[i|At>/nON\ 
 
 a Jgxt Book, 
 
 -H A- Clarke 
 
Digitized by the Internet Archive 
 in 2014 
 
 https://archive.org/details/systemofharmonyfOOclar_0 
 
A SYSTEM 
 
 or 
 
 HARHONY 
 
 POUNDED ON KEY RELATIONSHIP 
 
 By means of which a thorough Knowledge of 
 the rules that govern the combinations and 
 successions of sounds may be easily acquired 
 
 WITH OR WITHOUT A TEACHER 
 
 H. T\. CL3RKE, MUS. DOC. 
 
 pr-joressoi? or nusic in the university or Pennsylvania 
 
 ^rjiladelprjict- 
 
 Copyright, 1898, by Theo. PRESSER 
 
PREFACE. 
 
 This work is not meant to be a theory of harmony, but a simple 
 practical system, by means of which a knowledge of the mass of facts 
 that form the basis of the art of composition may be acquired. Theo- 
 retical questions are therefore carefully avoided, and the tempered 
 scale is accepted as the foundation of modern music. 
 
 The principal assumption or hypothesis upon which the system is 
 built is the following : 
 
 No scale is an independent entity, but is only the principal one 
 in a group of six called the related group. 
 
 The other is the reference of all dissonant groups to two roots in 
 each scale. 
 
 The related group is of course familiar to all musicians, but it has 
 never been used as the basis of a system of teaching harmony, to any 
 great extent. The derivation of dissonarit groups from a few roots 
 is also quite familiar now, yet some departures from the usual manner 
 of treating them will be found in this work, not for theoretical rea- 
 sons, but for the gain of greater simplicity. 
 
 The plan of teaching laid down in this work is entirely new in 
 several respects, and is based on the following maxims : 
 
 Teach one thing at a time. 
 
 Arrange the subject matter in such way that each step is a natural 
 outgrowth of the last. 
 
 Teach the pupil how to use his knowledge, instead of simply try- 
 ing to follow out the rule. Another departure from the usual prac- 
 tice is the complete discarding of the figured bass, with the result 
 that all merely mechanical rotework is eliminated, and the pupil 
 writes the chords because he knows what they are. 
 
 Many of the rules usually found in text-books are omitted ; many 
 of them are modified. For the reason that the so-called rules of 
 
PREFACE. 
 
 composition have all been arrived at empirically, they are in a great 
 measure, and ought to be altogether, deductions from the practice of 
 those best qualified to say what should or should not be; viz., the 
 great composers. It is a common subject of complaint on the part 
 of the student that such and such things are laid down in the text- 
 books as rules that must not be broken, and when he turns to the 
 work of some great composer he finds them totally disregarded. His 
 complaint is generally met by the reply, "When you can write like 
 so and so, you may break the rules also." A wiser reply would be, 
 Whatever has been sanctioned by a great writer becomes the property 
 of all, provided they can use it with taste and discretion. 
 
 We do not wish to be understood as recommending to the pupil 
 the instant disregard of all rules, because no one can learn how to 
 break them until he has learned thoroughly well how to use them. 
 
 It being the business of harmony to teach the combinations and 
 succession of sounds, very little is said in this book about the move- 
 ment of parts, that being the province of counterpoint, which may 
 be defined as the art of making the best use of the materials placed 
 at our disposal by harmony. 
 
 H. A. CLARKE, Mus. D. 
 Professor of Music, University of Penna. 
 
 January, 1898. 
 
CONTENTS. 
 
 I NTRODUCT70N PAGE V 
 
 Chapter I. page i 
 
 Intervals. 
 
 Chapter II. page 6 
 
 Major Scale. 
 
 Chapter III. page q 
 
 Major Scale and Common Chord. 
 
 Chapter IV. page 13 
 
 Positions of Common Chord and Succession of Common Chords 
 with Roots at Bass. 
 
 Chapter V. page 16 
 
 Sequences of Common Chords. 
 
 Chapter VI. page 22 
 
 First Inversion of Common Chord. 
 
 Chapter VII. page 27 
 
 Second Inversion of Common Chord. 
 
 Chapter VIII. page 30 
 
 Harmonizing of Melodies with Common Chords and their In- 
 versions. 
 
 Chapter IX. page 33 
 
 The Minor Scale. 
 
 Chapter X. page 38 
 
 The Group or Circle of Related Keys. 
 
 Chapter XI. page 43 
 
 Chords of Parallel Minor, Lowered Supertonic, — and Chords in 
 the Related Keys not Found in the Given Key. 
 
 Chapter XII. page 51 
 
 Chord of Dominant Seventh, — First Progression. 
 
 Chapter XIII. page 56 
 
 Chord of Dominant Seventh, — Second and Third Progressions 
 and Succession. 
 
CONTENTS 
 
 Chapter XIV. page 60 
 
 Chord of Dominant Ninth. 
 
 Chapter XV. page 6i 
 
 Chord of Dominant ElevCiVtn. 
 
 Chapter XVI. . page 72 
 
 Chord of Dominant Eleventh Continued, — Additional Remancs 
 on Second Inversions. 
 
 Chapter XVII. page 76 
 
 Progression of Dissonant Chords by means of Related Sounds. 
 
 Chapter XVIII. page 83 
 
 Chord of Thirteenth. 
 
 Chapter XIX. page 87 
 
 Supertonic Harmony. 
 
 Chapter XX. page 91 
 
 Altered Chords, — Augmented Sixth, — Augmented P'ifth, — 
 Passing Seventh. 
 
 Chapter XXI. page 97 
 
 Suspensions. 
 
 Chapter XXII. page 99 
 
 Retardation. 
 
 Chapter XXIII. page 109 
 
 Changing Notes or Appoggiaturas. 
 
 Chapter XXIV. page 112 
 
 Passing Notes. 
 
 Chapter XXV. page 119 
 
 Minor Scale. 
 
 Chapter XXVI. page 123 
 
 Open or Vocal Harmony. 
 
 Chapter XXVII. page 126 
 
 Pedal or Organ Point. 
 
 Chapter XXVIII. page 130 
 
 Transition. 
 
 Supplement. 
 
 Tempered Scale, — Figured Bass. 
 
 page 145 
 
INTRODUCTION. 
 
 Sound is produced by the motion of the air. This motion is com- 
 municated to it by the vibration of some material body. If the vibra- 
 tions are irregular, the sound produced is called Noise ; if they are 
 regular, the sound produced is called Musical. 
 
 The means used for producing musical sounds for artistic purposes 
 are : 
 
 ist. The vibration of a Column of Air enclosed in a tube, as in the 
 flute and the flue-pipes of the organ. 
 
 2d. The combination of the column of air with a Reed, as in the 
 clarinet, hautboy, and ( in some degree ) the human voice. 
 
 3d. The vibration of Strings set in motion by the fingers, or by a 
 bow, or by hammers, as in the harp, violin, and piano. The brass in- 
 struments may be included among the reed instruments, as the lip of 
 the player in this case performs the function of the reed. 
 
 4th. The vibration of the free reed, as in the harmonium. 
 
 Musical sounds are distinguished among themselves in various 
 ways : 
 
 ISt. As high or low ( acute or grave ) , called Pitch. 
 
 2d. Loud and soft (forte and piano), called Intensity. 
 
 3d. Quality (timbre). By quality is meant that property of a 
 musical sound by which we distinguish whether it is produced by a 
 violin, or flute, or voice, etc. 
 
 4th. By the relative length of time the sounds last, called Du- 
 ration. 
 
 Notation is a system of signs designed to represent the Pitch, Du- 
 ration, and Intensity of sounds. 
 
 The signs used to designate Pitch are the Staff and the Clefs; to 
 designate Duration, the Notes ; 
 
 (v) 
 
vi 
 
 IN TROD UC TION. 
 
 To designate Pitch and Duration together, the Position of the 
 Notes on the Staff and their Form. 
 
 The Staff consists of five parallel lines, on, between, and above or 
 below which the notes are placed. When the staff is insufficient, addi- 
 tional lines called Leger Lines ( generally but erroneously written 
 ledger ) are used, and the notes are written on, between, above, or 
 below them. 
 
 The Clefs, three in number, are placed at the beginning of the staff ; 
 they determine the letter name of the line upon which they are placed. 
 
 ist. The treble or G clef, used now only on the second line. 
 2d. The C clef, Sr or use d on the first line, is called the 
 
 soprano or descant clef ; on the third line, called the Alto Clef ; and 
 on the fourth line, called the Tenor Clef. The use of this clef on the 
 first line is gradually being discontinued. 
 
 3d. The Bass or F clef, CJj, used now only on the fourth line, 
 
 was formerly used on the third line also, and then called the baritone 
 clef. 
 
 The Pitch of the G indicated by is that of the sound given by 
 an open pipe sixteen inches long ; of the C indicated by that of 
 one twenty-four inches long ; of the F indicated by ^f, that of one 
 
 thirty-six inches long. 
 
 In vocal music the use of the G clef for the tenor voice has become 
 almost universal. When so used its Pitch must be understood as 
 being an octave lower; viz., that of the sound produced by a pipe 
 thirty-two inches long. 
 
 The Forms of notes indicate their relative duration ; their Positions 
 on the staff their letter names. 
 
 Eight forms of notes are used ; the duration of each is half that of 
 the one that precedes it. The first and last forms are less used 
 than the others ; they are named : 
 
 Breve, or Whole Half Quarter Eighth Sixteenth Thirty-sec- Sixty-fourth 
 double whole note. note. note. note. note. note. ond note. note. 
 
 iM! - f r Z % % % 
 
INTRODUCTION. 
 
 vn 
 
 When eighth, sixteenth, thirty-second, and sixty-fourth notes are 
 
 0 0- #■ 0 0- 0- 0 0- 
 
 used in groups they are joined, thus, — tZH — - in instru- 
 
 mental music, but not in vocal, unless they are all sung to the same 
 syllable, when they must also be enclosed in a line called a slur; 
 
 thus : F 9^ = ^zj ^ij:j When sung to separate syllables they must not 
 
 fair 
 
 be joined ; thus : f — * — J — 
 
 sup - pli - ca - tion 
 
 A dot placed after a note, thus, ^ • increases its duration by one- 
 half of itself, making it equal to three of the note that follows it in the 
 table above, thus, <s> . — & & & • a second dot increases the duration 
 
 by one-half of the first dot, thus, <s> . . — & ^ & 
 
 Each note has an equivalent sign for silence, called a Rest, thus : 
 
 Whole Half Quarter Eighth Sixteenth Thirty-second Sixty-fourth 
 rest. rest. rests. rest. rest. rest. rest. 
 
 i * r i 3 
 
 Dots modify the duration of rests in the same way as that of notes. 
 
 The essential rhythm of music is indicated by dividing it into por- 
 tions of equal duration by lines drawn across the staff, called Bars. 
 The enclosed spaces are called Measures, but in ordinary speech are 
 also called bars. 
 
 To indicate the rhythmic content of the measure, signs called 
 Time Signatures are placed after the clef ; these are the following : 
 
 ijz E or | called simple common time. 
 
 £1 il ii 
 
 S ^ § Ifl' ca ^ e< ^ simple triple time. 
 
 8 § M § ' ca ^ ec ^ compound common time. 
 
 ^ g g»' called compound triple time. 
 
viii 
 
 INTRODUCTION. 
 
 The lower figure indicates the note taken as the unit of the beat or 
 pulse \ the upper figure, the number of these units that each measure 
 must contain. 
 
 The first two signs, and g, are survivals of the old sign for 
 what was called imperfect time ; viz., a broken circle, which signified 
 two beats in the measure. The first of these signs, |Jj, always means 
 two beats in the measure, and is called alia breve time ; the g with- 
 out the line is the same as i. e., four beats in the measure. 
 
 The first four are called Simple Common Time. Common time 
 means an even number of beats in a measure ; simple means that 
 
 a single rhythmic unit is contained in each measure, (g or ^ is, 
 
 strictly speaking, a compound of two rhythmic units, but custom includes it among the simple 
 times.) 
 
 The second four are called Simple Triple Time because each meas- 
 ure contains three beats, or one rhythmic unit of 1, 2, 3. 
 
 The Compound Times are all made from Simple Triple Time. If 
 
 the upper figure is 6, it signifies that two measures of simple triple 
 are made into one; if the upper figure is 12, four measures of simple 
 triple are made into one. Then, as 6 and 12 are even numbers, it is 
 called Compound Common Time. 
 
 The last four consist of three measures of triple time made into 
 one; and as the upper figure is the odd number 9, it is called Com- 
 pound Triple Time. 
 
 A Scale is a succession of sounds ascending or descending from a 
 given sound. There are two kinds of scale, Diatonic and Chromatic. 
 A Diatonic Scale moves through the letters without omission or 
 repetition. A Chromatic Scale repeats the letters, changing their 
 pitch by means of signs called sharp ($), flat (b), natural (fc[), double 
 sharp (x), double flat (bb). 
 
 The interval between a given letter and the next above or below is 
 called a whole tone if another sound comes between them, and a half 
 tone if no sound comes between them. Natural half-tones are found 
 between E and J?, and B and C; in every other case, if a half-tone 
 is desired between two letters, one or the other must be modified in 
 pitch by means of a sharp or flat. 
 
IN TR ODUC TJON. 
 
 IX 
 
 The sharp raises the pitch of a letter ; the flat lowers the pitch of 
 a letter. Therefore, to make a half-tone between F and G, the F 
 
 There are two forms of the Diatonic Scale. First, called the Major 
 Scale, has the sounds so arranged that there is a half-tone between the 
 third and fourth, and seventh and eighth. If the letter C is chosen as 
 the starting note of a scale (called the Keynote), we get a scale of 
 this kind without having to use a sharp or flat; therefore the scale of 
 C is called the Natural Major Scale. 
 
 If we take the sounds of the scale of C and rearrange them, begin- 
 ning with A as a keynote, we get the other form of diatonic scale 
 called the Natural Minor Scale. 
 
 The chief difference between a major and minor scale is, that in 
 the major there are two whole-tones from the keynote to the third 
 letter ; in the minor, a tone-and-a-half from the keynote to the third 
 letter. 
 
 As the scale of A minor is a rearrangement of the sounds of the 
 scale of C major, it is called the Relative Minor of C. 
 
 If a scale is begun on any other letter as a keynote, it is necessary 
 to use sharps or flats to make the whole and half-tones fall in the 
 proper places. When a piece of music is written in any of these 
 scales, the sharps or flats that the scale requires are put at the begin- 
 ning, and are called the Signature. Sharps and flats to the number 
 of six may be used in a signature. These signatures are here given : 
 
 must be raised or the G must be lowered, thus : 
 
 P- 
 
 Keys with Sharp Signatures. 
 
 i . 
 
 1. Key of G, or of its relative minor, F minor. 
 
 2. Key of D, or of its relative minor, JB minor. 
 
 3. Key of A, or of its relative minor, F$ minor. 
 
 4. Key of F, or of its relative minor, C$ minor. 
 
 5. Key of B, or of its relative minor, G% minor. 
 
 6. Key of F\, or of its relative minor, D$ minor, 
 
2. 
 
 INTR OD UC TION. 
 Keys with Flat Signatures. 
 3- 4- 5- 
 
 
 
 
 
 & — 1" 
 
 
 
 
 1 . Key of F or of its relative minor, Z> minor. 
 
 2. Key of .Z?b, or of its relative minor, G minor. 
 
 3. Key of or of its relative minor, C minor. 
 
 4. Key of Ab, or of its relative minor, F minor. 
 
 5. Key of Z>1?, or of its relative minor, B\> minor. 
 
 6. Key of Gb, or of its relative minor, F\> minor. 
 
 Observe that the sharps always begin with F§, and that they are al- 
 ways written in the order in which they are here set down. So also 
 with the flats, which always begin with B\> ; also, that F§ and G\} are 
 identical in pitch. 
 
 If the number of flats be increased to seven, the keynote would 
 be Cb, this being the same as F, which has five sharps. It is preferable 
 to write in F, it being easier to read in the key which has the fewer 
 modified letters. Keys with more than six sharps or flats often occur 
 in the course of a piece of music, but the sharps and flats are then 
 placed before the letters to which they belong. 
 
 When any sharp 01 flat, not found in the signature, occurs in the 
 course of a piece of music, it is called an Accidental. 
 
 Accidentals affect all the letters on the same degree on which they 
 are written, but their influence never extends beyond the measure in 
 which they occur, except when they occur at the end of a measure and 
 the same letter is repeated at the beginning of the next measure. 
 
 (This rule is very generally disregarded now, and the accidental is repeated.) 
 
 The Natural is never used in the signature, except when in the 
 course of a piece a change of signature occurs, when the old signa- 
 
 ture is canceled, thus : 
 
 When the natural 
 
 occurs in the course of a piece to cancel one of the sharps or flats in 
 the signature, it is an accidental. But when it occurs for the purpose 
 of restoring an altered note to its place in the scale, it is not an acci- 
 dental. 
 
INTR OD UC TION. 
 
 xi 
 
 The natural cancels the double sharp and double flat also. Therefore, 
 if the double sharped letter is to be restored to its original place, the 
 natural and sharp are combined, thus, t$ ; if the letter is double flat, 
 thus, t[b. The following illustration gives examples of all the subjects 
 treated so far. 
 
 In piano music two staves are used, joined with a sign called a 
 Brace. Immediately after the brace the Clefs are placed ; then the 
 Signature, then the Time Signature. In the second measure the 
 natural is an accidental. A quarter and a half -rest are also found 
 in this measure. After the fourth measure the signature is changed — 
 also the time signature. Whenever either one of these is changed a 
 Double Bar must precede the change. 
 
 The clefs and signature must be put at the beginning of every line, 
 but not the time signature. Observe that in every measure the 
 united duration of the notes and rests equals the rhythmic unit indi- 
 cated by the Time signature. 
 
 In the eighth measure a whole-measure rest is indicated in the 
 lower part. A whole-rest is always used for this purpose, without 
 regard to what the time signature may be. 
 
xii 
 
 INTR OD UC TION. 
 
 The duration of a note may be varied in another way; viz., by 
 tying it to another or to several more on the same degree. This sign 
 - — ^ is called a tie. The tie must be repeated for each note when 
 
 several are tied, thus : j 5 * ^ ^ j 5 * j* J 
 
 If the first note is marked with an accidental, it is not necessary 
 to repeat it as long as the tie lasts. 
 
 The duration of a note is also indefinitely extended by means of a 
 sign called a pause or fermata The pitch of the G clef is often 
 
 raised an octave by writing 8va over it. The octave higher 
 
 lasts until the dotted line ceases. 
 
 The pitch of the F clef may be lowered an octave by writing under 
 
 it 8vb Sva is an abbreviation of ottava alt a (octave 
 
 higher) ; 8vb is an abbreviation of ottava bassa (octave lower) . 
 
 The' Rate of Movement, called Tempo, is indicated by Italian 
 words, as, allegro, andante, etc. ; 
 
 The Intensity, by p, pft, ppp, which stand for piano (soft) , piu 
 piano (softer), pianissimo (softest), fiffifff, which stand for forte 
 (loud), piu forte (louder), fortissimo (loudest) ; sudden access of in- 
 tensity, by or a, ox fz\ gradual increase of intensity, -===; grad- 
 ual decrease, z==-. Many other words and signs are used, but they 
 may all be found in the Dictionary of Musical Terms. 
 
 Rules for writing the chromatic scale in any given key : In ascend- 
 ing, raise all the letters except the third and seventh. 
 
 In descending, lower all the letters except the first, fifth, and 
 fourth. 
 
 When any one of the major chords in the scale accompanies it, 
 think of it as a tonic chord and write accordingly. 
 
 Write in the same way, if the accompanying chord is its domi- 
 nant. The notes that must be changed in accordance with this rule 
 are marked x. 
 
INTRODUCTION-. 
 
 xiii 
 
 of AJf. 
 
 
 
 
 FJt. 
 
 1 V 
 
 
 
 
 -w-J 
 
 
 
 9± 
 
 :or: 
 
 Mi 
 
 Ctf , not 
 
 Db. 
 
 -S: 
 
 5 th 4th 
 
 If the accompanying chord is one of the minor to?iics, or its dom- 
 inant, write as though in that key, as follows : in ascending, raise 
 all but the second and fifth ; descending, lower all but the first and 
 fifth. 
 
 ->5>- 
 -'5'- 
 
 9£ 
 
 m 
 
 Ml 
 
xiv 
 
 INTRODUCTION. 
 
 The advantages gained by this method of writing the chromatic 
 scale are two. 
 
 i st. It reduces the accidentals to the smallest number possible. 
 
 2d. It does not introduce an accidental that may not be found in 
 the dominant harmonies of the related group with one exception, viz., 
 A$\ and even this is possible as the augmented fifth in the dominant 
 of G, and as the third in the supertonic harmony of its relative minor, 
 E. 
 
 DEFINITIONS. 
 
 Motion is similar when two parts or voices ascend or descend to- 
 gether ; oblique when one part is stationary while the other moves ; 
 co7ttrary, when the parts move in opposite directions. 
 
 A degree is from one letter to the next above or below, whether 
 distant a whole-tone or half-tone. Conjunct motion is motion by de- 
 grees ; disjunct motion is motion by leaps ; diatonic motion is from 
 one letter to the next; chromatic motion is from any letter to an 
 altered form of the same letter ; as, A-A\> or A-A\. 
 
 Enharmonic change is the substitution of one letter for another 
 without changing the pitch ; as, Cjf, D^. 
 
HARMONY. 
 
 CHAPTER I. 
 Intervals. 
 
 Harmony treats of the combinations of sounds of different pitch, 
 and the successions of these combinations. 
 
 The basis of modern music is a series of sounds, each one of 
 which differs from the one lying next above or below by an interval 
 called a half-tone, semitone, half-step, or minor second. 
 
 If the two contiguous sounds are expressed by the same letter, as 
 C, Cjf. B,£b. it is called a Chromatic half-tone; if by different 
 letters it is called a Diatonic half-tone. 
 
 When the same sound is represented by different letters, as C$, 
 Z>b, it is called an Enharmonic change. 
 
 The difference in pitch between two sounds is called an Interval. 
 
 The number of letters included decides the name of the interval, 
 without regard" to the number of whole or half-tones it may include. 
 Thus, C-D$ is called a second because it includes two letters, 
 while C—E t>, which sounds the same ( in the modern scale ) , is 
 called a third because it includes three letters. 
 
 The names of the intervals within the limits of the octave are : 
 Second, Third, Fourth, Fifth, Sixth, Seventh, Octave. 
 
 But every interval may be written in several ways; as, C-T)\>, 
 C—D, C-D\. It is therefore necessary to distinguish between the 
 different kinds of interval bearing the same name. 
 
 This is done by the use of the following terms, added to the 
 name to denote the kind : Minor, or small ; Major, or large ; Per- 
 fect, Diminished, and Augmented. 
 
 Intervals are also classified as Consonant and Dissonant. A con- 
 sonant interval is one that gives repose to the ear. A dissonant in- 
 
 (i) 
 
2 
 
 HARMONY. 
 
 terval is one of which it is necessary that one or both the sounds 
 must move in a certain way to satisfy the ear. 
 
 Consonant intervals are farther divided into Perfect and Imperfect. 
 
 A perfect consonance is one that cannot be altered without produc- 
 ing a dissonance. An imperfect consonance is one that is equally 
 consonant, whether major or minor. 
 
 A diminished interval results from the contraction of a minor or 
 perfect interval. 
 
 An augmented interval results from the expansion of a major or 
 perfect interval. 
 
 All aug.nented and diminished intervals are dissonant. 
 
 The motion of the member or members of a dissonant interval is 
 called their resolution. 
 
 If the dissonance is minor or major, only one member is compelled 
 to move ; if it is augmented or diminished, both members must move, 
 towards each other if the interval is diminished, away from each 
 other if it is augmented. 
 
 Although there are five kinds of interval, there are not five kinds 
 of every interval. Thus of seconds there are three kinds, viz. : 
 C-D\>, one half-tone, called minor second. 
 C-D, two half-tones, called major second. 
 C-Z>$, three half-tones, called augmented second. 
 
 It is quite possible to put a diminished second, or a doubly aug- 
 mented second on paper ; but as neither are to be found in any possi- 
 ble combination or succession, they are excluded as of no practical 
 use. 
 
 The third also exists in three forms, viz. : 
 Cj-jE'b, diminished, two half-tones. 
 C—Jlb, minor, three half-tones. 
 C-E, major, four half-tones. 
 The fourth exists in three forms, viz. : 
 C\-F, diminished, four half-tones. 
 C-F, perfect, five half-tones. 
 C-jFJ}, augmented, six half-tones. 
 
