OND YEAR rºomas rapper *NUp ºrmiſſing É sº E. B | i THE GIFT OF Anne Hamer P nº m., " " . . . . 22 F.T. - P ** = y - is --- . BALLARD; RECoRos-sheet Music . . 13 O G SEREET - N.W. Phones: NABL (M1404.5 ° AUGMENTED AND REVISED EDITION Second Year Harmony (A Sequel to “First Year Harmony”) BY THOMAS yarres, Litt. D. →r Price, $1.25 met THE ARTHUR P. SCHMIDT CO. BOSTON NEW YORK 12o BoyLSTON STREET 8 West 40TH STREET Copyright 1912, by ARTHUR P. ScHMIDT Copyright 1932, by THE ARTHUR P. SCHMIDT Co. Cº.; 1940, by THOMAS TAPPER ternational Copyright Secured * //7. 3/2 . . .72% //40 PREFACE This book is divided in two parts. In Part I, close position is used, and all chords not pre- sented in FIRST YEAR HARMONY are taken up for study. In Part II, open position is used, and the harmonization of a given soprano is required. - The opening chapters follow a definite plan of presenta- tion. This plan includes: * (a) The chord selected for study, shown and described in both modes. (b) Tone Study, by the practice of which the student learns the chord, its character, and resolution through the voice. The value of this practice can- not be over-stated. (c) Questions designed to bring the salient facts before the student in question and answer form. (d) Bass and soprano melodies to be harmonized. The items that make up the working vocabulary are pre- sented in detail, and many examples are given to illustrate the English text. . g - In the Appendix will be found some test papers in harmony, which have been set in schools and colleges. w { THOMAS TAPPER. NEW YORK, December 4, 1911. A. P. S. 9420 |JU$/€ . GitH Arne Heſſler 10-30-78 SECOND YEAR HARMONY PART I CHAPTER I THE SUPERTONIC SEVENTH CHORD 1. The first chord to be added to the vocabulary is the supertonic Seventh chord. In C major and in C minor this chord appears thus: AC major oG minor f II? f IIOT - 2. A seventh chord, being a dissonant tone-group, re- quires resolution. This resolution may take place in several ways, the most usual of which is found in its progression to the triad of the tone a fourth above its root. Thus, the seventh chord on D, in paragraph I, resolves regularly to the triad a fourth above D, which is G. This form of reso- lution, applicable to nearly all seventh chords, is based upon the authentic cadence formula, in which the dominant pro- ceeds to the tonic, thus: - MozArt -º- º º f : I- * > h— I w L fº. gº t º–14--|| EEEEEEE=E=E====EEE H Note in these examples (1) that the first chord is the domi- nant seventh of the key, (2) that the second chord is the tonic triad of the key. The bass G moves up a fourth (or, what is equivalent, down a fifth) and the other tones, on the treble staff, connect directly with the tonic triad. The tenor G, in examples (a) and (b), is common to both chords. The leading tone, B, moves up to C, and the seventh of the dominant seventh chord, resolves down, regularly, to the third of the tonic chord. 3. Applying this form of progression to the supertonic seventh chord, there is produced an exactly parallel resolu- tion: - - a C major . a Q minor ==#===HE 4. All seventh chords admit of three inversions. (See FIRST YEAR HARMONY, Chapter L, page 131.) In the first inversion, the third of the seventh chord appears as bass tone; in the second inversion, the fifth is the bass tone; and in the third inversion, the seventh appears in the bass. Thus: C mai a C major e —# - #H#H#H IIT 3 3. § 3 3 NOTE. In C major the supertonic seventh is numbered thus: II+. In minor, a small circle is added, thus: II9, to indicate the diminished fifth. a 9 minor -º- - --~~IIT-FILTE –––. IIOT g 3. ; 3 . 3 5. The full figuring of the inversion is rarely used. # is generally abbreviated to 3, § to #, and # to 3 or 2. 6. The regular resolution of the fundamental II, (see paragraph 3) applies also to its inversions, and all follow the authentic cadence formula. (See paragraph 2.) 7. The dominant triad, or seventh chord, often proceeds, not to I, but to VI, making the deceptive cadence. Note that in the authentic cadence resolution, the V, may appear complete, or without its fifth. In the deceptive form of cadence, however, the seventh chord must be complete to avoid faulty progressions. 8. The deceptive cadence in C major V, VI, and in C minor V, VI: * * a C major a C minor g===#H# §====== I VI Vr V Wr 9. This progression, applied to the II, chord results as follows in C major. It is not applicable in minor as a com- plete resolution of the Supertonic chord, because the third degree in minor is an augmented triad. C major C minor Io. Seventh chords may appear complete, with root, third, fifth, and seventh, or the fifth may be omitted and the root doubled in one of the upper voices. Hence: With fifth Without fifth g ſh zº- TONE STUDY II. Before the student proceeds to harmonize basses which include this chord and its inversions, he must familiar- ize himself with it by repeatedly singing the chord and its resolution. 1. Sound with the voice, taking the pitch from the piano, the tonic and its octave: 5 2. Then the following, using the Italian syllables,” singing slowly: * —fl. Iºw tº a I º fºr . T_- fºssº [-e- «---- W. º - tº II? V 3. Then embody the entire group in metrical arrange- ment: - V T =e II? 4. Similarly, in C minor, sound the tonic: * #E: •eº- -->= 5. Then the following, with syllables: —fl. 1. Tºſi A L ——-a-— === 2=ſ. L. II.O 7 V * , g 7. Sound on the piano the supertonic seventh chord, fundamental position, of the major keys of: C, A5, Eb, B, G, F. . * For the application of the Italian syllable names, see First Year Melody, Page 1. 8. Sound on the piano the supertonic seventh chord, fundamental position, of the minor keys of: E, B, Eb, C#, F#. 9. Sound the tonic of each of the following keys, then sing the tones of the Supertonic seventh chord ascending, and resolve upon the leading tone, falling to the dominant: - s (a) Major — D9, Eb, Ab, BP, F, G, E, C. (b) Minor — C, D, G, B, A, F, E, Eb, F#. Io. Sing the following in the major and minor keys given in Question 8: . - C major —f) ſº —l A- 3– -º-º: EEEE|| -º’ |- —L. wº LTw T- Tº P- I V7—I W I 12. This vocal practice should not be discontinued until the chord has become thoroughly familiar. Once the II, chord is grasped mentally in its progression to V, other pro- gressions, which will be shown in succeeding chapters, will be easily mastered. & QUESTIONS I. What is the interval structure of the II, chord in major? - . . * 2. What is the interval structure of the II9 chord in minor? . . 3. When is a seventh chord in its fundamental position? 4. How many inversions has a seventh chord? 5. Write the full figuring of each of the seventh chord inversions, and its abbreviated figuring. 7 6. How does the bass move in the regular resolution of a II, chord? - 7. What is the usual progression of the seventh of a seventh chord? 