I "'"■"""'1i::!M!iii;!U!!i:iimii . ^lOilQ s>4> PRACTICAL LESSON PLANS IN HARMONY BY HELEN S. LEAVITT • : . ■• X • GINN AND COMPANY BOSTON • NEW YORK • CHICAGO • LONDON ATLANTA • DALLAS • COLUMBUS • SAN FKANCI8CO COPYRIGHT, 1916, BY HELEN S. LEAVITT ALL BIGHTS RESERVED 216.6 Tgfte fltbenaeam jgretf* GINN AND COMPANY • PRO- PRIETORS • BOSTON • U.SA. PEEFACE " Practical Lesson Plans in Harmony " is not a treatise on the subject of harmony. It aims to present in a direct and lucid manner an outline of the principles governing har- monic composition. The student is supposed to have a thorough knowledge of the rudiments of music, as outlined in Lesson I. Until such a knowledge is acquired, progress in the study of harmony is hopeless. These outlines are the result of practical teaching experi- ence. They are suitable for both teacher and pupil. It will be advisable, however, to use them conjointly with a textbook on harmony, in order that the student may have the advantage of more minute discussion and illustrations from the works of famous composers. Purposely these outlines are brief, definite, and free from the detail which is found in the exhaustive treatises on the subject. This volume presents one method. Experience has shown that if students are thoroughly grounded in the simpler forms of harmonic composition, they may gradually add to their chord vocabulary without the confusion which results from having too great a choice of chords at the outset. Greater progress will be made when the student has specific directions as to the best mode of harmonization than when too much stress is laid on forbidden progression^. To this end, positive statements are made as far as possible in these outlines. From the outset the student is encouraged to make his own choice of chords. In order that free melodic expression may iii iv LESSON PLANS IN HARMONY result from harmonic study, mechanical figured basses are discouraged. It may be the judgment of some that certain of these lessons should receive more comprehensive treatment. But the underlying principle has been to present clear and concise plans, with only the essential points defined. For further details and more exhaustive discussion the student is referred to the textbook " Cumulative Harmony," by William J. McCoy. Ear training is an important factor in all harmonic study, and, as each lesson is undertaken, the teacher will find it help- ful to direct the student to associate with the ear as well as the eye all the chords which are presented. This development of hearing the actual sounds of chords has a twofold effect: first, accuracy as to intervals and chord relations; and second, a mental conception of the real sounds of the symbols ; that is, to hear with the eye. This will be particularly valuable as the study progresses to modulation. The student is urged to illustrate the points of each lesson by writing original melodies and basses and by making two- part and three-part vocal arrangements. HELEN S. LEAVITT CONTENTS LESSON PAGK I. Introduction to the Study of Harmony ... 1 II. Intervals 5 III. Chords 10 IV. Harmonization of Melodies 13 V. Harmonization of Basses 18 VI. Inversions of Triads 20 VII. The Dominant Seventh Chord 24 VIII. Inversion of the Dominant Seventh Chord . . 27 IX. Cadences 30 X. The Dominant Ninth Chord 32 XL Construction of Accompaniments and of Melo- dies OVER Accompaniments 36 XII. Directly Related Keys 41 XIII. Modulation 44 XIV. Secondary Triads 48 XV. Suspensions, Passing Tones, and Appoggiaturas . 53 XVI. The Minor Mode 59 XVII. Secondary Seventh Chords 63 XVIII. Diminished Seventh Chords 68 XIX. Remote Modulation 73 XX. Chromatically Altered Chords ....... 80 XXI. Sequences 85 XXII. Irregular Resolutions of the Dominant Seventh 89 XXIII. Elementary Ear Training, Melodic and Rhythmic 91 XXIV. Elementary Ear Training, Harmonic . . . . . 97 INDEX 99 V PRACTICAL LESSON PLANS m HARMONY LESSON I INTKODUCTION TO THE STUDY OF HAEMONY Aim 1. To develop a working vocabulary of chords and the ability to construct harmonic progressions in a melodic, musical manner. Definition of Harmony 2. Harmony is the grammar of music. In general, it applies to any combination of tones or chords which produce music, embracing rules for the treatment of those chords. Specifically, it applies to a group of tones of different pitch sounded as a chord and represented by corresponding notes on the stafE. Preparation 3. A thorough knowledge of key signatures, note val- ues, and use of chromatic characters in writing. A review of these principles is suggested. 2 '^ LESSON PLANS IN HAEMONY Presentetion ' ' < ' ' ' ' ' ' 4. Tones are musical sounds of definite pitch and are perceived by the ear. 5. Notes are representations of musical sounds and are perceived by the eye. 6. Staff degrees are lines and spaces of the staS and are perceived by the eye. 7. Steps and half steps are tonal distances and are perceived by the ear. 8. Scales. A scale is a series of eight different tones from any basic tone to its octave, which succeed each other according to a fixed law. The scale names are 1, 2, 3, 4, 5, 6, 7, 8. A half step is the smallest interval (see Lesson II) used in any scale. A whole step is an interval equivalent to two half steps. A diatonic step is a progression between contiguous degrees of the same major scale, and may be a half or a whole step. a. The Major Scale, The major scale ascending is step 4 step 5 Btep 6 step 7 ste] The major scale descending is INTRODUCTION TO THE STUDY OF HARMONY 3 b. The Minor Scales. Natural — ascending 1 step 2 step d step 4 step step y step 7 descending step 8 b Step 7 step D step 5 step 4 step 9 .A_ 1 Step ^ step Melodic — ascending descending 8 step 7 step 6 ^tep 5 step 4 step o step 2 step 1 Harmonic — ascending J step ^ step o step ^ step Q step^^ steps I step o descending 8 step 7 steps 6 step 5 step 4 step 3 step 2 step 1 c. 7%e Chromatic Scale. The intervals are all half steps. 1 #1 2 #2 3 4 #4 5 #5 6 #6 7 8 8 7 b7 6 b6 5 b5 4 3 b3 2 b2 1 4 LESSON PLANS m HABMONY d. Technical Names, The technical names of the scale tones of the major or minor scale, in distinction from the numerical designations, are as follows : The first tone is called tonic. The second tone is called supertonic. The third tone is called mediant. The fourth tone is called suhdominant The fifth tone is called dominant. The sixth tone is called suhmediant. The seventh tone is called leading tone. The eighth tone is called tonic. e. Melodic and Harmonic Relation. Tones are related in scale and in chord. Chords are related in key. A key comprises a series of tones forming any given major or minor scale, considered with special reference to their melodic and harmonic relationship to each other, and to a fixed tone called a keynote. LESSON II INTERVALS Aim 9. To define the relationship of any two notes appear- ing in combination or succession ; also the relationship of any two tones in regard to pitch. Definition 10. An interval is the difference in pitch between two tones and is measured from the lower tone upward. Preparation 11. Review of scale structure. Presentation 12. Names. There are two kinds of interval names, general and specific. a. General Name. The general name indicates the number of staff degrees an interval covers and is ex- pressed by some one of the ordinals — prime, second, third, fourth, etc. The general name depends entirely on the position of the notes on the staff. If the two notes of an interval are on the same staff degree it is a prime; if on contiguous staff degrees it is a second. 6 LESSON PLANS IN HAEMONY In all other cases add to the two degrees which the two notes occupy all the scale degrees between, and the sum expressed by the ordinal is the general name of the interval. The largest interval is a ninth, and notes more than a ninth apart are reckoned as though they were within the same octave. ft. Specific Name. The specific name indicates the aggre- gate of the component parts (steps and half steps) an in- terval contains, and is expressed by such terms as major, minor, perfect, augmented, and diminished. If a third is composed of two whole steps it is a major third ; if it is composed of one whole step and one half step it is a minor third ; if two half steps it is a diminished third ; and so on. In studying intervals determine first the general name and then the specific name. Major, minor, perfect, augmented, and diminished intervals are all found in a major diatonic scale. 13. Character of the Intervals. a. Major or Minor Intervals. The scale ladder is a graphic representation of the major diatonic scale in any key. Note that from 1 to 2 is a second, major ; from 1 to 3 is a third, major; from 1 to 6 is a sixth, major; from 1 to 7 is a seventh, major ; from 1 to 2 is a ninth, major. These are all the different kinds of major intervals there are, and an example of each is readily recalled from the fact that each begins on 1 of the scale. INTERVALS Note that from 7 to 8 is an example of a second, minor ; from 6 to 8 is a third, minor ; from 3 to 8 is a ^ -i i a sixth, minor; from 2 to 8 is a seventh, minor; from 7 to 8 is a ninth, minor. These are all the different kinds of minor intervals there are, and an example of each is readily recalled from the fact that each ends on 8 of the scale. b. Perfect, Augmented, and Diminished Intervals, Jl 4 l_-..i.-4.. -^ — ? 