 The remaining intervals within the limits of the octave may be 
 found by'inverting the letters of those just given. It will at once be 
 evident that any interval and its inversion must together make an oc- 
 
HARMONY. 3 
 
 2d. 7th. 
 
 tave, thus, C D C; and since twelve half-tones make an octave, 
 
 an interval and its inversion must make twelve half-tones. There- 
 fore, to find the number of half-tones in the inversion of a given in- 
 terval, it is necessary only to subtract the number in the interval from 
 twelve, the number in the octave ; thus, in the second C-D there are two 
 half-tones, therefore there must be ten in its inversion, D-C\ and as the 
 number of letters from D to C is seven, we also find that the inversion 
 of a second produces a seventh. Then the inversion of a third must 
 produce a sixth, and the inversion of a fourth must produce a fifth. 
 
 Then, as there are three kinds of each interval, three kinds of 
 sevenths, sixths, and fifths must result from their inversion ; and the 
 nearer each other the sounds are in the smaller interval, the farther 
 apart they must be in its inversion. Therefore the inversion of a 
 given interval always produces one of the opposite kind, with one ex- 
 ception; viz., the inversion of a perfect interval produces a fieifect 
 one. 
 
 The foregoing explanations will make the following table of inter- 
 vals clear. (See page 5.) 
 
 Intervals may also be divided into diatonic and chromatic. Dia- 
 tonic are to be found in the major scale and in the natural minor 
 scale ; chromatic result from the introduction of sound's foreign to 
 the scale. 
 
 Questions on Chapter I. 
 What is the smallest interval in the scale ? 
 
 What is the difference between a chromatic and a diatonic half-tone ? 
 What is an enharmonic change? 
 What is an interval ? 
 
 What determines the name of an interval ? 
 
 Give the names of the intervals included within the limits of the octave. 
 What terms are used to distinguish between the different kinds of intervals 
 
 with the same name? 
 How are intervals farther classified? 
 What is a consonant interval? 
 What is a dissonant interval? 
 
 What farther division is made of consonant intervals? 
 What is a perfect consonance? 
 What is an imperfect consonance? 
 How is a diminished interval produced? 
 How is an augmented interval produced? 
 
 What is the nature of all augmented and diminished intervals? 
 
4 
 
 HARMONY. 
 
 What is meant by the resolution of a dissonance? 
 In what kind of dissonances must one member resolve? 
 In what kind of dissonances must both members resolve? 
 When both members of the dissonance must resolve, in what case do they ap- 
 proach each other? In what case do they separate? 
 Are there five kinds of every interval? 
 How many kinds of seconds are there? 
 W T hat is the smallest one called? 
 How many half-tones does it include? 
 How many half-tones in the major second? 
 How many half-tones in the augmented second? 
 How many kinds of thirds are there? 
 How many letters are included in a third? 
 What is the smallest third called? 
 How many half-tones does it include? 
 
 What is the difference between a diminished third and a major second? 
 
 How many kinds of fourths are there? 
 
 What is the smallest one called? 
 
 How many half-tones does it include? 
 
 How many half-tones in a perfect fourth? 
 
 How many half-tones in an augmented fourth? 
 
 What does inverting an interval mean? 
 
 What interval results from any given interval and its inversion taken together? 
 How many half-tones are there in an octave? 
 How many half-tones in an interval and its inversion? 
 Given an interval, how is the number of half-tones in its inversion found? 
 What is the name of the interval produced by inverting a second? A third? 
 A fourth? 
 
 What kind of interval is produced by inverting one that is major? One that 
 is minor? Perfect? Augmented? Diminished? 
 
 NOTES. 
 
 ( i.) These questions must be asked over and over, and the various intervals must be written, 
 until the whole chapter is understood and committed to memory. 
 
 ( 2.) The half-tone is used as a measure for the intervals, it being more convenient than it 
 would be to use both whole and half-tones. 
 
 (3.) Whole-tone and half-tone are used in preference to the German whole-step and half-step, 
 their meaning being perfectly clear ever since they were first used in English. 
 
 (4.) Dissonant intervals are by many writers called discords. A dissonant is pleasant; a 
 discord is something that never should appear in music. 
 
 ( 5.) The perfect fourth and fifth are by some writers called major. The diminished fifth is 
 also called imperfect. The augmented sixth is called extreme, or extreme sharp sixth. The 
 names adopted in this work seem more logical and less likely to contuse the student. 
 
HARMONY. 
 
 5 
 
 < 
 
 03 
 % 
 
 in 
 
 Q te 
 Z> ° 
 ^ .S 
 
 5 5 
 
 H . 
 
 <u 
 ,£ 
 
 IP 
 
 vv 
 
 51 
 
 -1 
 
 ro O 
 
 ft 
 
 ft- 
 
 4w 
 
 Mill 
 
 VI 
 
 CO 
 
 4 
 
 •c ft 
 
 hi PL, 
 
 3 I -U^ 
 
 CO • 
 
 I o 
 X S 
 
6 
 
 HARMONY. 
 
 CHAPTER II. 
 The Major Scale. 
 
 A Scale (from Latin, ^/« = a ladder) is a succession of sounds gradually 
 rising in pitch from any given sound to its octave. 
 
 A Chromatic scale is one that ascends (or descends) by half-tones. 
 
 A Diatonic scale is one that ascends (or descends) by whole and 
 half-tones. 
 
 Two kinds of diatonic scale are. used in the modern musical sys- 
 tem : ist, called the Major Scale; 2d, called the Minor Scale. 1st, 
 the Major Scale : in this succession a half-tone is found between the 
 third and fourth, and seventh and eighth degrees ; consequently, if the 
 scale is divided into two groups each containing four sounds, it will 
 be found that these two groups are alike in consisting of two succes- 
 sive whole-tones followed by a half-tone, and that these two groups 
 are separated by a whole-tone, thus : 
 
 C, £>, I G, A, B^C. 
 
 These groups are called TetrachordS (from two Greek words meaning four 
 strings) . 
 
 A major scale may therefore be defined as being formed of two 
 Tetrachords separated by a whole-tone. 
 
 As the Tetrachord must consist of a succession of two whole-tones 
 followed by a half-tone, if it begins on any letter but C or G it is 
 necessary to alter the pitch of one or more of the letters to make it 
 conform to this succession. It is for this purpose that sharps, flats, 
 double sharps, and double flats are used. For example, if it be desired 
 to write a Tetrachord beginning on A, the succession of letters will 
 be A, B, C, D; but as the interval between B and C is a half-tone, 
 and that between C and D a whole -tone, it is necessary to move the 
 
 C closer to the D ; therefore it is written A, B, C§ D. 
 
 If a Tetrachord is to be written beginning on B, the letters will be 
 
HARMONY. 
 
 7 
 
 F, G, A, B ; but as j5 is a whole-tone above A its pitch must be 
 lowered by making it flat; thus, F, G, A, 2>b. 
 
 By examining the following series of sounds it will be found that 
 the Tetrachord that makes the second half of the scale of C is also 
 the first half of the scale of G, and the Tetrachord that makes the 
 first half of the scale of C is also the second half of the scale of F. 
 
 Scale of F. 
 
 Scale of G. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 L_ — _ — g^Iei- 
 
 
 
 
 i 
 
 Scale of C. 
 
 Therefore, Every Tetrachord belongs to Two Scales, that of the letter 
 it begins with and that of the letter it ends with. These two scales 
 are called related scales. 
 
 Therefore every major scale has two related major scales, one be- 
 ginning on the last note of the first Tetrachord, the other on the first 
 
 note of the second Tetrachord. (The easiest way to remember is, the related major 
 scales begin on the fourth and fifth of the given scale.) 
 
 Every Tetrachord must contain four successive letters, and every 
 scale must contain all seven letters and the octave of the letter it begins 
 with. 
 
 It is this that necessitates the use of double sharps and double flats. 
 Thus, if a Tetrachord is to begin on D§, the letters will be F, F, 
 
 G ; but to make a Tetrachord they must be, F3i~ lp— j^ = t^ = t ==: | : | 
 Or, if the Tetrachord begins on F\>, the letters will be F\>, G, A, 
 B\ but they must be written. 
 
 Questions on Chapter II. 
 
 What is a scale? 
 
 What is a chromatic scale? 
 
 What is a diatonic scale? 
 
 How many kinds of diatonic scale are used? 
 
 Where do the half-tones occur in the major scale? 
 
 How may a major scale be divided? 
 
s 
 
 HARMONY. 
 
 Of what do these groups consist? 
 What are they called? 
 
 What definition may be given of a major scale? 
 
 Of what use are sharps, double sharps, flats, and double flats? 
 
 To how many scales does a Tetrachord belong? 
 
 What determines the scales to which it belongs? 
 
 What are these scales called? 
 
 How many major relations has a given major scale? 
 Upon which notes of the given scale do the related scales begin? 
 The pupil should write Tetrachords beginning with every sharp, flat, and natu- 
 ral, and should write over them the names of the scales to which they belong. 
 
HARMONY. 
 
 9 
 
 CHAPTER III. 
 
 Major Scale Continued, and Common Chord. 
 
 The following names are given to the degrees of the diatonic scale : 
 First, or keynote, is called the Tonic ; 
 
 Second, SllpertOniC (upon or over the tonic) J 
 
 Third, Mediant; 
 Fourth, Subdominant ; 
 Fifth, Dominant ; 
 Sixth, Submediant; 
 Seventh, Leading Note. 
 
 Mediant (from Latin medius= middle) is so called because it is half-way 
 between the tonic and the fifth above, or dominant. 
 
 Subdominant (Latin sub = under) is so called because it is the same 
 distance below the Tonic (a fifth) that the Dominant is above. 
 
 Dominant (Latin dominans = ruling) is so called because its harmonies 
 
 rule or determine the Scale. (Originally the dominant was so called in the eccle- 
 siastical system because it was the principal reciting note of the chant.) 
 
 Submediant is so called because it is half-way between the tonic 
 and the subdominant. 
 
 Leading Note is so called on account of its tendency to ascend to 
 
 the keynote. (This note is also called the subtonic, in Latin nota sensibihs, in French note 
 sensible = sensitive note, on account of this tendency.) 
 
 COMMON CHORD, OR PERFECT CHORD OR TRIAD. 
 
 A Common Chord consists of three sounds. The sound on which 
 the chord is built is called the Root ; the next is the Third above the 
 root; the next is the Fifth above the root. 
 
 The third over the root may be major or minor : if major, the chord 
 is called a Major Chord; if minor, the chord is called a Minor Chord. 
 
 The fifth over the root must be perfect ; if it is not, the chord is not 
 a common or perfect chord. 
 
HARMONY. 
 
 As there are only seven letters used in music, it follows that seven 
 groups of letters must make all the common chords possible, as each 
 letter may be the root, or the third, or the fifth of some chord, thus: 
 
 Fifths, E, E, G, A, B, C, D. 
 
 Thirds, C, D, E, E, G, A, B. 
 
 Roots, d, £, C, Z>, E, E, G. 
 
 It will be seen that to form a chord on any given letter, for exam- 
 ple, A, it is only necessary to skip one letter to find the third, C, then 
 skip another letter to find the fifth, E ; thus, A (B) C(D)E. There- 
 
 ^ ' s s 
 
 fore, there is an interval of a third between the root and third, and 
 an interval of a third between the third and fifth. If from I to 3 
 is a major third, from 3 to 5 is a minor third ; if from 1 to 3 is a minor 
 third, from 3 to 5 is a major third ; if from 1 to 3 and 3 to 5 are both 
 minor thirds, the chord is called a Diminished Chord (or imperfect ) ; if 
 from 1 to 3 and 3 to 5 are both major thirds, the chord is called 
 
 an Augmented Chord ( neither are common chords) . 
 
 In every major scale Six common chords may be written, (i.e. with- 
 out using any accidentals) . Three of these chords are major, three minor. 
 The chords take the names of the degrees of the scale upon which 
 they are written ; therefore the chord on the 
 First is called the Tonic Chord, and is Major ; 
 Second is called Supertonic Chord, and is Minor ; 
 Third is called Mediant Chord, and is Minor ; 
 Fourth is called Subdominant Chord, and is Major ; 
 Fifth is called Dominant Chord, and is Major ; 
 Sixth is called Submediant Chord, and is Minor. 
 The seventh or leading note may not be used as a root, because the 
 fifth over it is diminished. (Diminished and augmented chords will 
 be treated of in the proper place.) 
 
 2. 3. 4. 5. 6. 7. 8. 
 
 * 
 
 & g- 
 
 N. B. 
 
 N. B. If B is taken as a root the perfect fifth is E§, which does 
 not exist in the scale of C. 
 
 It is important to remember that no change in the order in which 
 
HARMONY. 
 
 the three letters forming a chord are written, changes the name of 
 the chord. Thus the following example contains the chord of A 
 only, because each group consists of the letters A, C, E. 
 
 -<s>- 
 
 — Z? g? II 
 
 & _ % IJ 
 
 Therefore, to rind the root of a chord arrange the letters composing 
 
 it to read (upwards) One, three, five. (This rule should be borne in mind; it 
 will be extended farther on.) 
 
 The pupil should be required to write major and minor chords, using- every natural, sharp, and 
 fiat as roots. The following remarks will aid in remembering the perfect fifths. 
 
 I. Every fifth that may be struck on two white keys is perfect, 
 except B-F; to make a perfect fifth between these letters, either B 
 must be flat or F sharp. 
 
 II. Every fifth that may be struck on two black keys is perfect. 
 
 III. There are only two perfect fifths that have the root a white 
 and the fifth a black key, viz., B-F§ and Cb- G\> ; only two that 
 have the root a black and the fifth a white key, viz., Bb-F and A\- 
 
 Write the following chords in their natural positions, that is, root, 
 third, fifth, and mark every chord major or minor, as the case may 
 be. 
 
 Questions on Chapter III. 
 Give the names of the degrees of the diatonic scale. 
 
 What does supertonic mean ? Mediant? Subdominant? Dominant? Sub- 
 mediant? 
 
 Why is the seventh degree called the leading note? 
 Of how many scunds does a common chord consist? 
 What is the sound on which the chord is built called ? 
 
12 
 
 HARMONY. 
 
 What is the interval between the root and the next member of the chord ? Be- 
 tween the root and the third member of the chord ? 
 What kind of third may a chord have? 
 
 What is the chord called when the third is major ? What when the third is 
 minor? 
 
 What kind of fifth must a chord have? 
 
 How many groups of letters make all the common chords? 
 
 What is the interval between the third and fifth of a chord ? 
 
 What kind of third is this in a major chord ? In a minor chord ? 
 
 If both these thirds are minor what is the chord called ? 
 
 If both are major what is the chord called ? 
 
 Are either of these common chords? 
 
 How many common chords may be written in a major scale? 
 
 How many are major ? How many minor ? 
 
 How are the chords named? 
 
 Give the names of the major chords. 
 
 Why may not the leading note be used as a root? 
 
 Does changing the order in which the letters of a chord are written change its 
 name? 
 
 How may the root of a group of letters that form a chord be found ? 
 
 Note. The teacher should insist that when pupils are giving the letters that form a chord, 
 they must mention the sharps or fiats always. 
 
HARMONY. 
 
 13 
 
 CHAPTER IV. 
 Position and Succession of Common Chords. 
 The lowest note of any group sounded together is the Bass. 
 
 (This word should be spelled base, because the proper meaning of bass is a deep sound.) 
 
 It is not at all necessary that the bass note of a group be written 
 on the "bass" staff. 
 
 Avoid any confusing of Bass with Root. The root may be the 
 bass, but the bass may be any member of the chord. The first step 
 in learning to use chords is to learn how to write successions in 
 which the Roots are always the Bass Notes. 
 
 The most effective harmony is that written in four parts (or for 
 four "voices"). Since the common chord has only three letters in 
 it, it is necessary to repeat one of the letters to make a fourth part. 
 When the root is used as a bass, the root itself is the best member to 
 repeat ; thus, C, E, C7, C. It will be evident that while retaining 
 
 the root C as a bass, it is possible to make three different arrange- 
 ments of the remaining letters. Thus, instead of having the repeated 
 root at the top, the third, E, might be, or the fifth, C7, might be. 
 Therefore we have this rule : 
 
 Every chord with its Root at the Bass, and with the Root repeated, 
 may be written in Three Positions. 
 
 If the repeated root is at the top, 
 it is called the Octave Position (1) ; 
 if the third of the chord is at the top, 
 it is called the Tierce Position (2) ; 
 if the fifth is at the top, it is called 
 the Quint Position (3). 
 
 For the present these positions are indicated by placing over the 
 top of the group, 8 for octave, 3 for tierce, and 5 for quint position. 
 
 (Pupils should be required to do this until they are quite familiar with the positions.) 
 
HARMONY. 
 
 It is necessary to remember that the term Position always means 
 that the Root is at the bass. The first and most important rule to be 
 observed when writing a succession of chords in Positions is — Two 
 Chords must never occur in Succession in the Same Position. 
 
 < 
 
 ^ <S> 25 
 
 a. 
 
 — a. & — i_ps 
 
 (5. c. d 
 
 
 
 *—&-\* 1 
 
 
 
 "7 f> 
 
 
 
 
 (3;. The first chord being in the octave position, the following chord 
 may be in either the third or fifth position. 
 
 b. First chord, third position; the next may be octave or fifth. 
 
 c. First chord, fifth position; the next may be third or octave. 
 
 d. Both chords in octave position forbidden. 
 
 e. Both chords in third position forbidden. 
 
 f. Both chords in fifth position forbidden. 
 
 Consequently there is always a choice of two positions; viz., either 
 of those in which the last chord is not written. 
 
 In general a better effect is produced when the three upper parts 
 move in the opposite direction to the bass, especially when the bass 
 moves only one degree. (More exact rules for this will be given 
 later.) 
 
 ?d 
 
 
 
 
 
 9t 
 
 m 
 
 EE 
 
 § 
 
 to. 
 
 I [, 
 
 The motion from first to second chord is called oblique — that means 
 one part (the top) is statioiiary, the bass moves. 2 to 3 is contrary 
 motion; the bass (a) moves one degree. 3 to 4 is direct or parallel 
 motion ; bass and top both ascend. At b the bass moves one degree. 
 
HARMONY. 15 
 
 The following basses are to have the chords written over them in 
 accordance with the foregoing rules. Do not be satisfied with simply 
 getting the chords right, but try the effect of different positions. 
 
 II. 
 
 3*B : g 
 
 d — 1 
 
 
 PS 
 
 -4— i 4~ 
 * - 
 
 — j 
 
 1 1 
 
 11 
 
 L ^ L 
 
 III. 
 
 EEEFEEt: 
 
 — t 
 
 
 - d 
 
 
 
 
 
 IV. 
 
 
 -4- 
 
 — 
 
 2=t= 
 
 ± 
 
 0- 
 
 - t 
 
 — 1 # 
 
 ..- •' ! 
 
 
 — F 
 
 V. 
 
 
 ==l= : 
 
 i 
 
 — h— r- 
 
 
 1 
 
 
 \ — 
 
 ~m 0- 
 
 
 
 
 II 
 
 VI. 
 
 ==^7^=1= 
 
 3 fj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 These exercises should be transposed repeatedly and rewritten. 
 
 Questions on Chapter IV. 
 
 What is a bass note? Must it be written on the bass staff? 
 
 How is four part harmony made from common chords? Which member is 
 
 the best to repeat when the root is at the bass? 
 Do bass note and root mean the same thing? 
 What is meant by the position of a chord ? 
 
 In how many positions may a chord with the root repeated be written? 
 
 What are they called and why? Which member of the chord is at the bass in 
 all positio?is? Give the first rule for writing successions of chords in posi- 
 tions. 
 
 If a chord is in the octave position, what positions may the next chord have? 
 What if it is in the third position? What if it is in the quint position? 
 
 What is meant by oblique motion? By direct or parallel motion? By con- 
 trary motion? 
 
 Which kind of motion is considered the best? 
 
 In what case is it especially to be observed? 
 
 Name the keys, the tonic, subdominant, and dominant chords, and leading 
 notes of the exercises marked I. to VI. 
 
i6 
 
 HARMONY. 
 
 CHAPTER V. 
 
 Sequences of Common Chords. 
 
 The movement of common chords is absolutely free; that is, any 
 chord in the scale may be followed by any other one. Some of 
 these successions will be found to be much smoother than others, 
 but there is no succession that cannot be made to sound well when 
 used in the right place. For example, the following passage 
 
 — 1:| may be harmonized in the following ways : 
 
 1 is smooth but commonplace. 
 
 2 is more vigorous. 
 
 3 is rugged almost to harshness. 
 
 4 is dignified, with a savor of quaintness. 
 
 In 2 the progression from first to second chord, (i. e., from a major 
 
 chord to the minor chord on the third above,) was not considered good at one time. 
 
 In 3 the progression from first to second chord, (i. e., from a minor 
 
 chord to another minor chord one degree above or below,) was forbidden. The pro- 
 gression from the second to the third chord, (i. e., from a minor chord to the 
 major chord a third higher,) was not considered good. 
 
 No rule can be given as to when one of these harsh progressions 
 will sound well and when it will not. The judgment of the composer 
 as to the effect he wishes to produce is the only guide ; but pupils should 
 avoid this class of successions until they have thoroughly learned all 
 those that are smooth and natural. 
 
HARMONY. 
 
 There is one other progression that should be avoided; viz., from 
 the subdominant to the dominant, except the subdominant is in the 
 eighth and the dominant in the fifth or third position, thus: 
 
 5 3 
 
 N. B. The above remarks must be 
 understood as applying only to Suc- 
 cessions of chords in Positions ; i. e., 
 with their roots at the bass. 
 
 Common chords are frequently written in what are called Sequen- 
 ces (Latin sequens= following). In a sequence the roots move in a regular 
 
 order or pattern, for example : 
 
 -a — 
 
 P 
 
 up four, down three. The result is three pairs of chords, each one 
 degree higher than the last. 
 
 The most usual sequences are here given, both ascending and de- 
 scending. The pupil should write them in various keys and should 
 also exercise his ingenuity in constructing others. 
 
 a, 6, c, are ascending sequences. 
 d, e, f, are descending sequences. 
 
i.S 
 
 HARMONY. 
 
 It is allowable to use the dimin- 
 ished (leading note) chord in a 
 sequence for the sake of preserving 
 the "pattern," thus: 
 
 The use of the diminished chord 
 was sometimes "dodged" by the 
 older writers in the following way : 
 
 The jE>Q is retained in the chord 
 of G because B\ would necessitate 
 a chromatic progression, B\>, 2?tj, 
 which was forbidden in strict coun- 
 terpoint. 
 
 Sequences composed of common chords natural to the scale are 
 called Diatonic or Contrapuntal. They were much more largely 
 used by the old school than by the new ; still it is absolutely necessary 
 that the pupil should familiarize himself with them. The reason why 
 will appear farther on. 
 
 The Positions of the chords may be changed in all these examples; 
 thus, Example a, page 17, may be jive, three, or three, eight, or 
 three, Jive, or eight, three, alternately, thus: 
 
 5353 3838 3535 8 38 3 
 
 This is not as 
 good as the others. 
 
 Observe that the best effect is produced when the outer parts move 
 in opposite directions. 
 
 It does not sound well to move to a chord in the Octave Position 
 with the Bass and upper part (soprano) moving in the same direction, 
 except in the following cases: 
 
 I. From Dominant to Tonic Chord. 
 
 II. From Tonic to Subdominant chord. (The relation between these chords 
 is the same as that of the previous chords.) 
 
HARMONY. 
 
 l 9 
 
 g2. 
 
 — r 
 
 i 
 
 Another rule is often given, viz., that the eighth may occur in 
 Direct Motion when the upper part ascends a half-tone ; but whenever 
 this is the case, it must be either a progression from Dominant third 
 position to Tonic octave, or Tonic third position to Subdominant octave. 
 
 N. B. It is owing to the infraction of this rule that this passage does 
 not sound well. Another progression that does not sound well is 
 that to a Chord in the Quint Position with the outer parts (bass and 
 soprano) moving in the same direction, except in the following case: 
 
 From any chord to another, the roots of which chords are a fifth 
 apart (ascending), or what is the same, a fourth apart (descending). 
 
 4= 
 
 r 
 
 i 
 
 __L 
 
 --r 
 
 i 
 
 Tonic. Dominant. 
 
 Subdom- Tonic, 
 inant. 
 
 :=J: 
 
 Two chords may be WTitten in succession in the Tierce Position by 
 doubling the third of one of them. 
 
 If the roots ascend, double the third of the Second chord. 
 If the roots descend, double the third of the First chord. 
 
 V ^ -<5»J .&r -&r\ -©J ° & -&r 
 
 (What sequences may be made of chords in the third position?) 
 
20 
 
 HARMONY. 
 
 Two chords may be written in succession in octaves, fifths, or thirds 
 when the outer parts move in opposite directions. 
 
 8 8 5 5 3 3 
 
 1 The last example (3) is fre- 
 
 9± 
 
 2. 
 
 quently used. 2 is the most 
 unusual. 1 is common at the 
 |_| end of a piece. 
 
 Exercises. 
 