8. Name the major key in which each of these inverted II, chords is found: - 9. What is the authentic cadence resolution? Io. Write the authentic cadence resolution (V,I) in C, Ab, Eb, Gb, and F major; and in B, D, F, E, A, and C minor, BASSES TO BE HARMONIZED Harmonize the following, in four parts, close position. First copy the bass correctly, adding the figuring. Then sing the bass. When the three upper parts have been added, play at the piano. Finally, proceed thus with every exercise: (This practice should be followed with all written work.) I. Sing the Soprano, playing alto, tenor, and bass. 2. Sing the alto, playing soprano, tenor, ard bass. 3. Sing the tenor, playing soprano, alto, and bass. 4. Sing the bass, playing the soprano, alto, and tenor. Vocabulary: The triads and their inversions. The dominant seventh and its inversions. The II, and its inversions. Gonº Lºº ÉEEEEEEEff==#| L | 2. № №s qosh —l —1– #EEEEEEEEEEEEEEH = H I– up— T- 9 a " a 3 7 6 3 # (2 II? V7 II.7. VT IO NOTES ON THE PRECEDING EXERCISES No. 2. Measures three and four, modulation to the domi- nant. Measure six #9, passing modulation to the sub-domi- nant. The tones required above D are f, ab, bb, No. 4. Measure seven the 5%, requires the triad of D with augmented fifth (ał) which must resolve up to b in the next measure. - - - ** No. 6. Both 6 chords (second and third measures) re- quire the double third. • No. 7. Sixth measure: second chord. . The seventh of this chord (b5) resolves by holding over into the 3 chord of the next measure. No. Io. In the first four measures use fundamental triads only; and in sequence. No. II. Third measure, second chord, use an inversion. No. 14. First measure, second chord, the II, in the # position. - - Seventh measure, first chord, the tonic-3. I I' CHAPTER II * sub medant THE SEVENTH CHORD ON THE SUPERB8%Hºt C major C minor ### —es— —tº-º- asº– - poor : - es-— -º-ax Tº —at-– WI7 II VI, II The seventh chord, upon the sixth degree of the scale, differs widely in effect in the two modes. In the tone study suggested in the previous chapter the student will have noticed the comparative mildness of the supertonic seventh chord, both in major and in minor. Further, he will, by analysis of the exercises, have remarked that the II, chord is admirably adapted to precede the V or V7 chord. In fact, this progression IIT, V., I is the commonest form of the authentic cadence. Fundamentals rising a fourth, or falling a fifth, are particularly satisfactory because based upon the natural progression of V to I. Hence, as V pre- cedes I, so II precedes V; and in like manner, VI precedes II. Thus: * É=== -T- VI II W I But, to avoid the awkward progression, which results from a series of rising fourths in the bass, the rising fourth is I2 . . * often replaced or expressed by the falling fifth (its equiva- lent). Hence the above passage is better thus: ÉÉ== VI II V I - That the adaptability of the VI, chord to precede II is greater in major than in minor, is seen when the tone effect of the chord is closely observed in both modes: C major C minor WI7 VI, § In interval structure the VI, chord in major is exactly like the II, in major; both chords consisting of root, minor third, perfect fifth, and minor seventh, a combination of tones that is comparatively mild in its degree of dissonance. † By analysis of VI, in minor, we find that it consists of a fundamental, a major third, a perfect fifth, and major seventh. The presence of the major seventh produces dis- sonance so harsh that the chord is less adapted in minor for pure four-part writing than it is in major. Before taking up the tone study of this chapter, the student should sound on the piano the VI, in minor, funda- mental position and inversions, and listen attentively to the effect of the tone groups in each case: - * VI, VI,(:) VI,(i) VI,(i) I3 The presence of the minor second (G-AB) renders the inversions particularly harsh. Again, the natural progres- ..sion of the bass (Ab) up a fourth (to D) is not practical with this chord, ordinarily, as the fourth is augmented; hence, less satisfactory melodically than a perfect fourth. Nor may the bass VI rise a second to II° as in the deceptive cadence formula (VVI) owing to the presence of the aug- mented second from VI to VII° in minor. Consequently, the roughness of the VI, in minor, in any position, and the impracticability of its progressions taking place as with VI, in major, make the chord impractical in pure four-part writ- ing as a chord of regular resolution. TONE STUDY I. Sound the tone C on the piano, and sing the major scale up and down from that pitch, to establish the key in the mind. 2. Then sing, or play, the following tones, noting the natural progression; that is, the plan of the tone groups, as they are indicated in Roman numerals, below the tones: t ... } . - =#EEEE========E===== —H –D–– I- cº L– I * *; * C major : WI7 WI7 II? V, I' 3. Sing this progression in several major keys, first writ- ing out the chord (in small notes) and the melodic seventh chords (large notes) as is shown above. - I4. 4. For comparison, sing the same progressions in minor: f #=E=========== I lºſ f *— C minor: VI, VI, II? V7 I 5. Sound the tonic of C major again, sing the following inversions, and observe the resolution of VI, to the triad of II. C major: WI7 II . VI7 II WI7 II 6. Write and sing these in several major keys. QUESTIONS 1. What is the interval structure of v1, in major P 2. What is the interval structure of VI, in minor P 3. To what triad does the VI, naturally resolve (on the authentic cadence formula) in C major, G major, Ab major, D5 major, E major, F# major P -> 4. Why is VI, in minor less practical in pure four-part writing than VI, in major P 5. In what major key does each of these occur as VI, P I5 6. Resolve each of these chords (a vi, or its inversions): f : * 6 - 7 - * > H # H 6 7_2~ *s ==== =E====H BASSES TO BE HARMONIzºd Vocabulary: The triad and its inversions: e, 3. The V, and its inversions. The II, and its inversions. The VI, and its inversions. 6 3. i 6 & T_5\ º 7 5 5 §4. E}: * I ſº E —P- IT AL I | T #E:( ) -Hº-Hºº-º-Es-a-FES F-2–C–H–H *" || || || 2–1– —ſº ll-e -2 Lºſ | g u ºr Vi' ºr # 5 7 7 F. l 2- w"Ts w” * : *, 7 * : . • * * * * # , 1– №s * * ( (osſeaQ ©vº 17 NOTES ON THE PRECEDING EXERCISES No. 1. The 5}, following the 5 in the last measure but one, requires the dominant triad to appear with augmented fifth a #." - No. 3. Soprano begins, in first chord, on #= In the second chord it moves to b: (third line). No. 4. Measures four and seven. See note No. I. No. 5. Begin thus, in the upper parts: = etc. :3: -º- • No. 6. Second chord. The seventh g, resolves up to ab. Mo. 7. Measure four: The dominant triad (d—f{–a) is emphasized by the # chord. The tones required in the first chord are g-a-ch. 18 CHAPTER III. THE SEVENTH CHORD ON THE MEDIANT ºC major a , C minor - #=#== III, III; In the major mode the III, chord is a comparatively mild dissonance; in minor, it is exceedingly harsh. The figuring of this chord in major shows in the small numeral, III, that to a major triad (root, minor third, and perfect fifth) there is added a minor seventh. In the minor mode, III; indicates, in the large numeral, III with the sign + to the right (III*) that the root, third, and fifth form an augmented triad; to this a major seventh is added. -- While the III, in major is constructed of intervals exactly parallel to those of the II, chord, there is a greater degree of dissonance in III.7. This is probably due to the difference in the fifths, D–A, and E–B in