by resolving into the G-major I ; the f-sharp is indispensable. In the next measure its appearance (notation) is not confirmed in this manner, but, progressing into the I of C major, it proves to have been a C-major chord. Altered; the f-sharp (4th step raised) in this case is arbitrary and optional. — The other examples are demonstrated similarly. Compare 190, and observe that the identity of a chord depends upon what it does (i. e. upon its progression). 1 94. The most frequent alterations in Major are : 1. The LOWERED 6th Scale-step, in all chords which contain that step; 2. The RAISED 2D STEP, in Dominant Triads; 3. The RAISED 4TH STEP, in all 2d-class chords (Ex. 112) ; 7 4. The RAISED 2D AND 4TH STEPS TOGETHER, in the II. For illustration : Lowered 6th step Ex. 129. C-Major. h Raised 2d step : oVlr I IVl? Raised 4th step : wl?nb vit> n 7 V I i Raised 2d and 4th steps : W^ I 7 7 n I IVJt I h I •i) The chord of the Dim.-7th can thus be used «■» ^(j^Vr as well as in Minor! See 165, last clause. — *2) An exceptional, but not uncommon, Resolution. 195. Other alterations are possible, but _/ar /«j «j«a/. Namely; 7 1. The raised 1st step (in the I or VI, always resolving into the Domyjth). 2. The raised 1st and dth steps together (only in the VI'^, followed by the V^). For example .* Ex. ISO. C-Major. Raised Tonic : I» 7 V T-! •i) Raised ist and 6th steps : 7 7 -« -« — t— •2) ALTERED CHORDS. 103 *i) Not thus, into the II, as this would corroborate the preceding chord as legitimate, in D minor. — »2) In connection with Altered chords, such unusual interval-progressions as c-a-sharp, etc. are permissible. Additional illustrations : Lerdo. Ex. 131, •i) fTT ^ onjtt ■«*- tt^ f i3= ^fiT?" ^ S i TT ..... ••-_ ^ i =fT ^^ nutt ^ i i Later : =t i ^^ ^F it± ^ 1^ =1= •2) m ^ •3) •4) fe M 1 OIV Vjj! _ 7 dv- ^ Sl^ •s) :i i •s) Schumann. Op, 2. J^t -(»-i ^ ^ ^^ p * 3? onjtjj- • v„ 7 -V- SCHUMANN. Op. 21,4. Allegro. ^m i m ^ ^ •6) ^ iM^ l-=f= ^ ^ ^ ^= D Major I04 ALTERED CHORDS. •i) The altered IF of C major (raised 2d and 4th steps); repeated two measures later.— •2) Here a transient modulation is made into d minor ;— *3) and here C major is re-entered, through its IV.— #4) The lowered 6th step of C major.— *5) *s) The comparison of these two measures illustrates the distinction between an Altered and a legitimate chord. At first, the d-sharp-f-sharp-a-c is an altered Il7 of C, because it resolves into the I of that Key ; two measures later, the same chord proves to be the legitimate Dim.-7th of e minor, because it pro- gresses into the V7 (and then into the I) of the latter.— *6) The Dim.-yth in the major xaa^ft, Ex. 129, note *!). See also : Chopin, Mazurka 34, measures 33-68 (raised 4th step). 196. The treatment of Altered chords is very simple, not differing materially from that of the corresponding unaltered chords. Raised notes resolve diatonically upward, (with rare exceptions, as in Ex. 129, note *2): lowered notes always downward. Altered tones should not be doubled. Observe smooth voice-prog'resston. Avoid the Cross-relation. (187). Lesson 42. Harmonize the following Melodies, each in two ways, with an Altered chord at each • : I. * J. 2. * * * •?. ;i ^p ^ ^a B e w d2t St -A^ ^ q ±^±i wmf^r^rr^rf^ - s^^ ?jt^ ■g- hJ g ■Hy-fi^ ljg'' i?fc ^ (Chord of the Dim.-yth at each *). ^ ^ ivb ^^S iqe ■ g e i :& * tr To THIS Lesson, add Appendix C, No. 8. ttt CHAPTER XXXV. Altered Chords in Minor. (Mat. Mus. Comp. §§ 249—255). 1 97. Review, carefully, 85, 86, 87 and 88. The Alterations in Minor are defined on the basis of the Harmonic Minor Scale. Their purpose in Harmony consists almost exclusively in obviating the awkward interval- progression between the 6th and 7th steps of the Harmonic scale, by substi- tuting a melodious succession which gives rise to the Melodic minor scale. 198. For this purpose. The 6th step is raised in the ascending scale, and the 7th step is lowered in the descending scale. ALTERED CHORDS. "5 Thus: Ex. 132. C Minor, Melodic. i N.B. *2) N.B. I^JJit rP-^ 2*^; '«»*tM 3S 13 8 4 5 6 4 3 2 1 Compare Ex. 56. •i) yyxe ascending scale thus re-approaches the original Major form (C major).— •2) The descending scale corresponds to the historic "Aeolian" mode, and exactly resembles the Relative Major Key, from which the minor Signature is derived (see Ex. 58, note *i). 1 99. The external proportions of these various Minor scales may be systematized without confusion as follows : 1. The first 5 tones, from Tonic to Dominant, are the same in all the forms of minor, and contain ^dowered (or minor) yi step; (in c-minor, c-d-e-flat-f-g). 2. In the Harmonic scale, the Dominant and Tonic are each followed by a half-step, in passing beyond this central group of 5 tones just described, in either direction ; thus : i C Minor, Harmonic. w i^sBSl -}f- ^^S^ ftpsr 3. In the Melodic scales, the upper series of tones, between Dominant and upper Tonic, consists of "whole-step, whole-step, half-step" in both directions ; thus : i C Minor, Melodic. 3e-s: Efc^ Lte: ±g=^- =8 \ \ 200. From this the important principle is deduced, that The 3d, step is the only characteristic and distinctive tone, between a Iffajor scale and its derivative minor, being If ajor in Major, and Minor in Minor, and subject to no alteration. 20 1 . The raised 6th step is applied and treated as follows : *i) 1 *3). Ex. 133. ) C-MlNOR. J ^m isa s^?T? ±3!: *2) ua V I ±=^ *-~i— ^ T iJ- 7 7 IVt] ^ Trrr 444J4 i±±i mf ii J4 7 s f^ ^ i 7 , via 7 via ^ *i) The progression of these chords is defined by the resolution of their Altered step, — not by 193 I Here, ZJoOT/waw^ chords »!«j^ follow.— *2) The Resolution of this 7th (c in Alto) corresponds to Ex. 100. — *3) ACf followed by at* (Tenor) produces the Cross-relation. See 187. The diatonic progression of Has first tone invariably removes this error. io6 ALTERED CHORDS. 202. The raised 4th step often accompanies the raised 6th step, imd- class chords. In this case only the 4th step requires the ascending resolu- tion ; the 6th step may rise or fall. For illustration : Ex. 134. C-MlNOR. EF^ ^. ^ 4^ r^ ^^ 1 1*" W- *=t=f Jz *2) I F«Pf se=n n i •s) •3) *>-&:= ^ I I 9-UJ-4 M ha, XVJttjI njftv I *i) See Ex. 114, note *2). — *i\ Resolution into the I ; stationary dissonances. — •3) Anal- ogous with Ex. 129, note *2); rare. — *4 ) Comp. Ex. 133, note *3). — *5 ) The resolution into the Concord V resembles a modulation. The Dom.-discords, or the I, are more genuine ( 193). 203. The lowered yth step is applied and treated thus : Ex. 135. C-MlNOR.^ ^^ ^ e^ ^M i^£3::i: I I r \vi ^ Htt labTj n gte g^g fe "ITT m A-f-:?: vbr7 vW, *i) Comp. Ex. 133, note *!). — *2) Compare loi, and Ex. 67. — ^*3) The Lowered 7th step is rarely employed in Z)o«B.-chords ; especially not in the Discords of the Dominant. 204. Aside from these Alterations, which are identified with the Melodic minor mode, there is one other very common alteration, namely, the lowered 2d step, which occurs in the 1st Inversion of the II (more rarely in the II itself). For illustration : Ex. 136. GMlNOR. ieJ=i »I) #2) I i I t ^Tf i I I -# « — -^ ^^^ T-r-f- i I I d=^ r-f- =y=^ -^ — i — t tf i^^ ^ ^ nb I 7 V ni7ivjfa *i) See Ex. 130, note *2). — *■£) Two different Altered chords in succession. ALTERED CHORDS. 107 Additional illustrations : Ex. 137. ^. Allegretto . *i) Mendelssohn. f|( minor. i^ t=^ ^- 7 1^ :tt*= -■Ti- 7 • -J- 7 ifl 'IV — ' V— Prestissimo. Htte P f-- Beethoven. i^^i^^^ ^ ^; UJlTj f minor. •2) iS^^^ ^ S^ 7 fV- 7 oV Vo r^Sfl la i 3- Allegro. W i. BEEtHOVEN. 3E ^fe -« — r- ^^^^ P SS i±^^ *3) ^3 *3) SB=^ P=1^ ^ -VltjVo 7 7 V-VIjJVo I i Lento. ^3=t ^ Chopin. i^ ¥« ^^ zsn •4) I I :ii :*3 *4) I I 'S^ 4i ^ i^ ^-J- Si t=F=l=p I nii?(ii) V VI iijl? S 7 V V V *i) Lowered 7th step. — *2) Raised 6th and 4th steps. — *3) Raised 6th step. — ^*4) L(w» ered zd step. io8 ALTERED CHORDS. Lesson 43. Harmonize the Melodies of Appendix C, No. 9. Harmonize the following Minor Melodies and Basses, introducing altered steps at each • ( in some cases definite, in others optional ) ; and modulating as indicated : i.*i) i ^s a ^'^rf^ g a§ •-ii-& ♦-♦ ^-P-f- #t ^ ■9-4- t. * • s « pc minor 1 pBJ? major""] pg minor" 3. pc mmor 1 pB7 major"^ pg minor 1 i M .■-D- ~) f Jf minoi ^ ^4t^ S 5^ ? F^§-/ ^- i *^ ^2- F™^^ i I — a!? 1 Gb 1 pbt> minor"! P^^ minor" 3£^ i :&p: ^■^^j i^^^^^ =F i^ i^=ffi*s -bt> i ^^^feEti rail. itSt g^^ li ifcfii ?=^»^ i^=i ^ E4=t # 6 4: =i=ic:U^ ^=t 2.*2) * ^g =P=«p: =lt* "7 VI 7 V w. i -tQ— ^ •1) This Melody (and the next one also) may be harmonized in two or three different ways. — *z) Close Harmony; one Melody-note to each slur, strictly. MIXED CHORDS. 109 CHAPTER XXXVI. Mixed Chords in Major and Minor. (Mat. Mus. Comp. §§ 256 — 261). 205. Mixed chords, usually called Chords of the Augmented Sixth (because they all contain that peculiar interval), have an illegitimate or deformed shape, resulting from the more or less unnatural association of steps which are peculiar to different scales. They are very effective, fre- quent, and easy to manipulate. Besides the rules in 193 and 196 (which re- view) it must be observed, that The interval of an augm. 6th is rarely inverted; and Mixed chords nsnally resolve into the Tonio chords. 206. Mixed chords in Major are obtained, firstly, by raising the 2d step oi the scale in Dominant Discords ; secondly, by lowering the 6th step in conjunction with the raised 4th (or raised 4th and 2d ) steps, in Second-class chords. Thirdly, and very rarely, by lowering the 2d step in the Dominant Seventh. Dom.-chords : Ex. 138. C-Major m^^ F=^ r 2a-ciass cnoras : ^g . I *l) The augm, 6th arises from the association of d-sharp with f-natural. — *2) Here the augm. 6th is inverted (to a dim. 3d, d-sharp — ^f-natural), which sounds ambiguous, and even disagreeable.— *3) The augm. 6th arises froni associating d-flat with the Leading-tone b.— *4) The augm. 6th (a-flat — f-sharp) is here again inverted (to a dim. 3d, f-sharp — a-flat).