 The pupil should be required to point out all the sequences that may be 
 found in these exercises, also the places where examples of all the progres- 
 sions mentioned in this chapter may be used. For example, in the first exercise 
 the first two measures form a sequence ; the three chords marked x may all be 
 in the third position. 
 
 I. 
 
 — I- 
 
 Avoid unnecessary skips from one chord to the next 
 II. 
 
 iH§8 
 
 III. 
 
 ^2: 
 
 3 
 
 IV 
 
 si 
 
 V. 
 
 E=Id2:2: 
 VI. 
 
 2^: 
 
 zest 
 
 2=t=±E 
 
 11 
 
HA RMONY. 
 
 21 
 
 VII. 
 
 
 
 
 
 
 1 1 Li. i_2 § 
 
 m — -0 \—S 
 
 "n — ^ 
 
 1 1— M 
 
 
 — 1 « <p — | 1 1 
 
 
 
 
 r * ^ -=3 li 
 
 + £ * t» +1 
 
 VIII. 
 
 
 
 1 
 
 £2- 
 
 
 
 It 
 
 
 
 -0 T 
 
 h- 
 
 
 
 
 -TP- 
 
 - II 
 
 Questions on Chapter V. 
 
 Is there any restriction on the movement of common chords? 
 Give the successions that are mentioned as lacking in smoothness. 
 What is a sequence ? 
 
 Is the use of the diminished chord permitted in a sequence? 
 
 What are sequences composed of chords natural to the scale called ? 
 
 Give the cases in which an octave position may be taken in direct motion be- 
 tween the outer parts. 
 
 Give the cases in which a fifth position may be taken in direct motion between 
 the outer parts. 
 
 How may two chords be written in succession in the third position? 
 Which of the chords has the third doubled when the roots ascend ? 
 Which when the roots descend ? 
 
 State the cases when two chords may be written in succession in octave, fifth, 
 and third. 
 
 Note. When writing exercises draw a slur > under all the roots that form the sequence^ 
 
 also under succession of chords in third position. 
 
3 2 
 
 HARMONY. 
 
 CHAPTER VI. 
 
 First Inversion of Common Chords. 
 
 If the preceding chapters have been thoroughly mastered, the pupil 
 will know all that may be done with the Common Chords natural to 
 the Scale, with their Roots as Bass notes; i. e., in Positions. 
 
 The next step is to Invert the chords. Inversion means using some 
 other member of the chord as a bass. 
 
 If the Third of the chord is used as a bass, the Chord is said to be 
 in its First Inversion. 
 
 The First Inversion of a Chord is subject to no restrictions; that 
 is, any chord in the scale may be written with its third at the bass. 
 
 When the Third is used as a bass, the Root or Fifth may be re- 
 peated (to make the fourth part) ; it is immaterial which. 
 
 b. 
 
 d. 
 
 a. Chord C, E, G, with the third, 
 E, at the bass, the root repeated. 
 
 b. Same, with the root repeated 
 at unison. This is signified by 
 doubling the note. 
 
 c. Same, with the fifth repeated. 
 • d. Same, with fifth repeated -at unison. 
 
 It is a rule that No two Voices or Parts must ever move together 
 
 in Fifths Or Octaves (making what are called parallel or consecutive fifths or octaves). 
 (This rule will be largely modified in the proper place, but must be strictly observed at present. ) 
 
 It is in consequence of this rule that it is forbidden to write two 
 chords in succession in the same position. 
 
 a. Both in octave position; 
 therefore the Jirst and fourth 
 parts move together in octaves, 
 the second and fourth in fifths. 
 
 b. Both in third position; 
 second and fourth in octaves, 
 third and fourth in fifths. 
 
HARMONY. 
 
 c. Both in fifth position, first and fourth in fifths, third and 
 fourth in octaves. 
 
 The doubling of the third, when two chords are written in suc- 
 cession in the tierce position, is sure to avoid the parallel fifths and 
 octaves. 
 
 In writing the same Position twice in succession, the parallel fifths 
 or octaves will always be found between the bass and one of the 
 upper parts. If two First Inversions are written in succession, the 
 parallel fifths and octaves will occur between two of the upper parts, 
 thus : 
 
 a. Octaves between first and 
 third parts, fifths between second 
 and third, caused by repeating the 
 root in both chords. 
 
 b. Octaves between first and 
 third parts, fifths between first and 
 second, caused by repeating the 
 fifth in both chords. 
 
 Therefore they may be avoided by repeating the Root in one 
 chord and the fifth in the other, or repeating one at unison, the 
 other at the octave. 
 
 a. Both roots repeated — one at unison, the other at octave. 
 
 b. Fifth at unison, root at octave. 
 
 c. Root at octave, fifth at octave ; but the repetition of the root 
 makes an octave between the frst and third parts, that of the fifth 
 an octave between the second and third parts, and to be parallel, 
 they must occur between the same two parts. 
 
 d. Both fifths repeated. The first and second parts being in 
 unison, there is a fifth between them and the third part; but the 
 second fifth is between the first and second parts. - . .. 
 
HARMONY. 
 
 e. The repeated C is root of one and fifth of the other chord ; but 
 these octaves are not consecutive because they are stationary. To be 
 consecutive they must move. 
 f and g. Roots repeated, unison and octave. 
 
 Parallel fifths and octaves may also be avoided by repeating the 
 Third of one or both of the inverted chords, provided the repetition 
 of the Third is made by two parts moving in opposite directions. 
 
 The Third of a chord may be repeated at any time, if the repeti- 
 tion occurs in parts moving in opposite directions. 
 
 s 
 
 j- 
 
 3 I 
 
 1 
 
 ipzzzzp 
 
 a. First and second chord 
 inverted, the third of 2 re- 
 peated. 
 
 b. Second chord only invert- 
 ed, its third repeated. 
 
 c. Third of second chord repeated. 
 
 d. Same. 
 
 e. The third of the same chord repeated. This case is peculiar as 
 it really makes parallel octaves between the first and fourth parts, but 
 they occur in opposite ( contrary ) motion. The long skip of the 
 bass also helps to hide them. 
 
 f. The third repeated in both chords. 
 
 The above examples should be written in all the keys, until they 
 are thoroughly understood and memorized. Then the exercises fol- 
 lowing should be written, care being taken to introduce examples of 
 all the progressions here given. 
 
 Any bass note may be treated as a Root, or as a Third.* When it is 
 treated as a third, put a 3 under it, and no figure over the upper part. 
 
 * Note. It is perhaps necessary to repeat that the leading note cannot be a root; therefoie 
 the second of the scale cannot be a third. 
 
HARMONY. 
 
 2 5 
 
 When a chord is Inverted it is not in any Position ; therefore the 
 chord that follows it may be in any position. 
 
 Analyze the following example, give the Name, Position, or Inver- 
 sion of every chord. State which member is repeated, and give the 
 reason of every repetition. 
 
 4-1 
 
 -0- -m- 
 
 1— rn~r 
 
 ^-=4— •-*- r - a -#- = t 
 
 
 
 IT 
 
 T ' 
 
 A- r & -g-- 
 
 0 1- 
 
 
 
 
 
 
 »-F^ — # 
 
 
 This example should be copied, and the chords numbered, and the 
 analysis of each chord written out, thus : 
 
 1. Tonic chord, tierce position. 
 
 2. Supertonic, first inversion, third doubled by parts moving in 
 opposite directions, and so or. 
 
 I. 
 
 Fc^-^-^-^-F^ - — ^-F-h — i-^P-=l=iF;^ 
 
 II. 
 
 III. 
 
 IV. 
 
 / j/ ir?TifT?i ii iii ! j ; i i ii 
 
26 
 
 HARMONY. 
 
 V. 
 
 VI. 
 
 ±_f: : 
 
 4- 
 
 
 1 1 ^ 
 
 it Fl 
 
 ff 4 * * p- 
 
 ±=p 
 
 
 
 *- * ^ - 
 
 
 Questions on Chapter VI. 
 What does the inversion of a chord mean? 
 
 Which member of the chord is at the bass in the first inversion? 
 
 Which chords in the scale may be used in the first inversion ? 
 
 Which members of the chord may be repeated ? 
 
 What is meant by parallel or consecutive fifths or octaves? 
 
 Between which parts will the parallel fifths or octaves be found, when two 
 
 chords are written in the same position? 
 When two first inversions are written in succession, where will the parallel 
 
 fifths or octaves be found ? 
 How may these be avoided? 
 
 What is the rule in regard to the repetition of the third ? 
 
 Which degree of the scale may not be a root? Which not a third? 
 
HARMONY. 
 
 .27 
 
 CHAPTER VII. 
 
 Second Inversion of Common Chords. 
 
 When a chord is written with its Fifth as a bass note, it is called 
 the Second Inversion of the Chord. 
 
 The use of Second Inversions is very much restricted. 
 
 A Chord in its Second Inversion is either a Tonic, a Subdominant, 
 or a Dominant. 
 
 The Second Inversion of a Tonic may be used at any time, pro- 
 vided it is followed by the Dominant Chord. (Note the author is well aware 
 of the rule which says, it must never enter with a leap in the bass, but fails to see the utility of 
 rules that the greatest composers disregard.) 
 
 In Second Inversions, the fifth (bass note) is the best to re- 
 peat. 
 
 a. Second inversion of tonic, preceded by tonic, b. By supertonic. 
 c. By mediant, d. By subdominant. e. By submediant. f. By first 
 inversion of supertonic with third doubled. This succession and that 
 at d are very smooth and orthodox. 
 
 Cadence (Latin cado= to fall). This term is applied' to various kinds of 
 endings. The Perfect or Authentic Cadence is the final tonic pre- 
 ceded by the dominant with its root at the bass. This is emphasized 
 if the dominant is preceded by the second inversion of the tonic, and 
 still more emphasized if the second inversion of the tonic is preceded 
 by the subdominant (as at d) or supertonic (as at /) . 
 
28 
 
 HARMONY. 
 
 Examples of Perfect Cadence. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 ^ — 
 
 
 
 i 1 
 
 
 -<5« 
 
 
 The Second Inversion of a Subdominant must be preceded by the 
 Tonic Chord with its root at the bass. It is generally followed also by 
 the Tonic Chord with its root at the bass. 
 
 
 -g 
 
 j — l-Jf— g — 
 
 & 
 
 tr | r 
 
 
 
 
 ==1 =1 
 
 — i 
 
 
 
 
 
 
 X 
 
 X 
 
 X 
 
 The Second Inversion of the Dominant chord is preceded by the 
 Tonic Chord with its root at the bass, and followed by the Tonic Chord 
 with its third at the bass, or just the reverse. This second inversion 
 is not often used on the accent of the measure. It is apt, in this case, 
 to sound like a Tonic chord. 
 
 x x x x 
 
 a and b are better than c and d, on account of the contrary motion 
 between the outer parts. 
 
 Although the second inversions always enter as above, viz., if a 
 tonic, after any chord in the scale; if a subdominant, after the tonic, 
 root at bass ; if a dominant, after the tonic, root or third at bass — 
 they do not always conform to these examples as to the chord that fol- 
 lows them ; but the rest of this subject must be reserved for a later 
 chapter. 
 
HARMONY. 
 
 29 
 
 The exercises that follow are to be transposed to all the keys. 
 They are the last basses that will be given. 
 
 I. 
 
 Questions on Chapter VII. 
 
 What is meant by the second inversion of a chord? 
 Which chords may be used in the second inversion? 
 What must precede the second inversion of a tonic? 
 What must follow it? 
 
 What must precede and follow the second inversion of a subdominant? 
 What must precede and follow the second inversion of a dominant? 
 What is meant by a perfect cadence? 
 
3° 
 
 HARMONY. 
 
 CHAPTER VIII. 
 
 Harmonizing of Melodies, with Common Chords and 
 Their Inversions. 
 
 The knowledge of Common Chords now gained, must now be ap- 
 plied to the harmonizing of Melodies ; first, with the Chords in Posi- 
 tions. 
 
 As every chord may be written in three positions, it follows that 
 every note in a melody may be either the root, third, or fifth of some 
 chord belonging to the scale. If it is treated as a root, the bass will 
 be the same letter ; if as a third, the bass will be the third letter be- 
 low ; if as a fifth, the bass will be the fifth letter below. 
 
 It is evident that if two notes in succession in the melody are 
 treated as roots, or thirds, or fifths, the result will be two chords in 
 the same Position. 
 
 Begin and end with the Tonic Chord. Observe that the melody 
 may begin on the root, third, or fifth of the tonic. Be careful to 
 avoid using the Leading note as a root. 
 
 The first time the exercises are written, observe carefully the rule, 
 not to write two successive Positions alike. 
 
 The second time they are written, find as many opportunities as 
 possible to put two or three successive chords in the Tierce Position. 
 
 Sequences are indicated in the Melody as they are in the bass, by 
 the notes moving in a regular pattern. Thus, the following notes 
 
 hEEjzzfj indicate the following Sequence: 
 
 Others may readily be found 
 by referring to the sequences in 
 Chapter V. 
 
HARMONY. 
 
 3^ 
 
 ^33 
 
 ii. 
 
 fcd: 
 
 III. 
 
 <f. 
 
 as; 
 
 IV. 
 
 V. 
 
 t=i= 
 
 VI. 
 
 VII 
 
 F F-M-p — 
 
 VIII. 
 
 1 
 
 After harmonizing these exercises with chords in Positions, write 
 them over again, introducing First Inversions. Then, for the last 
 time introduce both First and Second Inversions. Analyze the fol- 
 lowing example of a melody, harmonized three times. 
 
HARMONY. 
 
 First time, chords in position. 
 
 Second time, first inversions introduced. 
 
 Third time, first and second inversions introduced. 
 
 — i — i — — 
 
 9t 
 
 Play these over, and observe how the musical effect improves with 
 the use of the inversions. 
 
 Questions on Chapter VIII. 
 
 What member of a chord may any note in the melody be? 
 
 If treated as a root, what will the bass note be? 
 
 If as a third, how far below will the root be found ? If as a fifth ? 
 
 May two notes in succession be roots, or thirds, or fifths? 
 
 When may two or more notes be thirds ? 
 
 What chord must begin and end the piece ? 
 
 Note. A piece does not always begin with the tonic choid. 
 
 Must the first and final chord be in the octave position? 
 
HARMONY 
 
 33 
 
 CHAPTER IX. 
 
 The Minor Scale. 
 
 The Minor scale historically seems to have preceded the Major. 
 Although its formation from two Tetrachords is not so evident as in 
 the Major scale, yet it is nevertheless true. In the oldest form of 
 Tetrachord the half-tone lay between the first and second letters ; thus, 
 
 E, F, G, A. A seven note scale (which preceded the octave scale) was 
 
 formed by joining two of these Tetrachords ; but the second Tetra- 
 chord began with the letter upon which the first Tetrachord ended ; 
 
 thus, E, F, G, A. 
 
 ' A, m, C, D. 
 
 This was called the scale of Conjunct (joined) Tetrachords. It was 
 made into an octave scale by adding a sound below the first Tetra- 
 chord ; thus, D, E, F, G, A. 
 
 A, ,Z?b, C, £>. This was . known as the 
 
 Dorian scale. 
 
 It will be seen that the half-tones lie between the second and third, 
 and fifth and sixth. This form is now called the Natural Minor 
 Scale. 
 
 It will be found that by taking the sounds of any Major scale and 
 arranging them in arvoctave succession beginning with the sixth of 
 the Major scale, it will give a succession identical with this ; therefore, 
 
 Every Minor scale is called the Relative Minor of the major 
 scale from which it is formed, and it has the same signature. (It is 
 
 perhaps easier to remember the relative minor as beginning on the third below the tonic, this being 
 the inversion of the sixth above. J 
 
 The requirements of harmony have made several modifications in 
 this scale. 
 
 I. It is necessary to modern ears to have a half-tone between the 
 seventh and eighth of a scale in ascending. If the seventh is raised, 
 
3.4 
 
 HARMONY. 
 
 there results the awkward interval of an augmented second between 
 6 and 7 ; to remedy this, 6 must also be raised. But the need of a 
 half-tone between 7 and 8 is not felt in a descending scale ; they are 
 therefore allowed to remain unaltered. This form of ascending and 
 descending scale is called the Melodic, because the raised sixth and 
 natural seventh are not found in any of the chords belonging to the 
 scale. (See note.) 
 
 We have nothing to do at present with either of these forms, but 
 with a third form called the Harmonic. In this the seventh is always 
 raised, both ascending and descending. So the minor scale is always 
 to be thought of at present as having a raised seventh or leading note. 
 These three forms of minor scale are here given. 
 
 Scale of A-Minor. The Relative Minor of C. 
 
 Natural. 
 
 
 
 
 
 ■ 0 
 
 — -s>— 
 
 
 
 9 bj- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — <s»— 
 
 
 
 -n \ 
 
 
 — rS>— 
 
 
 
 
 
 
 
 
 
 
 — <S>— 
 
 
 
 Four common chords may be written in the Harmonic Minor scale. 
 Two are minor, viz., Tonic and Subdominant; two major, viz., the 
 Dominant and Chord on sixth. 
 
 Dominant chords must be major. This is the harmonic reason for 
 the raising of the seventh; hence this scale is called the Harmonic. 
 
 Note. In the older writers the raised sixth was harmonized as the fifth or third of a chord. It 
 is rarely found in modern music. Another form of minor scale was also used by the older writers, 
 called the mixed minor. In this scale the 6 and 7 were raised both ascending and descending. 
 Consequently it differs from the major scale only in having the third above the tonic minor. This 
 scale will be found frequently in Bach and Handel. 
 
HARMONY. 
 
 3,5. 
 
 Scale of A-MinoR, Harmonic, with Chords, 
 i. 2. 3. 4. 5. 6. 
 
 -1- 
 
 Tonic, minor. 
 
 The fifth is diminished. 
 
 The fifth is augmented, owing to the raising of the seventh. 
 Subdominant, minor. 
 
 i 
 
 1 . 
 
 2. 
 
 3- 
 4- 
 5- 
 
 Dominant, major. Observe that this is the only chord in the 
 
 scale in which the raised note is found, and that it is the third in this 
 chord. 
 
 6. Submediant, major. 
 
 7. Leading note, diminished fifth. 
 Analyze the following example : 
 
 § gzz ^ 
 
 J-L-4 
 
 4 
 
 -<5t- 
 
 9i 
 
 -F- 
 
 :t 
 
 ^ 2::?: :f: ^ <^ 
 
 1 
 
 =t±E 
 
 1 
 
 A Major Scale and its Relative Minor are so closely bound together 
 that they may conveniently be looked upon as one and the same thing. 
 Consequently if the seventh of the minor scale appears not raised, it 
 is generally as a member of one of the chords in the related major 
 scale. 
 
 £f~®- 
 
 3=4 
 
 3= 
 
 2 is in the relative major. 
 
 3 and 4 in minor. 
 
 Part of 5 and 6 in major, the remainder in minor. 
 
HARMONY. 
 
 It was customary at one time to end all compositions in the minor 
 key with a major tonic. This major third was called the "Tierce de 
 Picardie." It is still occasionally used. 
 
 In harmonizing the exercises that follow, find opportunities for the 
 use of the relative major chords. The natural seventh of the minor 
 scale must (at present) be either root or fifth of a chord in the relative 
 major. 
 
 It is necessary now to speak of the Diminished Chord, but more 
 will be said about it later. 
 
 Diminished Chords may be used freely, with the proviso that they 
 are used in the first inversion. 
 
 In the Major scale there is but one ; viz., on the Leading note. In 
 the Minor scale in addition to one on the Leading note there is one 
 on the second (Supertonic) of the scale. This last mentioned chord is 
 very important in the minor scale. 
 
 The Bass note of this chord is the 
 best to repeat. 
 
 g pr- 
 
 
 m 
 
 w § 
 
 -! 
 
 
 
 
 
 
 t 
 
 
 First inversion, bass 
 repeated. 
 
 Diminished chord on second of A minor, (it will be seen that it is also the 
 leading note chord of the relative major.) The second inversion of the tonic 
 enters very effectively after this chord. 
 
 t Diminished chord on second, 
 
 ** first inversion. 
 
 X 
 
 III. 
 
 
 
 
 
 
 
 
 
 
 'i 
 
 
 -<s>- 
 
 
 
 
 
r-Q~b— It 
 
 
 1 — i % 
 
 =1 ^ -i 1 
 
 
 
 
 
 
 
 Questions on Chapter IX. 
 
 Where do the half-tones lie in the natural minor scale? 
 
 Why is a minor scale called the relative minor of a major scale? 
 
 Upon which degree of the major does the relative minor begin? 
 
 To what form of minor scale is the term melodic applied ? 
 
 To what form is the term harmonic applied ? 
 
 Where do the half-tones lie in the harmonic scale? 
 
 What is the interval between the sixth and seventh ? 
 
 How many common chords are found in the harmonic scale? 
 
 Which are major? Which minor? 
 
 What kind of fifth does the mediant bear? 
 
 In which chord is the raised seventh found? 
 
 What member of this chord is it? 
 
 If the seventh is not raised, how is it generally treated? 
 Where are diminished chords found? 
 In what form may they be used ? 
 Which member should be repeated ? 
 
3* 
 
 HARMONY. 
 
 ' ' CHAPTER X. 
 
 The Group or Circle of Related Keys. 
 
 In Chapter II. the relationship of Major scales through the Tetra- 
 chords is explained. In the last chapter the relation between a 
 Major and its Relative minor is explained. This relationship must 
 now be extended to include the Relative Minors of the Major 
 Relations. 
 
 Thus, given the key of C, the related majors are E, G. 
 The relative minors A, D, E. 
 
 Thus a given key always includes a group of six keys, three Major 
 keys and their Relative Minors. 
 
 Each of these scales must have a leading note ; thus, C being the 
 key, E, its first major relative has E as leading note. G, the sec- 
 ond major relative, has E§ as leading note; A minor has G§; D 
 minor, Cjf ; E minor, Z$. 
 
 So four accidentals may be introduced in the scale of C, as lead- 
 ing notes to the related scales. We found that the leading note of 
 the minor scale was only to be found in the dominant chord, in 
 which chord it is the third. From these facts we deduce the follow- 
 ing rule : 
 
 Notes raised by accidentals are Leading notes to Related Keys, 
 and they are always harmonized as Third in the Dominant Chord of 
 the key to which they lead. 
 
 The most natural progression of a Dominant chord is to its Tonic. 
 
 
 i. 
 
 2. 
 
 ' 3- 
 
 4- 
 
 
 5 . 6. 
 
 
 
 
 
 
 
 
 % * 
 
 — 1— 
 
 =1 & 
 
 A M 
 
 
 
 
 m= 
 
 sr 
 
 
 
 — 1 
 
 & 1 
 
 
 
 & — 
 _j 
 
 F CPHI 
 
 I. Dominant and tonic of D minor, relative minor of E. 
 
HARMONY. 
 
 39 
 
 2. Dominant and tonic of E minor, relative minor of G. (When there 
 
 are two raised notes in a chord, the last one to occur is the third ; therefore D$, which does not oc- 
 cur until after Ft, is the third, F must be sharped in F minor because it is sharped in G major.) 
 
 3. Dominant and tonic, F major. 
 
 4. Dominant and tonic, G major. 
 
 5. Dominant and tonic, A minor, relative minor of C. 
 
 6. Dominant and tonic of Key. 
 
 It is much to be regretted that one word, modulation, is used to 
 signify going into a related key transiently (especially by means of its domi- 
 nant chord), and going outside of the related groups. 
 
 The writer has thought that for clearness' sake, the word modu- 
 lation might be used only in the first sense, and that the word 
 transition better describes this passing to a new group of relations. 
 Therefore in this work these words will be used with this distinction 
 between them. 
 
 In all the modulations in the foregoing example, the idea of the 
 original key is never lost for a moment, — what is called the "Tonality." 
 The reason, perhaps, is that the Tonic chords are simply the six 
 common chords of the original scale. If one of these Tonics, when 
 preceded by its dominant is changed, for example, if the tonic of 
 D minor ( 1 ) is changed to major, the tonality of the original key 
 is at once lost, and a transition is made. 
 
 The following examples will show how these dominant chords may 
 be used. 
 
 -~ ! 
 
 9* 
 
 m 
 
 -0r 
 
 a. Is harmonized with chords natural to the scale. 
 
 b. Same melody, with dominant chords of related scales introduced. 
 Harmonize the following passages in the same manner ; follow 
 
 every dominant by its own tonic for the present. 
 1. 2. 3. 
 
 EH 
 
4 o HARMONY. 
 
 i^iipi^BIsilllligi^a 
 
 In i the dominant and tonic of D minor may be used. 
 In 2 the dominant and tonic of A minor and G major. 
 In 3 the dominant and tonic of A minor, G major, JF major. 
 In 4 the dominant and tonic of G major, twice; or second place 
 may have dominant E minor. 
 
 In 5 the dominant and tonic of E, G, A. 
 In 6 the dominant and tonic of D, E. 
 