8 LESSON PLANS IN HAEMONY Note that from 1 to 4 is an example of a fourth, perfect; from 1 to 5 is a fifth, perfect; from 1 to 1 is a prime, perfect; from 1 to 8 is an octave, perfect. Every fourth in the major diatonic scale is perfect except one, and that one is founded on 4 and ends on 7, and is a fourth, augmented. Every fifth in the major diatonic scale is perfect except one, and that one is founded on 7 and ends on 4, and is a fifth, diminished. Deduce from the ladder that •a major second con- tains one whole step, and a minor second, one half step; that a major third contains two whole steps, and a minor third, a step and a half; and so on. A perfect or a major interval .made a half step larger becomes augmented. A perfect or a minor interval made a half step smaller becomes diminished. Show the progressions major, minor, diminished ; minor, major, augmented; perfect, augmented; perfect, diminished. c. Consonances and Dissonances. Intervals are further classified as consonances and dissonances. By consonance is meant a combination of tones that is complete in itself ; a point of rest. By dissonance is meant a combination of tones which is incomplete in itself ; a point of unrest, or an interval of motion which demands resolution. Primes, octaves, fifths, fourths, thirds, and sixths are consonances. Seconds, sevenths, ninths, and all augmented and dimin- ished intervals are dissonances. I.. INTERVALS S 14. Inversions : Primes inverted become octaves. Seconds inverted become sevenths. Thirds inverted become sixths. Fourths inverted become fifths. Fifths inverted become fourths. Sixths inverted become thirds. Sevenths inverted become seconds. Octaves inverted become primes. Minor intervals inverted become major. Major intervals inverted become minor. Augmented intervals inverted become diminished. Diminished intervals inverted become augmented. Perfect intervals inverted remain perfect. LESSON III CHORDS Aim 15. To define and use two or more intervals simul- taneously. Definition 16. In general, the term " chord " refers to the har- mony of two or more tones of different pitch which are sounded simultaneously. Technically, a chord is a com- bination of three or more different tones, and is formed by erecting upon a fundamental tone, called a root, an ascending series of thirds, and is represented by cor- responding notes on the staff. Preparation 17. Review of Lessons I and II. Presentation 18. Triads. A chord which is composed of three differ- ent tones is called a triad. A triad consists of a root, a third, and a fifth. Triads may be built on any degree of the scale, and are designated by the names of the degrees of the scale upon which they are founded. Therefore a 10 CHORDS 11 triad having the first note of the scale as its root is called a tonic triad; one built on the second degree is called a snpertonic triad ; on the third degree, a mediant triad ; on the fourth degree, a subdominant triad ; on the fifth degree, a dominant triad; on the sixth degree, a sub- mediant triad ; and on the seventh degree, a leading- tone or subtonic triad. 19. Kinds of Triads. There are four kinds of triads — major, minor, augmented, and diminished. A triad can be erected on each of the seven tones in the major diatonic scale. («) ■ I J ^ (&) a= k± I II III IV V VI viio The large Roman numerals I, lY, and Y represent major triads and are designated as primary triads. The small Roman numerals ii, iii, and vi represent minor triads and are designated as secondary triads. The chord erected on vii° is a diminished triad. There is no augmented triad in the major diatonic scale. From (a) derive the definition of major, minor, and diminished triads. Deduce that a major triad consists of a root, a major third, and a perfect fifth; that a minor triad consists of a root, a minor third, and a perfect fifth ; that a diminished triad consists of a root, 12 LESSON PLANS IN HARMONY a minor third, and a diminished fifth. From (h) deduce that an augmented triad consists of a root, major third, and augmented fifth. 20. Progressions : Melodic. There are the following different kinds of melodic progression : diatonic pro- gression by step and by skip, and chromatic progression by step and by skip. ^ I wi §i i (e) ^m i j-^^j^ I m ^t m. rT 21. Progressions : Harmonic. There are the following different kinds of harmonic progression : parallel, con- trary, and oblique. From (c) deduce that parallel or similar motion occurs when voices move in the same direction; from (d) that contrary motion occurs when voices move in opposite directions ; from (e) that oblique motion occurs when one voice remains stationary while the other moves up or down. LESSON lY HARMONIZATION OF MELODIES Aim 22. To harmonize three voices under a given melody, using the primary triads, I, lY, and V. Definition 23. A melody is a series of tones heard successively. The variety is dependent upon the changes of pitch. A melody may be complete in itself, or it may be repre- sentative of changing harmony. It is sometimes used as synonymous with "tune" or 'air." A good melody should consist of a succession of tones rhythmically and symmetrically arranged. In this connection we regard the melody as the leading part, namely, the soprano. To harmonize a melody, therefore, means to construct under the given soprano a bass, alto, and tenor which shall represent the harmony suggested by the melody. Preparation 24. Review Lesson III. Presentation 25. Doubling. As a triad contains but three notes, one of them must be duphcated in four-part writing. For 13 . 14 LESSON PLANS IN HARMONY this purpose the root is the most suitable. While using the primary triads avoid doubling the third. 26. Voice Ranges. The exercises for the present are to be arranged for four voices — soprano, alto, tenor, and bass. The following compass for these voices is suggested : Soprano ^ Alto Tenor -^i Bass i-^i^ , — .. . ^-i -&U (*) For solo singers these limits are frequently extended. 27. Chord Selection. The primary triads of the major diatonic scale contain every tone of the scale, so that a melody may be harmonized with these chords alone. It is evident that the fifth of the tonic triad is the root of the dominant triad, and that the root of the tonic triad is the fifth of the subdominant triad ; therefore, the first and fifth degrees of the scale have two possible harmonizations, while all others have but one. It is evident also that there is no tone in common between the subdominant arid dominant triads. In harmonic progressions two successive chords fre- quently have a common tone. For example, when the triad C-E-G progresses to G-B~D, G is the common tone. It is possible, therefore, to utilize this common tone in the connection of these chords by observing the follow- ing direction : When a given chord progresses to another HARMONIZATION OF MELODIES 15 chord and has a tone in common with that chord, con- tinue this common tone in the second chord in the same voice in which it appears in the first chord. At the same time let the other voices progress from their positions in the first chord to the nearest possible positions in the second chord. Tones in common should be confined as much as possible to the inner voices, in order that the melody may be free and varied. In cases where two successive chords have no note in common, move the three upper voices in contrary motion to the bass. It is always true that triads founded on adjacent degrees of the staff (V and IV) have no note in common. A chord may be repeated in any one of its positions — that is, with the root, third, or fifth in the melody. When the melody has different notes of the same chord it is not necessary to change the harmony, but simply the position of the chord. When a melody repeats a note which is common to two different chords, the har- mony may be changed. This is particularly effective when the repeated note occurs on the accented beat of the measure. 28. Parallel fifths or octaves occur when two voices moving in the same direction progress in perfect fifths or octaves, either diatonically, chromatically, or by skip, and are generally disagreeable. It is, therefore, prohibited that two parts move in perfect fifths, unisons, or octaves. 16 LESSON PLANS IN HARMONY They are often skillfully used by composers with beautiful effect ; but until the student has acquired a broad har- monic foundation and experience, so that he can judi- ciously and effectively employ these progressions, it will be best for him to make no experiments in this direction. Points to be Emphasized 29. The melodic progression of each voice. 30. The harmonic progression of each part in relation to the whole. ^i^ (h) i gfflg d Si- 't^-- 31. Close Position. When the three upper voices — soprano, alto, and tenor — lie within an octave, the harmony is said to be in close position (a). 32. Open Position. When the voices are more equi- distant from each other and the three upper voices cover more than an octave, the harmony is said to be in open position (h). 33. The tones of the major diatonic scale may be har- monized as follows : 1 as the root of the tonic or fifth of the subdominant ; 2 as the fifth of the dominant ; 3 as the HABMONIZATION OF MELODIES 17 third of the tonic; 4 as the root of the subdominant ; 5 as the root of the dominant or fifth of the tonic; 6 as the third of the subdominant ; 7 as the third of the domi- nant ; and 8 as the octave of 1, and therefore harmonized similarly. The following is a typical melody : m g ^ jiJ r J i# ^ LESSON V HAEMONIZATIOX OF BASSES Aim 34. To construct over a given bass an easily flowing melody, with inner voices moving in correct progressions and harmony, employing only the primary triads. Definition 35. The bass is the lowest note in a chord or the lowest part or voice in a composition. To harmonize a bass, therefore, means to construct over a given bass a soprano, alto, and tenor, utilizing for the present the notes con- tained in the chord of which the bass is the actual root. Preparation 36. Review Lesson IV. Presentation 37. The rules given regarding motion and regarding consecutive fifths and octaves (which were treated in Lesson IV) in the harmonization of melodies apply to the harmonization of basses. In (a) we see triads constructed over a given bass, all the common tones being connected. At (h) we see another staff placed above this harmonization, and on it appears a free and easily flowing melody. This melody 18 HARMONIZATION OF BASSES 19 is constructed from tones contained in the chords in (a). By a process of eHmi nation it is possible to reduce