— *5) When the augm. 6th is inverted i^ycB^Mf ufAzB'; (i. e. as dim. /if«//4) the effect is much less objectionable. — ^*6) The d-sharp in these chords is quite frequently written e-flat, erro* weously. The latter is peculiar to the viinor mode ( 200 ). \ict MIXED CHORDS, I 207. Mixed chords in Minor are limited to the Second-class (II-II'- IV-IV), and are obtained by raising the 4th scale-step, while the 6th step vemains minor. For example : *1) «2) •!) *i) V I *3) Ex. 139. C-MlNOR *l) The identity of these chords in C major on one hand, or in C minor on the other, de- pends, as usual, upon the resolution — , here solely upon the tones e-flat, as above, or e-naturah as in Ex. 138, measure 6. — See 193, and 200. — ^*2) For the reasons given in note *i) the pro gression into the Dom. (instead of the Tonic) chord is too indefinite; the I must immediately follovr, at all events. — ^*3) The augm. 6th (a-flat — f-sharp) is here inverted, as dim. loth. Comp. Ex. 138, note *5). — ^*4) These perfect Jths are so seductive, that unusual caution must be observed in using the Mixed IV7; the only reliable safeguard is the resolution into a Tonic chord. See Ex. 118, note *i). Additional illustrations : Ex. 140. Moderalo. *i) *8) ^ ^Mi 9^ ffi ^ S ^ -^ Schumann. Op. 42. A- ^ -*-^ B ^ ? O- i dl OVb IFVJf I FI allj V" Allegro. *4) =1= f=p: i.J EB! I I I 3=^ m ^ P=4=t=^- r s) 4-4-4-4- ^^^ -J — \ — u t=t Eb V- Beethoven. (Bb V Et7 n Allegretto. , 7 Et^V I fJi u. ^ I Abvti Mendelssohn. S ^ ^ r S "j—l F "fW^- M & ^ *6) *6) f AfT r i ^ ^ £ I AVJ — I EilJ{jf-r AVff-I Ei? V MIXED CHORDS. Ill •i) Lowered 2d step j also premonitory of F major (as lowered 6th and raised 4th stepsV Comp note*4).— *2) Raised 2d step.— *3) Raised 4th step.— *4) Both analyses are tenabl* (6-flat and E-flat), though E-flcU major, as preceding and following Key, may be most proba> ble.— *5) Mixed Dom .-Seventh of A-flat major.— •e) *6) Here the modulations are both effected through altered steps (as indicated). Lesson 44. Harmonize the Melodies of Appendix C, No. 10. Harmonize the following Melodies and Basses; introducing a/Z^r^i/iT^-wiMriff/ chords at each note marked Al. or M. respectively ; and modulating as indicated : te 'I) IV> 2. ntftj =P==i- ^ ^ g%4^ — rfR :t:«t ^^ -jt=± -iH-'» :& Al. Al. lEbnBi? — -^-v* — ^ M. M. M. Al. •O i X^ \ ^\h:&}± pF— |Bir m ^tf=m^ :pj*: W M. s •3) ^fn ^ rrn^ a i •3) *3) Al. Vo n^Al. I -*L ^ ^ ^ jcl i3=t i^4J-&^-J+^ ^ M. Al. M. i •0 M. I M. I M7 I 7 iDVI ^ » ^ >'2J I Jit;j ^ aJ g^ -ffzy 1^ M. D- "? 1 A- 1*4) n *4) Al. D — Al. Al. »4j) •3) n •^ Al. Al. Al.^ °^ M. M. i ji D 1 b minor 1 ftt minor 1 ffFf I. M. AK Al. A1.2 AIT * ^ — -^ ^^^ ^ 7 n M. m^. H — f M. Al. 2. Lowered 6th step throughout. | IIVW tut ^^^ '**'*'^ IVt? Al. Al. aT^M. Al. , , (over) 112 EXTRANEOUS MODULATION. Al. Oj Al. I *M. lEV-IBIVJIIVt!^ *i) The raised 2d step in Soprano is most suggestive of a Mixed £>om.-chord. — *2) The raised 4/i step must be in a Seconti-class chord. — ^*3) The Mixed chords in Minor are exclu- sively Second-class. — ^*4) Lowered 6th step. — ^*s) Such an addition to the Perfect Cadence is called a "Flagal ending." ( Mat. Mus. Comp. § 155.) CHAPTER XXXVTI. Extraneous Modulation. 208. Extraneous modulations are such as extend beyond ^e Next-Re- lated Keys, in any direction. See 186, Rule I. The remote Key is usually reached by modulating through the Next-related Keys •which intervene, i. e. from Signature to Signature in the direction of the desired Key — , whereby either the major or minor mode of the interme- diate Signatures may be taken. For illustration : from C major (or a minor) to A-flat major (or f minor), the following Signatures fiiW be involved: tj— b— 2t> — 3!? — 4I7 (see Ex. 123). The modulation may there- fore represent any of the following lines of Keys : C (a)— F— Bir— Eb— a1? (f) " — d— g — c — ' " — F— g -Et>— ' « _d_Bb— c - — F— Bb— c - " — d— g — Eb— " Or, from Bb (or g) to A (or fj(), through the Signatures 2b — ib— J}— ij^2j(— 3J{. Or, from Db (or bb) to E (or cjf) thus: 5b— 6t>=6jfl-5jf-^4. Lesson 45. Harmonize the following Melodies ( Nos. 2 and 4 in several ways ), modulating at each * : i FTTTTTHi g a F d ^^ ^-^ Bb Eb g c EXTRANEOUS MODULATION. "3 ^ f=^ S ^X ^ l ir-^-^—r 3^iiri=t±t^ ^ "W bi?. ip 5 ^ ^ a i -<» — «»- :j^ «^ fi li «a l G e D b A cJt Lesson 46. Harmonize the following Melodies, in at least two ways, with a modnlation at each *, (Major or Minor) : cJt B G|7 bb _e:r * * • f^j ^^^W ga^ ^g ;^^ D G b e C ^F d ^ Wf^T i s '- f—r\^. I m liUt j5»- *t g ^is= Et> c F d C a i • Eb W- ^ # — y F d 114 EXTRANEOUS MODULATION. « « mi^ r |"f r cr^ im».i di J ji ^jjr ^ At? El? f Bi? F g E ctf -^ Bl7 'f C G S— ' g d a e "i) * Bt> g i) Raised 4th step of D major. CHAPTER XXXVIII. Direct Extraneous Modulation. (Mat. Mas. Comp. §§ 280—289). 209. Under certain favorable circumstances a Remote Key may be reached directly, i. e. without passing through the intervening Signatures. 210. The first and best of these cases is a direct transition of 4 degrees (or Signatures) for which the author has adopted the term "Modulatory Stride," and which is defined as follows : The "Stride" is a perfect 5th downward hom any Major Keynote, and upward from any Minor Keynote, with a change of Mode. For example : from C major down to f minor; or from c minor up to G major. The Stride-relation is represented in both directions by any perfect 5th, the upper tone of -which is a major Tonic, and the lower tone a minor Tonic. Thus : Ex. 141. i O A mfn. -P^— ©b "'J-- -^iS^Kb-'Jf «»i».- ^ ^-n- ^ etc. 211. Upon reflection it will become apparent that the remote transition of the "Stride" results simply from an ultimate exchange of Mode (minor for the expected major, and vice versa), without which it would be an ordi- nary Dom. or Subdom. modulation, respectively. That is, from C major to f minor instead of F major ; and from g minor to D Major instead of d minor. EXTRANEOUS MODULATION. "5 Confusion can however only be avoided by mechanically bbserving the formula in 210. Therefore this modulation has a certain bearing upon 213 — 215, which see. For illustration : Ex. 142. ^^ X X t=^ f r «r f -f — f- ^5— • — »- =i=F r r r rt2 ~»-t • 7 g V-- 7 -n- ^^ i •i) Chopin. Op. 23. ^ P=^ j^ I I -a«hr- X a. J- 4i X r T I I I ' I' I I ' J J 7 DV- 7 gV *i) With f-natural (instead of f-sharp) it would be the next-related Key, d minor. Why f-sharp should however be preferred to f-natural, in the vicinity of g minor, is very obvious, and affords one of the best demonstrations of the practically close intimacy of the Stride-re- lation, notwithstanding the actual difference of 4 degrees in the Key-signatures — , see g minor — D major, Ex. 123. Lesson 48. A. Indicate the Stride-relation (by Keynotes) from every major and every minor Key.— B. Harmonize the following Melodies, introducing the modulatory "Stride" at each * : ^^ Sfcbi t-Ml^('^^\YTtjT - fh M ^^ j=i^ 'AH^rXl^^f'} jt& I I pc min,-] • \\^'n'[fft-h^^-m\.i H'r r f-J l 4 j J i IIO i EXTRANEOUS MODULATION. ^A> maj. , , E ^^ A inaj._|» :^==5«- ^ §1 ^ ^ i i ^e min. ^_, • r TP~?"' i ^k^<^ W ^^ ^ ■«- ^ Al. *2) •i) The Stride from A-flat maj. is d-flat or c-sharp minor. — *■£) When the last chord of a Key is, as here, the Dom. chord of the prospective Key, the latter cau be taken up at once, without any additional intermediation. CHAPTER XXXIX, Direct Extraneous Modulation. Continued. 212. The next best direct transition to a remote Key is the Change of MoDK (from Major to Minor, or vice versa) upon the same Tonic ; for in- stance, from C to c, or d to D, or G-flat to f-sharp, etc. Although this tran- sition into the " Opposite Mode" actually effects a change of location in the modulatory circle (equal to 3 degrees — , see C — c, Ex. 123), it is hardly to be regarded as a "Modulation" in the strictest sense of the term. For it is only a modification of one and the same tone-family or Key, as was demonstrated in 84 and 87, which review. 213. The possibility of thus changing the mode of any Keynote is 7 7 traceable to the coincidence of the Dominant chords (V, V, Vg, V al- s tered and Vq altered) in the two Modes (see 88; 140; 155, Rule I; Ex. 129, note "i), by reason of which any Dominant chord may be resolved at op- tion either into the Major or Minor Tonic chords of the corresponding Key. See Ex. 91, note *8). The resolution into major is, however, always the more natural, example : For V I„: oV I Ex. 143. OT VI^oVVI fl, 4 EXTRANEOUS MODULATION. 117 *i) The tone upon which this exchange of mode solely devolves is the Mediant (3d step) •f the Key — , in this case e-natural for C Major, and e-flat for C Minor. See 200. 214. A Dominant chord, then, which enters from Major (i. e. in the capacity of a Major-Key Dora.) may resolve into the corresponding Minor Tonic (by substituting the minor Mediant for the expected major Mediant).; or, inversely, a Dom. chord which enters from minor, may resolve into the corresponding major Tonic ; thus effecting an "Exchange of Mode." This may be done at any point in a Phrase, and is only subject to such conditions and limitations as are patent to a cultivated ear. See 221 b. 215. The coincidence of the Dom. chords in major and minor is very frequently utilized as a means of reaching other remote Keys directly, by substituting' ihe opposite mode for what would otherwise be a n'ext-related Yijerj. This is always the case with the "Stride" (see 211); and also witb such examples as the following : Ex. 144. i •0 \y { { i l^d^a^^p=Tl •3) •2) •l) With b-natural it would be G major, a next-related Key of the C-major which pre- cedes. Substituting the minor Mediant h-Jlat makes the modulation remote. — *2) With f-natural it would be the next-related Key, A-minor; with f-sharp it is a remote Modulation.— *3) The Stride. Compare Ex. 142, note *i). 216. The exchange of mode may also be accomplished by the simple chromatic inflection of the Mediant itself (Ex. 145 a) ; Or through Altered chords with the lowered 6th step (Ex. 145 b) : Ex. 146. ^-^r^ f= Vl\) J_A ±t iv(0ivb)_o iiH EXTRANEOUS MODULATION. Additional illustrations : Schubert. Ex, Adagio. Beethoven. Op. 22. bbmin. , , I Hjjlf IVJft V Bbmaj. Andanle. Brahms. Op. 10. bmin. B maj. •1) The Dom. Triad of A minor, resolving into A.-major. — *2) A direct chromatic tran- sition from major to minor. — ^*3) The g-fiat is the lowered 6th step of the next-related Key». i)-flat major. — ^*4) The Dom. chords of B-flat major resolve here into b-flat minor. — •S) See Ex. 136, note •2).— •e) B-flat major here finally asserts itself.— •;) Direct chro- matic transition from b minor to B major. Comp. note *2). Lesson 49. Harmonize the following Melodies, introducing the Opposite mode at each *> * G 1 • i w djti ^3ii =f=BP= ^ g| EXTRANEOUS MODULATION. 119 i pc mm. ^^ ^^^^i ^^ gH> « d— D G — I c*3) Bt^ ai^— Ai? bl>— Bb ■Ei? i ^ g ^ ^ tip: ?=fg i ^=F 1^ t*i) B-b A a G e F— f El>-eb D^-] f" Ftt major. t t t t t t t •1) bl?-Bb c— C d— D e-E fj{ E— e i »j^«f r'rr i rTii.a i -# — W- =?«(== djat J2tUi P ?fS Ab major *4) t»i) t t *i) At each t the foregoing Dom. chord is resolved into the "opposite Mediant" of the (evaded) Next-related Key (215). — "2) Lesson 48, note *2). — *3) C minor is substituted for C major, thus effecting the Stride-transition (211). — *4) The "Cross-relation" (see 187) is very often unavoidable in Sequences, as here ; but, as usual, the Sequence justifies it (121). CHAPTER XL. Sequence and Cadence Modulations. 