the tempered scale. In major, III, may be resolved by either the authentic cadence formula, or by the deceptive. In the former case, the root rises a fourth or falls a fifth; in the latter, it rises to the next scale degree, a minor second above. . C major - Cl | º: at: º- gº-> º- wº-> ę e -e-II zº- e ſº | gºz tº- | & } H III, VI III, IV I9 The III; in minor may be resolved in several ways; its roughness, however, requires that its dissonant tones enter as passing tones, for smooth progression. Hence it is rarely used, in any position, as an independent chord. C minor e c, Lº & e #======== #== g -> III; VI III; V, I III; I At a the regular progression of the bass takes place, the other tones moving to the nearest position in the chord of VI. At b the root rises a major second, and the chord of V7 results. At c the leading tone ascends, the seventh regu- larly descends, the root and the third remain stationary. When the dissonant tones of this chord are properly pre- pared and resolved, the rough effect is reduced to a mini- mum, and the chord is useful in proper context. C minor & v III:y, III; TONE STUDY I. Sing the tones of III, in major until their scale re- lation as a group is clear. Do this in all major keys. zº- IT |ſ sº-º Tºsº, | I - || —T ſ É e e e- tº 2O 2. Sing the same group in conjunction with the tones of , the chord of resolution (VII) leading through II, Wr, to I. 25-e TT e=~HZ-2 TI a 2 lºſ I III, VI, II? Wr I 3. Note the regular resolution (authentic cadence form- ula) of the seventh chords in the following. Sing in all major keys. 4. In like manner sing the inversions of III.7. Thus: _ſh. —EE--->E=HEEEEEEEEEEH e—f- H-HE H-HE-e–E–F–H tº ** Toº -e- III.7 VI III, VI - III? VI 5. Sing each voice part alone, playing the other three; ... that is, (I) sing the soprano, playing alto, tenor, and bass; (2) sing the alto, playing soprano, tenor, and bass; (3) sing the tenor, playing soprano, alto, and bass; (4) sing the bass, playing soprano, alto, and tenor. 6. In C minor, sing: § III; VI 7. And the inversions, thus: III; VI III; VI III; VI QUESTIONs . What is the interval structure of III, in major? . What is the interval structure of III; in minor? . Why is III, more dissonant than II, in major? . 4. To what two triads may III, regularly resolve, in major? § - 5. Why must III+ (in minor) enter with especial prepara- tion of its dissonant intervals? - N 6. In what major key is each of these chords found? : Introduction.) 9. What is meant by resolution? Io. Construct on the following fundamentals: C, EP, F, A, G, B9, a II, chord in major; a II? in minor; a vir-in major and in minor; a III, in major and a III; in minor. 22 BASSES TO BE HARMONIZED Vocabulary: The triads and their inversions. The V, and its inversion. The II, VI, III; and their inversions. # • * 6 § 6 6 ° 4. + 3, 2, - . Š 8 5 5 6 6 5) : H r=r º | H T 2. 1– LL |--|-- L- | TIT | T 2. 6 6 *–4–4–4–4 __5 5: 5b % 4. "if : e2 - E9:Ez-ZºffaifeFE*=====HEEE|| T 2 | | H L' L L | | | I e ſº 3 - & ĐăHHHHHHHH. zºn Fºr 4. - . t 3 * 7 - 7 7_a_-a- 7 T T I- ==#| # 23 7 6 s 7 3 2 5 7 s at 7 7 7 T E9ärbä- aff H Ez H -H-Ez- H E-5–24–2 Ez–EEEEz–E–2-E e–H2–H -tº- 8 ge *—-i-º-º-º-º-º-º- Đ;#H#############| NOTES ON THE ABOVE BASSES No. 1. First measure, second chord: the dominant of A minor. . . - No. 2. Fourth measure, second chord: this is the aug- mented triad (G B Dž). The D# leads upward to E in the following chord. Fifth measure, second chord: The chord is C G B 9, dominant seventh of F major. The seventh, Bb, resolves on A in the next chord. No. 6. Fourth measure, second chord: G# in the alto, moving to A in the next measure. Fifth measure: The 4 requires C# in the dominant seventh chord on A; A C# E in the upper voices. - No. 7. Fourth measure: The Eb of the first chord moves up through E to F in the next measure. No. 8. Fourth measure, second chord: dominant seventh chord of F minor. The tones in the upper voices are C G Bb. MELODIES TO BE HARMONIZED 6 * VI, II? Is IV, VI; 11; V: Al I- C Aº IVIME ET | H-H L– |- L *TU tº I 6 –0 tº . | l 1- - 25 CHAPTER IV THE SUBDOMINANT SEVENTH CHORD C major C minor IV, IV, In major, the IV, consists of root, major third, perfect fifth, and major seventh. Sounded on the piano, this chord is harsh, particularly because of the force of the seventh F-E In minor, the IV, chord consists of root, minor third,' perfect fifth, and minor seventh; and because of its minor seventh (joined to a minor triad) it is smoother than th corresponding major scale seventh chord. & The IV, chord cannot make the authentic cadence reso- lution in either mode, as the interval a fourth above is, in both modes, augmented. Consequently, it follows the deceptive cadence resolution, and moves up one degree to the triad of V. Thus: . - ar C major AC minor This chord appears to best advantage when the third or fifth of the IV, is in the soprano. When the seventh is in the soprano the resolution of IV, to V produces fifths. The 26 seventh chord must always be complete when it resolves a degree upward; that is, in the deceptive cadence progression. In C major 5th in Soprano ... 3d in Soprano 7th in Soprano £h |ſ I 7 7 - 7 H H H IV, V IV, V IV, V In C minor - 5th in Soprano 3d in Soprano 7th in Soprano -—n i- TONE STUDY I. Sing the IV, chord in all major keys, with resolu- tion to V. o_C major - IV, V 2. And in all minor keys: a A minor * #=== 27 3. Sing the resolving IV, through V to I in major and minor: a C major Tº <-E º zº- E –H w HºH ======= _o_A minor e - -T- I ====== —L e 25–2-HD arº -º- IV, V., T g - g . . 4. The following illustrates the use of this chord in major. Play the exercise, then sing each voice part in turn, playing the other three, as explained On page 20. I IV II, V, I IV, V V, I IV viio VI II, V, I 5. The next example illustrates the use of IV, in minor. Play and sing as directed in No. 4. IW IIO I IV I IV I I I § V, 7 V V, II, V, I 28 QUESTIONS . What is the interval structure of IV, in major? . What is thé interval structure of IV, in minor? . Which is the more dissonant, and why? . Why is the authentic cadence progression not available with the IV, chord? - 5. What tone cannot appear in the soprano of IV, in its progression to VP Why? *, - 6. Write the fundamental positions and inversions of IV, in these major keys: C, F, Ab D9, G, B. - 7. And in these minor keys: C#, F# G#, A, E, F, B, D. 8. In what major key is each of these the IV,? - i EXERCISES Vocabulary: - The triads and their inversions. The V, and its inversions. - The II, VI, III+, IV, and their inversions. Y, 3. BASSES TO BE HARMONIZED 6 * a 7 2 6 #b 2 " ? 8-e 3 | v/7tſ? 72 T ... 7 %, # # r | PZººſ Ea-E. –EH Hºff-HE I ºf DNC TITUTITT SLICT-ILIT 36 * . IO v. Dv, I VI IWe - Mº. a tº ſe - º FV, VIe 1—1––. # HHHHHHHHHH. NOTES ON THE PRECEDING EXERCISES No. 1. Fifth measure, the seventh (c) of the first chord rises to d. - No. 8. Measures three and four are in sequence with one and two. No. 9. Third measure, first chord, must appear with doubled third. - No. 11. Second measure, second chord, VI. * No. 11. Third measure, second chord, the bass in E, modu- lating to F major. 