this melody, with the four-tone chords beneath it, to a four- part exercise, the inner voices being moved to places as nearly equidistant from each other as possible (c). ^m M^^^g^M e^if rg^^ t S l gJ m With bass given, write a soprano to give the effect of a duet. Avoid monotonous repetition and awkward inter- vals. Then harmonize this soprano and bass. If it is more melodious to place the third of the triad in the soprano rather than the fifth, do so, even if it involves the move- ment of a chord contrary to the suggestions given regard- ing continuance of connecting tones in the same voice. LESSON YI INVERSIONS OF TRIADS Aim 38. To harmonize melodies and basses with other tones in the bass than the root of the triad. Definition 39. By inversion of a chord is meant the placing of one of the notes other than the root in the actual bass. Preparation 40. Review harmonization of melodies and basses. Presentation 41. Since there are three tones in a triad, it is possible to have three different notes in the bass. With the root in the bass the triad is said to be in fundamental position. With either the third or the fifth in the bass the triad is said to be inverted. The inverted chord contains the same tones as when in root position, but the intervals are changed, and from the relation of these intervals to the bass the inverted chord receives its name. a. The tonic triad of C is C-E-G and is composed of a root, major third, and perfect fifth. With the third of the triad, E, in the bass we find that the root, C, is a sixth 20 INVERSIONS OF TEIADS 21 above, and the fifth, G, is a third above the bass, which is E. The name of this chord, therefore, would be 3, but for purposes of convenience the 3 is eliminated. b. With the fifth in the bass we have G as the bass note, and the original root and third form intervals of a sixth and a fourth with the bass ; this inversion is called a % chord. c. These chords should be treated as inversions and not as triads. Inverted chords may appear in two ways, singly or in succession. It is important now to distinguish between the root of the triad and the bass. 42. First Inversion. In the first inversion of primary triads (o) the bass is not doubled, but the root of the triad or the fifth of the triad may be doubled. If the bass is the third of the original triad the third must not appear in the melody. In harmonizing basses involving the use of triads in the first inversion it is well to observe the rule regarding connecting tones. Eight of the available uses of the chord of the sixth are here given. ^''^- 1 . . 1 .2 . . 3 , I 14 ii^^i^k^^^ mM^ -p- -m~ -0~ £* fife IVe IVe 22 LESSON PLANS IN HARMONY g- ti^Hf^^^^ ^i^mk^=^ ^m4#m 43. Chord of the Second Inversion. In the chord of the second inversion (1) the bass is usually doubled. This chord in many places is weak and should be used judiciously. a. Tonic %. This position of the triad is most effec- tive when used at the close of a phrase in a cadence^ (le, V, I) and denotes an establishment of key or a point of rest (h). It may also be used as a passing chord between two chords on V having the sanie bass (c). The tonic % may be used in a repetition of the same harmony to form a melodic bass (/). Barring the use of the tonic % in an authentic cadence, % chords are more melodic than harmonic. Never begin or end a piece with a 4 chord. It may be approached by step (g) or skip (h). When approached by skip it demands great care. {b) (c) {d) ^^ 8=g SEl m^ i ^1 I ^ F le V I V Is V I IV- 4 4 4 1 For definition of cadence, see Lesson IX. (e) IKVERSIONS OF TRIADS (/) (9) 23 m Bs^ Xibiblfai -25^ m J. J ^f:^ ^^ -.^- F ^ 221 J h I le I le I V^ le IV ^ b. The subdominant I is commonly used as a passing chord between two tonic triads having the same bass (d). c. The dominant % is common!}^ used as a passing chord between the tonic triad and the first inversion of the tonic (e). d. The 4 chord may be used between a triad and a chord of the 6th of the same harmony (i). (h) ii ^=^j-^-^,g g^ --& m^^ ^4^^^ ^^^^^ i i IV II h i^d^^ii^ k± V Vj V, I Ij I. :£=pr-S=f^=^=d r^ IV IVe IVe LESSON VII THE DOMINANT SEVENTH CHORD Aim 44. To introduce a new chord to enrich harmonic effects. Definition 45. A dominant seventh chord (sign Vy) is formed by adding to the dominant triad a minor seventh above its root. This is equivalent to adding a minor third to the dominant triad. It is composed of a root, major third, perfect fifth, and minor seventh. It is the same for minor and major keys. Preparation 46. Review of primary triads. Presentation 47. Value of Dominant Seventh Chord. It defines abso- lutely the key, though not the mode. Any combination of notes, therefore, which can be resolved to a major triad and a minor seventh is a dominant seventh chord in a certain key, regardless of the initial signature. In a minor key, however, the raised leading tone, which 24 THE DOMINANT SEVENTH CHORD 25 is the third of the dominant seventh, is always indicated by a chromatic sign. a. Classification. The Vj is a dissonant chord and therefore demands a resolution. By resolution is meant the progression of a dissonance to a consonance. The V7 regularly resolves to the tonic triad; the seventh descends one degree ; the root ascends a f oinrth or descends a fifth. The third (leading tone) may ascend to the tonic, or if it is in an inner voice it may descend to the fifth of the tonic triad. The fifth (when present) descends to the tonic. The root and seventh must always be present. The fifth, or sometimes the third, may be omitted and the root doubled. As there are four tones in the Yy chord it is possible to represent each tone in four-part writing. However, the root is frequently doubled, and in order that the progression of each voice may be more melodic the fifth is frequently omitted, the third less often. b. The Y7 chord may be repeated in different positions before the resolution. c. Entrance of the Dominant Seventh. The seventh may be a prolongation of a tone from the preceding chord (a), page 26 ; it may enter by step (b) ; it may enter by skip (c). Parallel motion is permitted, providing no faulty pro- gressions result {d). This chord permits another bass tone in harmonizing the fourth degree of the scale. 26 LESSOK PLANS IN HARMONY (d) «=*^^ -^ \-2=^ ^& -f^— ,-# w ^. J 22: e f p m ^ Examples of resolutions are seen at {e). (e) V7 complete 5th omitted s i#^ 3d omitted ^ Si f ^^ ?^ ■^t-0- P=T f l# -1*-^ f i SE LESSON VIII INVERSIONS OF THE DOMINANT SEVENTH CHORD Aim 48. To employ the dominant seventh chord in other positions than the fundamental so as to promote variety in the bass. Definition 49. See Lesson YI. Preparation 50. Review inversions of triads. Presentation 51. There are three inversions. Since there are four tones in the Y7 chord, it is possible to have four different notes in the bass. 52. Derivative Figures. The root and the seventh of the original chord are the two characteristic tones which define it, and the figure names by which the inversions of the Y7 are designated are derived from the relation of the root and seventh to the actual bass. The first inversion places the third in the bass, and the root and seventh form intervals of a sixth and fifth ; this chord is known as a 5 chord. In a similar 27 28 LESSON PLAKS IN HARMONY manner show that the V7 chord with the fifth in the bass (second inversion) is a 3 chord ; the Yy with the seventh in the bass (third inversion) is a 2 chord. No tone is omitted in the inversions of the dominant seventh chord. 53. Resolution. The regular resolution of the V7 chord in these inversions is the same as in the original chord; the seventh descends one degree ; the root, never being in the bass, is prolonged into the following chord in the same voice; the third (leading tone) will ascend to the tonic; the fifth may go to any tone in the following chord. The ¥7 inversions may be approached by preparation, stepwise, or by skip. 54. We have now the following possible harmonizations for the different degrees of the scale : a. In the melody, 22: I, le, n IV, IVe, IV| V, Ve, V6 ^7, Vg, vj I, le IV, IVf,IV6 V7, V|, V4 22: 32: k¥. It IV, iv« I ^2 V, V" V7, V|, Y, mVEBSIONS OF THE DOMIisANT SEVENTH CHORD 29 b. In the bass, — ^^ I, IVe ^r ^i IV, Va g IV« LESSON IX CADENCES Aim 55. To define the manner in which certain chords suc- ceed one another to form a harmonic turning point for a rest or close. Definition 56. A cadence is Hterally "a fall"; hence, it is the subsiding of a melody or harmony to a point of rest. Therefore it is any concluding strain in a melodic or harmonic phrase or sentence. It may be either momen- tary or entirely complete. Preparation 57. Review of inversions of triads and the dominant seventh chord. Presentation 58. There are four cadences : authentic, plagal, half cadence, and deceptive. a. The authentic cadence is formed by the dominant triad (often the V7) followed by the tonic triad (a). This form is strengthened when the tonic % precedes the Y7 chord. b. The plagal cadence is formed by the subdominant triad followed by the tonic triad (h). 30 CADENCES 31 c. In these cadences the soprano may end on the third, fifth, or root in the final tonic triad. When the root is in the soprano and the bass, the cadence is said to be perfect. With any other interval in the soprano or bass it is said to be imperfect. d. The half cadence may be considered a reversal of the authentic, for it ends with the dominant triad and is often preceded by the le (c). It is aptly compared to the semi- colon in punctuation, the authentic resembling the period. («) ^ (&) EE •=i< \ ?g=g 11 s grrrHlp_ | zg^ I f^ ^_^-=f^^^ l> V, I 4 IV I 'I e. The deceptive cadence is formed by the dominant triad (or V7), often preceded by the tonic %, and is fol- lowed by an unexpected chord (d). This receives further attention at a later period. /. The succession subdominant, dominant, tonic, is called the complete cadence (e). ^ 11 3? m S-i i fe^ •s ■ _- W LESSON X THE DOMINANT NINTH CHOED Aim 59. To add a chord to the chords already studied, in order to enrich the harmony and to produce a variety of harmonization for certain scale tones. Definition 60. A dominant ninth chord (sign Vg) is formed by adding to the dominant seventh chord a major or minor ninth above its root. This is equivalent to adding a major or minor third to the dominant seventh chord. It is composed of a root, major third, perfect fifth, minor seventh, and major or minor ninth. Preparation 61. Review of the dominant seventh chord and its inversions. Presentation 62. Character. In major keys the dominant ninth is usually major, though occasionally it is chromatically altered to a minor. In minor keys a similar chromatic change from minor to major takes place. 