217. In all the foregoing modulations, both Next-related and Ex- traneous, the fundamental rule given in 186 (Rule IV and context), has been strictly observed. But more abrupt and irregular modes of transition are possible, under favorable circumstances. The most auspicious conditions are afforded by the momentary breaks or interruptions which occur between Seqjjences, or at (i. e. after) Cadences of any kind. Hence : I20 SEQUENCE AND CADENCE MODULATIONS. 218. Upon passing a Cadence into a Sequence, or into a new Phrase, or distinct Member of a Phrase, an abrupt transition may be made into the desired Key (whether next-related or not) witiiont necessarily interposing the usual Dom. (or 2d-Dom.) modulatory chord. For example Ex. 147. SECyjENCES See §191. *4) cJt min. H ^V •i) The transition is made abruptly from the I of the old Key, into the I of the new (comp. 186, Rule II). There is no common tone connecting the Keys (219), but the Sequences are so close and coherent that the connecting-link may be dispensed with. — *2) This modulation is made in the regular way, but the Keys are not related. — ^*3) Here one single chord must suffice to represent a Key. Comp. 190. It is accounted for by the Sequence.— *4) The old Key is abandoned at its Dom.-7th (comp. 186, Rule IV). The connecting link (219) into the first Sequence (which is a very close one) is the tone cX = d (Leading-tone becoming a Tonic). SEQUENCE AND CADENCE MODULATIONS'. 121 219. The limitations for such abrupt modulations are : that there shall be a reasonable degree of coherency between the Keys ; and, as a general though not inexorable rule, that at least one tone be sustained from the old Key into the new one, as connecting-link. Of these "pivotal" mod- ulatory tones the best are tlie Tonic, Mediant, or Dominant of the old ICey, which may become at option respectively either Dom., Mediant, Tonic, or Leading-tone (perhaps 4th or 6th steps, as 7th or 9th of the Dom. -chords) in the new Key. Illustrations of abrupt Cadence-modulations, and "pivotal" modulations : Ex. 148. Cadences. Presto. D'Albert. Ffg^s:- ^^ fS £. *i) ^m iH a minor I~ -|| f minor I YI- Allegro. ^mtuUM ^ Brahms. hM Si u^fT* E*^^^ W- ^ 1t^ w=^ e& ^ m *2) ^i^ ±=3tiM: -MM ftr?- ^ ■& te f DI- -V — U 01- liqi I mi$ I Vivace. ^M f^ ±=A Hummel. ^ rj>- ^ g^'W •=P= ^ •3) ■!«- P Jf: ^ DI AV- P=^ s ^^ il 01 122 SEQUENCE AND CADENCE MODULATIONS. Lento. Schumann. Idem. *i) Cadence (Semi-) in A minor, followed by the abrupt announcement of the f-minor I. The connecting link is c-c (Mediant becoming Dominant). — *2) Dom. Semicadence in D, followed by the I of C. Connecting link e-e (2d step becoming a Mediant). — *3) Tonic cadence; connecting link e-e (Dominant becoming Mediant). — *4) Transient Tonic cadence ; connect- ing link c-c (Mediant becoming Tonic). — ^*5) Connecting link a-a (Mediant becoming Dominant). — *6) Dom. Semicadence in A minor, followed by the I of B-flat major. Lesson 50. Harmonize the following Melodies and Basses, with abrupt modulations as indicated : i *i) Dom.— fj± i Med. Med.=Ton. Bb aF^ W V Med.=Dom.Ton.=Med. Med.=Dom. i^^E ^? w -U ^^ > Bb Eb SEQUENCE AND CADENCE MODULATIONS. 8. •2) Ton.=Med. Med.=Dom. Ldg-tone=Ton 123 ^^ 1^ Iflfc Ldg-tone=Ton. n .e^ •3) «s ^ ET G ^m XP= ^W^ ^ ^ I ■«' — ^ g( min. E i inS dj( min. D B E cjf lAV lEHtlllVtl I gZ3 S 'ij g lJ ^ - g Z5l- Med.: ■^4) i-»S) Dom.=6th step. Ton.=Leading-tone. a ,. .^ Bb ^ Ton, C'^ Db ^ I F » T b ^ fft^ i il^cf: ^ te^ ii=^=i b" I U I cftS^J-u^^^ :3ttz:2*=-3t Ton.=Leading-tone. >^ ^ ^^ ^5=^: IfitJ: flt 5^ ^ **= maj. G maj. -maj. b min.- *i) The Bass begins on the first beat; the three upper parts follow on the second. — •2) Like note *i ) throughout. — *2) This irregular rhythmic form of the perfect Cadence is not unusual, and is justified here by its agreement with the Semicadence. — *4) Plagal end- ing. Comp. Lesson 44, note *5). — *5) Close Harmony. One Melody-note to each slur. CHAPTER XLI. Special Application of the Diminished-7th Chord, in Both IVIodes. 220. The most efficient and attractive form of the entire Dominant chord-class, and the most flexible chord in the whole range of Harmony, is the CHORD OF THE DIMINISHED 7TH. It is very frequently employed for the purpose of Modulation, and, on account of the unlimited facility of its connections, it serves as a transitional medium between any Keys, regard- less of Mode, and almost entirely irrespective of the ordinary consideration of Key-relation. 124 DIMINISHED-SEVENTH CHORt». 221. The following points must be borne in mind : a. The Chord of the Dim. 7th is the Incomplete form of the Dom.* Ninth, and is found upon the Leading-tone of the Minor mode (165). b. Though legitimately a minor-mode chord, the Dim. -7th is equally available (as Altered chord) in the Major mode ; i. e. it may resolve indif- ferently, either into the Minor or Major I. Ex. 129, note "i); Ex. 131, No. 2 (D major), and paragraphs 213-214. See also 166, and Ex. 91, note *8). c. A Diin.-7t]i may be introduced, in some form or other, after the Tonic chords (I or VI) of any other major or minor Key ; tke choice of Inversion and Position will depend upon the form and location of the preceding chord. d. The notation of the Dim. -7th must conform to the new Key (into which it resolves). See the table made in Lesson 29, B. — ^Whatever chro- matic inflections appear must be effected according to the Rule in 187, which see. — For illustration ; •l) •!) Ex. 149. i 1 1 1°" 1 1 A C G maj. ^ t=^ ^^^ ifeii"i •j) i i } s g min. F maj. min. ±^ f=^ ^ W^ *2) 4=4=4= ^ F^^ ^ \>i J " J i i I'd i ^ A ¥ i ^?^3f^ C B!^ maj. min. C d min. maj. •3) ^S ^ K J-^^J-rJ-V -HtJ-^J- -fzzii i J •ri ± ? s =t ltp= — ft C a min. maj. C EJ7 C e min. maj. C fjjf min. raaj. DIMINISHED-SEVENTH CHORD. "5 •i) With e-flat, instead of e.the first chord will represent the I of C minor also.— •2) Avoid that form of the Dim.-7th in which the 7th (the original 9th) lies in the Bass- See Ex. 108, note *4).— *3 In this example the VI of C major is used. It represents, at the same time, the I of a minor. Lesson 5 1 . A. Connect the I of every Major and Minor Key, with the Dim.-7th of C major (and minor), in the manner of Ex. 149.— B. Connect the I of G major with the Dim.-7thof every other Major (and minor) Key, as in Ex. 149. All Inversions optional. Lesson 52. Harmonize the following Melodies and Basses, introducing a Dim.-7th {choice optional) at each •: i -^ wf-f^ E^ p=5i ^ ^ a -eHn :^=#= - g-fig'- ^3 W- *I) *2) i SbJ^^J fe^-v- •3) * • '^ V ■• — •■ j=^-^ = gi=f -^ ^I ^^Si Ie5 *4) ^^m^^m *4) » a= i^ ^^— A BE^ I^?^-_^ *s) f|; gg^T^^^^3ifr--;T;^ :9^*:^=F ^ ^^ f^f^g^^^Bi G E D- *6) t^ ^ i ^■ ^^ 1^=^' Bt> G *r) The Dim.-7th of d minor, D major, or F major, at option. — *2) The Dim.-7th of C major, c-minor, or E-flat major, at option. — ^*3) The choice here is limited to c-sharp minor, in view of the approaching Cadence in that Key. — *4) The choice here is limited to D major or d-minor, in view of the following slur. — *5) Place the three accompanying parts together upon the Bass-staff (inverting the style of "close harmony"), and use one chord to each slur, strictly. See Ex. 98, note *2). The choice of Key is rendered evident by the slurs. — •6) The three upper parts rest on the ist beat of each measure, excepting the Cadence, and enter together (close harmony) on the 2d beat. Thus : S J J I 12$ CONSECUTIVE DOMINANT CHORDS. CHAPTER XLII. Consecutive Dominant Chords. (Mat Mus. Comp. §§ 290 — 299). 222. Tlie most notable exception to the fundamental law of Dominant chord-progression given in 64, (Rule III) and adhered to strictly hitherto, is encountered when the Dominant chord, instead of resolving into the Tonic harmonies of its own Key, digresses into another Dominant chord (of some other Key). This very irregular but by no means infrequent pro- gression may be demonstrated on the ground that the obligations of the first Dominant chord are simply transferred to a chord of exactly similar obli- gations in another Key. And the connection is moreover usually effected by means of one or more chromatic inflections, which is the smoothest of aL modes of melodic progression. 223. The Chromatic inflection is directly opposed to the Diatonic progression, and consists, as has already been seen, in simply raising or lowering a certain Letter or Scale-step by an Accidental, without effecting an axAosi progression from one Letter or Step into another It does not conform to the line of the diatonic Scale, but is oblique to the latter. It is an abrupt digression from the natural order of tones, and its effect is therefore to cancel the Key instantly and completely. No Resolution, and no diatonic chord-progression of any kind, within the same Key, can include any chromatic inflection (only excepting the possible chro- matic introduction of Altered tones). Consequently the chromatic inflection (mtless in- cidental to an Altered or Mixed chord) invariably executes a change of Key, as abrupt as it is inevitable, and usually so quietly and smoothly that this species of melodic succession, i. e. "Chromatics," is properly regarded as the most powerful and seductive factor in Modula- tion. The fundamental principle of chord-analysis, that "the identity of a chord depends upon its progression" (Ex. 128, note *3), is also canceled by every chromatic inflection, which, as stated above, instantly severs the connection of the chord with its Key. From this, the peculiarity, but at the same time, the extreme importance of the chromatic inflection, and the frequency of its employment, especially in modern Composition, may be inferred. A great number of curious chord-progressions may be and are effected through the agency of Chro- matics, which elude all rational demonstration, and can be accounted for in no better way than as a manifestation of seductive chromatic agency. Therefore the chromatic inflection must be accepted as one of the chief excuses for the peculiar harmonic connection of which this chapter treats, viz. the direct succession of different Dominant Chords. 224. This principle of chromatic Dominant succession is to be applied in the most general and comprehensive sense ; i. e. the Dominant chords of 779 9 one Key in any form (V, V, Vg, V or V^,) can progress into any form 799 9 of the Dominant of another Key (V, V, Vq, V or Vj,), either Major oh Minor. CONSECUTIVE DOMINANT CHORDS. 127 225. The new Dominant chord may resolve properly into its Tonic, or may be followed again by another Dominant chord. When the series of Dominant Chords is thus protracted, either the Soprano or the Bass is likely to progress in continuous chromatic descent or ascent (Ex. 150, B). 