3I CHAPTER v . THE SEVENTH CHORD ON THE LEADING TONE C major C minor VIIo, VIIo, The chord, in both modes, is a mild dissonance, the minor VII? being somewhat less harsh than the major viſº, owing to the presence of the diminished seventh from the chor fundamental (leading-tone). ---, Many theorists present the leading tone seventh chord as the dominant ninth chord, with root omitted. The chord in its complete form of five tones, is shown in the following example: Employed in four-part writing, the Vo chord must appear with one of its tones omitted; the omitted tone is usually the fifth. The Tone Study work, and the basses for harmoni- zation given in this Chapter will treat this chord as a seventh chord. In Part II, this chord as the Vo will be studied. Interval analysis of VII? in major, shows that it consists of a root, minor third, diminished fifth, and minor seventh. In minor, the intervals above the root are a minor third, diminished fifth, and diminished seventh. 32 From the fact that the VII? has for its root the leading tone, it invariably makes the deceptive cadence resolution; : that is, the root following its usual strong impulse (as leading tone) rises to the tonic. The chord, however, may resolve a fourth up, in major, after the authentic cadence formula, in sequential passages; that is, when the bass moves in regular intervals. Thus: s Except in sequential passages, this chord usually resolves upon the triad of the tonic. Thus in C major: C major g I -T- a * | L. | | | VI Io, I VIIo, I viio, I 1. Sound the tonic of C major, and sing the VII? and its resolution: a C major : Tºz. H. . e=2 "ar cº -º- VII '7 I 33 2. Sing this group in all major keys. 3. Proceed likewise through the minor keys with the following: a C minor TZ Tºyº - L i L | tºº -º- VIIo, I 4. In both modes, in this rhythmical form: a C major - ſº # EEE=====El —º-P-e– -- a---- (z)— I. VII 9, I 5. Sing the inversions, testing the pitch from time to time at the piano: * a 9 major - ~-ºr ==n== #########EH I VIIor I_VIIor I. VIIo, I *. 6. And similarly in C minor. - 7. Sing the diminished seventh in the following keys, continuing the practice until the interval is familiar: Model D minor r—£2. L *—ſ. –E–e5–E | Tº Lºſ f a #25. -e- sº I "*7—I C, F, E, D, A, B, F#, Bb minor. 34 QUESTIONS 1. What intervals occur in the minor scale (harmonic) that are not found in the major scale? . 2. What is the interval structure of the diminished seventh chord (VII?) in this inversion ? #= 3. To what minor key does each of these chords belong P 4. Which is the milder dissonance, VII? in C major or in C minor, and why P 5. Write on the dominant of the following keys, the Vo chord; first as a five-tone chord, then as a four-tone chord: Major — B, Cb, DE, G, F, D. " Minor — Bb, Eb, A, AP, C, E. - 6. When may the VII° in major progress to the triad of a fourth above P - 7. Why, ordinarily, does it not make this progression ? 8. What other seventh chord in major progresses to the triad of the next degree above P BASSES TO BE HARMONIZED Vocabulary: The triads and their inversions. The V, and its inversion. - The II, VII, III+, IV, VII?, and their inversions. 35 Aº 7 A-, LL ray Î> ## ÇO —l sº *–97 # TTLøT I I- | || T T tº i- I ſ • & © 2 B E-i-ti 5: . EEEEEEEEEEEEEEEEEEEEE|| Qomæ 5 8 r— II I | | || L | | EE L oſo §§ 6 S TTI | TLE *_L | T -] Aº tºº L– =h =H | DTITLTTET TIt I- L l— L == GNTII | || =HEEE +H: —t—O H 2 E; , ſh 6 6 # H № №r Gosſi –4 6 - § 5 2 -a- zºº zºº z Como º 36 MELODIES TO BE HARMONIZED 9 - Q— IVr III'ſ Is . . II" -e II —ſ Höß # =#| TUT i T I r I-T- T- I IO IV7 VII°r III+ v17 II+ Vir “ I F#3==FF I I I L I Hº: L Lº | –F | E-e—He H TVSDMZºº. L Tu JT II v1.1°7 II? V7 v1 IIT - a 4 | ſ —ſ —t º º 1—1 |-22.É9. T H– |-|--| Lº Ú --! |-|-- I T. E6*::===#EEEEEEEEEz=E=#EEEEEEEEEEEH U—I- -- n I2 - A minor v1.1°7 VIIe I V7 *:::: HE # HEH al) 37 CHAPTER VI THE TONIC SEVENTH CHORD C major a C minor 7 7 The tonic seventh chord in both modes is a harsh disso- nance. In major, the interval of the major seventh, includ- ing the leading tone, takes from the chord that characteristic of most sevenths, to fall to the next scale degree below. This chord may, however, be used in two ways, by either of which its dissonance is made less forcible through the con- text. (a) It may appear in sequential passages, entering and resolving as satisfactorily as do the milder sevenths. (b) In close connection with other chords, triads or sevenths, in which the leading tone enters as a passing note and brings the Ir into evidence with smoothness. Thus: C major & I V, I, IV, VII* in, vi ii, V I, IV I V, I C major 38 While the I, in major is thus practical even in pure part writing, the corresponding chord in minor is not. By close chord connection the It may be made to enter and to give a passing suggestion of its independent character. Thus: A minor *—a 3: 6 8 4. 7 ſº-ºº: F-E- —2-3–-e- *Pººl I V Ir, VI W. CFE See Chapter VII of this book for further explanation of this and other extremely dissonant sevenths. - In interval structure I, in major consists of a major triad and a major seventh. In minor, it consists of a minor triad and a major seventh. In both modes, the seventh has a strong tendency to resolve upward, being the leading tone; it may be led downward in major, but not in the harmonic minor scale, for, in the latter, the progression of an aug- mented second from the leading tone to the sixth degree of the scale is unsatisfactory. Note the use of this chord in the following example: 39 While the second chord in measures one, three and five ap- pears as independent seventh, the passage is merely a suc- cession of triads, in a two-measure sequence group, the groups being closely connected by a passing tone that, in the above example, gives the impression of independent seventh. - * " . TONE STUDY 1. Sing the tones of I, in order, and observe the ten- dency of the seventh. - * - G major Tºz I zº- e–H– zº-sº lº | -ex. T“’ IT IV 2. But observe in singing the following that, through the momentum of the sequence, I gives the impression of resolving to IV naturally. C major 4o f 3. Sing the following, and observe that when the tones of the triad on I continue through the leading tone, descending, that the seventh in Ir appears as passing tone: - 4. Sing the following, observing the pronounced ten- dency of the leading tone to ascend: 5. Sing the next example, observing the tone group of - I, and also that the underlying Ir-IV resolution brings the leading tone down to A naturally: 6. All examples given in the above questions should be practiced in several keys. QUESTIONS 1. Write the I, in C, G, B, D5, Ab, Eb, major. F, D, A, C, F#, E9, minor. 2. What two forms of triad are contained within the I, in major P - 3. What two forms of triad are contained within the 1, in minor? 4 | 4. Write and resolve the I, in the keys of C, G, B, D5, Ab, Eb, major, in four parts, resolving the chord (a) upon the triad of the fourth degree; (b) upon the triad of the second degree. 5. Locate each of these chords in a major or minor key, as Ir: - 6. Chromatically alter one tone in these chords, to pro- duce a dominant seventh in each case: BASSES TO BE HARMONIZED I. All triads and their inversions. 2. All seventh chords and their inversions. 