32 THE DOMINANT NINTH CHORD 33 63. As this chord contains five tones, we must omit one when but four voices are used. No tone may be doubled. If the seventh is absent the chord loses its character; therefore the root, seventh, and ninth must be present. As with the V7, the chord is stronger if the fifth is omitted. The third, however, is sometimes omitted in order to obtain a better voice leading. The ninth may be prolonged from a preceding chord (a) or may enter by step or skip (6), not needing to be prepared. (a) 4-v4- is y=j^j=^ k± s ±=t ^ m ^^ i b 4 ^ ^^ ^ V« V» 64. Resolution. This chord, resembling the dominant seventh in harmony, resolves usually to the tonic chord, the ninth descending parallel to the seventh. 34 LESSON PLANS IN HARMONY The customary resolution is for the ninth to descend one degree, the root ascending to the tonic, the seventh descending one degree, the third, if present, ascending to the tonic, and the fifth, if present, either ascending or descending (c). In some cases the ninth descends while the other voices remain stationary, the second chord thus being a chord of the dominant seventh {d). The ninth frequently resolves upward (e). Sometimes it descends a seventh to the third of the dominant seventh (/). If the fifth is present in the chord and lies below the ninth, it must ascend to the third of the tonic to avoid the consecutive fifths which would arise from parallel motion with the ninth (g). (g) Poor Good 65. Inversions. The first (h) and third (^) inversions are the most practicable, although the second (j) may be used if the ninth lies in the upper voice. The fourth is rarely used. The ninth most often is placed in the soprano. It may, however, be in either the alto or the tenor. It is THE DOMINANT NINTH CHOED 35 necessary in four-part writing that the ninth shall always appear above the root and be distant at least a ninth from it. 66. The dominant ninth is effective in harmonizing the descending major scale on the sixth degree {k). LESSON XI CONSTKUCTION" OF ACCOMPANIMENTS AND OF MELODIES OVER ACCOMPANIMENTS Aim 67. The aim is twofold : first, to develop from chord structure rhythmic figures which may be effectively used in accompaniment form ; and second, to exert more free- dom in melodic construction. Definition 68. For definition of melody see Lesson IV. By accompaniment is meant the supplementary part or parts which attend the principal part or parts in a musical composition. The purpose of an accompaniment is to enhance the musical effect. Although the accom- paniment may be independent, it should be subservient to the chief part. Preparation 69. Review Lessons V, VI, VII, VIII, and X. Presentation 70. Accompaniments. Accompaniments are formed in various ways — broken chords, arpeggios, and so on. The 36 CONSTRUCTION OF ACCOMPANIMENTS 37 table given below exemplifies some of the different figures that may be used in accompaniment writing, (a) in the left hand and (b) with both hands. (°) 1 fe ^m^^ ^ ^ ^^ m ^^^^^ m b-^ ^ 10 m ^ tS^rt r U=^ (b) 1 It will be noted that there is constant repetition. This is necessary in order to preserve the fundamental 38 LESSOK PLAKS IN HAEMONY harmony. Embellishments, either chromatic or diatonic, may be used. The student is cautioned, however, against employing these until skill has been developed along more simple lines. At (c) a simple melody is harmonized, employing only such chords as have been used in the foregoing lessons. 'H- w ^ i^4 ^ ^g^g * ^ -»- -f=- ^ Ct%~d -l-i^-j-r+c t-^ f=£==^=^=F^- ^ 1-» 9 p- pS>-r, "^^ it 1 - 1 1 - p— •-A 1 -U '^-- At (d) this same melody appears with simple accom- paniment, based solely on the chords represented in (c). i -^- m "^m t^ k^-^^ d: f CONSTRUCTION OF ACCOMPANIMENTS 39 ^^ ^ ^m * k± m 2^ Experience in writing accompaniments for melodies already harmonized will develop facility and originality. The primary use of an accompaniment is to furnish for the melody a harmonic foundation with strong rhythmic characteristics which shall emphasize the beauty and value of the melody itself. 71. Melodies. In constructing a melody over an accom- paniment such as has been worked out at (d) we may use the notes which are contained in the three upper voices at (c), for at (c) we find the basic harmony for the accom- paniment which is developed. In constructing this melody 40 LESSOK PLANS EN" HARMONY any of the notes may be duplicated; but doubling and faulty progressions forbidden between the bass and any of the upper voices (according to the rules contained in Lesson IV) are also forbidden between the bass and this melody. After a melody has been constructed, passing tones, either chromatic or diatonic, may be introduced as a means of embellishment. a. Characteristics of a Good Melody, The two principal requirements of a good melody are first, that it should be attractive ; second, that it should wear well. While these are more or less indefinite, yet it must be remem- bered that the melodic progression should be of broad song style and as tuneful as possible. 6. The tones of the scale, so far as melodic progression is concerned, are divided into active and inactive tones. The inactive scale tones are 1, 3, 5, and 8, because they inherently suggest rest. The active scale tones are 2, 4, 6, and 7, because they inherently suggest action. The natural tendencies of the active tones are as follows : 7 to 8, 6 to 5, 4 to 3, and 2 to either 3 or 1. Melodies are usually built in phrases of eight measures or a multiple of eight. Melodies in song form are frequently divided by points of partial repose. In this connection " Exercises in Melody Writing," by Goetschius, will be helpful. c. The melodic phase of harmonic study should be emphasized and melodic construction should be carried on conjointly with harmonic instruction. LESSON XII DIRECTLY RELATED KEYS Aim 72. A musical composition of any length would be mo- notonous if it remained always in the same key. In order, therefore, to progress into other keys than the one indi- cated it will be necessary to define those keys whose tonal- ity is so closely related to the original key that transitions may be made without radical harmonic changes. Definition 73. The keys which are most directly related are those whose signatures differ only by one sharp or flat. Preparation 74. Review scale construction. Presentation 75. Different keys are said to be related in proportion to the number of common tones. It follows, therefore, that the dominant and subdominant and their relative minors are the nearest in tonality to any given key. For example : Scale of C : C, D, E, F, G, A, B, C Scale of G; G, A, B, C, D, E, F#, G Scale of F : F, G, A, Bb, C, D, E, F 41 42 LESSON PLANS IN HAEMONY Every tone in G major exists in C except FjJ. Every tone in F major exists in C except Bb. Two major tonic chords may be mutually related to the same key. The tonic triad of C and the tonic triad of D are the subdominant and dominant respectively of G major. A change of tonality convincing to the ear must be accompHshed by means of connecting chords which con- tain one or more tones which are not found in the origi- nal key and belong to the new key. a. When a melody abandons its own key temporarily, it does not usually wander farther away than to one of these related keys. Certain triads are related to more than one key. These triads are the primary triads — the tonic, dominant, and subdominant; and the secondary triads, — supertonic, mediant, and submediant, — which are related to other keys but preserve their function as secondary triads. Their tonality therefore is ambiguous, and the key to which they are related can be determined only by the harmonic context. b. The seventh chords also, on every degree of the scale except the fifth (and seventh of the minor only), may be related to more than one key. c. Transitions into directly related keys are at all times permissible and easily accomplished, but if the change is to be made permanent the modulation must be followed by a complete cadence. DIRECTLY BELATED KEYS 43 76. Relative Minor. Each major key has a minor key rightly called its relative minor; 1 of this minor key is 6 of the major key. These keys have the same signature, the only existing difference being in the raised seventh of the minor key. 77. Parallel Minor. Each major key also has another key related to it called its parallel minor. In such case the tonic of both the major and the minor key is the same note, but the signature is different. LESSON XIII MODULATION Aim 78. To enrich harmonic effects by transitions into other keys without changing the signature. Definition 79. Modulation is a change of key without a change of signature. It is final when the new tonality is definitely fixed. It is transient when the original or a different tonality is speedily reaffirmed. Preparation 80. Review of the dominant seventh and its inversions. Presentation 81. Modulation is effected melodically by the use of chromatic intervals. Illustration : major scale founded on C ; major scale founded on G, involving the chromatic change of F to FJ). A modulation is indicated by the presence of one or more tones found in the key to which we are going. Turn the attention to the harmonic modulation to di- rectly related keys only. For discussion of directly related keys see Lesson XII. 44 MODULATION 45 The triad C-E-G may be the tonic triad of C, the subdominant of G, or the dominant of F. By introducing a dominant seventh founded on C {Q-E-Q-Bp) we have the dominant seventh chord of the key of F. This may be definitely fixed by an authentic cadence, or it may be transitory. 