226. Rule I. The Seventh of each Dominant Discord must be cor- rectly resolved (diatonically downward), if possible. Rule II. The chromatic progression should be approached, if possible, in the corresponding direction. See also 187, and 55. A.«i) *2) *3) •4) Ex. ISO. i i i i i ^!^^ J-^ i J J_J. »S) *5) •6) til ^ -"•.-f- ■J-J- i ■±tL 7 7 OV FV *7) C A C c a c Bb C D C Eb bt? c d c eb *7) »8) J^- '8) :;tt; iE -i-~--tt- — *L r »: I /r ? I 1 ki :J^^ii=i I • I i ItJ \L =r=»f=P=f c c At? C c B b C c Db C c G g C c E e B. *9) •10) i -^ i - ^i -- j i d=± -!>— Inl- i i i r I f u ^=jy 'tiJi: =tA=#^ :|?=5 ^-przzpltpf^ 7777 V V V V 7 7 7 7 V V V V •i ) May also be c minor. — *2) May also be any other form of the Dom.-harmony of C 7 99 (V, Vo, V, Vo). — *3) May be any other Dom. chord of F. See 224 ; and 226, Rule II. — *4) May also be F minor. See 213. — *S)*S) I" both of these cases there is no chromatic inflection involved. — *S) Here the Seventh of the Dom. chord remains stationary ; comp. 9 149. — *7) The substitution of the Diminished-yiYi ( Vq) for the Dom.-7th, is an effective means of facilitating all such awkward successions as these. — ^*8)*8) In both of these cases the 7th is obliged to ascend. See 226, Rule I. Therefore the connections are somewhat objection- laS CONSECUTIVE DOMINANT CHORDS. able.— *9) See 225 ; and 226, Rule II. The identity (i. e. the Keys) of each of these chords can only be determined by conjecture. See 190^ and 223. — *io) The notation of the Dimin- ished-7th, in chrom. succession, cannot be definitely regulated, because the Keys represented are only conjectural. In descending succession ^^o/x, and in ascending succession sharps, are apt to prevail. — ^*ii} Comp. Ex. 133, note •3). Additional illustrations : Andomie. Ex. 161. Brahms. AndaviA. i^ ^ z^ ^-f-^^ .7 7 11,1 B!7V gVOV— VFYBl^V— I I ^ i ^- Brahms. Aliegro. Brahms. m ^^ m='m f^ -m ^ i^ % ^^ ^ trti ^ % .7 e 9 ,7 Bt?V gVo PVo Bt?V- Modtraio. F IV I V F V 1 Schumann. #^^1^ t^^ ^p=g; §Ste P ^: ^ ^^ 5=i^S=^ dVo oX To I aVoBtJVo Vq I gVoB^IV 1 Allegro Schumann. i ^=#: =»t ^=g P^=*^ n ^s^ simile.. a:ft lit p i OE -%f^ fffVo 9 0S »o ^O ^O 9 7 Vo JSV V — I CONSECUTIVE DOMINANT CHORDS. 129 Lesson 53. A. Connect the following chords, in open 4-part Harmony, Inversion (Bass) optional ! A maj. V— D V; El? V-c V; D V— F V ; f Vo— DlT V; E '^— C V; Bb V— Al> Vq; 9 77 9 9 9 9 90 9 9 9 G V-A V ; B V-fjf Vo ; g Vo-d V^-a Vo-e V^ ; c}{ V^-i^ V^-b Vq-c X^-*^) B. Find and play these successions at the pianoforte, in close Harmony. C> Harmonize the following Melodies, with successive Dom. chords, as indicated at each * (Inversion optional) : feS ■tt"fln r r ^r i ^r te m H* ? M ^ -)- ■ r >■ ^ lp=Sf=ttic: ^^ ijt 4=tai "C Db bI? Et? aFdF CAD G C- At>- i ?=^ ^ H^rliS i *2) 4- * F D F d- 'm-r =fl^ S -f2 (2- 1^ t=P ^^rS^ •2) 9 V D g V 7 7 7 •i) The V at each * in these Melodies. — *2) Either V or Vq at each •. — ^"3) At each* a 9 Dim.-yth (Vq). — ^*4) Resolve the last chord, in each case. CHAPTER XLIII. Enharmonic Treatment of the Chords of the Diminished-7th and Dominant-7th. (Mat. Mus. Comp. §§ 300^308; 314, 3). 2 2 T. The ' 'enharmonic change, " or ' 'exchange, "is obtained by inflecting the next higher or lower letter so that it agrees in souxd with the original 13© ENHARMONIC EXCHANGE. tone. Thus, the tone g-flat is "enharmonically identical" (in musical practice) Wx^f -sharp, and either of these two tones may be enharmonically '•exchanged" for the other. The enharmonic equivalent of b is c-flat ; of f, e-sharp ; of d there are two enharmonic equivalents, c-double-sharp and e-double-flat ; and so on. Review i8i ; and Ex. 123, with its note. 228. The enharmonic exchange involves an inevitable change of Key, or modulation, as the two enharmonic equivalents cannot belong to the same Key. 229. This modulatory factor is most commonly applied in the chords of the D1MINISHED-7TH, which admit of the enharmonic exchange to a very remarkable extent, and with that facility and flexibility which characterize every movement of these extraordinary chords. (165.) 230. The wonderful ambiguity of the Dim.-7th is chiefly owing to the peculiarity of its structure, consisting as it does of equal contiguous intervals (of three half -steps each), which divide the 12-tone chromatic octave into four equal parts. This is best seen and understood at the Keyboard of the Pianoforte. Thus : Ex. 1 52. e DVo ^^^ idfe "etc. In consequence of this uniformity of structure, there is no external mark of recognition by means of which the various forms or Inversions of the Diminished-7th chord might be dis- tinguished IN SOUND from each other. The four forms (Inversions) of the above chord; % ^' all present the self-same external form, upon the keyboard of the Pianoforte, and are not dis- tinguishable from each other as chords of the 7, f , f and a, respectively j because the actual difference in the size of the interval b-flat — c-sharp (augm. 2d) while recognizable on the paper, in the notation of the Dim.-7th chord (comp. Ex. 93, note *i), disappears in the sound of the chords, on account of the enharmonic coincidence of the augm. 2d with the minor 3d. 231. As the different Inversions of the Dim.-7th-chord can therefore not be distinguished from each other in sound, it follows that the identity of the separate intervals is not distinctly definable, or recognizable by ear. That is, it is impossible to determine, by ear, which of the four tones is the Leading-tone, which the original gth, which the yth, etc. Hence, each tone of the Diin.-7tli chord may be assumed in torn to be a Leading-tone, whereby it will represent in each case a dif- ferent Key. and will be subject to a corresponding alteratioa of dotation. ENHARMONIC EXCHANGE. 131 As the alteration in notation does not alter the sound of the interval or chord, it will simply be an "Enharmonic Exchange." For example, adopting the Dim.-yth chord of b minor : Ex. 153. (at piano- forte.) *l) i-Ss I •2) i Ra5= "7 Leading-tone a-sharp, resolving into B MINOR OR B MAJOR : Leading-tone c-sharp, resolv- ing into D MINOR OR MAJOR : - gyigg 1*- ^ n >>. 0=^ i U _ Ilia- 0_ -0 ^ r — 'iiob "g*^ — &^-^^^^ — -^ ) g— « C^ 7 Leading-tone e, resolving into F MINOR OR major: i ho iig o Leading-tone g (or fx),resoIving into A- FLAT (or G-SHARP) minor or major: *i) The form and notation of each chord of the Dim.-7th is defined by the formula given in 165 (which see); viz. it must constitute a chord of the Seventh upon the Leading-tone of each Key, respectively, and correspond in notation to the minor scale of its Key. — *z) Here the |-form of the original chord (Vo in b minor) on c-sharp, is transformed into a chord of the 7th on the tone c-sharp, whereby an enharmonic change from a^sharp to b-flat is involved. The selfsame procedure gives rise to the other two enharmonic exchanges which follow. 232. The same system of enharmonic exchange is applied with sim- ilar results to the other two chords of the Dim. -7th, which lie respectively a half-step above and below the one upon a-sharp (manipulated in Ex. 153). For illustration : Ex. 154. (AT pianoforte). * izfe: -^^%^^g sf- w9- Leading-tone : a. fjjL dj(, bjf. Keys: bi^ (Bt». g (G). e (E). cj (CJ). Leading-tone : b Key*: c (C). a (A), «(Flt). m- d. el? (Efe). 13* ENHARMONIC EXCHANGE. 233. The application of these "exchanges" in Enharmonic Modula- tions is made as follows : the chord of the Dim. -7th is introduced in its own Key (i. e. in the notation corresponding to its scale, — but in Minor or Ma jor indifferently), and, upon repetition, or during a series of repetitions, the notation is altered, according to the given tables, to agree with that of the desired Key. For example : Ex. 15S. i •i) •3) i -^ A f - S ' *2) . n f^ r ^ •4) Brahms. S P J H ^^ A te ^ ^^1^4-^-fl^ 9 9 9 9 C min. Vo= a Vq-I e min.Vo=Bi? Vq— I ^ PW *i) Or C majors— *2) A-flat is enharraonically exchanged for g-sharp. And, as is here shown, the exchange need not be made in the same part. — ^*3) Or A major. — ^•4) The en- harmonic coincidence of the chords renders all such peculiar melodic progressions (as here in Soprano) excusable. Enharmonic Transformation of the Dominant-7th. 234. The chord of the Dom.-yth is identical in sound with a mixed second-class chord of the tninor and major Keys upon the Tonic im- mediately (i. e. a half-step) below the original Tonic. By means of this enharmonic exchange, a modulation may be made, in other words, into the next lower Key (fi\e Leading-tone becoming a Tonic). For example, from C (or c) to B (or b) ; from B (or b) to A4t= Bb (or W). Thus : Ex. 156. ' B V l)t>]^5.1 b 'b V Bbnjtj-i *i) Raised 4th step in minor (IV); see 207 ; Ex. 139, measure 7. — *2) Raised 4th and 2d, and lowered 6th steps, in Major (in); see 206, second clause ; Ex. 138, measure 9 — 11. — ^*3) Gen- erally, the 7th, or the 7th and 5th, of the Dominant chord are enharmonically changed (see the first measures) ; but here, owing to the unusual location (or Signatures) of the Keys (B majoi progressing into A-sharp minor), the 7th remains, and the lower intervals are changed. ENHARMONIC EXCHANGE. Additional illustrations : Allegro. Ex. 157. »33 F Maj. V Vo e min. IVjjT Mozart. ij? ^£5=^ -&a^^ -^R=^ -^^^:;n F=^ F^ ¥ 4 1^ =^ H: — ' -#- — ^ -*- ■ I E maj. i Allegro. n-Q n Haydn. :^^E ^^^ t-n P g=fx S ^ 7 DV- cJIVx 7 -vv- ^{fo Schubert. ^ • i ;-^m i Mr-r-:. ,m JTl ^ * — ; Nj J *— Ird l-i — H-=» hi ^ — i — I ^ * tn 1 — ^ g« Hr-fr ^ as f ^ :1=4: =i=4 ^fS U-^^-t-^rf^ -t- -t -t- El? Major 7 dIVJt »J4 ENHARMONIC EXCHANGE. Lesson 54. A. Harmonize the following Melodies, introducing a chord of the Dim.-7that each*, with enharmonic exchange at the following^*, as indicated by the Key, and according to Exs. 1 53 and 154: i ^ ^itp^^ ^^s mi 1^ ^ Tt=* 4- _Bl7_ i a=B « « •^Nf S SE^^ fjy^ ^eS ^o^ d f- Ab- •i)"^^-^ C a A Eb eb -^fe2l!l=^^ •i) The three lower parts together on the|Bass-staff, as in Lesson 52, note *5). — B. Transform the Dom.-7th-chord of every Key, enharmonically, in exactly the manner shown in Ex. 156. C. Harmonize the following Melodies, with an enharmonic change at each *, according to Ex. 156: ^ --^ gE5 £ «t±jtoi=±fl* V 4 _IVfl&V_ ^ --r I WWf=f • — J ritard. i Wfs>- *«=F t^^ss^ ^ ^-Stt :?»t^ t^ tf D- ■Vcjt:. 7 V c_ 7 ' .V B- V bl>_ 7 V a_ SUPPLEMENTARY EXERCISE. Harmonize each of the following fragments, in as many keys as may be found I* contain the notes, either as legitimate or as Altered Steps : 6. S ) r TIE I li-r I It H '^'^ J I I 'g-feg- •i) •i) *i ) An excellent general rule for chromatic successions is : to harmonize the first ton* with some ( almost any ) 3-tone chord; and the second tone with some Dominant harmony. DIVISION FOUR. INHARMONIC TONES. Introductory. (Mat. Mus. Comp. §§ 325—335). 