6 6 5 8 7 6 6 Šb : 6 6 6 4. Lºc I T- L 2-5 | || | | º Dº Is | 2-2. [ 2 L-rz Leº T] | | T | E TL’ tº TC’TL L Lt- aw I - | I | | Tº T. | L | | –– LTE-ITI e; 2 t 7 4. 6 3 T # - ? 6 a 5 2 6 5b • £n | I Fºº ſº I A-, £2 | 22 r- º T- I- 3 8 * 7 Aj -º’- 7 a 7 7, 6 6 6 –, sººn | TºTI L-5 I EzTI I/2 I | L | | [H !--- I | 4. BºžH=#EEEEE|| 8 ,- 7 -5° v1.1°r Vr II°7 v1.1°7 - !--------> 1–1–1 EEEEEEEEEFFEEE E653;-H=a++2 | TºSººſ" T H-i-H-E-HT I e-Ee-2-H2–2H2–H | | || I l I NoTE. – From this point the harmonization of melodies, in close position, will not be required. - In Part II, melodies alone (soprano, alto, or tenor part) will be given for harmonization in open position. Beginning with Chapter VII, harmonic analysis of part music is introduced and continued to the close of Part I. 43 CHAPTER VII REVIEW The basses to be harmonized which are given in this chapter, present a general review of the fundamental and inverted seventh chords, thus far studied. The chromatically altered triad (with augmented fifth) is introduced, and an occasional modulation to a nearly related key. - It is suggested, in harmonizing these exercises, that th student adopt the following process: - I. Write the soprano throughout. 2. Then add the alto. 3. Lastly, add the tenor. - - Each part should be sung as it is completed, and the whole tested, when finished, by the chord progressions. QUESTIONS (Applicable to the Exercises of this Chapter.) I. In which of the following exercises is the augmented triad used, as a chromatically altered chord? . 2. Where are consecutive seventh chords used sequentially? '3. What cadence form is employed in No. 6, fourth meas- ure? - 4. Where is the passing modulation employed? . 5. When may the VII? proceed on the authentic cadence formula (that is, its root rising a fourth)? - - I 6 6 s: 6 6 3, 4, 6 A e -º- ºr 6 , 6, 5 4 7 . L * F | || ITU-T-I-I I LI II TI I ITT, I I —I- $. r— º ſº 6 3 5 # 6 — 6 6 * I 5 : zºz gº =#| l º I- e 4 + s: 5$__6 7 7 7_7 , Ełż H L E E l_ſ TI I ITT T. H T] | | | 5 § 6 3. # - e_T, 7, 7 7, 7 z \ 6 T_T_-a- 6 6 7. 7 T # 16 - 6 4 # e 6, 7–3 # 2, Ež =========H ſ E E y | III] I L I II TI TIT I | I T J —I- t J I- 45 8 3 ſº 7 3, 7 7 —l 5: - 6 3. _l - E}+z===Hºff-a-E-BEEEEEEEEEEEEEEEH 9 7. § 7 se 37 E}#: * T E ſº |-2 L T | ſ -H |. |- | 2– H F-I-H HE | == E I ANALYSIS In each chapter, from this point to the end of the book, chord analysis is taken up. This work will require frequent references to the preceding chapters of this book, and to the text of FIRST YEAR HARMONY. LUDwig van BEEThoven ! l . What is the key? . . What is the key at the end of the first phrase? . In what key is the second phrase? . Where is the 3 chord used? . In what key is the augmented second Eb-F# found? . What seventh chords are used in this example? Give the root of each. i 47 CHAPTER VIII . NON-CADENTIAL RESOLUTIONS Thus far we have observed the seventh chords chiefly in their cadential progressions. The root rises a fourth, fol- lowing the authentic cadence formula, or to the next scale degree above, following the deceptive cadence progression. In nearly all cases the seventh has been regarded as a tone that proceeds downwards in its resolution. Thus: In major: - It proceeds to IV or II II, proceeds to V or III III, proceeds to VI or IV IV, proceeds to V (to viſ” only rarely and through th impulse of sequence) - V, proceeds to I or VI - - VI, proceeds to II (see note on IV7) VII? proceeds to I (see note on IV.) In minor: - • IV, (see Chapter V) II? proceeds to V III; (see Chapter III) IV, proceeds to V V., proceeds to I or VI VI, , (see Chapter II) VII? proceeds to I In practical music all these chords may be used in many other ways. The most dissonant seventh chords may be gradually introduced and made to pass over to the other less dissonant chords before resolving. 48 } Through the motion of the other voices, the seventh itself (of a seventh chord) may resolve: 1. Downward (regularly) or 2. Upward, or 3. It may remain stationary. Careful observation of the progressions found in the exercises at the end of this chapter will show that these progressions are practical. Note the following: ` e=#=E= P-E- | | At a, the seventh (F in the alto) moves up because the bass proceeds to E, the tone of resolution. Should F also proceed to E, the seventh would resolve in two yoices and produce hidden octaves. At b, the seventh, F, moves up to F#, producing another V, chord, which, in turn, progresses regularly, its seventh C, resolving on B, in the soprano. * At c, the seventh, F, remains stationary and passes over in the third chord to the V., of D minor. Other examples of the same, and similar resolutions: 49 At a, the seventh (EP) proceeds upward to E. yADASSOHN At a, the seventh (D) remains stationary and becomes the root of the following six chord. fº (2) - =#####H#H At a, the seventh (F) may move either up to G, or down to E. r At a, the seventh (G#) moves up to A. BASSES TO BE HARMONIZED 1 a 7, 6 7 6 - # 6 3. ū I T- 25- : • , * 7 * 6 6 6 * 2 8, 12-4 g 5 § 3 #23 -º- * 7 4 & 5 # 3 e : a 5 -, i. 3 # E3: 5– H | E E IIT [-L- L | || | I * * * * y . 5 e 65 t i * 7 3, 5 ## 6, 7 # …, # 3 : E}}#E E=E= :F == a-É EPH2=HEEZEE=H | 2. | L | - ECI- I | TT P I–– LE.L. 6 6 - 6 a S.A. EMERY 6 a , 5 at . , 82 6 5 # 7" e Aº I- I– wº 51 ANALYSIS Sir Joseph BARNBy E-i-T-- | TITLºl — || FE f cº- - –Jºl 1. What is the key? 2. Why may the second chord (first measure) be in the 3 position? - 3. What modulation occurs in A major, through the tone E sharp? - 4. Through D sharp? 5. Bass of measure six: what effect on the key has D natural? C natural? 6. What chord prevails through the penultimate meas- ure? -- y 7. Why is the unison used twice in measure one (bass clef)? 8. Is the melody of this composition confined to the soprano? 52 9. Are any of the chords in close position? Io. Why may the third of the tonic triad be doubled in the second measure? - II. What is the purpose of having the parts cross in meas- ure four?" * 12. How many dominant seventh chords are used? What is the key of each? 53 CHAPTER IX cHROMATICALLY ALTERED CHORDs In four-part writing, of simple character, any one of the melody lines may be enriched by introducing chromatic tones as modification of the chord. The following example is of simple chords throughout and illustrates the basis of chromatic alteration: * * - In this, the melody lines may be given character and greater impulse by introducing chromatic tones, a process with which the pupil is already somewhat familiar. (See p. 15.) The first chord to be so modified is the triad, and the strongest melodic tendency may be given to it by allowing its fifth to proceed chromatically upward. In the next example, this modification occurs at the points marked with the 5%. 54 Such modification of the triad rarely produces a modu- lation. The preceding example begins and ends in C major. At the points where the 5% occurs an enrichment of the melody line occurs. The effect of these chromatically altered chords is to emphasize the following chord as an integral part of C major. A triad may be chromatically altered, not only in its fifth degree but in its third. The following are the various chromatic inflections that may be used. Major triads: 5% or b3. Minor triads: 5; 3:#. • Diminished triads: (6 chord position) 5%, 39. All these are illustrated in the examples that follow: | *H+H=H b #e. fºr a + I L -º- ! !