 When these dominant chords of related keys are used in sequences, 
 the sequence is called harmonic ( or chromatic ) . Sequences will be found 
 in 2, J, 5, and 6 of the above examples. A few more are here given. 
 They and the foregoing exercises should be transposed to every major 
 key. 
 
 Exercises Introducing Related Keys. 
 
HARMONY. 
 
 4 1 
 
 III. 
 
 IV. 
 
 t=*=n 
 3=d 
 
 v. 
 
 VI. 
 
 fa 
 
 ±=d: 
 
 let 
 
 The rules about second inversions may now be extended so as to in- 
 clude the Tonic, Dominant, and Subdominant chords of the Related 
 keys. 
 
 r 
 
 X 
 
 0 
 
 zt: 
 
 :pz=: 
 
 -251- 
 
 -(2- 
 
 1 1 5 s- 
 
 L -t--5-^- 
 
 
 -4- 
 
 
 
 
 
 
 
 
 rr rr-r i~ 
 
 
 9z a 
 
 
 
 
 
 
 1. Second inversion of some related tonics. 
 
 2. Second inversion of subdominants. 
 
 3. Second inversion of do-minants. 
 
 Although the dominant chords generally progress to their tonics, 
 
HARMONY. 
 
 being Common chords — have othe-r progressions, which 
 
 1 
 
 42 
 
 they may - 
 
 may occur singly or be arranged in sequences, 
 r. 2. 
 
 4- 
 
 6. 
 
 1. Dominant, followed by the chord on the sixth of the scale to 
 which it belongs. 
 
 2. Dominant of minor, followed by tonic of relative major. 
 a. Both roots at bass. b. Tonic, with third at bass. c. Dominant, 
 third at bass ; tonic, fifth at bass. 
 
 3. Two dominants in succession. In this case the roots must be a 
 fourth apart (ascending), or fifth apart (descending). 
 
 4. Dominant of a minor, followed by chord on minor third above. 
 
 5. Dominant changed chromatically to natural chord of scale. 
 
 6. Same as 4, but second chord with fifth at bass. 
 
 7. Dominant of a major key, followed by dominant of its relative 
 minor. 
 
 1, 3, and 7 are of special importance. 
 Transpose these examples to all keys. 
 
 Questions on Chapter X. 
 
 How many scales are included in the related group? 
 How many are major ? How many minor ? 
 
 How many accidentally raised notes may be introduced in a given scale? 
 What are these accidentals? 
 
 What is the natural progression of a dominant chord ? 
 
 What is the difference between a diatonic and a harmonic sequence? 
 
HARMONY. 
 
 43 
 
 CHAPTER XI. 
 
 Chords of Parallel Minor, Lowered Supertonic, and 
 Chords in the Related Keys not Found 
 in the Given Key. 
 
 In addition to the Dominant chords of the Related keys there still 
 remain some Common chords which may be used without making a 
 transition. 
 
 Taking C as our given key, the related key of F possesses two 
 chords, C7, Z?b, D and D, F, that are not found in C. The 
 related key of G possesses one that is not found in C, — F, D, F$. 
 See accompanying table of chords. 
 
 K 
 
 ey of C. 
 
 </. <r. /. 
 
 k 
 
 
 
 K 
 
 eyof F. a. j 
 
 ( . ^ i X | /• | x 
 
 
 b _-J— ~d 
 
 
 
 «_ 
 
 K 
 
 eyofG. 
 
 
 »EI_f* « ^ 
 i 1 
 
 -—I , d 
 
 y i 
 
 m — id 
 
 «g f*-n£=-r s= * - 1 
 
 
 l -' Tl 
 
 The use of these chords in the key of C is somewhat restricted, 
 owing to the fact that they are not owned in common by the scale in 
 which they are found and the given scale. Their use generally 
 indicates a transition to one or the other of these related keys, which 
 is continued for some time. The following examples are given of 
 their use without a transition : 
 
44 
 
 HARMONY. 
 
 if* 
 
 1HH 
 
 None of them, especially 3, sound quite at home. 
 
 The Major and Minor scales that begin on the same keynote are 
 called Parallel scales. The chords belonging to a Minor scale may 
 be used in its Parallel major. The Minor scale (harmonic) differs from 
 its parallel major in two of its degrees only; viz., the third and sixth, 
 which are minor, counting up from the keynote. 
 
 n Third. Sixth 
 
 These sounds are found in three of 
 the chords in the minor scale, thus : 
 
 ■i9- 
 
 One of them, the sixth, is also found in the Diminished chord on 
 
 :2s: 
 
 1 
 
 the Supertoni C (which must be used, as already explained 
 in its first inversion) , thus : 
 
 The Minor Tonic and Subdominant are often preceded by the 
 major form of the same chord (1) ; or, the Minor Tonic by the 
 Dominant (2) ; the Minor Subdominant by the Tonic (3), or by 
 the Dominant (4). 
 
 1. 2. 3. 4. 
 
 The chord on the 
 sixth of the Parallel 
 minor may be pre- 
 ceded by the Tonic or 
 Dominant. 
 
 jGL 
 
 is 
 
 i 
 
HARMONY. 
 
 45 
 
 The chord on the sixth of the 
 Major may be followed by the 
 Minor Subdominant or Tonic. 
 
 1— t 
 
 I 
 
 The Minor Tonic may also be 
 preceded by the Dominant of the 
 Relative minor (i) ; and by the 
 Dominant of the Relative minor 
 of the first major relation (2). 
 
 li 
 
 The first inversion of the dimin- 
 ished chord on the supertonic is 
 generally followed by second in- 
 version of tonic ; it may be pre- 
 ceded by any chord but the 
 mediant. 
 
 m 
 
 1 
 
 The foregoing examples show what may follow as well as precede 
 these Parallel Minor chords. The pupil should try the effect of all of 
 these successions in different positions and inversions (in all the keys) . 
 It will be found that some progressions which sound well with one 
 arrangement of the chords, are intolerable with another arrangement. 
 
 The last Common Chord is a Major chord on the Lowered Super- 
 tonic of the scale. 
 
 In the key of C, the Lowered Supertonic is Z?i? ; a Major chord on 
 this root is, Db, jF, Ab. This chord, although used freely in the Ma- 
 jor key, seems to sound more at home in the Minor key. If used in 
 the Major key it may be preceded by the Tonic, Subdominant, Domi- 
 nant or by any of the chords of the Parallel minor. It is followed by 
 the Tonic or Dominant. 
 
4 6 
 
 HARMONY. 
 
 This chord is more frequently used in its first inversion (as in ex- 
 amples 4, 5, 6, 7) and is then called the Neapolitan Sixth. 
 
 In the example that follows, all the chords and progressions so far 
 learned will be found. The analysis of it should be well studied. 
 All analyses should be made on the following principles. 
 
 I. Every chord bears some relation to the principal key ; that is, it 
 is either to be found in that key or in one of its relations. 
 
 II. Every chord bears some relation to the Chord that precedes it. 
 
 III. Every chord bears some relation to the Chord that follows it. 
 
 IV. Every Major chord may bear five possible relations; viz., 
 Tonic, Subdominant, Dominant, sixth of a Minor scale, Lowered 
 Supertonic. 
 
 V. Every Minor chord may bear five possible relations; viz., 
 Tonic, Subdominant, Supertonic, Mediant, Submediant. Thus, 
 the Major chord C, E, G, in 
 
 1, bears the relation of Tonic to the preceding chord. 
 
 2, bears the relation of Dominant to the following chord. 
 
 3, bears the relation of Subdominant to the following chord. 
 
 4, bears the relation of Submediant to the following chord. 
 
 5, bears the relation of Lowered Supertonic (of B, followed by 
 dominant) . 
 
 
 2. 
 
 
 3- 
 
 
 4- 
 
 5- 
 
 
 
 
 
 -i 
 
 
 
 
 
 
 
 
 
 
 w & — 1 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The Minor chord A, C, I?, in 
 
 I, bears the relation of Tonic to the preceding chord. 
 
HARMONY. 
 
 47 
 
 2, bears the relation cf Subdominant to the following chord. 
 
 3, bears the relation of Supertonic to the following chord. 
 
 4, bears the relation of Mediant to the following chord. 
 
 5, bears the relation of Submediant to the preceding chord. 
 
 r. 2. 3. 4- 5- 
 
 A Chord always bears a relation to the Chord that follows it differ- 
 ing from that it bears to the Chord that precedes it (unless the same chord 
 precedes and follows) . 
 
 This relationship may or may not make a modulation. 
 
 1. The chord A, C, E, enters as Tonic, and is followed by Sub- 
 dominant chord, — all three in A minor 
 
 2. A, C, E, enters as Tonic, but is Subdominant to the following 
 
 chord, modulating to E minor. 
 
 3. Dominant of C, followed by chord on sixth of parallel minor. 
 This chord, A\>, C, E\>, is then treated as the Lowered Supertonic 
 of G, followed by Dominant of G. 
 
 '■'•<' " 1. 2. 3. mi^M 
 
 
 
 — 
 
 -h 
 
 
 -id 
 
 ^= 
 
 
 
 
 — <s — 
 
 
 
 
 
 
 H 1 r 
 
 
 
 1 1 
 
 
 - 
 
 II 
 
 Common chords have been treated at great length and with especial fullness, because a 
 thorough familiarity with them and their progressions is by far the most important part of har- 
 mony. The dissonant chords that follow will be found easy if the common chords have been 
 thoroughly mastered. 
 
 I. 2. 
 
 P 
 
 3. 4. 5. 6. 
 
 9. 10. n. 12. 13. 14. 15. 
 
 
 
 
 
 
 
 
 
 
 
 ±=t== 
 
 
 1*9 
 
 
 
 4. 
 
 r - 
 
 
4 8 
 
 HARMONY. 
 
 1 6. 17. l8. 19. 20. 2F. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 9fc 
 
 31. 32. 33. 34.35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 
 
 r— t 
 
 1 1 — L - f— J — p- -p^ — ^ — % 
 
 <s*- -<^- -IS- 
 
 1. Tonic. 2. Tonic parallel minor. 3 and 4. Dominant. 5. 
 Submediant. 6. Supertonic. 7 and 8. Dominant A minor. 9 and 
 10. Tonic parallel minor. 11 and 12. Submediant parallel minor. 
 13. Lowered Supertonic followed by (14) dominant. 15. Tonic 
 16. Submediant is Subdominant to the next chord. 17. Tonic E 
 minor. 18. Dominant E minor. 19. Tonic E minor. 20. Sub- 
 dominant E minor, but mediant to the next chord (21) which 
 is dominant to (22) Z?b, which is lowered supertonic of A, followed 
 by dominant (23) and (24) tonic A, treated as subdominant to E, 
 25. 26. Dominant of E minor, followed by chord with root a 
 minor third above, 27. 28. Dominant of D minor, followed in the 
 same way. 29. C minor, parallel minor. The two bars make 
 
HARMONY. 
 
 49 
 
 a sequence. 30. Dominant. 31 to 38. All belong to parallel 
 minor, except 35, which belongs to both major and minor. 39 to 42. 
 Are easily "parsed." 43. Subdominant of parallel minor, preceded 
 by Submediant of major. 44. Tonic treated as sixth of E minor. 
 The rest is easy. 
 
 It will be seen that the chords of the parallel minor may be written 
 in succession. 
 
 Exercises Introducing All Possible Common Chords Without 
 Going Outside of the Group of Related Keys. 
 
 I. 
 
 1=3 
 
 p=t 
 
 P 
 
 -i n 1 n r - 
 
 i 
 
 11. 
 
 in. 
 
 St 
 
 1= 
 
 22: 
 
 IV. 
 
 sir 
 
 - [ 1 H -2 — = 
 
 5 
 
 =2 - 
 
 1 
 
 V. 
 
 Questions on Chapter XL 
 
 How many chords are common to the scales of C and F ? Which are they ? 
 
 How many to the scales of C and G ? Which are they? 
 
 Are there any chords common to all three scales? Which are they? 
 
 What chords in F are not found in C ? 
 
 What chords in G are not found in C? 
 
 What is meant by parallel scales ? 
 
5° 
 
 HARMONY. 
 
 In what respect does a minor scale differ from its parallel major? 
 In how many of the chords of the minor scale are these notes found ? 
 Does the dominant of a major scale differ in any way from that of its parallel 
 minor ? 
 
 How is the minor tonic preceded? The minor subdominant? The chord on 
 sixth ? 
 
 What other chords may precede the minor tonic? The minor subdominant? 
 How is the diminished chord on supertonic of parallel minor generally used? 
 Is any other common chord possible? Where is its root? Is it major or 
 
 minor? By what is it followed ? By what may it be preceded ? In what 
 
 form is it most frequently used ? 
 What name does it bear in this case? 
 How many relations may a major chord bear? 
 How many, a minor chord ? 
 
HARMONY. 
 
 5* 
 
 CHAPTER XII. 
 
 Chord of Dominant Seventh, First Progression. 
 
 Dissonant chords are those that include a sound that must move in 
 some specific direction. This motion is called the Resolution of the 
 
 Dissonance. (The term resolution is rather loosely applied to the movement of chords. 
 Chords progress, their Dissonant members resolved) 
 
 All Dissonant chords are formed by additions to Major Chords. 
 The most important are the additions to the Dominant chord. 
 
 Dissonances that are members of a chord are called Essential (to 
 
 distinguish them from those that are merely ornamental, or that are used as Suspensions or Re- 
 tardations). 
 
 The whole series of dissonances that may be sounded with a given 
 root are called its Harmonies. 
 
 The first addition to the Dominant is the seventh over the root. 
 
 This seventh is minor; it resolves by descending. 
 
 Three Inversions may be made. The rules about second inversion 
 of common chords do not apply to Dissonant chords. 
 
 The Dominant seventh chord may have Three Progressions. 
 
 The First progression, the most natural, is to the Tonic Chord. 
 
 Rides. The seventh descends one degree. 
 
 The fifth may ascend or descend; it generally descends. 
 
 The third must ascend one degree. 
 
 The root when at the bass ascends a fourth or descends a fifth, to 
 the root of the tonic. When the chord is inverted the root is stationary. 
 
 It will be seen that the freedom of movement of common chords is 
 lost when a dissonant is added, for the reason that they must move to 
 a chord of which the note that the dissonant resolves on is a member. 
 
 First inversion. 
 
 . ... . L or ! 
 
5^ 
 
 HARMONY. 
 
 Second inversion. 
 
 — =1 
 
 Third inversion. 
 
 Every possible arrangement of this progression is given here. 
 Write in the same way the dominant seventh chords of the keys re- 
 lated to C, taking care to insert the necessary accidentals in every 
 case. 
 
 Observe I, that when the Root is at 
 the bass, the fifth of the Tonic has to be 
 omitted. This is often avoided by omit- 
 ting the third of the dominant and repeating 
 the Root, thus : 
 
 hi 
 
 7^- 
 
 3 I I 
 
 £ 1 LI 
 
 or, by omitting the fifth, etc., (2). 
 
 II. The fifth is often made to ascend, when in the soprano or at 
 the bass. When at the top in the third inversion, it may ascend to 
 the third or to the fifth of the tonic. 
 
 III. When the Root of the dominant is at the top in the third 
 inversion, it may ascend to the root of the Tonic, (it might do so when at 
 
 the top in the other inversions, but does not sound so well.) 
 
 The introduction of this additional member of the dominant chord 
 adds very much to our resources in harmonizing a melody, as any 
 note in the melody may be harmonized as the seventh of a dominant, 
 provided it is followed by the note on the next degree below, and 
 provided it will be the seventh in one of the dominant chords of the 
 Related Group. 
 
 2. 
 
 
 1 
 
HARMONY. 53 
 
 In the above descending scale, harmonized twice, will be found all 
 the dominant seventh chords of the group of C, and its relations, ex- 
 cept one; viz., the dominant of J?, the seventh of which is B\>. 
 Observe that the third and seventh are the only notes in the scale 
 which may not be sevenths. 
 
 The Bb, needed to make the seventh in the dominant of F, makes 
 the fourth chromatically lowered note — (the others being, two belonging to 
 
 the parallel minor, and the lowered supertonic) . 
 
 For the present the lowered leading note of the scale must be har- 
 monized as a dominant seventh. 
 
 Analyze the following example before writing the exercises that 
 follow. 
 
 Proceed thus in analyzing : 
 
 First. Chord is tonic of key, quint position. 
 
 Second. Dominant of A minor, second inversion, third at top, 
 followed by 
 
 Third. Tonic of A minor, octave position, mediant to the chord 
 following. 
 
 Fourth. Dominant of JR major, second inversion, seventh at top, 
 followed by 
 
 Fifth. Tonic of 7% tierce position. 
 
 Sixth. Dominant of D minor, second inversion, seventh at top, 
 followed by 
 
 Seventh. Tonic of D minor, tierce position. 
 If any sequences are found point them out. 
 
54 
 
 HARMONY. 
 
 ii. 
 
 EE3 
 
 III. 
 
 «J ' 
 
 IV. 
 
 Si? 
 
 "HE* 
 
 Ms- 
 
 13 
 
 b 
 
 z2 
 
 PHIEI 
 
 VI. 
 
 —A- k 4 -MM- _ _ r- -1 1 r, 1 k 1 _ 1^2- -^=5 _ , -k.- 
 
 
 
 
 — 1, — H — 
 
 
 ±3=1= 
 
 
 VII. 
 
 s 
 
 There are a few exceptional cases in which the seventh "does not 
 descend in the first progression. They can only occur with the 
 chords- arranged exactly as follows. 
 
 " US 
 
 IE! ^ j2_ 
 
 -©» 
 
 r — r — r ■ 
 
 3 
 
 -<S>- -fS?- 
 
 (Si ~~ ^) 
 
 7 
 
 ;ezee 
 
 ii 
 
HARMONY. 
 
 55 
 
 r. The bass and top part ascending in thirds with each other. 
 
 2. Root at bass going to third, and seventh ascending to fifth. 
 
 (This is more common in the older composers than it is now.) 
 
 3. Dominant, tierce position, followed by first inversion of 
 Snbdominant. 
 
 4. Diatonic scale in contrary motion. 
 
 5. Same, but the seventh is doubled; one ascends, the other 
 descends. 
 
 Questions on Chapter XII. 
 
 What is a dissonant chord ? 
 What is this movement called? 
 How are dissonant chords formed ? 
 
 Which is the most important chord to which they may be added ? 
 What is an essential dissonance? 
 
 What name is given to the series of dissonances that may be added to a given 
 root ? 
 
 What is the first addition to the dominant chord ? 
 Of what kind is this seventh? 
 How does it resolve? 
 
 How many inversions may be made of a dominant seventh chord? 
 How many progressions may it have? 
 What is the first progression? 
 
 How do the members of the dominant seventh move in this progression ? 
 When may the fifth of the dominant ascend ? 
 
 When the root of the dominant seventh is at the bass, which member of the 
 
 tonic following it must be omitted? 
 How may this omission be avoided? 
 When may a note in the melody be a seventh ? 
 How many and which notes in the scale may be sevenths? 
 How must the chromatically lowered leading note be harmonized ? 
 How many notes in the scale may be lowered accidentally? 
 Which are they, and how may they be harmonized ? 
 
56 
 
 HARMONY. 
 
 CHAPTER XIII. 
 
 Dominant Seventh, Second and Third Progressions, 
 and Succession. 
 
 A dominant seventh chord may be repeated indefinitely, with 
 changes in its position and inversion, provided that the dissonance 
 is resolved when the Progression 
 
 s*g- 
 
 1 
 
 4=t 
 
 takes place. In the following 
 example, the Dominant chord 
 is struck four times before the 
 progression to the Tonic takes 
 place. 
 
 The Second Progression of the dominant seventh is to the Sub- 
 mediant (sixth of scale) . 
 
 This progression only takes place with the Root of the Dominant 
 at the bass. 
 
 The Seventh and fifth descend. (The fifth must descend, otherwise it would 
 make parallel fifths with the root.) 
 
 The Third ascends except when the fifth of the dominant is at 
 the top. When this is the case it may descend. 
 The Root ascends to the root of the submediant. 
 
 i. 2. 3. 4. 5. 6. 
 
 1, 3, 5. Dominant seventh, followed by submediant. 
 
 2, 4, 6. Dominant seventh, followed by submediant of parallel 
 minor. 
 
HARMONY. 
 
 57 
 
 In 5 the third descends, the fifth of the dominant being at the top. 
 
 Same in 6. This sounds better in instrumental than vocal music, 
 owing to the awkward skip from 
 
 Third Progression. The dominant seventh of a Major Key may 
 be followed by the Dominant of its Relative Minor. 
 
 This progression may take place with any inversion. 
 
 The seventh descends; the fifth and third, being common to both 
 chords, either remain stationary, or they may change places ; that is, 
 while cne voice moves from the third to the fifth, another may reverse 
 this, moving from the fifth to the third. 
 
 The Root ascends chromatically. 
 
 The seventh of the first chord may skip to the seventh of the 
 second, while the fifth ascends to the Root ; or the seventh may skip 
 to the fifth of the second chord ; last, the seventh may be omitted 
 from the second chord. 
 
 6. 7. 8. 9. 10. 
 
 1, 2, 3, 4. Third progression with root at bass and the three in- 
 versions. 
 
 5 and 6. Third and fifth changing places. 
 
 7. First inversion of one followed by second inversion of the other. 
 
 8. Seventh of first chord skipping to seventh of second chord. 
 
 9. Seventh of second chord omitted. 
 
 10. Seventh skipping to fifth of second chord. 
 
 Note. More will be said about this third progression in the chapter on chord of ninth. 
 
58 
 
 HARMONY. 
 
 It is necessary to observe that this progression may only be used 
 with melodic passages that will permit of the resolution of the 
 second chord as indicated by the small notes. 
 
 In addition to the Three Progressions of the dominant seventh 
 chord, it is possible to make a Succession of dominant seventh chords, 
 as follows : 
 
 The third of the chord, instead of being made to ascend, is lowered 
 chromatically, and is made the seventh in the succeeding chord. 
 
 This Succession has the root and fifth, or third and seventh alter- 
 nately at the bass ; or all the chords may have the roots at the bass 
 by omitting the fifth from every alternate chord. 
 
 
 -is>-k«>- 
 
 2. 
 
 ■ ^ ^ ~& & 
 
 
 
 tr h | 
 
 
 
 r- -5> 
 
 1 1 
 X 
 
 ISP 
 
 
 
 
 
 a. (22 |_ 
 
 — ^ 
 
 22 - 
 
 1. Root stationary, fifth descends, root and fifth at bass. 
 
 2. Root stationary, fifth descends, third and seventh at bass. 
 
 3. Root at bass goes to root of next chord; the fifth is omitted 
 from chords marked x. 
 
 This succession should not be continued for more than two or three 
 chords, as it soon grows monotonous. 
 
 Questions on Chapter XIII. 
 
 What is the second progression of dominant seventh? 
 
 How do the members of the chord move? 
 
 Which member of the dominant must be at the bass? 
 
 Does the third always ascend? 
 
 What is the third progression ? 
 
 Can the dominant of a minor key have the third progression? 
 How do the members of the chord move in this progression? 
 What is it necessary to observe when using this progression? 
 How is a succession of dominant sevenths made? 
 How do the other members of the chord move? 
 
 What members of the chord may succeed each other as bass notes in this suc- 
 cession ? 
 
 What must be omitted when the notes are at the bass? 
 
HARMONY. 
 
 59 
 
 Exercises for all the Progressions and the Succession of 
 Dominant Sevenths. 
 
 I. 
 
 mm 
 
 III. 
 
 # s b-4 f i* » 
 
 r 1 
 
 
 X 
 
 
 • 
 
 
 
 
 
 
 
 
 
 1^ 
 
 !I1 
 
 IV. 
 
 X X 
 
 t4= 
 
 Use third progression at the signs x x. 
 
6o 
 
 HARMONY. 
 
 CHAPTER XIV. 
 
 Dominant Ninth. 
 
 The next addition to the dominant chord is the Ninth over its root. 
 
 The ninth may be either Major or Minor. 
 
 Major ninth contains an octave and a whole-tone. 
 
 Minor ninth, an octave and a half-tone. 
 
 In Major keys both kinds of ninths are used. 
 
 In Minor keys the minor ninth only may be used. 
 
 The ninth resolves by descending one degree. 
 
 The ninth may not be used as a bass. 
 
 The ninth may not be written close to, or below the root; hence 
 three inversions only may be made of this chord. 
 'The fifth must ascend when below the ninth. 
 
 In four-part harmony, the third, fifth, or seventh may be omitted. 
 The first progression only is possible when the ninth is added. 
 The Succession of dominant chords may be made, provided the 
 ninth is used only with alternate chords. 
 
 In general, the minor ninth sounds better than the Major when it 
 
 
 }t at the top of the chord, 
 i. 2. 3. 4. 5. 6. 
 