235. A chord, as cluster of accordant tones, is defined in 26 as the combination of 3, 4 or 5 tones in thirds., or in inverted forms reducible to thirds. The simultaneous association of more than j different tones ; or the association of even 3 tones in any other interval-relations than those em- braced in the definition ; or, in a word, the addition of any tone which is foreign to the legitimate (harmonic) chord-structure, — results in a so-called WBJJL- MOKIC DISCORD. For illustration : Chords : Inharm. Discords : Ex. 159. i ^^ i :§= *1) •2) *3) •4) •s) M *i) .SVIr different tonss can not accord. — *2) Association of two 2ds (c-d and d-e).— *3) Association of two 4ths. — *4) Two 5ths. — ^5) These four harmonic bodies would be rendered "Inharmonic" by the addition of the false tones (marked •), which are foreign to their legitimate chord-form. Review 22 —26. 236. The tone which is foreign to the chord is called the Inharmonic dissonance, and it is invariably either the upper or lower diatonic neighbor of one of the le- gitimate chord-intervals. It is eTident that the identity of an Inharmonic dissonance can not be determined until the identity of the chord with which it is associated has been clearly established. For examplci in the combination c-g-d (Ex. 159, note *4), the d will be Inharmonic if the chord can be proven to be the Triad of C (c-e-g)j but if it prove to be the Triad of G (g-b-d) then the e is the foreign tone. The identity of the chord will depend, as usual, upon its relations t» the at^acent chords, particularly to the one which follows (Ex. 128, notes, last clause). (1») 136 INHARMONIC TONES. 23 T. There are four varieties of the Inharmonic dissonance, distin. guished from each other by the manner in which they enter or progress, namely, the Organ Point, the Suspension, the Anticipation and the Neighboring or Embellishing Tone. CHAPTER XLIV. The Organ-Point. 238. The natural pre-eminence of the Tonic of a scale renders it ad- missible to prolong" {or sustain) thai tone, for a reasonable length of time, while the other farts continue their harmonic progression, almost or quite irrespective of the sustained tone. 239. The tone thus held or reiterated during a series of chord-pro- gressions is called an Organ-point, and it will almost inevitably become Inharmonic from time to time (i. e. at those points where the other voices progress into a chord to which it is foreign) . If the sustained tone is the Tonic of its Key, it will be called a Tonic Organ-point. 240. Organ-points appear most naturally and most frequently in the Bass voice, but are possible, especially when more brief, in Tenor, Alto, or even Soprano. Rule I. The Organ-point should begin, and also end, as harmonic in- terval; i. e. it should not make a progression during any chord to which it is foreign. Rule II. It should not be associated with chord-progressions (or Mod- ulations) which render it too obstinately dissonant, or ^protract its inharmonic condition past 3 or 4 consecutive beats. BULE m. The other voices may progress freely, and modu- late transiently into any related Keys, but must all move as smoothly as possible. For illustration (Tonic-organ-point in D major ; close harmony) : •i) *i) •i) Ex. 160. P-Major. H=^W Tonic THE ORGAN-POINT. »37 Luj *2) •2) *i ) It is natural that the Dominant chords of the Key should constitute the simplest means of making the Tonic (as Organ-point) inharmonic. — ^•2)*2)*2) These measures illustrate dif- ferent forms in which the Organ-point may be reiterated, instead of being simply held. — *3) The modulation into f-sharp minor, though a next-related Key, is somewhat doubtful, on account of the harsh dissonance involved. — •4) On the contrary, the modulations into g minor (the "Stride") and d minor (the Opposite mode) sound perfectly well, for obvious reasons. — *5) This Dom. chord of B-flat is very harsh, because of its location on the accented beat. It is however admissible, because brief. 241. The Dominant, which is barely less important than the Tonic itself, may also be sustained or reiterated as Organ-point, upon the same con- ditions. For example : •2) Ex. 16t. F-Major. Dominant. *j) The Dominant-note (as Organ-point) becomes inharmonic upon association with Sub. domtftani choTds. Comp. Ex. 160, note *i). — *2) Dominant Organ-point in the Soprano, as duplication of the Bass. — *3) The first 4 measures might also be f minor. 242. Occasionally both the Tonic and Dominant are sustained together, as double Organ-point in the perfect 5th, in the lowest voices. This is called the "Pastoral Organ-point." For example: Vivace Chopin. 138 THE ORGAN-POINT. 243. The other steps of the scale are not adapted to this mode of treatment, on account of their comparative inferiority. Still, isolated examples of Organ-poiuts upon the Mediant (or even the Subdominant) occur, especially in modern Composition, which are justified by the simplicity of the attendant harmony and modulation. For illustration : Ex. 163. C maj. a min. Additional illustrations : C maj. ^^ Andante, Ex. 164. EE =^ Al^V ^ Tonic lizri: Org.-Point. ^ 1 T^w Ilt>V I |*E| Beethoven. -t e^ *-Hi I i£ -Hr=- f i Allegro. ^ Beethoven. m w^^ -v — ' — Dominant Organ-Point. §M -f: m D maj. ^ Allegro. *2) ^ Schumann. i • 7 g i^ Organ-Poi EI pY" 7 AV I Pastoral nt. ^^M ^ 4zd= rat Tonic Org.-P( /int. *i) In this curious Modulation the Tonic (e) is transformed into a Leading-tone (219).- *2) Transition from one Dom.-chord into another (222). THE ORGAN-POINT. 139 Lesson 55. Complete the following Organ-point Periods, by filling out the inner voices {in close ffar- ttony) : 1. Alleqro, t =EEeE ^ -^+^FP Wrr^ m EE 2. Lento. i *^ ^ ^ — t -6 -i- -^ i ^S trtz;; g^ rt<. ^rp QE -f— »- -^—^ s Vi±* ^-^ =t i AlUgre tto. \ | -kH ,^ .F^^ !>» rO -B f^^ — I* ^ i I * I f j * -j— ^ «— 4- 1 * < *— I— |- ^& *2) f» ^=i^ ^ I ^ Tfrfr V V « ■^ J J J-J- j J-J-i. ^= ^ -j-^^iM — r-^i- m^S^: ■i-t^.-H-f fe ^^±ii:^a]i -j-^ tj rit. 9^g=^ J — -<-> — V :i=:i=t=;)= :i— JtH *i) Plagal ending. Comp. Lesson 44, note *5). — *2) 0«? inner voice will suffice, except ing at the two Cadences, where the Harmony should be fuller. N.B. In connection with, or instead of, this Lesson, the pupil is to take a number of the 4-measures Phrases from Lessons 9 to 36, and add to them a Tonic or Dominant Organ-point in the lowermost (extra) voice. I40 THE SUSPENSION. CHAPTER XLV. The Suspension. (Mat. Mns. Comp. 244. i 336—340). The Suspension is a tone which becomes foreign or inhar- monic by being projected or held over from the preceding chord. The tone which is thus sustained past the limits of its own chord, displaces or defers (literally "holds in suspense") the expected legitimate tone of the following chord, hence the appellation "Suspension." The displaced tone is called the "suspended tone," and it must obviously follow immediately, as resolution of the Suspension, 245. For this reason it is evident that the prolongation of a tone as Suspension can only take place in a voice which has a diatonic {step-wise) progression. And it is also evident that unless the prolonged tone become foreign in the following chord, it will not produce the impression of "sus- pension" or displacement. For illustration (given the chords "Tonic-Dominant" in C major): Ex. 165. C-Major AND Minor. *5) The^ofthel, by being held over into the V'/, becomes inharmonic.lt ipen (theFiFTHoi suspends" d S. S.*i) s. *3) *4) f theVy) whose place it u- surps, and to which it must sooner or later five way. bus: •2) S=*-^ «2) i± u. TT "S. S •i) As indicated, d is the suspended or displaced tone, by progressing into which the Suspension e effects its diatonic resolution. — *2)*2) The_/<»-»» (Inversion or arrangement) of the chords has no essential influence upon the Suspension. — ^*3) The same Suspension may occur in either inner voice, nearly or quite as well as in Soprano. — *^ In Bass, Sus- pensions are somewhat rare.— *5) Play each example in minor, also. THE SUSPENSION. 141 246. In these same chords, the tone c may be held over, as Suspension of 6 (the Third of the V or V7), to which it will diatonically descend, as Resolution. Thus : Ex. 166. C-Major AND Minor, IV IT IV •i) Comp. Ex. 165, note •2). The efiect is substantially the same whether the Dom.- Seventh or the X)om.-Triaii is employed. 247. If the tone ^ be held over from the I into the V or V7, ii will not become inharmonic^ because it is the common-tone. But if held over into the V'l the g will be a Suspension. See Ex 167 A. And the tone e can be sustained (as in Ex. 165), as Suspension oi f (the Seventh of the V7), in which case it will resolve diatonically upward. See Ex. 167 B. A B «I) S.»2) *2) jl] Ex. 167 C-Major / AND Minor. J ^ -gLJ^ TT \M I V ^9 r. -r- I v„ f= M q^i J, ^ ^ & rr 7 V ^ r ^ f=ft 4J- P ^ ^=s 3 9 I v„ •o ^ » -1 »o *3) •1) G is the common-tone between I and V or V, and does not produce the effect of a Suspension. — *2) In connection with the Dom.-JVtntA, however, the g becomes inharmonic. — •3) See Ex. 165, note *4). 248. The tones c and e, in the same chord-progression, may 6oiA he sustained, as Double-Suspension. And, on the same principle. Triple and even .:^«a(/ra//c-Suspensions are obtainable. For illustration : Ex. 168. C-Major AND Minor, ^=4 ^ ^ V p g ^y f 1 ^ ^ *i) *2) •3) ^ij P -fZ- I ■v 7 V L- *6)- •8)- g =l=FF=p -rTr^ « ^^ m jt if 144 THE SUSPENSION. ^ a. O.-^ f-/> ^M'^^hiiMm •9) •i ) Every note which is thus repeated (whether tied or re-struck) may be treated as a' Sus- pension, by harmonizing the FOLLOWING note in its stead,— ex3.c\i\y as in Exs. 165—167. — *i) Sus- pension on the 1st and 4th beats o£ each measure. — *3) The dot is to be a Suspension. Comp. note *5). — *^) In this Melody, ZJowW^suspensions may occasionally be used to good effect. — *5) Each dot, in this melody, is to be a Suspension, as if the notation were JJ#i as in the 1st measure. — *6) A Suspension in the Alto. — *j) Suspension in Tenor. — ^*8) Double- suspensions in Soprano and Alto. — ^*9) Every repeated note a Suspension. Use close har- mony. CHAPTER XLVI. Irregular Resolutions of the Suspension. (Mat. Mus. Comp. §§ 341—344). ■ 250. Simultaneously with the diatonic progression of the Suspension into its resolving-tone, the other voices may make any smooth frogression •which does not interfere with the Resolution of the Suspension. This progression of the other parts, at the moment when the Suspension is resolv- ing itself, may be limited to a simple alteration of the form or Inversion of the same chord ; or it may effect a change of chord, or even of Key. For illustration : Ex. 1 7 1 C-Major. S.