-EEE ſº lº * : | 3. * * L- —LI |- † —l e f | * Lºº Tº- I & º Zºº TE → I Lº sºr A TWT I El I- E ETI L ºl- w ſt —a º —l º ſ _l |-|-- —I | TI-I —l I- H. 5: I- L–C. f : ſº IT II t IT 2-, i º I r Lºï- I LTT I I Tºſs [−: P-- n w º TU The use of chromatically altered chords produces a thor- ough bass notation that is complicated beyond what we have hitherto seen. While some of the signs used in this chapter have already appeared, the following list may be of service for reference: - - I. 2 4 5 etc. A stroke through a numeral is equivalent to the # sign (as applied to the tone in the key of the exer- cise). 2. § # 5 used above a note refer to the modification of the third. t 3. 5x means a double sharp to the fifth of the bass note. 4. # 7. The short line under the seven means to carry the sharp in both chords. 5. ; – a The line means continue the previous chord (#) as second chord; the g requires the same chord again (#) but with chromatically altered fifth. TONE STUDY 1. The impression of the chromatically altered chord in its progression is best perceived, in this exercise, by singing the given notes, sounding at the same time on the piano, the fundamentals indicated below the melody line. 2. Sing the following in several major keys: A t--a y —A— +—a-e-He º -º- As I-I V I 3. Sing each voice part separately, in the following exam- ple, at the same time playing the other three parts. GENERAL RULES REGARDING CHROMATICALLY - ALTERED CHORDS , 1. The sharp sign requires the modified tone to move upward to the next scale degree. 2. Similarly, the flat sign requires the modified tone to move downward to the next scale degree. - - : 3. The chromatically altered tone must not appear in more than one voice. 57 4. Rules for chord progressions, thus far learned, are not set aside through the use of chromatics. - - 5. A chromatically altered fifth, if held into the next chord as new leading tone, creates a modulation: 6. If the chromatically altered tone appears in the bass, it must not be used in the upper voices. 7. Sharp five, as non-modulatory progressions, cannot be used in the triads of VI and III in major, owing to the minor seconds between three and four, and seven and eight. 8. Flat three cannot be used in the triads of VI and II in major, owing to the minor seconds between three and four, and seven and eight. QUESTIONS I. How must the sharp inflex be resolved? 2. How must the flat inflex be resolved? 3. Which triads, in major, cannot take the sharp five? The flat three? Why? 4. Why must the altered tone be restricted to one voice? 5. Do chromatically altered chords always produce a modulation? & 6. What is the value of the chromatically altered chord in four-part writing? - 58 / - 7. In what manner may chromatic alterations be made to produce modulation? i. - 8. When does the augmented triad appear as a natural to the key? * - 9. When may the diminished triad admit of its fifth being led upward, by the sharp? * ANALYSIS 5 6 7 8 1- - N ſº I TUI ITC ( a *Tº TL*T Tº —l- Lº 32–Lºg * —l e - (Cº- |-|3|º 1. First measure. What two tones are chromatically altered? - - 2. What chord is emphasized by this alteration? 3. What is the effect of the F# in measures three and four? . . 4. Measure seven: How far does the influence of the first chord extend? What is this chord? 5. What is the first chord in measure nine? . 6. What is the first chord in measure eleven? Where does the D9 resolve P - 7. What is the effect of the F# in measure thirteen P 8. What is the position of the triad in measure fourteen P CHAPTER X CHORDS OF THE AUGMENTED SIXTH By chromatic alteration the augmented sixth may be made a component of three chords: (1) the first inversion of a triad; (2) the first inversion of a seventh chord; (3) the second inversion of a seventh chord; that is, of a 6, #. and #. • The presence of the augmented sixth in these chords is indicated by a stroke through the 6, thus g; or by the sharp sign following the six (according to the key), thus 6:#. These chords may appear either in major or minor. They may be made to enter so as not to change the key, or they. may be used for modulatory purposes. } The following illustrates the chord of the augmented sixth in C major: - - In all instances the augmented sixth chord is a chromatic- ally altered minor triad. The following illustrates its use in G major: S. JADAssoHN G I - V., I a v III*W* I e Vº VI Gri, V. V. I. The derivation of the augmented sixth chord, from the minor triad, shows (1) the minor triad itself, (2) the minor triad with raised fundamental, (3) the first-inversion in which the third of the triad becomes the bass tone, and the raised root appears in one of the upper voices. Thus with the minor triad on D: () (2) (3) This triad may appear, thus chromatically altered, in the keys of C major (II); A minor (iv); F major (v1); D minor (1). Though this triad, D–F–A, is found in B5 major, it may 62 not be thus chromatically altered in that key. The D# conflicts with the sub-dominant, Eb, and cannot be led upward to E. . . - The chord of § may be employed in major and in minor. In C major: In A minor: : º =ºſº †-ºTIº === Cº- Tº º-Tº-ºº: Tº =#| ' > *** ne *** ©aſo Gosł №wºsº AQ *** Gosſ Quae 6 FH-57FFF Ea-EH viſ- | cº Jº H &º ba ©aº èsseſſº № ++; № $$ №sſº Dr. PAUL. aº * => I- 64 CHAPTER XI THE SUSPENSION A tone may be prolonged from a chord of which it is an integral part to the next chord in which it does not belong, by the nature of the chord structure, This prolongation causes a dissonance, which requires preparation and resolu- tion. At a, the triad of G follows that of C, the common tone, G, being retained in the alto. * - At b, the soprano tone, C, holds over, so as to sound in the triad of G. The C being tied over from the previous chord is thus prepared, and its motion to B is its resolution. . The soprano C (in Ex. b) merely delays the B (third of the G major triad). In order to indicate, in thorough bass figuring the presence of the suspension, it is necessary to figure the C-B independently from the given bass note G. Thus: Ex. c. | - 65 A great variety of suspensions (and hence of thorough bass figuring, indicating suspensions) may occur. The entrance of practically any tone of a triad, of a triad inver- sion, a fundamental seventh chord, or of its inversions, may be delayed and thus create a suspension. - e——H–e—=H-e— - 6 6 9 8 6 4, 8 5 5 - or 5 [. L I The following general rules for suspensions must be care- fully observed: ** (a) The suspended tone must be prepared and resolved in the same voice-part. - (b) The regular and desirable progression of chords must not be disturbed by the suspension. 66 ANALYSIS Name each chord, as to root. State whether the chords are fundamental or inverted. What figures are required to indicate the suspensions? I "7 - B 4, 8 Ag 8 4 3 9 8 4 3 Lºcº Iº | Eº | zºº L | T sºft I L | ſº | tºr L _e_2 –H H Lºº ºn. Tº L I –I | | TU Teº T U 2. | l I L L TUI T *7 – - - V 2 3 6 5 4L 3 º jº LººYo ſººn º | [ | } | [. I Tº Lºzº L 2- [Tºy L– >3 I I Ł -º " ºn Lºcz | | º cº’ [ T | Zº ſ L L | 2-, T tºº 3 6 5 9 8 7 | ! º 67 7 B 4 3 Aſºº Gosh 4 3 I &º 23 cº’ L’E E | † @ f A —T- H-62–H zº LTTLII | TUI LTT | gº ty L 4. 