 7- 
 
 U 1 f~ 
 • a 1 . 
 
 r r r 
 
 r r 
 
 T — r — & TT 
 
 <s> a \& — _L 
 
 ^ T ^- 
 
 
 
 :p ^|=t-^^:= 
 
 Third. Fifth. Seventh. 
 
 8. 9. 10. 11. 12. 13. 14. 
 
HARMONY. 
 
 61 
 
 1. Dominant of C, with major ninth. 
 
 2. Dominant of C, with minor ninth. 
 
 3. First inversion. 4. Second inversion. 5. Third inversion. 
 
 6, 7, 8. The third omitted in 6 and 7, the ninth is minor, not being 
 at the top of the chord. 
 9, 10. The fifth omitted. 
 11, 12, 13. The seventh omitted. 
 
 14. Succession of dominants. The ninth is not added to the sec- 
 ond chord, but is to the third. If the succession were continued the 
 fourth chord would be without the ninth. This example should be 
 written in several keys. 
 
 We found ( page 56 ) that it is possible to change the arrangement 
 of a chord at will, and that there was no Progression until the har- 
 mony changed; but as the ninth in descending moves to the root of 
 the chord, there may be Resolution without Progression, thus : 
 
 The ninth and seventh may also move 
 freely to any other member of the chord be- 
 fore progression takes place. 
 
 1. Ninth leaps to seventh, then seventh to fifth. 
 
 2. Ninth ascends to third. 
 
 3. Ninth leaps up to seventh. 
 
 4. Seventh leaps up to ninth. 
 
 This shows that resolution, although it may ( in the case of the 
 ninth ) take place without progression, is not compulsory. 
 
62 
 
 HARMONY. 
 
 The chord of the ninth is much used with the Root omitted. The 
 remaining notes may be inverted in any form, and may have the first 
 and third Progressions. 
 
 The omission of the root from a chord with Minor ninth makes 
 it what is known as the Diminished Seventh Chord. 
 
 The fifth may descend in the diminished seventh chord when it is 
 below the ninth, if the ninth is not at the top. 
 
 i. 2. 3. 4. 5. 
 
 1. Third, fifth, seventh, major ninth, first progression. 
 
 2. Third, fifth, seventh, major ninth, third progression. 
 
 3. Third, fifth, seventh, minor ninth, called diminished seventh 
 chord, because the interval from third to minor ninth is a diminished 
 seventh. 
 
 4. Diminished seventh from dominant of C, and diminished seventh 
 from dominant of A, its relative minor. Observe that three of the 
 letters are common to both chords, and that the remaining sounds are 
 enharmonically identical. It is owing to the fact of these two chords 
 
 (viz., the dominant of any key, and the dominant of its relative minor) having SO many 
 
 sounds in common, that it is so easy to pass from one to the 
 other. 
 
 5. Z>, the fifth, is at the bass and descends because ^4t>, the ninth, 
 is not at the top. 
 
 Some more examples of the third progression. 
 
 1. First chord has seventh ; the second, ninth without root. 
 
 2. Both chords have the ninth without root. Of course, in both 
 these cases the notes that are common to both chords may change 
 places in a variety of ways. 
 
 3 and 4. Give examples of the reversal of this progression. It is 
 possible with other arrangements of the chords, but is most effective 
 in the two here given. 
 
HARMONY. 
 
 i 
 
 The study of the following example will give an idea of the 
 wealth of harmonic possibilities there are in a given key and its re- 
 lations, and we are by no means at the end of them yet. 
 
 Take as given key C; relative majors -/FJ G\ relative minors A, 
 
 £>, E. 
 
 2. 
 
 3. -S-oife. 5- -^-ks?- 
 
 '9— 
 
 IS 
 
 12. 
 
 7. 8. 9. IO. IT. fo^L 3 ' j?<2_ 14. 15. 
 
 „ piliiMiiii ii^pi 
 
 1. The natural chords of the scale. 
 
 2. Chords from parallel minor. 
 
 3. Chord on lowered supertonic (during a modulation into a re- 
 lated key, its parallel minor and lowered supertonic may be used.) 
 
 4. Dominant harmony of the key. 
 
 5. The three groups derived from it. 
 6 and 7. Same in key of E. 
 
 8 and 9. Same in key of G. 
 10 and 11. Same in A minor. 
 12 and 13. Same in D minor. 
 14 and 15. Same in E minor. 
 
 Remember especially, that in using these dissonant chords no 
 transition is made, because their Tonics are the Natural Chords of the 
 Given Key. Observe also, that though there are several ways of 
 harmonizing the chromatically lowered notes, they may all be ninths. 
 
6 4 
 
 HARMONY. 
 
 It would be time well spent to write out a number of tables like the 
 preceding, taking care to get in the accidentals correctly. 
 
 Observe, that the seventh in the dominant of a major key is the 
 ninth in the dominant of its relative minor; therefore all the notes in 
 the scale that may be sevenths (Chapter XII.) may also be ninths on 
 the same conditions. 
 
 Analyze the example that follows before writing the exercises. 
 Give the name, root, and progression of every chord. 
 
 6>— 
 
 <5>- 
 
 IB 
 
 1= 
 
 :£s: Bfe-g; g-g©- 3^±§f&?fHgzg: -^-^ H 
 
 3 
 
 m 
 
 -1=2- 
 
 II 
 
 The succession of dominants may be made with diminished seventh 
 chords. Mistakes are often made in writing this succession ; but by 
 applying the simple rule that the lowered third becomes the seventh 
 in the next chord, and remembering the roots of these chords are 
 the dominants of the related group, no mistake need occur. Observe 
 that after writing six, all the dominant chords in the group, if you 
 wish to continue the passage, return to the first chord — it being enhar- 
 monically the same as A, C, E\>, Gl?, the chord that would follow 
 jB\), D\>, G, according to the rule. In other words, when the 
 lowering of the third will give a chord, the seventh of which is outside 
 of the related group, substitute the diminished seventh chord belong- 
 ing to the key of the mediant. 
 
HARMONY. 
 
 65 
 
 4- 
 
 9i 
 
 X 
 
 1 
 
 53 
 
 i II 
 
 (This is treated at length not on account of its beauty, but because so many who do use it 
 write it wrongly, overloading it with accidentals that should never appear in the key.) 
 
 Diminished seventh chords may move up as well as down (i) ; the 
 seventh when at the bass may fail to the tonic (2). 
 
 :2s: 
 
 I'- 
 
 ll 
 
 II 
 
 Note. All examples and exercises should 
 be played as well as written. This is the only 
 way to learn to remember the sound by the 
 sight, an absolute necessity to the composer. 
 
 Exercises Introducing the Ninth. 
 
 Use the ninth without the root more frequently than with it. 
 I. 
 
 II. 
 
 II 
 
 in. 
 
 =2. 
 
 IB 
 
 IV. 
 
 F— F 
 
 -0—90- 
 
66 
 
 HARMONY. 
 
 Questions on Chapter XIV. 
 
 What is the next dissonant after the seventh that may be added to the domi- 
 nant chord ? 
 Is the ninth major or minor in major keys? 
 What is it in minor keys? 
 How does the ninth resolve? 
 May the ninth be used as a bass? 
 May the ninth be close to, or below the root? 
 How many inversions may be made of the ninth chord ? 
 How must the fifth move? 
 May the fifth ever descend? 
 
 What members may be omitted in four-part harmony? 
 What progression may the ninth chord have? 
 
 How may the succession of dominant chords be made when the ninth is 
 added ? 
 
 What kind of ninth sounds best when it is not at the top? 
 In what form is this chord most frequently found ? 
 What progressions are possible without the root? 
 What is the origin of the diminished seventh chord? 
 When may the fifth descend when below the ninth? 
 
 How many letters are common to the dominant of the major and the dominant 
 
 of its relative minor? Which are they? 
 What sound have they in common? What member is it in each chord? 
 In what one way may all chromatically lowered notes be harmonized? 
 
HARMONY. 
 
 67 
 
 CHAPTER XV. 
 
 Chord of Dominant Eleventh. 
 
 The eleventh from the root is the next addition to the dominant chord. 
 The third of the chord must be omitted.* 
 
 The movement of the eleventh is either down to the third, or up 
 to the fifth. 
 
 The ninth moves with it or after it, when the eleventh descends ; 
 with it, when the eleventh ascends. 
 
 The remaining members of the chord are stationary, therefore no 
 Progression takes place. 
 
 3- 
 
 2. 
 
 
 
 
 
 5 r r ^t= t= 
 
 
 1. Eleventh and major ninth 
 descending. 
 
 2. Eleventh and minor ninth 
 descending. 
 
 3. Eleventh and major ninth 
 ascending. 
 
 The major ninth may be changed to minor before descending to 
 the root. 
 
 1 
 
 9; 
 
 -2- 
 
 S3 
 
 1. Major ninth descending 
 after the eleventh. 
 
 2. Major ninth changed to 
 minor before descending after 
 the eleventh. 
 
 3. Eleventh stationary; of- 
 ten used in terminations. 
 
 As is the case with the sev- 
 enth and ninth chords, so with 
 the eleventh ; leaps may be 
 made freely from one member 
 of the chord to another. 
 
 * Some weighty authorities say the third may be sounded with the eleventh. It is almost too 
 harsh for sensitive ears. 
 
68 
 
 HARMONY. 
 
 The eleventh chord is much more used without, than with the root. 
 The notes that remain, viz., the fifth, seventh, ninth, eleventh, may 
 have the Three Progressions of the Dominant. First Progression : 
 
 The eleventh is stationary. 
 The ninth descends. 
 
 The seventh may go to any member of the tonic chord. 
 The fifth must ascend a second or a fourth. 
 The fifth, seventh, or ninth may be at the bass, 
 i. 2. 3. 4. 5. 6. 
 
 Fifth. Seventh. Ninth. 
 
 1. Fifth at bass ascends a second; seventh at top descends. 
 
 2. Fifth at bass ascends a second ; seventh at top ascends. 
 
 3. Fifth at Dass ascends a fourth; seventh at top descends. If it 
 •ascended here, the tonic would have no third. 
 
 4. Seventh at bass ascends to fifth of tonic ; fifth at top ascends a 
 second. 
 
 5. Seventh at bass descends to third of tonic; fifth at top ascends 
 a second. 
 
 6. Seventh at bass descends to tonic ; fifth at top ascends a fourth. 
 
 7. Seventh at bass falls to root of tonic ; fifth at top ascends a second. 
 
 8. Ninth at bass. 
 
 Observe that all through C the eleventh does not move, as it is the 
 root of the tonic. 
 
 In all these examples, A, the ninth, may be ^4b, because the ninth 
 may be major or minor in major keys. 
 
 Second Progression. (To Sub- 
 mediant, chord on sixth.) The 
 eleventh and ninth are stationary ; 
 the seventh descends one degree ; 
 the fifth ascends one degree ; the 
 fifth or seventh mav be at the bass. 
 
 9± 
 
 Fifth. 
 
 Seventh. 
 
HARMONY. 
 
 69 
 
 Third Progression. (To dominant of relative minor.) Owing to 
 the number of sounds common to these two chords (Chapter XIV.), 
 this progression takes several forms ; any of the notes may be at the 
 bass. 
 
 II 
 
 1. Fifth at bass, ascends to root of dominant relative minor; elev- 
 enth, ninth, and seventh descend. 
 
 2. Fifth at bass, stationary; eleventh, ninth, seventh descend. 
 
 3. Fifth at bass; seventh and fifth stationary ; eleventh and ninth 
 descend. 
 
 4. Fifth at bass; ninth, seventh, fifth stationary; eleventh de- 
 scends ; result is that both are eleventh chords. 
 
 *This chord may have the same root as the preceding, in which case it 
 would be third to ninth. 
 
 Write this progression out with every possible arrangement of the 
 notes ; also the first and second progressions with different arrange- 
 ments of the upper notes. 
 
 The eleventh and ninth may descend while the seventh and fifth re- 
 main (as if the root were present), or the fifth may ascend to the 
 root. In this last case, if the fifth is at the bass and ascends to the 
 root of the dominant, the eleventh and ninth may ascend. 
 
 N. B. The descent of a fifth is always the same as the ascent of 
 a fourth. 
 
7 o 
 
 HARMONY. 
 
 The following example gives in one view all the dominant har 
 monies so far, and tells how they may be distinguished. 
 
 a. r. 2. 3 % 4. 5. 
 
 a. Dominant of C, with added 
 notes as far as the eleventh. 
 
 Broken into five groups of four 
 sounds each. 
 
 HI 
 
 First group, counting from lowest note, consists of major third, 
 perfect fifth, minor seventh ; is therefore Root to Seventh. 
 
 Second group (counting as before) consists of minor third, dimin- 
 ished fifth, minor seventh ; is therefore Third to Major Ninth. 
 
 Third group consists of minor third, diminished fifth, diminished 
 seventh ; is therefore Third to Minor Ninth. 
 
 Fourth group : minor third, perfect fifth, minor seventh ; is there- 
 fore Fifth to Eleventh, with major ninth. 
 
 • Fifth group is like 2 ; therefore a group consisting of minor third, 
 diminished fifth, and minor seventh, may be either Third to Major 
 Ninth, or Fifth to Eleventh, with minor ninth. To decide which it 
 is, it is only necessary to remember what the roots of the dominant 
 chords of the Related group are. Therefore Z>, F, A\>, C, if found 
 in the key of C, must be fifth to eleventh, with minor ninth, because 
 if it were third to major ninth, it is evident that Ffo would be the 
 root. 
 
 As to the other group, B, D, F, A, it may be third to ninth, 
 dominant of C, or fifth to eleventh in the dominant of the relative 
 minor of C. 
 
 Arrange the following groups in thirds, and find the roots. State 
 to what keys they belong, and write their progressions. 
 
 ?— a. 
 
 I 
 
 Questions on Chapter XV. 
 
 What member of the chord must be omitted when the eleventh is added ? 
 How does the eleventh move? 
 
HARMONY. 
 
 What member moves with it? 
 
 Does the ninth always move with the eleventh? 
 
 In what way is this chord generally used ? 
 
 What progressions may it have when the root is omitted ? 
 
 What are the movements of the notes in the first progression? 
 
 What notes may be at the bass? 
 
 Give the movements of the notes in the second progression. 
 
 What may be at the bass ? 
 
 Give movements of notes in third progression. 
 
 Which notes may be at the bass ? 
 
 May eleventh and ninth move as if root were present? 
 
 How many groups of four sounds each may be derived from the dominant 
 harmonies? 
 
 Of what intervals does the first group consist? The second ? The third ? The 
 
 fourth? The fifth? 
 Which two groups are alike ? 
 
 How may the roots of these similar groups be determined in a given key ? 
 How must a group be arranged in order that the root may be found ? 
 
7' 
 
 HARMONY. 
 
 CHAPTER XVI. 
 
 Chord of Dominant Eleventh, Continued. Additional 
 Remarks on Second Inversions. 
 
 In the following examples will be found the passages in which 
 the eleventh is most frequently found. 
 
 i. 2. 3. 4. 
 
 1 . Melody moves from first to third of major scale. 
 
 2. Melody moves from third to fifth of major scale. 
 
 3. Melody moves from first to third of minor scale. 
 
 4. Melody moves from third to fifth of minor scale. 
 
 5. Melody ascends from fifth of dominant to fifth of tonic. 
 
 6. This passage is frequent in terminations. In the last bar but 
 one the seventh ascends instead of remaining stationary. 
 
 We have found that the succession of dominants might take place 
 when ninth was added ( page 64 ) . It may also take place when 
 eleventh is added. 
 
HARMONY. 
 
 73 
 
 6. 
 
 i 
 
 1- 
 
 s-^— fit 
 
 "25^ 
 
 =t=i= 
 
 ±= 
 
 i 
 
 1. First chord, seventh ; second, yz/*^ eleve7tth. 
 
 2. First chord, third to ninth; second, fifth to eleventh. 
 
 3. First chord, third to minor ninth ( at bass ) ; second, fifth to 
 eleventh. 
 
 4. Both chords, fifth to eleventh. 
 
 5. First chord, fifth to eleventh ; second, first to seventh. 
 
 6. First chord, fifth to eleventh ; second, third to ninth. 
 Observe that in every case the ninth may be major or minor. 
 All these progressions may be reversed. 
 
 The rule as first given for the Succession ( page 58 ) may now be 
 expressed as follows, since the succession may take place when the 
 third is absent. 
 
 The harmonies of two or more roots descending by fifths may be 
 written in succession. 
 
 _g . Harmonies from all the 
 
 t> s> g — k g— 1 1 dominants of the related 
 Roots. B. E. A. D. G. C. group in succession. 
 
 -M-- 
 
 Additional Remarks on Second Inversions. 
 
 The second inversion of a chord may be followed by any chord 
 with the same bass as that of the second inversion, or with a bass one 
 degree above or below that of the second inversion. The second in- 
 version of the tonic may be followed by the first inversion of the tonic. 
 
 i 
 
 Eg: 
 
 (2- 
 
74 
 
 HARMONY. 
 
 5- 
 
 1. Second inversion of tonic, followed with various chords. 
 
 2. Second inversion of subdominant, followed by dominant. 
 
 3. Second inversion of dominant. 
 
 4. The chord of ^4 minor, second inversion, enters as a tonic; 
 but as it bears the relation of mediant to the key of F, advantage is 
 taken of the fact that a second inversion may be followed by any 
 chord with the same bass, and the dominant of F follows it. 
 
 5. Second inversion of tonic, changed to a dominant by the addi- 
 tion of the seventh to which the fifth skips. 
 
 Exercises for the Eleventh Chord. 
 
 In the first two the places are marked where an eleventh chord 
 may be used. 
 
 '^J 
 
 mm 
 
 11. 
 
HARMONY. 
 
 75 
 
 III. 
 
 IV. 
 
 II 
 
 V. 
 
 at* 
 
 i 
 
 VI. 
 
 FEE 
 
 I 
 
7 6 
 
 HARMONY. 
 
 CHAPTER XVII. 
 
 The Progressions of the dominant so far given, are the most natu- 
 ral and most usual ; but successions may be made of which no satis- 
 factory explanation can be given, in accordance with the following 
 rule : 
 
 Any two of the Dominant Harmonies of the Related Group may 
 be written in succession (with a few exceptions) , provided they have at 
 least one sound in common. 
 
 The dissonant notes are not always resolved in these successions, 
 nor are these successions agreeable, except in certain arrangements 
 of the chords. 
 
 The first thing to be done, is to find in which dominant harmonies 
 each note in the scale may be found as root, third, fifth, seventh, 
 ninth, or eleventh. 
 
 Connecting Note C. 
 
 Root. 
 
 Seventh. 
 
 Ninth. 
 
 Eleventh. 
 
 C is root in dominant of F\ seventh in dominant of G ; ninth in 
 dominant of E minor; eleventh in dominant of C. 
 
 Connecting Note D. 
 
 Root. Fifth. Seventh. Ninth. Eleventh. 
 
 D is root in dominant of G ; fifth in dominant of C; seventh in 
 dominant of A minor ; ninth in dominant of F\ eleventh in dominant 
 of D minor. 
 
HARMONY. 7 
 Connecting Note E. 
 
 Root. Third. Fifth. Ninth. Eleventh. 
 
 E is root in dominant of A minor ; third in dominant of F\ fifth 
 in dominant of D minor ; ninth in dominant of G ; eleventh in domi- 
 nant of E minor. 
 
 Connecting Note F. 
 
 Seventh. Ninth. Eleventh. 
 
 
 
 - 1 #~1 J 
 
 
 U * i i i II 
 
 
 F is seventh in dominant of C\ ninth in dominant of A minor; 
 eleventh in dominant of F. 
 
 Connecting Note G. 
 
 Root. Fifth. Seventh. Eleventh. 
 
 G is root in dominant of C; fifth in dominant of F\ seventh in 
 dominant of D minor; eleventh in dominant of G. 
 
 Connecting Note A. 
 
 Fifth. Seventh. 
 
 mm 
 
 Ninth. Eleventh. 
 X 
 
 A is root in dominant of D minor; fifth in dominant of G ; seventh 
 in dominant of E minor; ninth in dominant of C; eleventh in dom- 
 inant of A minor. 
 
 Root. 
 
 m 
 
 Connecting Note B. 
 
 Third. Fifth. F \s root in dominant of E 
 
 minor ; third in dominant of 
 C; fifth in dominant of A 
 minor. 
 
 m 
 
78 
 
 HARMONY. 
 
 The chords marked x cannot be written in succession, although they 
 have a connecting sound. 
 
 We give some examples below of these successions, in the arrange- 
 ments which are most effective. The pupil should try other arrange- 
 ments and should write them in various keys. No other exercise can 
 equal this in giving the student a sure grasp of the possibilities of 
 chord successions without transition. 
 
 The successions that come under rules already given are omitted ; 
 viz., the third progression (page 57), and the succession by lower- 
 ing the third (page 58.) 
 
 Connecting Note C. 
 
 N.B. 
 
 N.B. 
 
 1. From C, E, G, .Z>b, to chords derived from D. This will 
 serve as a model for all successions in which the connecting note is 
 the root of the first group, and seventh in the second group. 
 
 2. Connecting note root and eleventh. 
 
 3. Connecting note, root and ninth. 
 
 4. Connecting note eleventh and seventh. This sounds well in any 
 arrangement. 
 
 Connecting Note D. 
 
 As root and fifth, any arrangement, succession of dominants. As 
 root and seventh, see Model (i. e., C, E, G, B\>, to derivatives 
 of D). 
 
 9- 
 
 — 11 
 
 1. Root and ninth; the second group may 
 be either third to ninth, ox fifth to eleventh. 
 If considered as third to ninth, the root is 
 dominant of E; if as fifth to eleventh, root 
 is dominant of the relative minor of E. 
 
HARMONY. 
 
 79 
 
 Connecting Note E. 
 
 3Z- 
 
 : 5 f-%l_ : 
 
 JS2 
 
 9i— -F 
 
 :t=: 
 
 1 . As root and third. 
 
 2. As root and ninth or eleventh (root of second chord, D or B). 
 As root and fifth, succession of dominants. 
 
 Connecting Note F. 
 As seventh and ninth, third progression. As seventh and eleventh. 
 
 Connecting Note G. 
 
 As root and fifth, succession of dominants. As root and seventh. 
 ( See Model.) 
 
 „ i. N.B. 2. 
 
 i — 
 
 8 rg — 
 
 ff — p§ — | 
 
 I 
 
 9^ 
 
 -|2 12- 
 
 1 
 
 1. Gives an. example of the reversal of the rule for the succession 
 of dominants; i. e., raised seventh becoming third when the root of 
 the first chord is present. First measure gives the arrangement that 
 sounds best. 
 
 2. As root and eleventh. 
 
 II 
 
 II 
 
 Connecting Note A. 
 
 As root and fifth, succession of dominants. 
 As root and seventh. ( See Model.) 
 
 Root. Ninth or 
 eleventh. 
 
80 HARMONY. 
 
 Connecting Note B. 
 
 As root and fifth, succession of dominants, 
 i. 
 
 i 
 
 iP=^=jLr p h t^=y 
 
 i 
 
 i. As root and third. 
 
 These examples, with two exceptions, only give the movements 
 from the first -chord to the others containing the same connecting 
 note ; but the movement may take place from any chord of the group 
 to any other, with scarcely an exception. All the successions given 
 may be reversed. 
 
 The two chords marked N. B. in the first example are identical in 
 sound, because the diminished seventh derived from the dominant 
 of a major key, and that derived from the dominant of its relative 
 minor, are enharmonically the same, thus : 
 
 B, D, F, ufi^G% B, D, F 
 Dominant of C, dominant of A minor. 
 
 B, G, B\>, J3vTc% B, G, B\>. 
 Dominant of F, dominant of D minor. 
 
 F% A, C, B^B^ Fl A, C, 
 Dominant of G, dominant of B minor. 
 
 The minor ninth in the dominant of the major is enharmonically the 
 third in the dominant of its relative minor. 
 
 Observe in all these successions that the connecting' note must re- 
 main in the same part. 
 
 The following successions in which there is no connecting note 
 may be made. 
 
HARMONY. 
 
 Si 
 
 i and 2. The second chord resolved as a dominant; in 2 the 
 seventh falls to the root of the tonic. 
 
 3 and 4. Diminished seventh chord resolves as a supertonic har- 
 mony (Chapter XVIII.). It may resolve as a dominant, but the first 
 is more agreeable. 
 
 Exercises for Eleventh Chord, and the Unusual Progressions 
 Treated in the Previous Chapters. 
 
 Eleventh may be used at x. Look for opportunites for some of the 
 successions given in last chapter. Where two notes in succession 
 are marked x x there is an opportunity. 
 
 I. 
 
82 
 
 HARMONY. 
 
 IV. 
 
 in 
 
 XXX 
 
 ^ 7rS~ 
 
 
 
 =t==t 
 
 X 
 
 
 F — 
 
 -U i'. 
 
 
 
 
 3 
 
 Seventh. Root. 
 
 VI. 
 