82. Deduce the fact that to modulate from a given key to the key founded on its subdominant we take the tonic triad of the original key and add a minor third to form a dominant seventh chord, which resolves to a tonic triad founded on the subdominant (a). . 83. To modulate from a given key to its dominant. In the key of G the dominant seventh is D-Fjf-A-C. It is evident that the seventh of this chord is the tonic of our original key and that the root is the supertonic. There- fore if we build up a dominant seventh on the supertonic of our given key, this dominant seventh chord of the new key may enter by preparation from the tonic triad of the original key, and we may modulate to the key founded on the dominant (h). («) (f>) C*^) i ;i^s :ia— s^ :1P2: 1^ (<0 9^^. ^^ -JtZMl j^ ^ -p- -f^-^ -^^-^ m \t^ i^zzz^ s r CI FVt I CI GV7 I CI aV^I 46 LESSON PLANS IN HARMONY £^E r1: I w. f=r=h s* 1*=^=^ ££ ^ ^ ^^ f r^ 84. At (c) is indicated the modulation from a key to its relative minor. We note that by taking the mediant of our original key and building up a dominant seventh upon it we modulate to the relative minor. The third of our original key, which in (c) appears in the alto, becomes the root of the dominant seventh of our new key and so forms a point of connection for this modulatory chord. a. The new key is usually first indicated by the pres- ence of the new sharp (which appears on the leading tone) in sharp keys and by the presence of the new flat in flat keys. Modulations, however, take place when the melody is written in such a way as to indicate a modulation with- out chromatic evidence (d). In such cases it is possible to feel the modulation by hearing the melody. No rule can be given for the introduction of such modulations. They result from constant experience. b. On page 47 appear two melodies (e) and two basses (/). In the first exercise of each the modulation is indicated by chromatic changes. In the second exercise in each case the modulation is indicated by a cross. Plenty of drill and experience in modulation should be developed MODULATION 47 by applying the foregoing discussion to the harmonization of melodies and basses. $ (e)l m a: ^ ^S3 It* *-a^ t=tl k=^- m m^ i i^ ^■-^■i I=t: tFH=2= -^=2- 4=# < = ^ * # s: ==t ah'^^ t/ DVj GI DV, — $ » r ^ » =t: t=f 1=^ H I V7 I IV I — V7 V GV7 I I CV I X J n ft 1 1 , 1 X X i yS 1 m 1 l>r J i J J >• j» r 1 ~— ^ ^ N*- ■ l/p \ -=- ^^ i=^ -iS> — frg^ Bbv, FV CVe P^ ^^ 3=3 m s^ FL GVj I DVj P A_^ ^__^ r-r-r t=^ -^^ I GV^ I CVo LESSON XIV SECOND AEY TRIADS Aim 85. To introduce the minor triads of the major diatonic scale. Definition 86. The secondary triads of the major scale are those triads formed on the supertonic, mediant, and submediant of the diatonic scale. The leading-tone triad is practically never employed in fundamental position. Preparation 87. Review of primary triads. Presentation 88. Relation. The secondary triads may be regarded as the relative minors to the primary triads : supertonic to subdominant, mediant to dominant, submediant to tonic. 89. Supertonic Triad. This triad is the most important of the secondary triads. In using the subdominant triad the root is always doubled, and as the supertonic is the relative minor of the subdominant, the third of the super- tonic triad is often doubled, especially after a tonic chord. a. Uses : (!) To precede the dominant seventh or a tonic 4 triad in a complete cadence as a substitute for the 48 SECONDAEY TRIADS 49 subdominant (a) ; (2) as a passing chord between the tonic triad and its first inversion (&). It may also be used before the subdominant in any position (c) or before the dominant in the first inversion (d). b. When the supertonic triad is followed by the domi- nant in root position contrary motion is preferable to the prolongation of the common tone in the next chord. One reason for this is that contrary motion produces a smoother effect on account of the two consecutive major thirds which would otherwise result between the alto and the tenor. For example, the supertonic triad in the key of C is D-F-A. If we double the root, D, and continue it in the same voice in the next chord, which is G-B-D, we find that the bass will move to G, and the two voices which in the first chord occupy the staff degrees F and A will progress to the staff degrees G and B. These are the only two consecutive major thirds in the diatonic scale, and the effect indicates a false relation of the tri- tone, which is the augmented fourth F-B and contains three whole tones. t fe =i^=j-l^dJJ l ;3' l J j | g-t-l F m .^ .^^ .^2. :^2: fe£ EmpFfF ^^ II IV II IV« He IV 50 LESSON PLANS IN HARMONY (d) (e) (/) (g) g^i^#rtl##^ II V II . Vs V7 VI I VI IV I III IV 90. Submediant Triad. The submediant, the relative of the tonic, follows in importance. It is used (1) instead of the tonic, to succeed the dominant or dominant seventh and forms a deceptive cadence (e). In the succession Y vi it is customary to double the third in vi. If the leading tone, however, is in the soprano voice it may descend to the root of the submediant triad. (2) The submediant triad is used as a connecting chord between the tonic and subdominant triads (/). Other progressions are submediant, dominant seventh; sub- mediant, tonic 1; and submediant, tonic 6. It may also be followed by the supertonic triad. It is best to retain the connecting tone in these progressions in the same voice, or move in contrary motion to the bass. 91. Mediant Triad. This chord is the least important of the secondary triads. Its principal use is to harmonize the leading tone in the descending melodic succession 8, 7, 6 (g). As the third of this triad is the root of the dominant, it is frequently doubled. It is best preceded by the tonic or dominant and succeeded by the tonic or subdominant. / SECONDARY TRIADS 51 92. In general, the progression of a secondary triad to its relative major is not desirable, but the progression of a major triad to its relative secondary triad always produces good effect. General Rules for Progression 93. When there are no connecting tones, employ con- trary motion. When there are connecting tones use parallel motion when these tones are prolonged in the same voice in the next chord. When they are not prolonged, use contrary motion. Move to the nearest position of the succeeding chord. Avoid awkward progressions of augmented intervals in all voices. Avoid too frequent harmonic changes. The third of the secondary triads being the root of the subdominant, dominant, and tonic, respectively, is fre- quently doubled. In two successive chords of the first inversion double the root or fifth, then the third, or vice versa. In three successive chords of the first inversion with ascending diatonic bass double the fifth, third, and root in succession. Some very common progressions with triads are I-IV, I-V,I-vi,I-iii; ii-Y,ii-vi; iii-vi, iii-IY ; lY-I, lY-ii, lY-Y, Y-vi, Y-iii, vi-IY, vi-ii, Yi-iii, Yi-Y, and I-yi- lY-ii when the bass descends in thirds. 52 LESSON PLANS IN HARMONY 94. The various degrees of the major scale may now be harmonized with chords and their inversions as follows : a. In the melody, n ^ 1/ Irr X ^-■, f^ iV^iy "-^ J f) ft IV, IVe, IVJ VI, vie^ vi| 11, He, Vs I, l6 4 4, /ft c:^ ^^ \ l>f^ rLJ 1 lir \ 1 Iv J 1 t> IV, IVe,V, V9, II I, III V, V7, v« IV,IV6. V9, vi' II V, V„ V, III &. In the bass, P ^ I, IVe, Vl6 Ve, V4. II, 4 8 III. Vlfl ^^ 22: :22: IV, Va, V« V, V7,V9,l6 IVe, "e, vi lie iiie * * Ve. V«, V» IIIr * LESSON XV SUSPENSIONS, PASSING TONES, AND APPOGGIATURAS Aim 95. To introduce into the melody, or other parts, tones common and foreign to the fundamental harmony, but which do not demand special harmonization. Definition 96. Since the tones of a chord are called harmonic tones, nonharmonic tones may be defined as tones com- bined with a harmony to which they do not belong. Preparation 97. Review triads and chords of the seventh and ninth. Presentation 98. Passing Tones. Passing tones are nonharmonic tones that occur between harmonic tones of two successive chords. They may be either diatonic or chromatic and may occiu* in any one of the four voices (a), page 54. 99. Auxiliary Tones. An auxiliary tone is a non- harmonic tone which returns to that tone from which it started. It produces a dissonant effect with at least a part of the chord with which it is sounded. It proceeds 63 54 LESSOK PLANS IK HAEMOKY upward or downward from its principal tone by a major or minor second, and is unaccented (h). 100. Changing Tones. The changing tone is a non- harmonic tone occurring on the unaccented part of the measure. It usually moves over the skip of a third (c). 