3 4 3 9 8 Ez=E=E=E | I 4 3 *2 HG) H L^TAL L- | º №sił 9 8 L | <！\ a 7 Gosh -I- LT TTL I– LTE E �4 ț¢ (E) ț¢ć ț¢ ț¢ ∞ e-4 ķī: g ºg 52 · @ - ÇO ] © co = A2-, \ſº | gº E. | | º I | 2. tº | T-I- F į <łº -tº-Q---- eglº I J1|| aºſoį (o<;:ºrº-i- |–||–||–|- ŠTIN №Tų į Ō o.|()|| || →– ÇO* Io T I- I- LººYº Gº I & © Lºc 68 • CHAPTER XII THE SUSPENSION The following bass should be harmonized in all three positions of the first chord, that is, with three, then five, then eight, in the soprano. Note the effect in the soprano, alto, and tenor. Care must be taken, as previously stated, to prepare and resolve the suspended tone in the same voice-part. Suspensions are also available in the bass. Thus: The figuring 3 is, in full, § Or # according to the position of the sixth chord with doubled fifth or doubled root. 69 ANALYSIS Play the following. Add below each bass note the figur- ing to represent the chord. . . Note, and mark the suspensions. CHORAL - |7 J. S. BAch 7o CHORAL J. S. BACH EEEEEE |-ºf- T = Tai TE.T. |Tºº Tººlſº ! \ } ſº-P-P-- Kºź gº Cº-ºf-º’-azºf gº -º- == Ee Hºe H T-I--—- I- L | E- L' O). VUTC) _- L * E-T II LTE’ſ I | | | Aº a 2 | 2- Ú-sº —l —l T] a.º. I º —l- _2 –0 l- T I |-2^+12–2 zºº ſ | | | | || E. VLTT | | H-s—z-a-E a J I-1--- lº —l L | L–– Al U L VLVF E 8 O | I * I C | L | | | | # | H(€B4–C G *—L- TTL TT |Tºll I | f\ | | LZ - —— —L TITL III | J i w r– r— —I- 9 ( ) zºº a £2 T i —s ſº gº # J IO Gº TT H I TL L- H aſh fºy A * LVII.EET- | | | L | | |-- II n 4 - Q. t |-22 ºf 2-. Tº av |--|-> –––. H EUSB-t- | L. " IT | -L-L- | | | J. | | I I | ſº ass== 1 HAZ-4– D. | | a h P--- A-s—- T] C–H– Jº in n I– I º —l —º I H22–––. H– T J ºn | I fº-CEE-FEEſº-CEEEE| HS2 | i | TETI |--|--|- NOTES ON THE EXERCISES No. 1. Transpose to G minor. No. 2. Transpose to F minor. No. 3. Transpose to A minor or to Ab minor. No. 4. Transpose to D minor. No. 5. Transpose to B minor. 85 CHAPTER XV THE TRIADs on VI AND II In the exercises of this chapter, the Triads on VI and II are introduced. - The triad on VI may be approached from I, or it may follow V. The triad on II may be approached from IV, or it may proceed to V. - In the structure of the bass, the cadential progressions (authentic and deceptive forms) suggest the more direct form of procedure. Roots rising a fourth or falling a fifth are good. . Roots rising one diatonic degree are generally good. (But the triad on VII° may not be included in this.). Roots rising a fourth, by way of a third, are good. Thus: I–III–IV. The triad on II is much used in the authentic cadence group: sº II V I, or II 'I? V I. The use of v1 proceeding from V, and of II in the cadence group, is shown in this illustration from Beethoven: * 86 SUBJECTS TO BE HARMONIZED I –0. ex $. Fºx– g º => HéHzfff:##########| U I- J ..Tº I- lº | J VI II VI II U º m II VI II 3 * O - —l | & * —l —l E. W., 12 TI IT TI ſº Ea TTI | ſ I T VI II f) l- I —l º Fº 2- – ### u) *-sº I º n º * No. 1. Fourth chord. VI is approached from V. In measure five, VI moves to II, and II, in turn, to V. The cadence group (last three chords) II.V.I. 87 No. 2. In what position must the third chord be written to move to II (fourth chord)? 2. - No. 3. The second chord is V. Why? What form of cadence occurs at the end of the first phrase? Measure 6, II follows IV and proceeds to V. No. 4. Transpose to B major. No. 5. Transpose to G minor. .* ANALYSIS . Name each chord and its position. . What modulation occurs? . Explain the use of each six-chord. . Note the use of the triads on II and VI. . Why is the unison (tenor and bass) used in the second chord? - 6. What seventh chords are introduced? : 88 NoTE. – While the examples selected for Analysis present freer use of chords than is specified for the written work of the chapter, they still offer not only abundant illustrations of the use of certain chords, but also serve as models for part writing. * In every illustration, note: I. The distribution of tones throughout the total compass from bass to soprano. 2. The occasional use of a chord in close position. 3. The simple and direct manner in which modulation is effected. & 4. The melodic independence of each voice part. The student should not confine his studies in harmonic analysis to the single example given in each lesson. If he will play the four-part arrangements, such as those given in the Choralbuch of August Haupt, he will appreciate how rich the combinations of four voices may be made when only simple harmonies are employed. *. Further, it is admirable to play, for the purposes of analysis, simple piano compositions of the best composers. Nothing serves better, for this purpose, than the Sonatas, by W. A. Mozart, and the easier works of J. S. Bach. The first im- pression the student will receive on analyzing these works, is that comparatively few chords are used. These few chords are, through the impulse of melody and rhythm, spun out and prolonged. Direct and natural modulations provide color and contrast. Most of the secondary chords (except - II) are used invariably as passing chords, or they result from the use of passing tones proceeding from one primary chord to another. In fact, the usual chord simplicity of works of the classical school reveals, on close analysis, a wonderful effect produced by simple means. Modulation, 89 suspension, and the use of passing tones of various kinds are always sufficient to leave the simple chord-background undisturbed. Note in the analysis of the Mozart Sonatas, the absence of many of the secondary seventh chords in direct use. They appear, if at all, only as passing chords. - The subject of passing tones is generally included in a harmony textbook of this grade, but the subject is so easily mastered in the second to the fifth orders of Counterpoint that it is deferred for treatment in the author's First Year Counterpoint.* • * , In all analysis of chord procedure, the student should make constant reference to the Table of Progressions given at the end of this book. * See also First Year Harmony, Chapter LVII. CHAPTER XVI THE FOUR-SIX CHORD When triads are used 'exclusively in the fundamental position, the chord succession is stiff and angular. The voice part is invariably confined to so narrow a tone range that it loses any aspect of independent melodic progression. The soprano stands out as the most individual part, and the bass is confined to roots alone. By employing the six chord as a substitute for the funda- mental position, much greater melodic variety is secured. The six chord is never employed as first or final chord, and rarely as penultimate chord. It is available elsewhere when the third of the triad is not used in the soprano. Hence, with primary triads especially, the presence of root or fifth in the soprano discovers a possible employment of the first inversion; but the progression to and from a possible six chord must always be considered. As a rule, the six chord may be regarded as the equivalent of the fundamental triad to be availed of in certain instances - to improve the melodic trend of the alto, tenor, and bass. The second inversion of the triad (four-six chord) is intro- duced in this chapter. This chord has three distinct uses: (1) it may appear on the first of the measure in cadence groups; (2) on the non-accented part of the measure as a passing chord; (3) on any part of the measure following its own fundamental position. * This chord gives particular prominence to the bass, and its use, in conjunction with the six chord, affords considerable melodic variety to the voice parts. - 9I The following exercises illustrate the use of the second inversion of the triad: No. 1, in F major, should also be harmonized in F minor. No. 3, in E major, should be transposed to E minor. No. 5, in A minor, should be transposed to A major. These five exercises will afford ample preliminary prac- tice for the study of the four-six chord if it be accompanied by considerable analysis. —0– —! —l —l gº ºn Q — T] ITU- ºn |-> E*TIE’ 2 Tl £2— Eää.EEEEEEEEEEEEEEEf Jº 6 | 'a 6T' 6 4. 