 See 
 
 m 
 
HARMONY. 
 
 83 
 
 CHAPTER XVIII. 
 Chord of Thirteenth. 
 
 In the majority of cases the thirteenth may, for practical purposes, 
 be treated as a changing note, or as a retardation. Still there are 
 some cases in which its movement is such that it must be looked upon 
 as an essential dissonance. 
 
 The thirteenth, like the ninth, may be major or minor. The fifth 
 is generally omitted when the thirteenth is added, especially in those 
 cases in which the thirteenth descends to the twelfth (i. e., the fifth 
 of the chord). 
 
 Thirteenth. 
 
 <2- 
 
 H 
 
 Dominant of C, with all the available 
 overtones to the thirteenth. 
 
 ■>■ 11 
 
 In the examples that follow the cases are given in which the 
 thirteenth may be looked upon simply as a changing note. 
 
 1. 2. 3. 4. 5. 
 
 r 
 
 = P== ^ E^=^ =F=^ = ±=^4 1 
 
 1. Root, third, seventh; is the thirteenth, or a changing note. 
 
 2. Root, seventh, and ninth. 3. Third, seventh, and ninth. 
 4. Seventh, ninth, and eleventh. A may be flat or natural, at will. 
 If all the E's are made flat, the examples would be in C minor. In 
 this case Ab would be necessary also. 
 
 5. D\ is a convenient mis-writing for E\>, the minor thirteenth. 
 
 ( See remarks on augmented fifths.) 
 
8 4 
 
 HARMONY. 
 
 [n the following examples it is not possible to look upon it as a 
 changing note or retardation. 
 
 6. 
 
 5- 
 
 IS. 
 
 —i- 
 
 - g>— 
 
 rT 
 
 5>t 
 
 11 
 
 7. 8. 9. 10. 11. 12. 
 
 — ^ r 1- -4 -r—p * e • I <i ^ I * » f • II 
 
 i. The thirteenth, falls to the root of the tonic. 2. Same, 
 second progression. 
 
 3. Third progression, thirteenth falls to seventh of dominant of 
 relative minor. 
 
 4. This looks like a second inversion of E minor. It is the only 
 case in which a group of notes that form a common chord must be 
 considered as a dominant group. From the manner of its entry it 
 cannot be a second inversion of subdominant or dominant; and the 
 strong upward tendency of the B proves that it is not a tonic, but a 
 piece of dominant harmony. 
 
 5. Thirteenth stationary, seventh and ninth ascending to eighth 
 and third. 
 
 6. Major ninth, eleventh, major thirteenth, resolving within the 
 chord. 
 
 7. Major ninth, eleventh, minor thirteenth, resolving on tonic. 
 Minor thirteenth ascends chromatically. ( In this case the £0 is generally 
 
 written D$, making an augmented sixth chord.) 
 
 8. Same group with minor ninth and thirteenth resolved on tonic. 
 
HARMONY. 
 
 85 
 
 In this case the E\> must be used, as the combination of A\> and D\ 
 would be a monstrosity. 
 
 9. A succession of dominants, the first with minor thirteenth. 
 
 10. Same group as 8, resolving within the chord. 
 
 11. Dominant with minor thirteenth, followed by augmented sixth. 
 
 12. First chord, dominant, root, third, seventh, ninth; second 
 chord, dominant, root and ninth having changed places; viz., bass, 
 ninth; tenor, eleventh; alto, thirteenth; soprano, root. This passage 
 is the only one in which the root may be struck over the ninth with 
 good effect, owing possibly to the fact that the whole bar consists of 
 dominant harmony, and also to the diatonic contrary motion. 
 
 In analyzing harmony a good rule to follow is, take the most obvious 
 explanation, especially when the combinations may be ''parsed" as 
 common chords, instead of hunting for hidden "roots." For exam- 
 ple, the following passage from Tannhauser is thus explained by one 
 author. The note marked x is enharmonically B\>, consequently is 
 the ninth, C$ the third, and F\ the thirteenth in the dominant of D. 
 But if it is looked on simply as the second inversion of JF$ major, 
 changed to F\ minor, and followed by the chord on the sixth ( D 
 major), a much simpler explanation maybe given; viz., B minor, 
 the preceding chord, is the minor subdominant of F$, which enters 
 as a tonic; second inversion is changed to minor, and followed by 
 the chord on the sixth. 
 
 The beauty of the passage is owing largely to the uncertainty of 
 key and the kaleidoscopic rapidity with which the changes of key 
 take' place. 
 
 The following passage, also by Wagner, the same author, calls 
 an unusual form of augmented sixth, calling the Lfo a miswriting 
 for Cj}, in spite of the fact that the C is natural when the harmony 
 changes. 
 
S6 
 
 HARMONY. 
 
 It is much easier to say it is the diminished seventh chord, dom- 
 inant harmony of Bfo. The Lfo is a changing note which leaps to 
 another member of the chord, then runs to its resolution, C. The 
 chord A\, C, E\>, Gb, is enharmonically A, C, E^, a derivative 
 of the chord that follows. It follows that in both instances Wagner 
 wrote his chords properly. 
 
 x 
 
 WjP * * 
 
 i— -— /- 
 
 * - 
 
 J ii 
 
 -•- 
 
 * f — *— 
 
 
 > i 
 
 
 
 
 Chord of eleventh, dominant of Bb. Eleventh resolved. 
 
 The best way to become familiar with this chord is to transpose 
 the examples into all the keys. 
 
HARMONY. 
 
 *7 
 
 CHAPTER XIX. 
 
 Supertonic Harmony. 
 
 There is another progression of dissonant groups, that differs so 
 widely from any that they have as Dominant harmonies, that to dis- 
 tinguish them they are called Supertonic Harmonies, from the fact 
 that their progression is to the Tonic chords of the keys in which their 
 Roots are the Supertonics. 
 
 The major ninth is stationary. The minor ninth ascends chromat- 
 ically in Major keys, is stationary in minor keys. ( The major ninth cannot 
 
 be used in minor keys. ) 
 
 The seventh is stationary. 
 
 The fifth and third go to the fifth of the Tonic. 
 The root when at the bass goes to the fifth of the Tonic ; when not at 
 the Bass, to the third of the Tonic generally, but it may go to the fifth. 
 
 1. Supertonic harmony 
 of C, with major ninth 
 stationary. 
 
 2. Supertonic harmony 
 of C, with minor ninth 
 ascending chromatically. 
 
 3. Supertonic harmony of A minor, with minor ninth stationary. 
 As the root, third, and fifth all go to the fifth of the tonic, it will at 
 once be seen that the second inversion of the tonic generally follows. 
 
 1. 2. 3, 4. 5. 6. 7. . 8. 
 
 9 
 
 1 . First inversion, with root present. 
 
 2. First inverson, root omitted, major ninth. 
 
88 
 
 HARMONY., 
 
 3. First inversion, root omitted, minor ninth. 
 
 4. Second inversion, root present. 
 
 5. Second inversion, root omitted, major ninth. 
 
 6. Second inversion, root omitted, minor ninth. 
 
 7. When the root is at bass it is generally repeated, and the fifth 
 is omitted. 
 
 8. When the third is at bass and the ninth is minor, the third may 
 fall to the root of the tonic. 
 
 1=1 
 
 1. When the seventh is at the bass, it is generally repeated when 
 the ninth is at top. 
 
 2. Minor ninth, fifth at top. 
 
 3 and 4 give the usual way of writing these two chords; viz., 
 
 th D% instead of E\>. 
 
 5. Has the minor ninth at bass. 
 
 The supertonic harmony may be preceded by the eleventh 
 chord. 
 
 J-J- 
 
 1 
 
 ill 
 
 Also by the first inversion of the chord on lowered supertonic. 
 This is the only case in music in which it is possible to write in suc- 
 cession chords arising from two forms of the same root; viz., Z?b, 
 F, A\>, and D% F%, A\. 
 
HARMONY, 89 
 
 0 1 1 
 
 1 
 
 —&— 
 
 — 1 
 
 — 
 
 _[ 
 
 11= 
 
 1 
 
 :^|— 
 
 -tr-Si & 
 
 -I 
 — 1 
 
 
 
 
 
 — 
 
 — 
 
 
 
 
 
 
 
 
 + - 
 
 
 
 
 = 
 
 The eleventh of the supertonic harmony may be used. It sounds 
 best with the minor ninth. 
 
 1 and 2. Fifth at the bass. 
 
 3. Minor ninth at the bass. 
 
 4. Seventh at the bass. 
 
 Questions on Chapter XIX. 
 
 What distinguishes the supertonic harmony from the dominant? 
 
 How does the major ninth proceed? The minor ninth in major keys? The 
 
 minor ninth in minor keys ? The fifth? The third? The root, when at 
 
 bass? The root, when not at bass? 
 In what form does the tonic generally follow it? 
 Which members of this chord are used when the root is at the bass? 
 Does the third always ascend ? When may it not? 
 Give the rule for use of seventh as a bass. 
 What miswriting is often used in this case? 
 May the eleventh of supertonic be used? 
 
 Exercises on Supertonic Harmony. 
 
 When the second inversion of tonic follows the supertonic har- 
 mony, be careful to follow it according to rule. 
 I. x 
 
 az2= 
 
 EEE 
 
90 
 
 HARMONY. 
 
 II. 
 
 
 
 X X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 nn 
 
 in. 
 
 22: 
 
 tat 
 
 5^ 
 
HARMONY. 91 
 
 CHAPTER XX. 
 
 Altered Chords, Augmented Sixth, Augmented Fifth, 
 Passing Seventh. 
 
 There are a few chords that are produced by altering one of the 
 members of a given chord, chromatically. 
 
 Strictly considered, this altered note is nothing but a passing note 
 between the member of the chord and the note to which this mem- 
 ber moves. 
 
 The most important of these chords by alteration is called the Aug- 
 mented Sixth Chord. 
 
 This Chord results from the chromatic lowering of the fifth of a 
 dominant or supertonic harmony, root to seventh or third to minor 
 ninth. 
 
 The progression of the chord is unchanged. It maybe inverted in 
 any Way, but the chromatically lowered fifth is generally used as a 
 bass. 
 
 The chord gets its name from the fact that the interval between 
 the lowered fifth and the third of the chord is an Augmented Sixth ; 
 thus, D, Ah, F% 
 
 Root, Fifth, Third. 
 
 1. Progressing like a dominant, root present. 
 
 2. Progressing like a supertonic harmony, root present. 
 
 3 and 4. Same as 1 and 2, but the root is omitted and minor 
 ninth added. 
 
 5 and 6. Progressing like a dominant to a minor tonic. This pro- 
 
9 2 
 
 HARMONY, 
 
 gression of the augmented sixth is unusual. When it progresses like 
 a dominant, the chord to which it moves is (generally) also a 
 dominant. 
 
 The parallel fifths that occur in 3 and 6 are not at all unpleasant. 
 They may be found in the best writers. 
 
 The following inversions of the augmented sixth are used. 
 
 — tr-=-t- 
 
 9&- 
 
 m 
 
 1 . The upper notes may be arranged in any way ; the seventh of 
 the original chord is at the bass. 
 
 2. Minor ninth at the bass. 
 
 3. Third at bass. 2 and 3 sound best when arranged as here 
 given. 
 
 : , r ~; . || 
 
 , The rule for the succession 
 of dominant chords by lower- 
 
 ing the third chromatically 
 applies to this chord. 
 
 II 
 
 1. Root present. 2. With minor ninth. The Eft is suspended to 
 avoid the parallel fifths between the outer parts. 
 
 The minor ninth may be resolved and the lowered fifth restored 
 at the same time. 
 
 =t=: 
 
 3- 
 
 =t=A 
 
 4= 
 
 1. The ninth at top, lowered fifth at bass. 
 
HARMONY. 
 
 93 
 
 2. The ninth at bass, lowered fifth at top. This progression is of 
 singular beauty. It is often incorrectly written ; viz., the A\> written 
 GjJ, or the F$ written GP. 
 
 3. The same, but with the third lowered, making a succession to 
 fifth, seventh, ninth, eleventh, dominant of C. Then the ninth 
 {A\>) of this chord is resolved, and the fifth at the same time 
 lowered. 
 
 Rewrite the exercises on supertonic harmony, substituting an 
 augmented sixth whenever the supertonic harmony was used (ex- 
 cept with the notes marked x). 
 
 Questions on Chapter XX. 
 
 How is the chord of augmented sixth formed? 
 What progressions has it? 
 
 Which member of the chord is generally used as a bass? 
 
 Between which two members of the chord does the interval of the augmented 
 
 sixth lie that gives the chord its name? 
 Is the succession by lowering the third possible with this chord? 
 
 Chord of Augmented Fifth. 
 
 This chord may be produced in two ways : — 
 
 First, by chromatically raising the fifth of a Major chord. 
 
 Second, by chromatically lowering the root of a Minor chord. 
 
 The raised fifth must ascend ; any chord may follow that includes 
 the note to which the raised fifth ascends. 
 
 The fifth of the Dominant chord in Major keys may be raised when 
 the seventh is added; in general the raised fifth is put above the 
 seventh. 
 
94 
 
 HARMONY. 
 
 =5" 
 
 i 
 i 
 
 1 . C with augmented fifth, root at bass. 
 
 2. C with augmented fifth, third at bass. 
 
 3. C with augmented fifth, fifth at bass. 
 
 4. Dominant seventh, with augmented fifth. 
 
 5. Succession, first and third chords, with augmented fifth. 
 
 6. Dominant of C, augmented fifth, third progression. 
 
 The augmented fifth chord, produced by lowering the root of a 
 minor chord, is always followed by either the second inversion of the 
 tonic (Example 1 ), or by the dominant (Example 2 ) of its relative 
 major. 
 
 It is never inverted, being quite ineffective except with the root at 
 the bass. 
 
 1. 2. 
 
 
 
 
 
 
 
 — ^ — 
 
 
 
 ~3 — H 
 
 — ^ ^ 
 
 - * 
 
 
 
 
 
 f ¥ 
 
 
 »~r - - r 
 
 
 
 
 What is known as the chord of Passing Seventh may be conve- 
 niently included in this group of chords with passing tones. 
 
 The passing seventh may be added to any chord ; it may be either 
 Major or Minor ; it always descends. 
 
 11 J 
 
 1=4= 
 
 I— I— 1 
 
 I 
 
 1. Tonic, with passing seventh. 
 
 2. Subdominant, with passing seventh. 
 
HARMONY. 
 
 95 
 
 3. Mediant, with passing seventh. 
 
 4. Submediant, with passing seventh. In this case the seventh is 
 at the bass, as the chord may be inverted just as a dominant seventh 
 is. In fact, it will be seen that it progresses exactly like a dominant 
 seventh ; thus, first, third, fourth, fifth resemble dominant, followed 
 by tonic; 2 is like a dominant with second progression. 
 
 5. Tonic with passing seventh, with fifth at bass. 
 
 When the passing seventh is Major, which is only so with the 
 Tonic and Subdominant chords, the augmented fifth is often used 
 with it. 
 
 I. x 
 
 
 2- x 
 
 
 
 
 
 
 
 -X \l A. 
 
 — • 
 
 X 
 
 
 m *- ? • 
 
 
 
 
 The use of the Aug 
 
 •rnented fifth fu 
 
 rnishes a 
 
 new way of treating 
 
 raised notes. The only one that may not be so treated, without 
 going outside the Related Group, is the raised fourth. It enables 
 us to raise the sixth of the scale, thus : 
 
 First. 
 
 Second. 
 
 Fifth. 
 
 Sixth. 
 
 -1 
 
 r4- 
 
 -f- 
 
 J — X 
 
 =1 
 
 (5- — 
 
 -3- 
 
 fc=i 
 
 I 
 
 Questions on Chapter XX. (Continued.) 
 
 How may the chord of the augmented fifth be produced? 
 
 How does the raised fifth move? 
 
 What chords may follow the augmented fifth? 
 
 May the fifth be augmented in the dominant seventh chord? In both major 
 
 and minor keys ? 
 How is this chord generally arranged ? 
 
 By what chords may the augmented fifth chord, produced by lowering the 
 root of a minor chord, be followed ? 
 
HARMONY. 
 
 May this augmented fifth chord be inverted ? May the former one? 
 To what chords may the passing seventh be added ? 
 How does it move ? 
 Is it major or minor ? 
 
 May a chord with passing seventh be inverted? 
 What chord does it resemble in its progressions? 
 In which chords is the passing seventh major? 
 What may be used with it in these cases? 
 
 Which raised notes in the scale may be treated as augmented fifths ? 
 What new raised note may be introduced as an augmented fifth? 
 
 Exercises for Augmented Fifth and Passing Seventh. 
 
 
 
 
 s — 
 
 
 — 
 
 
 
 £2 
 
 
 
 
 
 
 
 
 
 u 
 
 
 
 
 
 
 
 
 23: 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 ^ 1 
 
 
 
 -HI 
 
 III. 
 
 2=t 
 
 Z2I 
 
 IV. 
 
HARMONY. 
 
 97 
 
 CHAPTER XXI. 
 
 Suspensions. 
 
 ( Note. Suspension and Retardation are treated in a new way in this work, the intention 
 being to bring out clearly the difference between them.) 
 
 The seventh and ninth, Major or Minor, may be added to any com- 
 mon chord by Suspension; i. e., by tying the note that becomes the 
 seventh or ninth from a preceding chord in which it is a consonant 
 member ( root, third, or fifth ) . 
 
 The Suspended seventh and ninth resolve by descending one degree. 
 The remaining notes follow the rules given for the progression of 
 the dominant seventh and ninth {<q. v.). 
 
 The rule may be put thus : the root of the chord in which the sus- 
 pended seventh is resolved is always the fourth above, second above, 
 or third below that of the chord in which the suspension occurs. 
 
 1. Chord of with suspended seventh ( D ) ; root ascends a 
 fourth ( like first progression of dominant seventh) . 
 
 2. Same; root ascends a second (like second progression of 
 dominant seventh ) . 
 
 3. Root (C) is third below (like third progression of dominant 
 seventh) . 
 
 Diatonic sequences may be made, in which every chord has a 
 suspended seventh. 
 
Any Diatonic Sequence may be turned into an harmonic sequence- 
 The above may be changed to the succession of dominant sevenths 
 ( by lowered thirds) . 
 
 II 
 
 
 i •— 
 
 
 
 
 
 
 n i- 
 
 - f 
 
 
 ■ i 
 
 The suspended seventh may be inverted like the dominant seventh. 
 
 The suspension belongs more to the old diatonic or contrapuntal 
 system than to the harmonic. 
 
HARMONY. 
 
 99 
 
 CHAPTER XXII. 
 
 Retardation. 
 
 When a note is prolonged from a chord in which it is a member, into 
 one in which it is not a member, thus becoming dissonant, it is called a 
 Retardation of the member of the second chord upon which it resolves. 
 
 The Retardation differs from the Suspension in the following 
 respects : 
 
 First, there is no change in the harmony when it resolves. 
 
 Second, the Suspended seventh and ninth are always found in con- 
 junction with a common chord, while the retardation may take place 
 in any group. 
 
 Third, the Suspension is always prepared by a consonant member 
 of some chord, viz., root, third, or fifth, while a Retardation may be 
 made by prolonging any member of a chord, consonant or dissonant. 
 
 Fourth, Suspensions always resolve by Descending, while Retar- 
 dations may either Ascend or Descend. 
 
 The member of the first chord is the Preparation ; the tied note 
 (or repeated note) is the Retardation. 
 
 The member of the second chord (that follows the tied note) is the Reso- 
 lution or Retarded note. 
 
 When a Retardation resolves by descendifig, its descent may be a 
 whole or half-tone. When it resolves by ascending it must be a half- 
 tone when the note to which it ascends is the root or fifth of the 
 chord; if it ascends to the third it 'may be a whole or half-tone. 
 
 The note upon which a Retardation resolves may be repeated in 
 a lower part, but not in a part above the Retardation. (Frequent excep- 
 tions to this last rule may be found, but they rarely, if ever, sound well.) 
 
IOO 
 
 HARMONY. 
 
 12. 
 
 (tt ia (2 ^ % -(22 - — ~ * 
 
 J -J- 
 
 2± 
 
 mm 
 
 3: 
 
 -(22- 
 
 -f=<- 
 
 I, 2, 3. Retardation of the root from above; the second chord has 
 root, then third, then fifth at the bass. 
 
 4, 5, 6. Retardation of root from below, etc. 
 7, 8, 9. Retardation of third from above. 
 
 10, II, 12, 
 
 13' H» I 5- 
 
 Retardation of third from below. 
 Retardation of fifth from above. 
 
 16. Retardation of fifth from below. 
 
 This Retardation may take place only in this progression ; viz., from supertonic harmony or 
 augmented sixth to tonic. 
 
 17. Seventh retarded from below. 
 
 18. Retardation of seventh from above. In this the root ( G) is 
 above the ninth {A). This is possible only when it is used as a 
 retardation of the seventh. 
 
 Two or three members of a chord may be retarded at the same 
 time. 
 
 1. 2. 3. 4. , 5. 6. 
 
 r r i 1 - — ' itt " 
 
 pE3 
 
 f 
 
 m 
 
HARMONY. 
 
 101 
 
 ^ "f ^^ S"""""-*' g Tl R°°t anQl third, retardation from 
 
 — F-^S-f H above. 
 
 2. Root below, third above. 
 
 3. Root and third from below 
 zj — U 4. Root and third from above. 
 
 5. Root, third, and fifth from above. 
 
 6. Root from below, third and fifth from above. 
 
 7. Root from above and below, third and fifth from above. 
 
 The next example gives the retardation in the bass, first of the third 
 from above. This is the best, because it is not necessary to have the 
 retarded note repeated in an upper voice, as is the case with 2 and 3. 
 
 § 
 
 9±= 
 
 
 
 - -i 
 
 A 
 
 1 
 
 -A— —A- J 
 
 
 
 l r 
 
 —6* 
 
 
 
 — # — 
 
 4 
 
 — & 
 
 . — * — 
 
 2 and 3 belong more properly to that kind of syncopation in which 
 one or more parts drag behind the rest, as follows : 
 
 t 
 
 e— g 
 
 — r r-r * ' 
 
 — s i- 
 
 The bass may move to 
 another member of the chord 
 at the same time the retarda- 
 tion resolves, or before it. 
 
 i 
 
 4SL 
 
 T T I 
 
 1 
 
 1 
 
102 
 
 HARMONY. 
 
 In the examples which follow will be found a series of sevenths 
 treated in three ways, which will serve to make the difference be- 
 tween Suspension and Retardation clear. 
 
 1 is a sequence which may be considered as a series of first inver- 
 sions with Retardation of the roots. 
 
 2 is a sequence of real Suspended Sevenths. 
 
 3 is so harmonized that the seventh over the bass is in turn the 
 Retardation of every member of a chord from root to ninth. 
 
 In 3, at a, the root ( G ) becomes a retardation of the seventh ( J?), 
 because the ninth ( Ah ) is below it. This is the only way in which 
 the ninth may be sounded below the root. b. The third is retarded. 
 At c the fifth ; at d the root ; at e the third ; and at f the ninth 
 ( A ) is retarded by the prolongation of B ( the third ) over C 
 
HARMONY. 103 
 
 (the eleventh). This is the only way in which the third and 
 eleventh may be sounded together ( with the third above ) . 
 
 Questions on Chapter XXII. 
 What is a retardation? 
 
 In what respect does it differ from a suspension ? 
 What accompanies a suspension ? What a retardation ? 
 How is a suspension prepared ? How a retardation ? 
 How does a suspension resolve ? How a retardation ? 
 When a retardation descends, what may the interval be? 
 When it ascends? 
 
 When may the note of resolution be repeated ? 
 May double retardations occur? Triple? 
 What retardations are possible at the bass? 
 What movement may the bass make ? 
 
104 
 
 HARMONY. 
 
 IV. 
 
 ^=1 
 
 :t: 
 
 
 
 
 1 hi — j — j — f—ff — «— * 
 
 II 
 
 V. 
 
 -| 1- 
 
 "i — r^f 
 
 Rewrite the following succession of chords with as many retarda- 
 tions as possible. 
 
 Proceed as follows : 
 
 Suspensions and Retardations do not always move directly to their 
 Resolution, but postpone it by the introduction of certain other notes. 
 This is called Ornamentation of the Dissonances. A Suspended 
 seventh or ninth may ascend one degree, then fall a third to the reso- 
 
HARMONY. 
 
 lution (Example i) ; or may fall a third, then ascend one degree to 
 the resolution (Example 2). 
 
 In both cases the descent of a third may be filled by adding the 
 intermediary note (Examples 3 and 4). 
 
 7799 
 
 
 __i — , — 1 — . 1 — -J^^-^^—m 
 
 
 
 
 
 g 
 
 -(2 h— 
 
 zj 
 
 _ 
 
 
 C f J- ' 
 
 T F 
 
 
 
 
 
 
 4— 
 
 
 
 
 
 
 
 The same ornamentation may be g'iven to a descending Retarda- 
 tion ( Example 1 ) . 
 