101. Appoggiatura. The appoggiatura is a tone foreign to the chord with which it occurs and must resolve upward or downward. It may enter freely from any tone of the preceding chord without preparation. It may appear in any voice, but is more easily distinguished when it appears in the upper voices.. It may occur in two or more voices at the same time. It differs from the suspension (see § 102) in not being prolonged from the preceding chord, but enters by step or skip (d). $ S=#=^.F^ta i i (&) ^^ m±:^. ^ ^-J^ ^ if-^-r-^F^ ^-^^ fe^ m m- ^ i M: (C) X X (<0 (0 1=1=3^ 1^ — I 3~ it=aL 2^ g ■* — * % m ^- m ^m- 4=t: ^ SUSPENSIONS 55 « 102. Suspension. A suspension is the prolonging of a tone in one chord to the following chord, in which it creates a dissonance and therefore requires a resolution. The tone of the first chord is said to be suspended, and is resolved by proceeding upward or downward to its proper tone in the final chord. a. The sounding of the tone in the first chord is called the preparation; its dissonant sounding in the second chord, the suspension; and the final progression of the suspended tone to its proper tone, the resolution (e). h. Any interval may be suspended in any voice, pro- vided it eventually progresses diatonically. When two or more tones are suspended the suspension is termed double, triple, and so on. c. The laws governing suspension are few. The sus- pended tone must usually be prepared in the same voice in which it is to be sounded as a dissonance (e), page 56. d. The suspension usually occurs on an accented beat, though not necessarily on the strongest accent. e. In a great majority of cases the tone of preparation is at least as long as that of the suspension. /. The characteristic of a good suspension is its dis- sonance and the strongest suspensions are those which form a second, seventh, or ninth with one of the tones of the chord (/). g. Suspensions without the dissonant element are generally weak (^). 56 LESSON PLANS IN HARMONY h. When double and triple suspensions occur they often form combinations of intervals identical with secondary triads and chords of the seventh (A). Triple suspensions occur frequently in the authentic cadence {i). i. The most difficult problem in the treatment of sus- pensions is to determine when the tone of resolution may be anticipated in some other voice. The resolution to the root in the soprano is often anticipated in any one of the other voices {j). (0 O") (k) Bad Good ^^^^^p^^a^ ^ -Aj. i^ j" \'j =p S Jr:^ iJ:rJ_j izs: 22: J. When the tone of resolution appears in the same chord with the suspension, a dissonant seventh or ninth is inevitably formed. Since the ninth never lies less than SUSPENSIONS 57 nine degrees above the root, it should be noted that (1) the resolution of a suspension may appear in another voice simultaneously with the suspension itself if it is a ninth below the suspension, but the two tones must never appear simultaneously in the same octave (k) ; (2) the effect is harsh when the suspension occurs in the bass and the note of resolution appears in an upper voice in the same chord (l). k. When the suspension takes place before the leading tone, the resolution should never be anticipated (m). /. At the same time that the suspension resolves, the rest of the harmony may be changed in any manner which does not interfere with the suspension itself. Some- times the suspended tone fails to resolve and is absorbed in the succeeding harmony. It is also occasionally re- solved chromatically. m. The resolution of a suspension may be delayed, either by the introduction of harmonic tones or by nonharmonic tones in the form of an embelHshment. i^ (0 (m) Poor (n) m -ll^r m^^-^ ^ r^r=r- g=^ ^ n. A suspension which resolves upward is called re- tardation. 58 LESSON PLANS IN HARMONY 103. Anticipation. The anticipation is the opposite of the suspension and is an unaccented tone which moves to its position in the next chord in advance of the other voices. The anticipation may occur in two or three voices at the same time (n). 104. Melodic Figuration. Melodic figuration indicates the process of elaborating a melody or theme in any voice by varying it with nonharmonic tones, as well as harmonic tones. Scale passages and arpeggios are frequently used. When the diatonic progression of any voice is chromati- cally altered, tones are introduced which are foreign to the key. Harmonically such tones may indicate modulation; melodically, however, they do not affect the relation of the chords to one another nor do they signify special harmonization. No rules can be given for the selection of nonharmonic tones in melodic figuration. Simply avoid unmelodious progressions and develop a melody which is rhythmic and tuneful. 105. Chromatic alterations may be written enharmoni- cally to facilitate greater simphcity of notation. For definition of enharmonic see Lesson XVIII, page 70, LESSON XVI THE MINOK MODE Aim 106. To construct and use triads and chords in the minor mode. Definition 107. Minor compared with major means smaller. The minor mode is founded on the minor scale, in which the keynote and the note on the third degree of the scale form a minor third, and the tonic triad is composed of a root, minor third, and perfect fifth. In the major scale the keynote and the third degree of the scale form a major third, and the tonic triad is composed of a root, a major third, and a perfect fifth. Preparation 108. Review of principal triads, chords of the seventh and ninth, secondary triads, and directly related keys in the major mode. Presentation 109. Every minor scale has the same signature as its relative major, and the raised leading tone is in every case indicated in the music itself. On each of the seven 60 LESSON PLANS IX HARMONY tones of the harmonic minor scale can be erected a triad. In classifying these triads we find there are two minor triads, two major triads, two diminished triads, and one augmented triad. The minor scale presents more variety than the major, as it has three dissonant triads (ii°, vii°, III+). fl. A marked feature of the harmonic minor scale is the augmented second between the sixth degree and the leading tone. The augmented second is of great effect when used in a melodic way, but it is better avoided in chord progression. On account of this fact, in the progres- sion from the supertonic triad to the dominant employ contrary motion (a). (a) Poor Good b. The points to be observed in the minor mode are the introduction and resolution of the three dissonant triads — supertonic, mediant, and leading tone. The augmented triad III + is seldom used in root position, but is more effective as a chord of the sixth. However, at (h) we see the augmented triad in root position resolved to the THE MINOR MODE 61 submediant. It may also resolve to the supertonic and to the subdominant. In the latter case it is better to double the third in the augmented triad. At (c) the mediant triad appears in the first inversion and it resolves to the dominant or dominant seventh. c. The diminished triad on the leading tone is seldom used in root position, but as a chord in its first inversion it is employed frequently (d). The bass is generally doubled, though the fifth may be doubled according to the leading of the voices. i id) (e) (/) (g) ^ ^ lEf^ ^^ w^^ 'H—:^ m=f ^^- ^ i f VI d. When the dominant is followed by the submediant (V, YI) in the minor mode, the voices must progress in certain directions in order to avoid consecutive fifths and augmented intervals. The leading tone ascends to the tonic or descends from it in order to avoid an augmented second (e), and two of the upper voices must move in contrary motion to the bass. In four-part writing the third is frequently doubled in the submediant triad (/). e. In the succession YI, Y the same arrangement of voices is followed. In a descending soprano or bass the 62 LESSON PLANS IN HARMONY melodic form of the minor scale is frequently used {g). The minor seventh when so used is generally harmonized with the chord of the sixth. 110. With this explanation of the minor mode, proceed with the instruction exactly as in the major mode, first employing the triads (i, iv, and V) and their inversions in the harmonization of melodies and basses ; then the V7 and its inversions, and so on until facility is developed in the minor mode, before combining it with the major. LESSON XVII SECONDARY SEVENTH CHORDS Aim 111. To introduce into the harmonic structure chords of the seventh f oimded on other degrees than the dominant. Definition 112. Secondary chords of the seventh are those chords whose roots are on other degrees of the scale than the dominant and are formed by adding a third to the upper interval of the tonic, subdominant, and secondary triads of the scale. Preparation 113. Review the dominant seventh chord and secondary triads. Presentation 114. In the treatment of secondary seventh chords we will confine ourselves mainly to the chords on the tonic, super- tonic, and leading tone. The harsh effects of secondary seventh chords are mitigated when the secondary seventh chord is prepared in the preceding chord (a), page 64. It is best that either the seventh be prolonged in the 64 LESSON PLAKS IN HAEMONY same voice from the preceding chord or that the root be prolonged, in which case the seventh may descend. (a) 1 2 (J) ^iS ^ . J- -i t i ^ r^ g f^ r 115. The chord of the seventh founded on the super- tonic is used to precede the dominant or tonic triad in a complete cadence (6). It is used similarly to the super- tonic triad, as the supertonic seventh chord is a combina- tion of the tones of the subdominant and the supertonic triads. The 1I7 will strengthen the harmonization where the supertonic triad has hitherto been used. • a. The seventh may appear in any voice and may be introduced as a connecting tone with the tonic triad (c). It may also be used as a descending passing tone between the second and seventh degrees of the scale (d). I le 117 I IV II 117 V IV 1I7 V7 IV II, SECONDARY SEVENTH CHORDS 65 b. There are two resolutions in common use: (1) to the dominant chord with or without the seventh (d) ; and (2) to the tonic chord or one of its inversions (&), in which case the seventh is prolonged into the follow- ing chord. The seventh may be prepared from the sub- dominant (e), may enter as a passing tone (d), or by skip from another note of the subdominant or supertonic chord (/). c. The inversions of the 1I7 chord present no new diffi- culties. The introduction, resolution, and uses are the same as when the chord appears in fundamental position and are similar in both major and minor keys. The seventh (when not prepared) enters most effec- tively in a 5 chord. Contrary motion between the root and the seventh is more harmonious than parallel motion. The first inversion of the supertonic seventh is the most useful, although the second and third may be used but are better when introduced