*i) S. *Z) S.«2) s. S. ^^^J- ff m p t+f: ^^^ mT*T w d:: w 01 F? *i) While the Suspension {e] is resolving to d, the Bass progresses in such a manner as to alter the Dom.- Triad io a 'Dom.-Seventh; in the next measure, to a 'Dom.-JVinth. — *2) During the resolution of the Suspension [c) a Modulation is made, in some other voice or voices THE SUSPENSION. H5 251. Other Licences, such as the prolongation of the Suspension ; the indirect resolution (through an intermediate tone of the same chord) ; and the exchange of Double-suspensions, are possible, but of comparatively rare occurrence. For example : S. res. S. — res. S. — res. S. — res. Ex. 172. C-Major J AND MlKOR. I ^=3 *2) m •3) 7 7, 7 7 01 V njfbv V V I- f T=t^ ^ *i) The Suspension (c) in Soprano is prolonged for 3 beats, before its resolution into b takes place. — ^"2) All 3 Suspensions are prolonged, while the Bass progresses. — ^*3) The Suspension {C_* ^-V-r i s. s. s. s. ^ n iJ.rj|Jj±q : fi'Q i ]f|rn s= -*^r •l)*2) *i) The accented note becomes a Suspension by harmonizing the following note in its place, as usual. But the preceding [fmaccented] tone must be harmonized with some chord which contains,or might contain,the Suspension! See 252, Rule. — *i) An additional (Double) Suspension, in Alto or Tenor, may in many places accompany the Soprano-Suspension." •j) Triple-Suspension.— *4) All the voices may rest together. 148 THE ANTICIPATION. CHAPTER XLVIII. The Anticipation. (Mat. Mus. Comp. §§ 348—357)- 253. The Anticipation is a tone which appears in advance of the chord and beat to which it properly belongs. It may appear in any part, but al- ways sounds most natural in the Soprano. Though possible at any point in the course of a Phrase, it is perhaps most effective at the Cadence. Rule. The Anticipation invariably appears on an unaccented beat, or unaccented fraction of its beat. The more brief it is, the less danger there will be of a misapprehension of the Harmony and Rhythm. Comp. 249, Rule 2. For illustration (given the chords "Tonic-Dominant" in C) : Ex. 175. C-Major / AND Minor. J (^ (|± The b is inhar- monic, or for- eign, in the I. It "anticipates" the Third of the V, into which it is immediately repeated Thus; Ant. 4=-. ■0-^S- A=L 7 V A. A. ^ r f ^=F ^ A. ^ f=p *l) Z)«I V EbVo I V T I oV i *# Allegro. Clementi. U- ^: ^ •i) i^ riuiS: z^d^zfcdi i. I- 7 -V Beethoven. fe^ iJ£_t- Andante. „ j. t° j. ^ .% ^ .^ ^ >54 THE NEIGHBORING-NOTE. Beethoven. Allegretto. ° S ^- & l^ S *i) o i ! i i J . n-T^-n J i I i J i , {^ \jz£. -t-=te m F I- 7 'V- ^wrfarafe. i Brahms. rn — ^^-s -1 — r^v^ i j u ,-7 ffc^ 9^ :1=q=i:=t Q j *— T>- Allegro. *i) Double Neighboring-note. — ^*z) Neighboring-chords; they are ^oi» brief to be essen- tial. — *3) Accented Neighboring-chords. Lesson 61. Bass. I. »i) ^ f7> ii rTrrr7??^ri.?^.r7rfFrrr i ^^^ bE— .M l M I Tl " f I -^-Q=f fi^^ ^-»-|L r^^^mnij i- LU MJ I H|p:£m *2) Soprano. 2- *3L •^ ^ 4 a4s#4=^ Se^ ^ -- H-U ^ J J J =:1^ ^ ^ J J J ^ ' THE NKIGHBORING^NOTE. 155 tt- EPS ^^ m ' niT P -i-ir-t J rTT ±s±=ii Vfiv- Tenor. 4- H^ *-^ " — ' ■^ ' ViJ Tenor. *6) Jf-T- 4- 4- 3=t "^ I -- -" I ■■■!■■" t H^U^HH H^H^HH 1 -^-F-^ . 1 1 l i rLtrn -^=p=? l^F^^H^ =HHfH^-f ^S =B -Btr •i) Add three upper parts to this "Running Bass," in close Harmony — ^•2) One melody' tone (and chord) to each slur, strictly. The Neighboring-notes are easily discernible.— *3) Ordinary open Harmony. See note •2). — *4) Add Soprano, Tenor and Bass to this Running Alto. See note *z). — ^*5) At this point the Alto pauses, and the Tenor takes up the Embellishment— *6) Add Soprano, Alto and Bass to this Running Tenor. See note *2). 156 THE FASSINQ-NOTE. CHAPTER L. The Passing-note. (Mat. Mus. Comp. §§ 363 — 369). 260. The Passing-note is an inharmonic tone which is touched in "pass- ing" step-wise^/Vo/w one chord-tone to another. Hence it serves to connect two different chord-tones. (Comp. 258, Rule I, for the distinction between Neighboring-riot^ and Passing-rxite) . 261. «• This connection is almost always made diatonically, along the momentary scale ; but occasionally it is also made chromatically^ espe- cially in ascending succession. h. Two, or even more, Passing-notes may occur in immediate succession if they follow each other stepwise in the same direction. This will depend upon the size of the harmonic interval to be "filled out," and also upon the choice of diatonic or chromatic Passing-notes. For example : Ex. 181. C-Major. *i) 4> i 01 + IV •2) r I r ^^M Bi 4- 4- 4- ■» *4) r r= ^s) \r ^M ^ — i r r *3) r f *i) The Passing-notes are indicated by +. — *2) Two Passing-notes in succession.— •3) Descending chromatic tones are generally written with flats, excepting the one immedi- ately below the Dominant of the momentary Key, which is written, as here, as raised 4th step (in C, as f-sharp). — ^*4) Four chromatic Passing-notes in succession. — *5) C minor; the change of notation in the minor mode is significant. 262. In the above example, the Passing-notes are all unaccented, i. e. they stand between the beats, as light fractions. But they may also occur at the beginning of the beat, as accented Passing-notes, and are then THE PASSING-NOTE. 157 usually much more efTective than the former, because more conspicuous. For illustration : Ex. 182. C-Major. t ^ g. + X ^a •■' ^ y u n *2) ^^^ ^ ■s-^4- w^ ttJBJ J J J. I r^r f f *i) The Accented Passing-note is indicated by x- — *2) These measures are also valid for C minor (with e-flat and a-flat) excepting tliis beat, which would read a-flat instead of g-sharp. 263. Rule I. Unaccented Passing-notes are admissible and effective in any voice. Accented Passing-notes are best in Soprano ; in ' the inner voices, or in Bass, they are apt to obscure the harmonic sense, and must there- fore be carefully tested (by ear) . Rule II. Passing notes usually necessitate the subdivision of their beat, and are therefore subject to the rule of rhythm given in 38, viz., the lig'ht beats must be broken first, so that the unbroken beats (if any remain unsub- divided) are the heavier ones of the measure. Rule III. Successive (parallel) perfect 5ths or 8ths, which may result from the insertion of Passing-notes, will only be objectionable in case the second 5th or Sve is ferfect and harmonic. For example : Ex. 183. "^r-iprn -r V A few of the very numerous forms of Embellishment with Passing-notes, Accented and Unaccented, are exhibited in the following example : J. S Bach. Allegretto. Ex. 184. ^^^ig + + P^ iE^ j^^^ —r—i f^^fe— —j—. — ■ GI- ■IV I5S THE PASSING-NOTE. i SiA Allegro. Beethoven. ^ d= §iS + X i^ ^3:4= I EI '7 V '!7 V Allegro Chopin. + X 5»a.. ojnti*!) Lento. ife=iz3 Chopin. Chopin. Mi — j»- *» g^p3^ ^=!^- -i— Jr -i- -t O O X , s ■3»2) g±g S fer#: -f-f- ^ =^^^ 7 ev- Dbi- Allegro. ^ x_ Chopin. Allegro. J. S. Bach. P±^^S^^ fe=3-_j^ !^i- ^^^S^^^5H S »4) -f-i-nm iS: e min. I~ THE PASSING-NOTE. 159 Allegro. S ti -h t| Chopin. ^M *s) 4t- :t i 08 V- Allegro.8 o ^) '' 1 f' Lt^ ^ •H-i-^ =ci= i^ -i— -^ =5= 01- -IV- "S. o CI. ^ ^ CZERNY. * 1 i I d^ A -^ ^ *i) The Lowered 2d step (d) of c-sharp minor.— *2) DoubleJPassing-notes. — ^*3) Pass- ing-chords. In such rapid tempo they are too brief io be essential. Comp. 180, note *2).— •4) The descending chromatic tones are Passing-notes, intercepted by the reiterated e.— *S) R'ptated Passing-notes. Lesson 62. Elaborate the following melodic sketches as " Running Soprano," in a uniform rhythm of first 2 notes, then 3 notes, 4 notes or 6 notes to each beat, as indicated ; using Passing-notes unaccented and (occasionally) accented. Neighboring-notes, and (when absolutely unavoidable Harmonic tones. The lower voices need not be added. Directions : The choice of intermediate embellishing notes depends (i ) on the size of the interval Uoxss. one essential tone to the next, and (2) on the number of tones to be used in a beat. If the space is just the right size for diatonic or (ascending) chromatic Passing-notes, these are to be taken in preference to any other form of embellishment. If the space is too small. Neighboring-notes will be necessary. If the space is too large (or in any respect incon- venient) Harmonic tones, of the momentary chord, may be used. By means of Neighboring-notes, any single tone develops into a group of 3 or 5 (7,9) tones I 3 3 5 5 Without involving the question of space (interval to next essential tone) at all. These groups i6o THE PASSING-NOTE. can then easily be extended to 4, 6 (and more) tones, by adding Passing-notes or Harmonic tones : 3d + ""T^ "^ '- 6~~^ 2d $ ' U^ M m-^ i=P= ?^=i=F P=S i =*t: IS I l£ ^ M Exercises. I. (2, 4 and 6 notes to each beat.) 2. (3 and 4 notes to a: ^= ie=^ each beat.) *3) *i) *2) ^ 3. (3, 4 and 6 notes to a beat.) M ■~^> iS^ *i ) The Cadence-tone is not to be embellished. — *2 ) See 258, Rules II and III. *3) The given melody-tones should appear, as a. rule, upon the first fraction of their re- spective beats, — where they stand ; occasionally, however, they may be shifted to the second fraction, — not beyond. CHAPTER LI. The Appoggiatura. (Mat. Mus. Comp. §§ 370 — 374). 264. The Appoggiatura is an unprepared Neighboring-note, which is simply placed before its principal tone, without reference to what precedes, i. e. without regard to the manner in which the Neighboring-note enters. Comp. 258, Rule I, for the distinction between the regular Neighboring- note and the Appoggiatura. 265. Either the M//e>- o>- /ower Neighboring-note may thus precede any chord-tone ; it may be long or short, and although it usually stands upon the accented fraction of its own beat, it may also appear upon an unaccented fraction of the f receding beat. Comp. 262. For illustration : Ex. 185. ^ 01 o ^^ o_ O— 3ES »4) it ^i ^ ^ EUt *i) THE APPOGGIATURA. 161 ^ i S ^^ M *2) *3) *l) These measures are all valid for C m<»0r also (with e-flat and a-ilat), excepting this d-sharp. — *2) It is usually possible, and always effective, to substitute a. Rest for the first (accented) tone of an embellishing group. — ^*3) When very short and accented the Neigh- boring-note is called an Acciaccatura. *4 ) N. E. The choice between upper and lower Neighb.-notes may conform with 258, Rule II ; or, as exception, the figures may all run in the same form. In the first case the groups will be regular ; in the other case, uniform and symmetrical, though irregular. 