 An ascending Retardation may leap to the note above, then fall to 
 its resolution (Example 2) ; or the ascent of a third may be filled as 
 in the preceding cases. Lastly, an ascending or descending retarda- 
 tion may leap to any member of the chord in which it occurs, before 
 going to its resolution (Example 3) ; and the interval from the 
 retardation to this note, or from this note to the resolution, may be 
 changed to a run (Example 4.) 
 
io6 
 
 HARMONY. 
 
 =3==t*=l=z 
 
 — I — 1-— I — I- 
 
 -t— 
 
 -I J r.^u.jjJU-. 
 
 
 
 
 
 
 
 
 
 
 
 =\— 
 
 
 
 
 i 
 
 
 — <Sf 
 
 
 o — 
 
 
 
 
 
 
 1 
 
 The ornamentation may be varied in many ways, but the underly- 
 ing principle is always the same; viz., a movement from one side to 
 the other of the Resolution note, upon which the dissonance finally 
 comes to rest, varied by a leap or run to some other member of the 
 chord. 
 
 J — , — J — U^-l — i — i — i — 1 — u=2:-i — t — , — i — ■ 
 
 
 — — 
 
 
 
 
 
 
 
 
 -ITS lAHTli J-;£3-£ 4- 
 
 9* z? p 9 
 
 ' " 
 
 1 . Retardation falls to another note of the chord, then leaps back 
 to the dissonance. 
 
 2. Same, but runs up to note below resolution, then leaps to note 
 above it. 
 
 3. Descends to note below resoluLion. 
 
 4. Runs to note above resolution. 
 
 5. There are two chords in this bar : first. A, C, is implied ; .the 
 
HARMONY. 
 
 107 
 
 E is at first a retardation of F, then of D in chord D, JR. A. From 
 this it may be seen that the passing' seventh (Chapter XIX.), al- 
 though itself a dissonance, may be used to prepare another disso- 
 nance. 
 
 6. Leap to another member of chord, then to note below and note 
 above resolution. 
 
 7. Leap to note below, then to another member of chord, from 
 which it runs down to the resolution. 
 
 Double Retardations may be ornamented, provided they move to- 
 gether in thirds or sixths, or provided the same variety of ornamen- 
 tation is applied to both. 
 
 I 
 
 ?5 
 
 11 
 
 Questions on Chapter XXII. (Continued.) 
 
 Do suspensions and retardations always move directly to their resolution? 
 What is this introduction of other notes called ? 
 
 Describe the various kinds of ornamentation that both suspensions and retar- 
 dations may have. 
 May the passing seventh be used to prepare a retardation? 
 May double retardations be ornamented? 
 
 Exercises on Ornamented Suspensions and Retardations. 
 
 
 — — - 
 
 
 
 
 
 
 
 
 -J-J-J-P- 
 
 m 
 
 
 
 
 
 • 
 
 
 
 
 
 M — 
 
 "-II 
 
io8 
 II. 
 
 HARMONY. 
 
 in. 
 
 era 
 
 IS 
 
 The augmented fifth may be used as a preparation of a retar- 
 dation. 
 
 IV. 
 
 
 
 =1 
 
 
 
 
 
 
 
 
 s^' ■ -1 ■ L f - 1 ■ 
 
 t3= 
 
 
 +^4 
 
HARMONY. 
 
 109 
 
 CHAPTER XXIII. 
 
 Changing Notes or Appoggiaturas. 
 
 These differ from Retardations only in being Struck instead of 
 being Prolonged from a preceding chord. They fall on the accentea 
 beats, or if there are two notes or more to the beat, on the first of 
 each beat. 
 
 They may fall on an unaccented beat if the accompanying har- 
 mony is syncopated. 
 
 When below the member of the chord upon which they resolve, 
 they must be a half-tone below it, except when they occur as part of 
 an ascending diatonic scale. 
 
 All accidentally raised notes that fall on the accented beats, or on 
 the first note of a beat, may be treated as Changing Notes, when they 
 ascend one degree. 
 
 They may be doubled in thirds and sixths like Retardations. 
 
 1. On accented beats. 
 
 2. On first note of beat. 
 
r 10 
 
 HARMONY. 
 
 3. On second beat (unaccented), the harmony syncopated. 
 
 4. The D, a whole-tone below E. Like the retardation, the 
 changing note may be a whole-tone below the third of a chord. 
 
 5. Raised notes on first of beat. 
 
 6. Doubled in thirds and sixths. 
 
 7. Same, with raised notes. 
 
 A Dominant harmony may be struck over the root or third of the 
 tonic, making Double, Triple, or Quadruple Changing Notes. The 
 dominant harmony moves according to the rule (1) and (2). 
 
 A changing note below the third and one above the fifth of a com- 
 mon chord may be struck over the root, or root and fifth (3) and (4.) 
 
 The Changing Note may be ornamented like the Retardation. 
 
HARMONY. 
 
 in 
 
 Questions on Changing Notes. 
 
 1. In what respect do changing notes differ from retardations? 
 
 2. On which beat of the measure do they fall? 
 
 3. May they occur in any other situation ? 
 
 4. When do they fall on an unaccented beat? 
 
 5. When may they be a whole-tone below the note of resolution? 
 
 6. When may accidentally raised notes be treated as changing notes? 
 
 7. May changing notes be doubled ? 
 
 Exercises on Changing Notes. 
 
 The note upon which the Changing Note resolves may not be struck 
 with it, but it may be struck at the octave below. 
 I. 
 
 H=f= 
 
 -t-0- 
 
 III. 
 
 Ornamented Changing Notes. 
 
 
 
 ft* 
 
 __j _l m. rrq 
 
 
 
 
 
 
 
 
 • — ^ — 
 
 0— 
 
 wir ~ t=t it: 
 
 
 
 
 
 =3 
 
 
 0 
 
 
 
 
 
 
 1 — A — * 
 
 
 
 
112 
 
 HARMONY. 
 
 CHAPTER XXIV. 
 
 Passing Notes. 
 
 The last manner in which Dissonant unharmonized notes may be 
 used is, as Passing Notes. 
 
 Passing Notes occur between the harmonies on the unaccented 
 beats, or on the second note of the beat. 
 
 There are Five Varieties. 
 
 The First Variety enters by degrees forming part of an ascending 
 or descending diatonic or chromatic scale. To get a passing note 
 of this variety there must be at least three ascending or descending 
 notes in succession, the middle one of which may be a passing note. 
 
 5EE 
 
 =t 
 
 a 
 
 a. The A must ascend and double the third ( B ) in the next chord, 
 to avoid making the parallel fifths, A, G, D. 
 
 b. The third (-£•) is doubled here, because if the root (C) were 
 doubled it would clash with the passing note ( D ) . 
 
 c. This is the only way in which a note may be natural and sharp 
 
 at the same time. (Theoretically this should be D\l, but for all practical purposes it 
 is -more convenient to treat it as a chromatic passing note.) 
 
 Diatonic or chromatic scales of any length may be played with a 
 single chord, provided the first and last, or second and last notes 
 are members of the chord. If the second and last are members of the 
 chord, the first note is a Changing Note. In passages of this kind 
 it is convenient to consider all the intervening notes as passing notes. 
 The chord may be changed with the last note. 
 
HARMONY. 
 
 "3 
 
 First and last. 
 
 Second and last. First and last. 
 
 Second and last. 
 
 The direction of the scale may be changed whenever a note belong- 
 ing to the chord is reached, or the scale may be abandoned when such 
 a note is reached. 
 
 0., 
 
 <r. d. 
 
 X X XX 
 
 a. In the first measure each time a member of the chord is 
 reached, the motion is changed, the next group of sixteenths begin- 
 ning with a changing note. 
 
 b. The change of direction begins with the member of the chord. 
 
 c. Is a passing note of the second variety. 
 
 d. The scale is abandoned. There is a leap from one member to 
 another of the chord. 
 
 The Second Variety enters by degrees above or below the harmon- 
 ized note, but returns to the same note. All varieties of turn, trill, 
 mordent are founded on this variety. 
 
 Like the Retardations this variety of passing note, when below the 
 harmonized note, sounds better if a half-tone ; but it may be a whole- 
 tone below the third of a chord. 
 
 9 
 
 i 
 
 g: .g. 
 
HARMONY. 
 
 The Third Variety enters by a leap from one harmonized note to 
 the degree above or below the next harmonized note. 
 
 When below it must be a half-tone. All accidentally raised notes 
 that occur on the unaccented beats, or the second member of the 
 beat, may be treated as passing notes of this variety. 
 
 x x 
 
 4 
 
 The Fourth Variety may be described as an Ornamented Diatonic 
 scale, made by adding to each note of the scale the note above or 
 below, or a third above or below. So many variations may be made 
 in this variety that it is only possible to give a few examples. 
 
 1 
 
 -g>- 
 
 ^2- 
 
 I 
 
 3 
 
 I 
 
 i is founded on 
 this diatonic 
 
 
 < — *5 = 
 
 * • a 
 
 
 P j i 
 
 < 
 
 
 
 
 
 
 
 ■i n* 
 
 6 on 
 
HARMONY. 
 
 Some apparently elaborate passages may be reduced to very simple 
 harmonic elements by eliminating the passing notes; for example, 
 the following from Handel. 
 
 I 
 
 
 
 — « — = 
 
 
 
 X 
 
 
 
 l *»r — ■ 
 
 r — i! 
 
 The Fifth Variety is called 
 the Anticipating Note. It just 
 reverses the Retardation ; i.e., 
 it anticipates the following 
 chord by sounding one of its 
 members before the preceding 
 chord is left. 
 
 X X X 
 
 In the example that follows, all these varieties are used in a cadenza- 
 like passage over a single chord. 
 
 x x 
 
 Observe that every change in the direction of the motion begins 
 with a member of the chord. 
 
n6 
 
 HARMONY. 
 
 All the ornamentation that may be given to the retardation and the 
 changing note may be given to the first three varieties of the passing 
 note. 
 
 i. 2. 3. 4. 5. 6. 
 
 
 0- 
 
 
 
 • 
 
 • 
 
 
 P 
 
 
 — — 
 
 • — 
 
 
 1 
 
 
 
 # 
 
 w- 
 
 
 
 9— 
 
 
 
 « 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 i 
 
 1. First variety, leaping to note below. 
 
 2. To another member of the chord. 
 
 3. Second variety, leaping to note below. 
 
 4. To another member of the chord. 
 
 5. Third variety, leaping to note above. 
 
 6. Leaping to note below. 
 
 The first three varieties may be doubled in thirds and sixths (1). 
 The first ( diatonic ) may also be doubled at the octave or third, 
 when moving in opposite directions (2). 
 
 The second and third varieties may be doubled at augmented 
 
 fourth or diminished fifth (like changing notes) (3). 
 
 A diatonic scale of first inversions may be written over a single 
 note or chord (4) . 
 
 Diatonic or chromatic scales may be written in contrary motion, 
 in either single notes, thirds, or sixths, provided the first and last 
 notes struck together belong to the same harmony (5). 
 
 A passing note is sometimes followed by a changing note (6). 
 
 The resolution of a passing note is sometimes retarded by repeat- 
 ing it (7) ; or by leaping to some other member of the chord and 
 returning to the passing note (8). 
 
 First. ^ Second. Third. ^ 
 
 9i 
 
HARMONY. 
 
 Third Sonata. Beethoven. 
 
 8va 
 
 Examples maj be found of changing and passing notes used in a 
 
 manner that does not conform to any of the rules here given, but 
 they are rare, and will cause the pupil no difficulty if these rules are 
 well understood. 
 
 Questions on Passing Notes. 
 What is a passing note? 
 
 How many varieties are there of passing notes? 
 Describe the first variety. 
 
 How many notes must there be in succession to have a passing note of this 
 variety ? 
 
 How may extended diatonic and chromatic scales be treated ? 
 Describe the second variety of passing note. 
 Describe the third variety? 
 
 When may accidentally raised notes be treated as passing notes? 
 Describe the fourth variety. 
 Describe the fifth variety. 
 
 May the ornamentation used with retardations and changing notes be applied 
 
 to passing notes? 
 To all varieties? . . 
 
 In what ways may passing notes be doubled ? 
 
 Exercises on Passing Notes and Changing Notes. 
 
HARMONY. 
 
 119 
 
 CHAPTER XXV. 
 Further Remarks on the Minor Scale. 
 
 (it was necessary to defer this chapter until changing and passing notes were explained.) 
 
 The changeable notes in the minor scale offer some difficulties to 
 the student. The following instructions will make this point clear. 
 
 In scale passages ascending, either the harmonic or melodic form 
 may be used when accompanied by the tonic chord (1) . 
 
 When accompanied by the subdominant chord, the harmonic or 
 natural form may be used (2). 
 
 When accompanied by the dominant, root to seventh, the melodic 
 or harmonic form ; but if the dominant harmony is third to ninth, 
 or jifth to eleventh, the harmonic form must be used (3). 
 
 Descending scale, tonic chord accompanying, use natural or har- 
 monic (4). 
 
 Subdominant accompanying, use natural form (5). 
 Dominant accompanying, use harmonic form (6). 
 The form given in 7 is much used by Bach and Handel. It dif- 
 fers from the major scale only in having a minor third above the tonic. 
 
120 
 
 HARMONY. 
 
 The raised sixth of the minor scale, when in the melody, may be 
 harmonized as in the example following, i ; when in the bass, 2. 
 These both belong to the old school of music. Some writers say that 
 2 should never be used, but 3, from the ''Duetto" (Songs Without 
 Words), is a sufficient argument for its use. 4 and 5 give the usual 
 ways of harmonizing it. 6. It is treated as a passing note on the 
 tonic chord. *j. It is treated as a changing note in the dominant 
 chord. 
 
 The natural seventh descending: 1. Diatonic harmony, rugged 
 but effective on occasion. 2. The same passage in the bass. This 
 manner of using the first inversion of the minor chord on the domi- 
 nant, viz., when the bass descends diatonically from the keynote to 
 the sixth or fifth of the scale, is very effective. Some authors say it 
 
HARMONY. 
 
 121 
 
 is the only way this chord may be used, in spite of the fact that 
 self-willed composers often use it otherwise with excellent effect. 
 3 *nd 4 give modern ways of harmonizing this note. 5 and 6 
 give examples of the use of the raised sixth in descending passages; 
 in 5 the sixth returns to the seventh. In 6 the sixth and seventh are 
 both raised, although in a descending passage ; the seventh because 
 the harmony requires it, the sixth to avoid the skip of augmented 
 second, which is very disagreeable in the bass. 
 
 cond, which is very disagreeable in the bass. 
 
 The augmented fifth on the third degree of the minor scale may 
 be used. It is generally used as a retardation, (1). 
 
 2 shows how the natural seventh may be used as a passing or 
 changing note with the raised seventh. 
 
 
 
 2. 
 
 
 
 (i * % 
 
 
 
 
 ik^ -i 
 
 % 
 
 0 
 
 =1 
 
 2. 
 
 ? 11 
 
 
 J 
 
 
 
 li 
 
 1 . 
 
 Exercises in Minor 
 
 I. 
 
 Keys. 
 
 1 I 
 
 
 
 
 
 
 1 1— 
 
 
 
 
 m 
 
 
 ^ 1 
 
HARMONY. 
 
 123 
 
 CHAPTER XXVI. 
 
 Open or Vocal Harmony. 
 
 The way in which the exercises have been written so far is called 
 Close Harmony ; i. e., the three upper parts are kept as close 
 together as possible. 
 
 This has been done because it is the easiest way in which chord 
 successions may be written, and because of a belief that after the 
 pupil has learned the chords and the rules that govern their motions, 
 the writing of them in Open or Vocal score is very much easier than 
 when the pupil has not only the rules for open harmony, but also for 
 the formation and succession of the chords to remember at the same 
 time. 
 
 Any correctly written example of chords in Position may be 
 turned into Open Harmony by the simple expedient of moving the 
 middle note of the upper three down an octave, thus : 
 
 a. 
 
 This expedient fails when Inversions and Dissonant chords are 
 used ; for example, the following is right in close harmony, but when 
 written in open, three successive fifths will be found at <z, and a poor 
 arrangement of the voices at 3, the tenor and bass being too close, 
 and the soprano and alto too far apart. 
 
124 
 
 HARMONY. 
 
 Rules. All previous rules as to Progression and Resolution must 
 be strictly observed. 
 
 No two parts must ever move together in Octaves, Fifths, or 
 Unisons. 
 
 Avoid the following leaps: augmented second, fifth, sixth; 
 diminished third, fourth ; major seventh, minor seventh ; except when 
 from root to seventh of dominant chord, all leaps beyond the octave. 
 
 Avoid all long leaps in the Inner parts (Alto and Tenor). Never 
 allow the Alto and Tenor to be separated by an interval greater than 
 an octave. 
 
 Soprano. 
 
 Alto. 
 
 Keep the voices within the 
 following limits, using the 
 highest and lowest notes of 
 each voice rarely. 
 
 Tenor. 
 
 Bass. 
 
 9± 
 
 2? 
 
 This kind of writing should also be practised on four staves (one 
 for each voice) . It is customary now to use the G clef for the Tenor, 
 with the understanding that its pitch is an Octave Lower than when 
 used for the Soprano. 
 
 The example (marked A), page 124, is here given on four staves. 
 
 . Soprano. 
 
 0 
 
 Alto 
 
 Rewrite all, or as many as possible of the preceding exercises, 
 except those on changing and passing notes, in open harmony, after 
 studying the following examples. This department belongs more 
 especially to the study of counterpoint. 
 
HARMONY. 
 
 Observe that when a note belongs to two or more chords in suc- 
 cession, it may be written as a single note equalling the others in 
 value ; as in second measure, first example. 
 
 When a letter is altered by a sharp, flat, or natural, keep it in the 
 same voice. 
 
 — <5<-q 
 
 I 1^ I 
 
 (2— 
 
 m 
 
 9?l 
 
 is?— 
 
 Mil 
 
 n 
 
 — ,-•—-! — \-x~r^— n 
 
 f 2 - -<5<- - -<5>- 
 
 * . • 
 
 Ffff 
 
126 
 
 HARMONY. 
 
 CHAPTER XXVII. 
 
 Pedal or Organ Point. 
 
 By this is meant the prolongation of a single sound through several 
 measures, generally in the lowest part, while a succession of harmo- 
 nies related to the key is written over it. 
 
 These harmonies must be written as though the Pedal Note were 
 not present. But the Pedal Note must be a member of at least the 
 first and last chords. 
 
 The Dominant is most frequently used as a pedal ; next, the 
 Tonic ; next, the Tonic and Dominant together. 
 
 Examples of other ' degrees of the scale used as pedals are rare. 
 Examples may be found of tonic, dominant, and the fifth of the 
 dominant (i. e., the supertonic) used together. 
 
 Progressions may be written with the greatest freedom over the 
 Dominant; next, over the Tonic. 
 
 They are necessarily much restricted when both these notes are 
 used, and still more when the three notes mentioned above are used. 
 
 If the prolonged note is a member of all the chords written over it, 
 viz., root or fifth, it is not strictly speaking a Pedal. This kind of pro- 
 longed note is often used in an upper part. (The real Pedal is rarely so used, 
 and the harmonies that may be written with it are much restricted.) 
 
 In Pianoforte and Orchestral music the Pedal note is often repeated 
 or alternated with its octave, or with the half-tone below it. 
 
 A succession consisting of the Tonic, Dominant, and Tonic is 
 often written over the Tonic, which might then be termed a Pedal of 
 short duration. 
 
 ■ ¥ 
 
HARMONY. 
 
128 
 
 HARMONY. 
 
 1. Dominant Pedal. 
 
 2. Tonic Pedal. 
 
 3. Tonic and Dominant together. 
 
 4. Tonic, Dominant, and Supertonic. This is rarely used unless 
 a quasi rustic effect is desired. It must end by the supertonic falling 
 to the octave of the tonic. 
 
 5. Example of a prolonged note that is a member of every chord, 
 therefore not strictly a pedal. 
 
 •)■ sS jS 
 
 — 1 41 1 
 
 -0— i 1 1 L-H M 1 — 1 — h — # — £ \- v A \ 
 
 I. The Pedal repeated, alternated with its octave and with the 
 half-tone below. 
 
HARMONY. 
 
 129 
 
 2. Pedal on the tonic, of short duration. 
 
 3. Is a beautiful illustration of this variety of pedal, from Chopin's 
 Cradle Song. This accompaniment persists all through the piece. 
 It is simply a breaking or dispersion of the following chords. 
 
 I: i- 
 g@ II 
 
 Pedals of considerable length may be met with in which transitions 
 are made to non-related keys, but as a rule the harmonies are con- 
 fined to the Related Group. 
 
13° HARMONY. 
 
 CHAPTER XXVIII. 
 Transition. 
 
 Transition is the act of passing out of the related group. 
 A Transition is not established until a Tonic Chord foreign to the 
 Group is struck. 
 
 The presence of a Tonic chord may be indicated in two ways: 
 first, and most emphatically, by being preceded by the harmony of 
 its own dominant; second, by appearing in its Second Inversion, 
 provided the second inversion does not enter in the manner prescribed 
 for a second inversion of dominant or subdominant. 
 
 As this second means of making a Transition does not necessitate 
 the use of Dissonant chords, we will begin with it. 
 
 Taking first the Major chords in the scale, each one may be a Tonic 
 without transition. 
 
 The first and fourth may be Subdominants without Transition; 
 but if the fifth is treated as a Subdominant, and is followed by the 
 second inversion of its Tonic, it gives a transition, thus : 
 
 I 
 
 i 
 
 The chord G, B, D is treated 
 as subdominant of D, and is fol- 
 lowed by the second inversion of 
 D, which is outside of the group. 
 
 The three major chords may also be dominants ; the first and fifth 
 within the group, the fourth gives a transition, thus : 
 
 i fit : ' :! 
 
 ii 
 
 5t 
 
 F, A, C, as dominant, fol- 
 lowed by^b, D, F, out of the 
 
 ^=zm \\ group - 
 
HARMONY. 
 
 A major chord is also found on the sixth degree of the minor 
 scale. Of the three major chords in C, the first and fourth treated 
 thus remain within the group, but the fifth passes out of the group, 
 thus : 
 
 G, B, D is treated as sixth in B minor. 
 
 Transition by treating the major chord as sixth in a minor scale 
 maybe extended by treating the Minor scale as the parallel of a Major 
 scale, thus : 
 
 S 
 
 1. C, E, G, as sixth of E minor, the parallel of E major. 
 
 2. F, A, C, as sixth of A minor, the parallel of A major. 
 
 3. G, B, D, as sixth of B minor, the parallel of B major. 
 
 A major chord may also be treated as being the chord on the Low- 
 ered Supertonic of either a Major or Minor scale, thus : 
 
132 
 
 HARMONY. 
 
 1 . C, E, G, as lowered supertonic of B, Major or Minor. 
 
 2. 7% A, C, as lowered supertonic of E, Major or Minor. 
 
 3. G, B, E>. as lowered supertonic of Major or Minor. 
 
 For the sake of clearness the Tonic of the key to which the Tran- 
 sition is made follows directly after the chord by means of which the 
 Transition is made, but as a result of the rule already given, that the 
 movement of common chords is perfectly free, any of the chords be- 
 longing to the new scale may appear before the tonic is struck. 
 For example, C, E, G, is found in C, as tonic ; E^ as dominant, 
 G, as subdominant. It may therefore be followed by any chord in 
 these keys or their related keys. But when treated as sixth of a 
 parallel minor, or as a lowered supertonic, it is subject to the rules 
 already given for the use of these chords ( Chap. XI.). 
 
 The three. Minor chords in the scale, treated as tonics, remain 
 within the related group. 
 
 As subdominants, those on the second and sixth remain within, 
 unless treated as belonging to parallel minor scales, thus : 
 
 „ i- ! J I 1 2 - 3-ii. 
 
 i 
 
 pi 
 
 
 
 
 m 
 
 
 
 
 
 - r x 
 
 
 
 
 
 
 
 
 
 
 ^4 
 
 
 
 
 % - 
 
 1. D, E, A, subdominant, A minor, parallel of A major. 
 
 2. A y C, E, subdominant, E minor, parallel of E major. 
 
 3. E, G, B, subdominant, B minor; gives a Transition when 
 followed by either B major or minor, 
 
 A Minor chord is also found 
 on the third of the major scale. 
 The supertonic is the only one 
 that will give a transition when 
 treated this way. 
 
 t 
 
 9± 
 
 II 
 
 In the following example all the transitions are made by means of 
 common chords, treated in the various ways just pointed out. The 
 
HARMONY. 
 
 J 33 
 
 places where the transitions occur are marked. It is left to the pupil 
 to explain them. 
 
 N l ' I 
 JV! 
 