with preparation. Some of the common progressions are: I, lie, V; I, 1q, He; IV, lie, le ; II4, le; 114, Ye- 5 54 3 4.25 116. Leading-Tone Seventh. This chord of the seventh is like the dominant and never requires preparation. This is also true of the inversions. The tones are iden- tical with those of the dominant ninth minus the root. In the entrance of this chord the seventh may be pro- longed from the preceding chord or may enter by step or skip. 66 LESSON PLANS IN HARMONY a. The regular resolution is like that of the Y7 (see Lesson VII). The seventh descends one diatonic tone, the fifth descends one diatonic tone, and the third ascends or descends according to the circumstances. iJ) . (9) I {h) (i) ^m x=i mn ipp 1= \ Eg f V4 3 (A:) i4^-J-4-j=J4J==J--JH=i^i=^ y^^^^444^m 1V7 VI7 h. The root, being the leading tone, has a strong ten- dency to ascend to the tonic {g). Sometimes, however, it ascends to another degree (A). This may be observed also in the progressions YII7, Yi or Yii?, Y2. c. No note of this chord may be omitted or doubled when the chord is in either fundamental or inverted position. There are instances when the seventh may fail to resolve, being prolonged in the same voice into the next chord. d. In Lesson X we found that if the fifth of the Vg lay below the ninth, it must ascend in the chord of resolution SECONDARY SEVENTH CHOEDS 67 in order to avoid consecutive fifths (§ 64). As the third of the leading-tone seventh is the same as the fifth of the dominant ninth, it follows that in the yii° chord if the third lies below the seventh, it must ascend in the chord of resolution; otherwise it may ascend or descend. e. The most useful inversion is the second (^), although the first is frequently used. The third inversion is harsh, but may be used as a passing chord, in which case it usually resolves to the tonic 4. General Statement 117. The chords of the seventh formed by adding a third to the upper note of the tonic, subdominant, and secondary triads of the scale are much more restricted in their use than the dominant seventh and dominant ninth chords. All secondary sevenths, barring the supertonic and leading-tone seventh, may be regarded as suspensions and passing chords and be treated as such. The tonic seventh is best used in its first inversion in harmonizing the descending diatonic scale {j). At {k) see some progressions with secondary seventh chords other than those already discussed. Their similarity to suspensions is readily apprehended in these progressions. LESSON XVIII DIMINISHED SEVENTH CHORDS Aim 118. To introduce into the harmonic structure a chord foreign to the harmony and suggestive of modulation, but not necessarily productive of it. Definition 119. The diminished seventh chord consists of a root and succession of minor thirds and contains the intervals of a root, minor third, diminished fifth, and diminished seventh. Preparation 120. Review secondary seventh chords. Presentation 121. Character. The chord of the diminished seventh is ambiguous, forming a strong contrast to the dominant sev- enth. No note may be omitted or doubled in either the orig- inal chord of the seventh or any of its inversions. It may be freely introduced in either the major or the minor mode. $ a c e flat f sharp 68 DIMIKISHED SEVENTH CHORDS 69 There are three chords of the diminished seventh on the piano keyboard (a) ; each chord may be enharmonically written in four different ways (&). At (a) it will be noted that all the different tones contained within an octave on the keyboard are used in the spelling of these diminished seventh chords. 122. Relation. In determining the key to which the diminished seventh chord belongs, ascertain the root upon which the chord is founded, which is the leading tone of the key to which the chord resolves. It will be seen at (b) that the root or leading tone in the first chord is G^; in the second chord it is Bfcj; in the third chord it is Db^; and in the fourth chord it is E$t. These chords respectively resolve to the key of A (minor or major), to the key of C (minor or major), the key of Eb (minor or major), the key of Fjif (minor or major). In a similar manner the chords in the second and third groups under (6) may be resolved. It will be noted, therefore, that as each diminished seventh chord has four possible representations, we may introduce the chord most closely associated to the key in which we are and, by means of an enharmonic change, modulate to a key more distantly related. 70 LESSON PLANS IN HAEMONY 123. Enharmonic Changes. When we employ chromati- cally altered chords we must use enharmonic tones. En- harmonic tones are tones which appear on different scale degrees, but which are practically identical in pitch, as FJf and G>. By enharmonic change we mean changes effected in the harmonic relations of a tone or chord so that it may be identical in pitch with another tone or chord but differ in notation, as at (6), on page 68. The resolution of the first chord in this illustration would be to the key of a minor. By employing the enhar- monic change, however, of Gj:f to At? a different resolution results on account of the changed tonality, and the second chord resolves to c minor. (c) Poor (d) Good (e) y^ (/) 3^ji^i^"=r^r? ^g s^ ^ F^ ^ F r d E^3S & m ^- n (9) w^ ^ m {h) (0 i DIMINISHED SEVENTH CHOKDS 71 124. Approach. The diminished seventh chord may be prepared in the preceding chord or it may be approached stepwise or by skip. It may also be approached by paral- lel motion. It is sometimes approached in modulation in such a way that a so-called cross relation is formed. 125. A cross relation, sometimes called false relation, occurs when a note appearing in one voice simultaneously or in a succeeding chord appears in another voice but is chromatically altered. The effect is most harsh when we pass from a major chord to a parallel minor or vice versa (c). There are times, however, when this cross relation is of good effect {d). 126. Resolution. The diminished seventh may be fol- lowed or preceded by the same or another diminished seventh chord or one of its inversions (e), by a V7 chord or one of its inversions (/), but the usual resolution is to the tonic {g) in minor or submediant in major. It may re- solve to the tonic in major. The seventh may be resolved downward ; it may be prolonged into the next chord ; and it may occasionally ascend. The root usually moves to the tonic. It may, however, be prolonged into the next chord or even descend. This latter resolution takes place usually in modulation. When the chord of resolution is a triad, the third or the fifth of the triad is frequently doubled. 127. Uses. The diminished seventh chord is freely used in the major mode by altering the minor seventh chromati- cally (li). It differs from the dominant seventh only by 72 LESSOR PLANS IN HARMONY one semitone (^) ; therefore the second, fourth, and seventh degrees, which are common to both the dimin- ished seventh and the dominant seventh, may frequently be harmonized equally as well by one as by the other. The diminished seventh chord is most effective in modulations. 128. All the inversions are useful and the resolutions are as follows : the first inversion of the diminished seventh usually resolves to the first inversion of the tonic with the third doubled ; it may however resolve to Vie (IVe in major) or iVe (lie in major). The second inversion usually resolves to tonic triad (first inversion) or Vie, while the third inversion may resolve to the second inversion of the tonic or to VI or V in funda- mental position. 129. It is advisable that the student write out these resolutions of the diminished sevenths, both in root posi- tion and also in inverted form, and that he play them, so as to become famihar with the musical effect. LESSON XIX EEMOTE MODULATION Aim 130. To gain a knowledge of modulation to indirectly related keys. Definition 131. Remote modulation is modulation which proceeds from one key to a key foreign in tonahty, by introduc- ing two or more tones foreign to the key in which we are and belonging to the key to which we are going. Preparation 132. Review modulations as presented in Lesson XIII, and the minor mode as presented in Lesson XVI. Presentation 133. The succession of different keys does not neces- sarily constitute modulation. Modulation may be tran- sient, or it may be more permanent in character. (See Lesson XIII.) In the latter case it must not only define a new key but it should remain in that key long enough to necessitate a distinct modulation in order to return to the original key. 73 74 LESSON PLANS IN HARMONY a. It is possible to modulate to keys more indirectly related than the keys of the dominant and subdominant and their relative minors. We will now consider some specific modulations to indirectly related keys. In order to determine the modulations to these keys we will state the plainest and most definite means of harmonic progression. b. Modulation from a Key to the Major Key founded on its Supertonic. At (a) we note that the dominant seventh of the new key to which we are going is founded on the submediant of the original key, and by the pro- gression C I VI, D Vy I we effect a change of key which is pleasing to the ear. It is possible to go immediately from the tonic triad of C to the dominant seventh of D (6), as there are two tones in common between the tonic triad of C and the dominant seventh chord of D. This progression is equally satisfactory for modulating to d minor. c. Modulation from a Key to the Major or Minor Key founded on its Mediant. We may progress by the domi- nant seventh of our new key (c). In the progression C I, E Y7 1 it is best to double the third of the tonic triad REMOTE MODULATION 75 on C in order to avoid the progression of an augmented second from C to Dj;}. We note that the root of the dominant seventh chord of E is the leading tone of onr original key. We may, however, modulate through the diminished seventh chord, and this