266. Upon the same principle, both the upper and lower Neighbor- ing-notes may successively precede their common principal-tone, as Double- appoggiatura (broken) . And, here again, both the duration and the rhythmic location of the inharmonic tones are entirely optional. Thus : Ex. 186. E Minor. el ~ *? " Ex. 185, note *4). >- 2 6 7. The rules for the treatment and choice of these unprepared Neigh- boring-notes correspond largely to 258, Rules II and III, which carefully review. But see Ex. 185, note *4). This mode of embellishment in its manifold phases is illustrated in the following example : Vivace. Ex. 187.< =^fe ^ ^ Is g fi^P oi_ l62 THE APPOGGIATURA. Beethoven. Op. 120. Allegretto. o ^8 /"^ Beethoven. Beethoven. i Presto. ^ Alio. Schumann. A m ^^ -tr ^^ g ^ 4^ 3=33 7 7 ^ 1^* " OIV IV I FV I bl 17 I i Allegro. o -1^ Chopin. Ficace, o m Chopin. B-i=rii^^fas it ^-^ J-l' ^r^ ^ t ^ •2) i -t- i m -a £3= F4 r * LJ lu L^' FI. el_ Allegro. ■ g ^ Beethovek U-U^^ ± •3) *4) S on. THE APPQGGIATURA. 163 i Allegro. --5— ^ s" „- ■^ —^ IK Beethoven. 00 00 f^- ^^^^^^=t-^=a zsnr: ^ *3) §S^ - L -I- 1^ ^ Presto. I Chopin. 1^ .^ " fPJM r> : F Fg:a ^ * •3) ^^3 -1- «J ^ ■A— ^- o^fy- -nr Chopin. ij^ H^jgir'^ ^ :^ .I_ *S) Chopin. Agitato. Chopin. ^ te^ I 1 000 _0 OOP |_ " T| n. *6)o ^ r p:^"^ " ? ^ r± ^^ ^ "-^^ i ^ ' ^ ^ ^=^ f=kz -^ — ^ S S^ -jv- T • I_ 164 THE APPOGGIATURA. *i) This unprepared Neighboring-note (g) illustrates the resemblance which frequently exists between the Appoggiatura and the "Free Suspension" (see 252).— "z) The £-sharp is in reality an accented Passing-note, but its effect is precisely the same as that of the adjoining Appoggiaturas. Observe the effective chromatic Passing-notes in Bass. — ^*3) Double appoggiatura (266). — *4) B-naiura!, and not b-flat, because the chord is distinctly in C major and not in d minor. — ^*5) A TVi^/if-appoggiatura. — ^*6) An extraordinary passage. Each Neighboring-note in Soprano is repeated (comp. Ex. 184, note *s), and accompanied by an additional Appoggiatura in Tenor. The second chord contains the raised 4th ste^x (d-sharp). Lesson 63. Take the three melodic sketches given in Lesson 62, and elaborate each one as "Run- ning Soprano," as before, in a rhythm of two notes, then three notes, and then four notes to every beat (excepting the cadence-tone), according to some of the embellishing figures shown inExs. 185 and 186. Simple Chord-accompaniment may be added, on the lower staff. CHAPTER LII. Embellishment in Alternate Voices. 268. When these various classes of auxiliary tones, explained in the foregoing chapters, are employed in alternating parts, with a view to the embellishment of the entire harmonic structure., the following rules must be observed : Rule I. The adopted rhythm (of two, three, four or more notes to a beat, as the case may be) must be adhered to throughout. That is, every beat must be subdivided, in some voice or other, in similar proportion ; only excepting an occasional interruption at an accented beat, if desirable. . See 38. In Soprano, on account of its prominence, the rhythm should be regular, as a rule, irrespective of the other parts ; i. e. only the lighter beats should be subdivided in the Soprano. This restriction is neither possible nor necessary in Alto, Tenor or Bass. Rule II. The embellishing rhythm must not continue in any one voice longer than one or two (or three) beats, after which some other voice must take it up. The choice of voice is optional, and will depend upon cir- cumstances, and upon the taste or judgment of the pupil. Two (but rarely three) voices may occasionally embellish simultaneously ; probably in the same rhythm, but not necessarily. Rule III. Parallel and intercepted 5ths and 8ves must be avoided, ac« cording to 263, Rule III, which review. EMBELLISHMENT IN ALTERNATE VOICES. 165 Rule IV. Ties should be freely used, especially from a light beat over into an accented beat. They are most effective when they give rise to a Suspension. It is however usually awkward to tie any short note (less than a half -beat in duration) to the following tone. A similar advantageous effect is produced by a Rest^ which, as stated in Ex. 185, note *2), may generally be substituted for the_/?rj^ note of an em- bellishing group. — Observe the directions given in Lesson 62. Lesson 64. Embellish the following Phrase three times, first in a rhythm of 2 notes, then 3 notes, and then 4 notes to each beat. Employ Harmonic tones. Neighboring-notes, Passing-notes (especially unaccented), and occasionally Appoggiaturas ; -with reference to the above Rules (268), and to the subjoined Model (Ex. 188): ; see also Appendix B, No. 9. ^ M JL ^^ ^ -* — t- ^ fc f iii r IJUi 4-1 5 ^ Jj?=?= ^ OE n^. "nyrrt Model. Ex. 1 88. 2 notes to a beat : ^ *i) iw l>=4- ^ ^E=^ 0*2) I ^^ 3 notes: i t- n 4 notes: m ^p?^ i ii-fc g ^g =t •i) Each of these fragments represents but one of a. very great number of possible elab- orations ; they are to be imitated, but not copied literally. — *2 ) The ties, given in the original, may, as here, be removed by the Embellishment. i66 EMBELLISHMENT IN ALTERNATE VOICES. Lesson 65, Elaborate the following Phrase three times, precisely as in Lesson 64, with first two, the> three, and then four notes to each beat; see 258, Rule III. ^^ m l=>u ^ J ^ji *- rr-f ^z^fa-i^-ty £ 'M^i^ ^¥ rT=P=f CHAPTER LIII. Harmonizing of Embellished IVIelodies. (Mat Mus. Comp. §§ 379—382). 269. Before determining the chords for the harmonization of a florid melody, it is necessary to reduce the melody to its original unembellished form. Such notes as are obviously (or probably) only ornamental Inhar- monic tones will not be harmonized at all, and maytherefore either be omitted or imagined absent, while choosing the harmonic basis. 2 TO. Tones of short value, especially in diatonic or chromatic succes- sion, and tones with Accidentals (unless distinctly indicative of a Modula- tion) will probably be Inharmonic, and unessential. On the other hand, all comparatively longer tones, and all tones which progress with a skip, will generally prove to be Harmonic and essential. The indications of a Sus- pension or Anticipation havealready been given (Lesson57, ""'^^ *'^) > Lessons 58, 59, 60). Aside from these very general principles, the pupil will be best guided by his judgment, experience and taste. Lesson 66. Harmonize the following florid Melodies, with reference to the subjoined notes : I. Moderato. ^^^^^ e^^ EMBELLISHED MELODIES. 167 r^-ffl^ ^jd' f f u . f ^ m K ffrr rrw ^ o • j 2. Maestoso. wsm 4^t- ^ ^ ^^ I ' ^l?^ ^ *2) F^ -E5" l Lf^j^^gfe^ri' .i.J^ i ^ f i-uT -i—f- r^ ' f w ^ff • - . r " 3- Allegretto. ^^ 3 s s S ES -f-6*— ^ ^^w?^ =t=t=? I ! i^r *3) *i) n ^ . ill — r ! — ^^-•" M(-Sp- ii*H . 4. Lento. C « — J — *• s q-fe-^ ^^ u^ l ^J^ •4) »!) f f 1 ^ 1 i. ^^1^: ^' r£ ^ I CT% ^ *i) One Bass-tone (and chord) to eaeA slur, strictly — , or ignore the slurs altogether.— *2) For 6 measures, the rhythm of the accompanying lower parts will be I X J )( J I i after that, one chord on each J-beat. The number and location of the lower parts is optional.— ■3) The three lower voices together ou the Bass-stafi.- *4) Lower parts rest during thia beat 1 68 EMBELLISHED MELODIES. Lesson 67. Continuation of Lesson 66 : I. Andante. gS /^p- -f- -r~ :t" "f" iffe S & ii. Allegro. g ^-^^- S^ S: f-^-r-Ff= ±±ie Uj ^l-i-U j:^ *l) (B maj.) i li^ (a) ^ f-r^7n-,>^?=Fit . f^f fii . r ^^3=^ I ^^ pa =t:t S < — -i — «• X s F #f f^iTnTrrT~-CTT ^f= rT7^-^-f ii jj I i i J 11 ^ JiiJ J t^ (F) ^U 6 4, r S^'-ji-r-^i-^-^^-^^ i=B l#^=t s s v-_j: ' rail. ^)" ^"^ ^ '-J-=g^=^=^^=^ J ^ ^HW^-^tI 3. Orazioao. Plff^'^ahMAm *2) ^ EMBELLISHED MELODIES. [69 Soprano, Tenor Alto. 'P^ p^' L lI^f ^Ff- F^ ^ a * (onjltb) Soprano. IE i=£ f^"f :D3=:i= ^tt^^ES ^ ^ J, \ \i J_.L^L4 J=j J-^ *4) •i) One Basstone (and chord) to each slur. The three lower parts together on the Bass- staff. — *2} One chord to each slur. The harmony may be open or close, according to ne- cessity.^3) At each of the next 4 bar-lines the embellishment alternates, as indicated. Comp. Lesson 61, note *s).—*4) Bass. In the next measure, Soprano again. Plagal ending. Lesson 68. Harmonize the following Embellished Basses, with reference to 269 and 270, and the sub- joined notes : (l)_ ^^i^^p^^^^ ^ i=^ e^^ :r-Ff=rE^rS ["^j^2"*'T ^ i:i -t-*- ^P^ lyo EMBELLISHED BASSES. 2. »i) ^&i= ^ ^^ ggg^ ^i m '^gSTS- 3- *i) ^. A^ ^^s :B ;S^JL2_^ ^S rf^ 1 S. Adagio. 6. Andante. 7. Presto. -O?- tf_t_ im f—f- :t?= ^ *2) M- rall. aa^ - ^ H 1— ^ 5=f s^^s fzzEEM 5^SF f-h-^Y 8. Allegro. ^^^\ {«« pin , fl /^ r- /^ f ^f rt-^,. f eHeeS ± T ifJr I ^" t :L£ iSfe ^s -I — — ^ — I- EMBELLISHED BASSES. 171 •l) The first care must be to obtain a good, melodious Soprano, throughout, before adding the inner parts. Use one melody note to each slur, and place the inner parts (the number of which may occasionally be more or less than three) together on the upper staff. — *i) To be elaborated three times, in the given tempi, whereby the rhythm of the Soprano will be as follows : Adagio, one melody-tone to each bass-note ; Andante, three (or four) melody-tones in a measure ; Presto, two melody-tones in each measure. CHAPTER LIV. Analysis. 271. The following excerpts are to be copied out and analyzed. The Keys, (Modulations), Chords, and Inharmonic tones (Organ-points, Suspen- sions, Anticipations, Passing-notes, Neighboring-notes, Appoggiaturas) must be accurately indicated, m the manner shown in the foregoing examples. Rule I. Place the simplest construction upon every chord ; i. e. de- fine it as "Tonic" or "Dominant" chord if possible, but not overlooking the possibility of its being a "Second-class" (Subdominant) chord, especially if Altered or Mixed. Rule II. Look forward. The identity of a chord depends upon what it does, i. e. upon what follows. (Review Ex. 128, notes, last clause; and observe 223). Rule III. Take the Tempo into consideration. What will produce the effect of an essential tone or chord in moderate tempo (or upon a full beat), will probably be an unessential Embellishing tone or chord in very rapid tempo (or upon a short fraction of a beat). Every note must be accounted for. Lesson 69. Aiulyze any one of the following excerpts : Meitdelssohn's " Song without Words " No. 12 { Op. 30, F-sharp minor ). Beethoven, Pfte. Sonata op. 13, second movement i^ Adagio cantabile ). Chopin, Prelude, Op. 28, No. 3 (G major). 172 ANALYSIS. Lesson 70. Continuation of analysis (271): I. Adagio. i ^^ i ^-* 1^ Ig _. i -I tTTf ^ # e^^&f i i i i ■4- asfe :?=¥ rg ^^^ «i) i ^ ^s ^4>^-^— j- J J - -j «- J^t_2^ r t-r-f-r i ^^^ n^^. 1 i is^^ =ttr= f^^ S! f=f=tf^ =P=^ J. S. Bach. "Matthew"-Passion. fcr ^ e =5Pt=F i .i i "^ — r— r i: iffeiE^^g i^ =tt t^ ^ 2. Allegretto^ ^s fe2= ^=^=i « a llESEi i: '■j—f—r- jtlzzi i i ^ w J * ' * *'- :t=t=t *2) ^• ±S . -iS-h ^=X aaES i:^ ■^ r^ ANALYSIS. i i ^^-J-.' - 2Ff ;&. 4=4: I ^ 173 ■^ -*- A -!^-r-F-f=F -»-?