 ^ 1- 
 
 it- — 
 
 J2.- 
 
 
 
 • 
 
 - 5= 
 
 
 
 
 ■ — %- 
 
 0— 
 
 N.B. 
 
 4* 
 
 «3£ 
 
 r b f 
 
 N. B. The chords of C§ and D\> are enharmonically the same. 
 
 to 
 
 zf __ at 
 
 9- 
 
 r r r 
 
 f r 
 
 -• — & 
 
 i i 
 
 Transition by means of Dominant Harmonies. 
 
 Any Dominant Harmony may be followed by either a major 
 
J 34 
 
 HARMONY. 
 
 or minor tonic. Thus the following groups derived from G may 
 be followed by C major or C minor % 
 
 G B D F— B D F Ab—£>, F, A% C. 
 
 First. Third, Fifth. Seventh. Third. Fifth. Seventh. Minor Fifth. Seventh. Minor Eleventh. 
 
 ninth. ninth. 
 
 ( The ninth, if present, must be minor, as the major ninth cannot be used in a minor key.) 
 
 ~£ g*. or ~Z7~ 
 
 -J I- 
 
 u^j :szo r zs: 
 
 2£ 
 
 1 
 
 It will at once be seen that, by taking advantage of this fact, Three 
 Transitions may be made from a given key by changing the major 
 tonics to Minor, and three by changing the Minor tonics to major. 
 
 I 
 
 =t 
 
 afcrifc* 
 
 r 
 
 
 
 
 
 
 
 
 =^ 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 r 
 
 ^ J_ij 
 
 =3= 
 
 X 
 
 9 
 
 9 
 
 1. The tonic of the principal key is changed to Minor, and as C 
 minor is the relative minor of Eb, the Transition is from C to Eb. 
 
 2. The same process in the related key of G takes us to Bb. 
 
 3. The same process in the related key of F takes us to Ab. 
 
HARMONY. 
 
 l 35 
 
 This means of making Transition may be combined with that 
 first given. It would require volumes of examples to illustrate them. 
 We give a few, leaving it to the pupil to invent others, — an easy task 
 if the principles are kept in mind. 
 
 To analyze a Transition, always observe what relation each chord 
 bears to the chord and key that precedes it, and to the chord and 
 key that follows it. 
 
 r \ x x i x x 
 
 i. Dominant harmony of G, fifth to eleventh, followed by G 
 minor ( 2 ) . This is then treated as being a third of iii?, and is 
 followed by dominant of E^. 3. Same process repeated in E9, but 
 the minor chord ( 4 ), B\>, is treated as subdominant of E minor, the 
 parallel of E major. 
 
 In the next examples the supertonic harmonics of the three major 
 keys of the group are followed by minor tonics. 
 
HARMONY. 
 
 4* 
 
 zfe 
 
 Write corresponding modulations in all keys ; also make the 
 corresponding changes in the related minor keys. 
 
 A Third means of Transition is by Additions to common chords. 
 
 To a Major chord, the minor third below its root may be added ; 
 it then becomes fifth, seventh, major ninth, and eleventh of a domi- 
 nant. This addition to the first and fourth chords will not give a 
 transition, unless the ninth is minor ( see former rule ) , but it will 
 with the fifth. 
 
 m 
 
 1. C, E, G, with A, the minor 
 third below, added. If the E 
 were changed to E\>, the tonic of 
 G minor might follow, giving a 
 transition to 
 
 2. Same remarks will apply. 
 
 3. G, B, D, becoming dominant eleventh of D major. 
 
 The augmented sixth over the root may be added to any major 
 chord. This gives some startling Transitions. Like the supertonic 
 harmony, a major or minor tonic may follow. ( 1 and 2 ), if fol- 
 lowed by minor tonics, resolve within the group. (3)? out of the 
 group whether major or minor tonic be used after it. 
 
 0 
 
 9i 
 
 w 
 
 According to our rule the 
 raised note must be the third. 
 Therefore E$ is the root of 1, 
 and as F\ is the supertonic of E, 
 this is the augmented sixth of E. 
 Root of second is B ; of third, Cjf. 
 
HARMONY, 
 
 *37 
 
 A minor third below the root may be added to a minor chord. It 
 may be fifth, seventh, minor ninth, and eleventh of a dominant, or 
 third, fifth, seventh, and major ninth of a dominant or supertonic. 
 
 1. I), F, A, with B added, treated as dominant eleventh of A 
 major or minor. 
 
 2. Same, treated as dominant ninth of C. 
 
 3. Same, treated as supertonic ninth of F. 
 
 4 and 5. Are the remaining minor chords in C, with minor third 
 below added. 
 
 These and the preceding examples with major chords should be 
 all written out and resolved. 
 
 The addition of a minor third above a Minor chord has the same 
 result as the addition of a minor third below a Major chord. 
 
 x 
 
 The next means of making Transition is by the Chromatic Altera- 
 tion of chords; first, from major to minor, and the reverse; second, 
 changing a group of four sounds into some other group of four 
 sounds. 
 
 Thus the group G, B, D, F (first, third, fifth, seventh of domi- 
 nant of supertonic) may be changed into third, fifth, seventh, ninth, 
 by making G sharp. 
 
 Into fifth, seventh, ninth, eleventh by making B fiat. 
 
 Into fifth, seventh, ninth, eleventh, or third, fifth, seventh, ninth 
 by making B and D flat. 
 
 Into third, fifth, seventh, ninth by making B, Z>, and F flat. 
 
 Last, by flatting D it becomes an augmented sixth chord, Z)b, F, 
 G, and B. 
 
i3§ 
 
 HARMONY. 
 
 Write out these changes and resolve them. 
 
 In the course of this change 
 one or more of the sounds may 
 be enharmonically changed. 
 
 The last means by which Transitions may be made is by Enhar- 
 monic Change. 
 
 First, advantage may be taken of the fact that the dominant seventh 
 chord and augmented sixth chord sound alike, consequently the 
 seventh may be changed to an augmented sixth, or the reverse. 
 
 This change is not always expressed in the writing. 
 
 n I. 2.m u 
 
 :l2§gg j§~r^g-rj i . Dominant of F, changed 
 ~~1 1 1 to augmented sixth of E. 
 
 i. Augmented sixth of C, 
 h& (9 — i n changed to dominant of Lh» 
 
 —& — 
 
HARMONY. 
 
 At b the augmented sixth of B is changed back to the dominant of 
 C. The change is implied here also, but it differs from the first case 
 in that the chord is written according to its resolution, whereas in the 
 first case it is not. 
 
 The chief source of enharmonic modulation is found in the dimin- 
 ished seventh chords. 
 
 These chords consist of four sounds separated from each other by 
 three half-tones ; thus, B, A F, A\>. 
 
 Third Fifth. Seventh. Ninth. 
 
 It will be found that, no matter in what order they are written, 
 this will hold good ; therefore, any one of the sounds may be in turn, 
 the third, fifth, seventh, or ninth. Thus if A\> be put at the bottom 
 we get, ^4b, B, Z>, F, and the A\> being enharmonically 6$, the chord 
 may be written B, F. 
 
 Therefore, as there are four notes in the chord, it may be written 
 in four ways, and obtained from four roots, and resolved in four ways 
 as a dominant, and four ways as a supertonic harmony. 
 
 Take the group B, D, F, A\> and move every sound up a half- 
 tone ; we get C, Eb, F§, A\. Move these up a half-tone ; we get 
 Cjf, E% G\ B\>. Repeat the process, and we get the group with 
 which we began. It will be seen that in the three groups all the 
 sounds of the Chromatic Scale are included. 
 
 First group. 
 
 I. 
 
 :f=|= 
 
 Second group. 
 
 4- 
 
 Third group. 
 
 3- 
 
 Ww<2-W 4. 
 
 ii-llorbfelM 
 
 First group, i. Written as if derived from G ; therefore domi- 
 nant of C major or minor, or supertonic of F major or minor. 
 
 2. As if derived from E\ dominant of A, supertonic of D. 
 
 3. As if derived from Cjjj ; dominant of F$, supertonic of B. 
 
 4. As if derived from B\> ' ; dominant of Z?b, supertonic of A\>. 
 Second group. 1. As if derived from C; dominant of F, super- 
 tonic of B\>. 
 
 2. As if derived from A ; dominant of Z>, supertonic of G. 
 
HARMONY. 
 
 3. As if derived from F\\ dominant of B, supertonic of E. 
 
 4. As if derived from D% or E\> '; dominant of G# or A>, super- 
 tonic of C% or Z)b. 
 
 Third group, 1. As if derived from Z?; dominant of G, super- 
 tonic of C. 
 
 2. As if derived from B\ dominant of E, supertonic of A. 
 
 3. As if derived from G\ or A\> ; dominant of C$ or /)!?, supertonic 
 of F% or Gt>. 
 
 4. As if derived from F\ dominant of B\>, supertonic of E\> '. 
 
 Tt will be seen that each group is found twice in every key; viz., 
 in the dominant of the major, and in that of its relative minor. This 
 being true in the scale of C, it follows that it must be so in every 
 scale. 
 
 This fact makes it possible to change instantly from one key to 
 another by means of this chord in two ways. 
 
 First way, take the group that contains the leading note of the key 
 to which it is desired to go, and resolve it as a dominant harmony. 
 
 Second way, take the group containing the keynote of the key to 
 which it is desired to go, and resolve it as a supertonic harmony. 
 
 It is a good practice, unfortunately not so much observed as it 
 ought to be, to write the diminished seventh chord, when used for 
 Transition, as it would be in the key in which it is resolved. 
 
 r}' I ,£ I Jt I 2 J id I 3- I I I 4- 1 I I5-|,I I 6. , I I 
 
 , '-*y<-'\' !"^ "]'' T -y r r '|| 
 
 I. C to E§ by dominant. 2. C to E$ by supertonic. 3. C to Av, 
 dominant. 4. C to Z>b, supertonic. 5. C to Z?b, dominant. 6. C 
 to supertonic. Observe that in each case the diminished seventh 
 group is not written as it would be in C, but as it would be in the key 
 that is to follow it. 
 
 One great advantage of writing it this way is, that it simplifies the 
 reading, because a musician always reads the harmony as well as the 
 
HARMONY. 
 
 notes, and is much more likely to trip over a miswritten passage than 
 a difficult one. 
 
 The only way to master this protean chord is to write, or better 
 still, play on the piano all the changes indicated by the foregoing 
 remarks. 
 
 The diminished seventh may be changed into a group of first, 
 third, fifth, and seventh in two ways. First, since any one of the 
 notes may be considered as the ninth by lowering it half a tone, the 
 note to which it is lowered becomes the root. 
 
 i. 2. 3. 4- 
 
 1. Z?l?, lowered diatonically to C. 
 
 2. B lowered diatonically to A ; enharmonically changed to 
 
 3. G, lowered chromatically to G\> ; E, enharmonically changed 
 to FV. 
 
 4. E, lowered chromatically to E\?. 
 
 Second way, by retaining one note and moving the rest up a half- 
 tone, the note retained becomes the root. 
 
 In both these cases the note that becomes the seventh maybe enhar 
 monically changed into an augmented sixth. 
 
 Last of all, the rules given in Chapter XVI. may be applied to 
 this chord, which may be written in any of its four ways, as may 
 best suit the succession desired. 
 
 Transitions are often effected by means of Harmonic Sequences. 
 
 The Harmonic Sequence consists of a dominant, or supertonic, or 
 augmented sixth harmony followed by its resolution, repeated at 
 regular intervals ascending or descending. 
 
142 
 
 HARMONY. 
 
 The varieties that may be made are infinite, but the following ex- 
 amples will give a clear idea of the operation. 
 
 4-.-L 
 
 If 
 
 E- 
 
 a 
 
 1. Dominant and tonic; each a whole-tone below the last. The 
 succession of dominant seventh will explain this passage. 
 
 2. Dominant and tonic ; each a half-tone lower than the last. Each 
 common chord bears the relation of tonic to the dominant that pre- 
 cedes it, and of lowered supertonic to the one that follows it. 
 
 3. Dominant and tonic; the minor ninth added; the roots ascend 
 by fourths, each root a whole-tone above the preceding. 
 
 4. Is a reversal of 3. The roots descend by fourths, each root a 
 whole-tone below the preceding. 
 
 All these sequences may be inverted or rearranged in any way. 
 A Sequence may take in three, four, or even more chords, as in 
 the following examples. 
 
 I I i I *\ 
 
 1. Tonic, augmented sixth, dominant; ascends by whole-tones. 
 
 2. Tonic and dominant; each root has first a tonic, then a domi- 
 nant harmony. 
 
HARMONY. 
 
 H3 
 
 C~2 i — ± 
 
 =fc=t=Fi== 
 
 }=±=±=±==i 
 
 
 
 
 
 
 
 
 1 
 
 — 
 
 
 
 
 
 
 r — f I" — f— (— 
 
 — P — F F— i F--i — 11 
 
 g ^2 &J^=± 
 
 f 2 — <S> 
 
 1. Supertonic harmony; tonic, dominant; descending by whole- 
 tones. 
 
 2. The same, with supertonic harmony changed to augmented 
 sixth. 
 
 3. Augmented sixth and dominant, descending by whole-tones; 
 i. e., the roots. 
 
 4. Same, descending by half-tones; i. e., the roots. 
 
 Of course the sequence may be stopped at any point, when the key 
 is reached to which it is wished to make a transition. 
 
 Sequences may be made by means of the second and third pro- 
 gressions of the dominant, also with dominant eleventh. 
 
 -S» & (2 <2_ 
 
 fe — frg — 
 
 & <S>— 
 
i 4 4 
 
 HARMONY. 
 
 1 . A sequence of second progressions ; each dominant resolved as 
 in a major key. 
 
 2. Same; the dominants resolved as in a minor key. 
 
 3. Sequence of third progressions. 
 
 1. Sequence with eleventh chords. 
 
 2. Same, showing the sudden transition that may be made by sub- 
 stituting A major for A minor. 
 
 The pupil should write and play these sequences in all the keys 
 repeatedly, and should invent new ones, make inversions of them, 
 and arrange the chords in different ways. 
 
 If the plan of instruction mapped out in this book has been care- 
 fully followed, and each step mastered before proceeding to the next, 
 above all, if the Relationship of Keys making up the " Group " is 
 well understood, the pupil will have a knowledge and command of 
 the resources of harmony that will amply repay the time and labor 
 spent in acquiring them. 
 
SUPPLEMENT. 
 
 Tempered Scale. 
 
 There is among musicians such a vague notion as to what is meant 
 by the tempered scale, that it has been thought well to add a few 
 explanatory words, avoiding all minute details as much as pos- 
 sible. 
 
 To make all our chords in perfect tune it would be necessary to 
 divide the octave into so many parts that the result would be an un- 
 manageable mass of sounds ; but it was discovered that by dividing the 
 octave as nearly as possible into twelve equal parts, a series of sounds 
 was obtained, which while not corresponding exactly with the true 
 series, was yet so near that every sound in the series might be the 
 root, third, fifth, seventh, etc., in some chord, so nearly in tune that 
 the ear was satisfied. 
 
 . The gain to music was not alone in the simplification of the scale, 
 but, what was of far greater importance, the power of passing at 
 will from any key to any other, by taking advantage of the sounds 
 they hold in common, 
 
 On this modern music is founded. It is hardly too much to say 
 that modern music dates from the publication of the "Well Tem- 
 pered Clavier." 
 
 Practically the "tempering" of the scale is secured by a very sim- 
 ple means; viz., by tuning every fifth slightly flat. This secures the 
 twelvefold division of the octave. 
 
 The ratio between the vibrations, per second, of a given note and 
 its octave is i to 2 ; that is, the octave vibrates twice as fast. The 
 ratio between the vibrations, per second, of a given note and its 
 fifth is 2 to 3 ; that is, the fifth vibrates one-half faster than the 
 root. 
 
 (145) 
 
146 
 
 SUPPLEMENT. 
 
 Now suppose we begin with C, and tune in fifths and octaves as in 
 the following diagram. 
 
 Oc- Oc- , 
 
 Fifth. tave.Fifth. Fifth, tave. . 1 I ,1 
 
 I I ~2 3 2 4 . J " ~ ' 4 
 
 3 ^6 7 ^ 8 9 Y 10 116 12 
 
 It will be seen that by tuning up twelve fifths and down six oc- 
 taves, the octave of the first note is reached. 
 
 Now, if we allow 144 vibrations to the starting note, the octave 
 must have 2S8 ; but the C reached by the tuning given above will 
 have about 290, so that it is too sharp, about the one-eighth of a tone. 
 
 Tempering is dividing this small interval, called the comma of 
 Pythagoras from its reputed discoverer, as equally as possible among 
 the twelve fifths. The result is that the octave is the only interval in 
 our system that is perfectly in tune. 
 
 Below will be found the first six of the above sounds, with their 
 vibration numbers attached. It is an easy arithmetical problem to 
 find the rest. To find the fifth of a given sound, add half the num- 
 ber to itself; thus, C, 144; G, 216, because the half of 144 is 72, 
 and 72 and 144 are 216. When the octave below is to be found, 
 divide the number by 2. 
 
 144 Sj »4J ,t, X 
 
 It is not necessary here to go any deeper into this subject. The 
 student who wishes to become thoroughly acquainted with it will 
 find it exhaustively treated in many works on acoustics, especially in 
 Helmholtz, Tyndal, Blaserna, etc. There is also an excellent trea- 
 tise in 44 Grove's Dictionary," under the title Temperament. 
 
 The regret is often expressed that musicians do not adopt a more 
 perfect scale, but it should not be forgotten that custom rules in this 
 
SUPPLEMENT. 
 
 as in many other things. From our earliest infancy we are habit- 
 uated to the tempered scale. 
 
 It is the scale that has given us all the greatest music we possess; 
 it satisfied the musical instincts of Bach, Haydn, Mozart, Beethoven, 
 Mendelssohn, and countless others among the greatest composers. 
 
 Music means something more than mere sweet sound. To one 
 who feels this meaning, no possible exactness of intonation would 
 add to it in, say, the slow movement of the Sonata Path^tique (I 
 choose an illustration from piano music because the chief scorn of 
 the purists is directed against the piano), while on the other hand it 
 would quite destroy the unexpected modulation from A\> to E, and 
 back again. 
 
 There is but one way in which a change in our scale may be intro- 
 duced : some great composer must arise who will show us that its 
 possibilities for expression far surpass those of the tempered scale. 
 
 FIGURED BASS. 
 
 Called also Erroneously Thorough Bass, (Italian) Basso 
 Continuo, (German) General Bass. 
 
 Figured bass was devised as a sort of musical shorthand, by means 
 of which the chord each bass note was to bear was represented 
 by figures placed under or over the bass. Its use dates from about 
 the year 1600. It was intended to serve as a guide to the accom- 
 panist, to whose discretion it was left to arrange the harmony as he 
 pleased. It may easily be guessed that accompaniment did not have 
 the importance in the estimation of the old composers that it has in 
 their modern successors. 
 
 By one of those strange chances that so often happen, figured bass 
 has assumed a position never contemplated by its inventors, through 
 its adoption as the means of teaching harmony. Its original purpose 
 has long been disused, although conservatism still demands ''playing 
 
148 
 
 SUPPLEMENT. 
 
 from figured bass " as one of the exercises for candidates for degrees 
 at some universities. 
 
 It may be easily understood that it is quite possible for any one to 
 write over a given series of notes the intervals indicated by the fig- 
 ures, without having the least conception of the reasons for the 
 combinations or for their successions. Just as one may learn the 
 Greek alphabet so as to pronounce with facility the Greek language, 
 yet without knowing the meaning of a single word. 
 
 The principles upon which the system of figured bass is con- 
 structed are easily understood, and to anyone who has mastered the 
 system of harmony taught in this book, they offer no difficulties. 
 
 The simple combinations and successions of the older writers may 
 be represented with comparatively little complexity, but the most 
 ardent advocates of figured bass admit that the amount of complica- 
 tion made necessary in the figuring by the complexity of modern 
 music, is such that its unravelment becomes a veritable enigma. 
 
 The rules upon which the system is based are as follows (the 
 figures indicate the intervals over the bass): 
 
 When a note is without figures it bears the common chord. 
 
 1. But it is sometimes necessary, as for example, when a given 
 note is to bear two or more chords, to indicate the common chord by 
 
 8 
 
 a 3, or 5, or 6 or 5, etc. (As a general thing, the 3 is sufficient.) 
 
 2. The position of the chord is left entirely to the discretion, or 
 the reverse, of the student. 
 
 1. 2. 
 
 1 
 
 The figures must be w 
 with the largest unit at the 
 without regard to the member of 
 the chord that may occupy this 
 position ; thus, 
 
 ritten / 
 top, j 
 
 e 
 
 5 may be 
 3 
 
 9* 
 
 I 
 
SUPPLEMENT. 
 
 149 
 
 When this arrangement is de- 
 parted from, it means that the 
 intervals must be arranged in the 
 way indicated by the figures ; thus, 
 
 i 
 
 1 
 
 33 
 
 The first inversion of a common chord is figured *j, or 6 only ; the 
 rule being that where 6 is used 3 is understood to accompany it (i)» 
 The second inversion is figured J (2). 
 1. 
 
 2. 
 
 1 
 
 — &- 
 
 3 or 6 
 
 l 
 
 The figure 7 (for 5) indicates any of the following groups : 
 
 3 
 
 Dominant or supertonic, first to seventh, third to ninth, or fifth to 
 eleventh, or a passing seventh, or a suspended seventh (1). 
 
 -(2- 
 
 X 
 
 2 
 
 -1— 
 
 7 . 
 
 The first inversion of 5 is figured 5, a 3 being understood (1) ; the 
 
 7 
 
 seconl inversion of 5 is figured |, a 6 being understood (2) ; the 
 
 3 
 
 third inversion of 5 is figured * a 6 being understood (3) . 
 
 (As in the former case it applies to any four note group.) 
 1. 2. 3. 
 
 ^ 
 
 a. 
 
 
 
 5 
 3 
 
 6 
 
 5 or 
 3 
 
 4 or 
 
 4 or 
 2 
 
 8 
 
 9i 
 
 1 
 
SUPPLEMENT. 
 
 Accidentals- are indicated as follows: 
 
 When sharp, flat, or natural is placed over a note not followed by 
 a figure, it always refers to the third over the bass (i). When sharp, 
 flat, or natural is followed by a figure, it affects the member of the 
 chord for which that figure stands (2) 
 
 4 
 
 }— * q 
 
 
 
 
 
 F 
 
 6 4 % 
 
 1 
 
 
 There are two exceptions, viz., the augmented sixth is indicated by 
 a six with a line through it, thus, the augmented fourth is indi- 
 cated in the same way, 
 
 When a note is common to two or more chords in succession, its 
 repetition is indicated by means of short horizontal lines (1). 
 
 A long line placed after the figures, over the first note of a running 
 or arpeggioed bass, means that the chord is to be held until the end 
 of the line (2). 
 
 When there are several sets of figures over a single note, care must 
 be taken to get the value of the notes in which the chords are written 
 correctly. When there are two or four sets of figures over a note, 
 there is no difficulty; but when there are three or any other odd 
 number, it is not so easy to tell just how the values are to be dis- 
 
SUPPLEMENT. 
 
 trihuted. This is indicated in some degree by. the position of the 
 figures in the measure ; thus, 
 
 Various attempts have been made to improve on this system of 
 figured bass by the use of additional signs, but the increase in the 
 number of signs only increases the complexity. 
 
 One plan largely adopted, is to indicate the degree of the scale that 
 is the root of the chord by means of Roman numerals under the 
 chords. 
 
 Thus, 3 signifies that the chord is an inversion of the chord whose 
 V 
 
 root is the fifth of the scale. 
 
 Another plan that has never become general uses the letters of the 
 alphabet to indicate the member of the chord that is used as a bass ; 
 thus, 
 
 A signifies that the root is at the bass. 
 B signifies that the third is at the bass. 
 C signifies that the fifth is at the bass. 
 D signifies that the seventh is at the bass. 
 E signifies that the ninth is at the bass. 
 F signifies that the eleventh is at the bass. 
 G signifies that the thirteenth is at the bass. 
 
SUPPLEMENT. 
 
 —Q- — <s> ^> (9— : 5^ a — i n 
 
 
 
 
 
 
 
 
 
 
 c> 
 
 ^ 
 
 — H>« 
 
 ^ 
 
 17^ 
 
 
 
 
 
 
 
 
 
 A 
 
 7 
 
 B 
 6 
 5 
 
 C 
 4 
 3 
 
 D 
 4 
 
 2 
 
 E 
 
 F 
 
 h 
 
 2 
 
 G 
 5 
 3 
 
 Enough has been written to give the student a thorough under- 
 standing of the meaning of Figured Bass. Should any one wish to 
 pursue the subject farther there are innumerable text-books based on 
 this system that may be consulted. 
 
 That good musicians may be trained by this system countless num- 
 bers attest. We only claim for the system set forth here, that it 
 reaches the same results by a shorter and pleasanter route.