progression is smoother, because the root of the original chord becomes the seventh of the modulating chord {d). d. Modulation from a Key to the Key founded on its Suhmediant. As the tonic of the new key is the rela- tive minor of the original key, we may progress imme- diately by means of the dominant seventh (e), the root of which is the mediant of the original key. The effect, however, of the major triad immediately following the dominant seventh chord is unexpected, for the third of this chord is a chromatic alteration of the tonic of our original key. In order, therefore, to make this modula- tion more euphonious, we may have the progression Cvi, aVji, DVel, AV,I(/). (0 (/) pN^^^pg=js;EfeE8j^^ ^Ttffff^^ §^ ^ e. Modulation from a Key to the Major or Minor Key founded on its Leading Tone. The modulations upward 76 LESSON PLANS IN HARMONY and downward a diatonic semitone are important, although somewhat abrupt. They are effected through the domi- nant and diminished seventh chords and also through the augmented chords. (See Lesson XX.) In modulating a minor second downward by means of the dominant sev- enth chord we note that the third of the original triad is the seventh of the modulating chord and is written in the same voice. The fifth descends a semitone ; one of the roots is chromatically altered ; the other descends a minor third to the third of the modulating chord (g). The dimin- ished seventh produces a smooth effect at (h). (0 ^ U) 1 j ^-^i Ffe=n ■' ^ — -gy |-| < c? !7 ( C:? 221 m: ig: ^t p- - p gptff^ _ -p- -^ F'Ff=F ^ #=t==:^^-: ]to: ^^>- -■^tLs :(^)|^ ^2=^ ^-• ^g=|^ ^ p }j ^ -^ -(S^ -f^ bhs- ^ ?2: £ ii=^ b==fe /. In this connection we may consider the modulation a minor second upward, using the dominant seventh chord (i). The root of the original tonic triad becomes the REMOTE MODULATION 77 third of the modulating chord. The third becomes the fifth of the modulating chord (chromatically altered by a flat), and we have the progression CI, D!? V7 1. In modulating upward a minor second through the diminished seventh chord the root of the original chord becomes the root of the modulating chord. The third and the fifth are chromatically lowered, and the seventh is added to the chord (j). In this modulation it is better to write the diminished seventh enharmonically, as it avoids the visible augmented second caused by the descent from the root of the original triad. g. The most abrupt of all modulations is that of an augmented fourth or a diminished fifth, and is most effective when the third inversion of the dominant seventh chord is employed and all the upper voices progress in contrary motion to the bass (k). h. Below are given examples of other modulations to indirectly related keys, with the figures denoting the key and chord appearing beneath them. By analyzing these examples the student may deduce for himself the formula employed. 1 o ■^^ ^M t^ W=f-=f ^ ^M- fe^ :*K -^ :^=tE=^ F Ito: CI I fvii° le At7ii( 8 78 LESSON PLANS IN HAEMONY $ t ± 2fc:fe 3 ^ — ^-^1 g=Ffe ^^_ -.^ -<=2. ^^ :te=«tc rtt ? F -i — r CI dvii° Bble IV I, I CI fVa I ebvii° Eble z. When we modulate from a key to its dominant we add one sharp or its equivalent to the signature ; from a key to its subdominant, one flat or its equivalent ; to its supertonic, two sharps ; to its mediant, four sharps ; to its submediant, three sharps ; to its leading tone, five sharps. When we modulate from a key up a minor second we add five flats or the equivalent; up a minor third, three flats; up a minor sixth, four flats; down a major second, two flats; up a diminished fifth, six flats. Students are urged to work out a formula for each modulation and to play these modulating passages in different keys. 134. Since the modulating chords, the dominant and diminished seventh, may be preceded by and resolve to both major and minor tonics, the modulations already given are sufficient to cover all changes of key. a. Many enharmonic changes occur in modulations be- tween sharp and flat keys. The difference in tonahty between two keys is indicated by the difference in the num- ber of accidentals in the signature. The keys of Grb and FJf major, C# and J)\> major, may be considered as identical. KEMOTE MODULATION 79 b. Practically any chord may be used to effect a change of key. As secondary triads and the secondary seventh chords belong to more than one key, they may be used as a modulatory means. c. Abruptness and monotony should always be avoided. Generally it is not best to proceed by the most direct means, but it should be borne in mind that in all mod- ulation we should first choose the connecting chords which lead to the new key. Between certain keys there is very little logical connection and a modulation to keys so dis- tantly related is effected only in a roundabout manner. Proficiency in modulating is not acquired by learning rules. Individual investigation is necessary, and the stu- dent is advised to write out the following modulations and also to improvise similar ones at the keyboard : A to B, Db to F, B> to D, FJf to a, D to f, Ei? to b, B to g, and so on. LESSON XX CHROMATICALLY ALTERED CHORDS Aim 135. To introduce chords formed by chromatic altera- tion which do not have a definite key tonahty. Definition 136. Chromatically altered chords are those chords in which certain tones are chromatically raised or lowered and which are not found in regular scale series. Preparation 137. Review of Lesson III. Presentation 138. The third of the triad denotes the mode (major or minor). Either the root or the fifth may be chromatically altered, but those triads in which the fifth is altered are more commonly used. The most important altered chords are those which result from chromatically changing the minor third to a diminished third when the chord is in fundamental posi- tion. This may be done by chromatically raising the lower tone, or lowering the upper tone. When the chord is inverted, this diminished third becomes an augmented 80 CHROMATICALLY ALTERED CHORDS 81 sixth. It is from this augmented interval that some of the chords derive their names. It is customary to present these chords in inverted position. 139. A very useful altered chord may be formed from the supertonic triad in the minor mode. As this chord contains a diminished fifth the dissonance is somewhat unsatisfactory. It may be altered by lowering the root and usually resolves to the dominant or tonic. It is most useful when used in the first inversion, though the fun- damental position or the second inversion are not pro- hibited. This chord founded on the second degree of the minor scale, with its root chromatically lowered, when used in the first inversion is called the Neapolitan sixth (a). This triad on the second degree of the minor mode may be altered by allowing the root to remain unaltered and chromatically raising both the third and the fifth (h). Although derived from the minor mode, the Neapolitan sixth may be found in the major. 140. The Augmented Sixth Chord. The triad founded on the fourth degree of the minor scale, sometimes reckoned as the second degree of the major scale, may appear with 82 LESSON pla:n^s in harmony its root chromatically raised and usually appears in the first inversion. It is known as the augmented sixth chord or the Italian sixth (c). In four-part writing it is cus- tomary to double the fifth, and one or both of these fifths usually appear below the root. 141. The augmented sixth chord may be formed by raising the root of the minor triad (either the supertonic or the submediant) in a major key [d). The mediant is not useful because the raised root would resolve out of key {e). In the minor key in addition to the subdominant it may also be formed on the tonic ' {d), or it may be formed by lowering the third of a diminished triad on the leading tone of either a major key or a minor key (/). It is not usual to employ the supertonic in the minor. I (^) (/) 3: ig) 22: m n^^ ?=: H^ ^ ' C Major a Minor m-. 142. The Augmented % Chord. This is the first inversion of the chord of the seventh founded on the fourth degree of the minor scale, with its root chromatically raised, and is commonly called the German sixth {g). In sound this chord is identical with the V7 in B flat. This en- harmonic relationship is most useful in modulation. CHROMATICALLY ALTERED CHORDS 83 In addition a similarly altered chord may be founded on the degrees of the supertonic and submediant in the major (h). As the subdominant in the minor is the same as the supertonic in the major, we see the resolution of that chord at {g). A chord founded on the mediant would resolve out of key (see illustration {e)). It is possible to use the augmented 5 chord in fundamental position or in the third inversion. 143. The Augmented 4 Chord. This chord, called the French sixth, is the second inversion of the chord of the seventh founded on the second degree of the minor scale with its third chromatically raised [i). In harmonizing melodies the bass formed by lowering the second degree of the scale is often used instead of the dominant 4 (j). ii (0 01 ^g ii^ 3 :ff^ i: ^ > m 5^ ^^ ^^=^ :zz An altered chord need not be preceded by the original chord, unaltered, but it may be preceded by any chord which permits a correct progression. Generally speaking, altered chords resolve to tonic or dominant, but freer resolutions are allowed and the tonality is determined by the chord of resolution. 84 LESSON PLANS IN HAEMONY 144. We may also have the following chromatically altered chords. 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Renewed books are subject to immediate recall. M.a.R 1 1959 RECP Ml IS FEB 20 1959 OCT 2 3 1959 NOV 1 8 1959 iflN?7^4fl£0 jSnIX m FEB 23 1972 OCT 6 1977 MAY 1 2 1984 LD 21-50m-8,'57 (,C8481sl0)476 i General Library University of California Berkeley f^ MT50.L4 C0371 42394 U.C. BERKELEY LIBRARIES CD37mE3TM DATE DUE Music Library University of California at Berkeley .;tm 1 1 Wlmml iUitiiiuMittiiii IliiiiiittMtiiid