- -» f- lff=^=5=f=x: jr-f- r-f-r !f=Ff ig^3^^a=|jj ^^j j ] | .i^g ]^ X Haydn. (Symph. E-flat). gEF=f=FR s ^ ^"-^■'-~''~ ^ :hi?: =F^r-^ T i_^ i-fcift: *=t i 3. Adagio molto. tr g^=^^=1^ ^FF^ '-^ 1^ :P=-T: :fc=t I M M 1=:tq=t1: S -i i i J ; 1 -i It- ^^ "^t TSL yt r 1: Beethoven. (Variation). 174 ANALYSIS. *i) At this point the second Part of the choral begins. The Melody is an almost exact reproduction of the first Part, but attention is directed to the remarkable changes in its har- monization. The latter is prompted throughout, as will be seen, by the independent melodic progression oi the individual voices. — *•£) E-flat major (or minor) V^. — »3) The Modulation into C is effected at this place, through what proves to be the IV of the new Key. Lesson 71. Continuation of analysis (271) I. Moderaio assai. *2) , pa j:^nTa45 I I ui ^^ gg -V^-f b. 1^ b* ^ lT tj^g ^U^.^^ i few i± ^ m-iS =R: ^ 5?^5Jt g=f^ ^H=T tl£ :pJ?: -^ & -r^ jn^ tJ.i^,i^ ?=^f-l-r ■#— h-= ^ F 1 F ^— H-' ' ■ ' — ^— ^— ^— . g^^^g ^TTl ^ ^ i^ J. B. Cramer. (Etude.) J- -f — ^ PS S ^ 4i- S ^ ^ ANALYSIS. ^75 2. Allegro. «# ^ ^3= mj-j^m^^J -j^S 1=t -i— *-r- ^ -tP^ T—r -« — t. S3e 1=^ * ^^ -pf-piJ=j=:^=0£ ntiS f r p^ li * S ^—^ ^. 33^1 Chopin. (Mazurka.) 3 g irfer-i- 1^ 4 §^±^ tfZ f *i) The g-flat in Tenor is a passing-note, which might be written f-sharp. The chord is e-minor I. — *2) Like note *i ). The chord is f-minor I, with c-flat (b-natural) as passing-note. Lesson 72. Continuation of analysis (271) I. Lento. ^E* 23=15 -^ — i -I J -.-^- ^ i^^ "F r^ _^__^ I X76 ANALYSIS. r^ s I 1 ■/ *1 ;j; :* i^ J^J^- ^. ¥^ . » * • 1 Ij'' 1 .lnq -» — 1 " ' n — ; — ^-frf — =:--f — =i i Schumann. Op. 23. i p dm ^ ^^ =r 1= irvl trf •*- + JL^I-J - asEi 1 — » — — ^ — r- f=f nj Poco adagio. 1 [I ill ^^ ^f I * ' 1 hJ . « • i ii « m ^ i=i J^ ^ i^ - t-f-r *i) -®-. a »2) ^ ^eeIe (i ^ u:f4 iJr:^ Li-4c:i m ^ izi :^ -f— r-4 15 6f4 m ?=ff^ -p- ■s-nJ-J^ w »^ :^^==p= px: i i=t s lip" |: • tif . 1^ •!-)>■ . -f. Dvorak. (Requiem.) m=^ u- m £E fp=tt 1 — r i: tl-fi.. P^^ ^=t =t=t: ANALYSIS. 177 3. Orazioso, poco vivace. P='=n ^*=H -feT5»»- t dolce, sotto voce. ^^m uJiKU-U^ rrrriUri>> e=yj gt* ^ r '^ feS; r tr . . , r ^=i=q=4=^ ^::gH rii. ^^^ cfo^ce ed animato. ^^ =^ m m s ? r il l U^^bIb *3) IF 1 -4-i-J ^ Brakms. Op. 76, No. 8. -^ f — ® ±n: -f — ->- ^pP=& * n'i. ^ ^^ ioj: u m S±: =6^ fc±: -f- I *i) The a-flat is an Anticipation (possible gth) of the following chord. — *z) This ar&tA s the lowered 2d step of g minor. — ^*3) The C in Bass is an Organ-point. APPENDIX A. SUMMARY OF CHORD-CONNECTIONS. 1 . Triad-Progressions. The I : can progress into any other chord (of the same, or even of a different key). The V : can only progress into I or VI. The IV : can progress into any other chord of the same key, excepting into the III. The II : can only progress, readily, into V or VI. (Rare in minor.) The VI : like the I, can progress into any other chord — , excepting into the I, its own Prin- cipal Triad. The III : can only progress into IV or VI. (Rare in minor.) General Rules. 1. Tonic chords may progress in every direction. 2. The Dominant chords can only progress, legitimately, into Tonic chords. 3. A Subordinate Triad should not precede its own Principal Triad. 4. The VI laay follow any Triad. 5. Any chord may be repeated, after an accent. Table of False and Doubtful Progressions. ?? -^^ ? ?? ^0 ?? ^ ^ ?? ^ ^^ I =9 ; g a -zr _£Z. j2_ -O- v-iv v-n iv-m n-i n-iv n-m vi-i m-n m-i m-v 2. Chords of the 6th (First Inversions). General Rules. 1. The best First Inversions are the Ij-Vj-IVi and II^. The VI and III are very rarely inverted. 2. The progressions of First Inversions coincide, in general, with those of the respective fundamental Triads. The difference consists in greater freedom of movement on the part of the 6ths ; namely : 3. All doubtful and false Triad-progressions are improved by inverting the SECOND of the two chords, and are rendered quite admissible by inverting both. For illustration : V-IV or VI-I or IV-III wrong; but V-IVi or VI-Ii or IV-IIIj a little doubtful J and V,-IVi or VIj-Ij or IVj-IIIi good. <1T8) APPENDIX A. 179 (The inversion of thejlrst of the two chords, however, does not materially aSect the pro- gression. ) 4. Hence the rule, that chords of the 6th may be connected with each other in any order; especially when the chords are close, so that no wide skips are involved in the Basa- voice. 5. All repetitions are possible j even over an accent, if the Bass-tone changes. 3. Chords of the 6-4 (Second Inversions). 1. The best 6-4 chords are the la and IVg. All the rest are rare. 2. A 6-4 chord may enter from, or progress into, any chord upon (i) the same Basstone; (2) the next higher or lower Basstone ; or (3) any other form of the same chord (as Repetition). 3. The only exception is the leap in Bass from II to I3. 4. A diatonic succession of Second Inversions is only allowed when one of them is a Dis- rortZ-harmony. 77770 9 5. No form of the Dominant harmony (neither V-Vj-Va-V-Vi-Va-Vs-V nor Vq, etc.) can precede the Tonic 6-4 chord (I2) when the latter is accented: the progression V (any form] | la (accented) — is impracticable. 4. Connections of the Dominant-Discords. 7 1. The V, in its fundamental form, resolves into the I, la or VI. In its inverted forms, only into the I or Ii — not into the VI. 7777, , , 2. The progressions with stationary dissonance: V-IV; V-II; V-II (mversions depend- ing upon circumstances) are permissible, especially when the Dom. harmony returns. s 3. The connections of the V (Complete and Incomplete) coincide approximately with 7 those of the V. 4. Through the agency of chromatics, Dom. chords of different keys may be connected with each other. APPENDIX B. Summary of the Rules of Melodic Progression. i in ail cases, diatonic (conjunct, smooth) progression is preferable to leaps. 2. Any reasonable leap is, however, permissible during chord-repetition. 3. After a wide leap, the voice should turn. 4. The leap of an augmented ith is invariably objectionable. The progression of an augm. 2nd, dim. 3rd, and other awkward intervals, should be avoided. They are least disagreeabte i8o APPENDIX B. during chord-repetition, or when occasioned by an Altered step of the scale, or by an Appog< giatura. 5. The 7th scale-step (Leading-tone) should ascend ; the 6th and 4th scale-steps should descend. 6. The succession of the 6th and 7th scale-steps, in either direction, is invariably a viola- tion of the spirit of melody and harmony, and, when deemed necessary, should always be treated with great circumspection. In minor it is prohibited altogether. It is least objection- able when one of the tones is Inharmonic (a Passing-note, Neighboring-note, Suspension or Appoggiatura ): ^ Se± T T OIV IV I 7. Chord-sevenths and chord-ninths descend. 8. It is not well to leap either to or from any sensitive tone (e. g. Leading-tone, chord-7th or 9th, ckordfifth. Altered steps); but the skip to such a tone is nevertheless permitted in the direction opposite to the tendency of the second tone; i.e. the skip downward to the Leading- tone (because the latter has an upward tendency); the leap upward to a chord-7th or gth; and the leap downward to a raised scale-step, or upward to a lowered scale-step. 9. In rapid melodic figures (in melodic Embellishment) care must be taken to calculate the direction and distance to the next essential tone so as to reach the latter, if possible, at exactly the right instant (usually diatonically), i.e. neither too early nor too late. If the space is too wide for conjunct (diatonic or chromatic) progression, the necessary skips generally come first in the group. Examples : rhythm of 3 : rhythm of 4 : * good. (reaches c too early.) good. good. ^ ii?C (reaches c too late.) rhythm rhythm of 3 2. of 2 : ^ rhythm of 4: good. good, (reaches c good, good'; better, too early.) good. 3. rhythm of 2 : f^)>j^;iJ->'^fei rhythm of 3: rhythm of 4: too uneven. better. (reaches g good, too late.) rhythm of 6 ; good. ? good; better. APPENDIX C. i s No. 1 . ( To Lesson io, p. 34-35.) *i) i. *U ^ #-F#- B ^ its. #4- g Mr 4 j+j- *iti ^ p-^ • |5^SS^ P^Sl ^^ i E^ /• ^ »S:2: P^ p^ ■f=- i? s i i:^ ^ i 5i^ r^ ir rr ^ ^ ■<=- •?5^ a J g i "T^ ^^~^ ^ s =p=ff ^ ?^ ?=^ i iA ^^&:r5 ^^ffi i Fimczrr^ J ^ | --<^ u^ •l ) Observe that a wide skip in the melody generally calls for choxd-re/etititn. But see 64, Rule 4. *2 ) The slur indicates that the tones belong to the same chord. No. 2. (To Lesson 11, p. 37-38.) i fe tef m s fi * N ^^ 'Jl j V-^ 1f^ ^^ S^i^^^ m ih*-^ ^JJ U c p^ (i8i) 1 82 ^ APPENDIX C. d. if"^"iini,njrMii,,i i|iJjr| | irJjjlJj M ^M^ J ^J^J ^ ^ S r^' J *\f- -^ i No. 3. (To Lesson 13, p. 42-43.) (SI — •• &t:g: 6# W^ a) l< g g^=g=g^ *— -•- — — a l g' i N.B. g r 'M'Tr r jiJ^jjj | j r f-7^.;pF^!^^ i rJj i J r r i r^j ffl±i i N.B. i ^ ^ :e #ro! B..ft -"i I I . I I , I r <. ^ ^^^ = ^i ^* J ^ s# N.B. S- n •i ) N.B. ^9^r^\ » p\ fT\»^\\ \\f , L^. f \\J^ \ -*- ' TT ^^-P- S ^ \ i^i^\vn z m ' n *i ) Not the V, because of the skip to ( or from ) M* chord-fifth ; compare Ex. 62, note *3 ). i t^ No. 4. ( To Lesson 16, p. 52-53.) a. b. ^ ? f'— — ^ ^ ^g— s>- I TT. %■ III ^ i=S tirfJ'.jiJ T i fn%^^^ ^^ Hi V ii n. ^'\r<'^]\l^y ;lfTT^ ^ )»• r :g 119. flr APPENDIX C. $ SE /• 183 3 ^^^ rS' es ZS. — -(S j^ ff b*^ J f ? I «2) Claude Goudimkl. 1 «> ^ a ? ^ *l ) Lesson 16, note •2). — •2) See Ii8. No. 5. (To Lesson 18, p. 59-60.) i fc& ^^^i £^a r r r =f=F #=F^ ^ a e 4 4 i fc=* s d I > The same as b, but with the following ending : *I ) I 1 1 1 ? u «4 S ^ FL' I 'J' I ^^L' I rrJ * i* . --* S: 119. i s a •2) ^ r^'^-^jg^ fTr^ S gr^^ *'-*-^ if •i ) The entire melody in g minor. — *z ) This must be the IIj ( not the V ). See Ex. 81, note •£ ). No. 6. ( To Lesson 23, p. 70.) m ^m t ^ m^^ nmrjnrii ^ iifi'iiiiii'iiiiirijii ^Tj^rirmni 184 APPENDIX C. No. 7. ( To Lesson 25, p. 72.) i *5 ^ r-' ■ ■ ~ i ^ FT-ffi' l J^-^ fE^ •i) L— i— ' nl S' »H"i ^ *I) »I ) *I ) trt *2) *I) i!) ?«=F?=P^ fe^^ S) 4 J I J W: £?3 Ttatt* '• *3) b .. I I - 4^'^('' i 'd — F- Jt=:± i^ s *3) -1^— *- ■ -^v • |g e <^=^—^ — d I ■ 1 *i ) According to 149. — *2 ) Two Bass tones. — *3) According to 150. No. 8. (To Lesson 42, p. 104.) An altered chord at each *, choice and form optional. Q, ^ ^_ # * « ^—, --I'-f- r ^ I r ^r r^=fl^V=irFrT=f rJ? 1^ gn^ i u ^M^ - ^ itttiS #■9*- |fe §wi#s#f^j 1 1 Mim^ mm i ^ y~f Df 'f^~#= a^ I ^s -'g-^* 1* =»^ i / i;^ t ^^' ' '_f ^HV-^— J- ^!fc£^g -1^ s- -tf^ g « — ~r""??F r ^ i "^ /5. « 2. » • ^^Ji^^rfffi ^paJiMtiMg » » _ » ^^r ffmrrn^v^S^^^pJ-J^gai Gl;— DT APPENDIX C. 185 No. 9. ( To Lesson 43, p. 108.) An altered chord at each *, form optional. a. * » « VI Fr^ SFiyr-^^ s f^ -s^ftgO^ SS- d. * i^ ^ S ^ ^ J iiUrJ^ =s^ ]=4T^^ f— <■- ^^5E^ (|