4. 4. 4. n _`S —l º L LZ-. E. TT | T] | [ I —l D I H2=2–E–2—2–E–F–F–F–EEH | \SLA ! | I Cºz U2 a 2 2– Iº |T 'el) | 6 II WI - 4. 2 n! *_ * =s | * -- –E– $. J I-Pi—I Tºº-ººs 6 4. ok —l l —l Hºff========E=====E=H IVD/ cº L- y ſ |- I–– L | I tº T 6 6 | 6 : II 2 - 92 T TT C–H L– w 24 93 fº ſº Lº Wººl/ En IVSU/ DNSD/ TI º P- (osił qosh **. ANALYSIS 93 :i QUESTIONS (The measures are numbered) . What is the key? What passing tones are used in measure I? What inversions occur in measure I ? Measure 2, what cadence form? . Measure 3. What triad is used as a ?? . Measure 4. Cadence? . Compare with measure I. . Measures 6 and 8. Note the 3 as it proceeds through the dominant, to the tonic. 9. IO. II. I2. I3. 6? Measure 7. What key is used in passing? Measures 9–Io. Key? & Measure I2. Key? - Measure I5. Where has this measure occurred before? Measure I6. Why is this varied from measures 2 and 94 The student should count the number of fundamental chords employed in this selection and compare with the total number of inversions. Note, also, the comparatively infre- quent use of passing tones and of seventh chords. * Play soprano and bass (omitting alto and tenor) and note the use of opposite and similar motion between these two parts. * - Why is opposite motion, as a rule, to be preferred? Study the measures in which other keys than the tonic are suggested or introduced. What keys are closely related to that of the key-note of this selection? What is meant by Tonic minor? Relative minor? From the use of passing tones in this selection construct a definition of this device. - What is the difference between a modulation and a sug- gested key? Y What keys are most easily reached from C minor? From D major? *** CHAPTER XVII ~3. THE SEVENTH CHORDS In the following exercises, the chords of V., II, and IV, are employed. Transpose Exercise 1 to G minor; Exercise 3, to A minor, and Exercise 5, to F minor. All rules hitherto given for the preparation and resolution of sevenths should be carefully reviewed. . . The seventh of a seventh chord is prepared when it appears in the previous chord as a consonance. In the case of the milder sevenths (minor and diminished), the seventh itself is often satisfactorily prepared by being approached by con- junct motion. t .* A seventh may resolve on one of several ways. Regu- larly, it should move one diatonic degree downward. But it may remain stationary, or even move up a major second or an augmented prime. In the latter case, the effect of dissonance may be transposed to another voice, or, the movement of resolution taken up elsewhere than in the voice where the seventh occurs. Examples of these resolutions are found in Part I of this text. p The dominant seventh is a comparatively mild dissonance. The II, is a natural precursor of V, and the formula II, W.; I is frequently met with in cadence groups. - . - The sub-dominant seventh is harsh, and the entrance of the seventh must be carefully prepared. The IV, moves naturally to V or V, or to the four-six on V. (See Exercise 3.) The seventh chords introduced in the following exercises may be employed fundamentally or as inversions. It must 96 be remembered that used fundamentally there is less free- dom in the motion of the parts, while with inversions, the voices, particularly the bass, gain much melodicindependence. I - a 9. ——f-ze= * _l —l #H#HE=HEEHFEHEHEH Tº JT I- r— . r-I V7 Vr V7 • Viz | I- TUI I I- Wr IV, II.7 V, V, 2 £). I- | —ſ ſº I Höße ===EEEEEEE J r— V7 V, VI 3. V., II.7 Vr 5 # == if （ Wr IV, II7 , Wr - V7 - II.7. 3. V7 * 97 ANALYSIS J. S. BACH. 98. I. 2. a’ *--- What is the key? - - The chords are three voiced throughout; two tones in the right hand, group themselves with each bass tone. 3. shown in measures one and two. . Measure 4, what form of scale? . Measures 5 and 6, what key? . Measures 7 and 8, what key? . Is sequence employed? - . Measures 13 and I4, what key? . In what key is the final cadence? . First beat, first measure, what is the d? . Third beat, first measure, what tone of V is omitted? . Place under each bass tone, the Roman numeral, as . GENERAL REVIEW . Explain preparation of a dissonance. Resolution. . Why are preparation and resolution necessary? . . (a) What are the principal uses of the four-six chord? g - 99 (b) Which triad is not used in this position? - 4. How do inverted chords influence the melodic struc- ture, in four-part writing? 5. What triads and seventh chords are used in the authentic cadence? - 6. What bass progressions are most satisfactory? " 7. What are hidden consecutives? 8. When are hidden consecutives objectionable?] 9. Which are the most dissonant seventh chords? Io. Are they frequently used in music of the classical school? II. Does instrumental music present as frequent change of chord as choral music? - 12. What are the most direct modulations (through key relationship) from G major? I3. What is meant by a passing modulation? 14. When may close position be employed in open har- mony? ‘. - 15. When may the unison be employed between two parts? I6. What are passing tones? 17. What do you understand by “classical school”? 18. What composers are prominent in this school? 19. What name is applied to the school of Johann Sebastian Bach? - 20. Define chorale, sonata, consonance, dissonance, rhythm. - IOO . CHAPTER XVIII THE NINTH CHORD The following exercises should be harmonized by the students in two ways: (a) In simple chord progressions: (b) embodying the various chords specified by the numerals (Vo, V7, etc.). -- - . All exercises from Chapter XIV should now be treated in a similar manner, disregarding the chords specified in each lesson. In the re-writing of the work of this chapter, the student should attempt a simple harmonization, in which the effort to secure distinct melodic progression for each voice is the principal factor. - Also, from this point on, the student will benefit by writ- - ing four-measure phrases in open harmony, using all chords thus far introduced. The purpose of this original work is to stimulate original chord thinking. Let the first efforts be thoroughly simple. Aim for clearness and for as much chord variety as is consistent. When the four-measure phrase form is mastered, the eight measure period should be taken up; the period permits more elasticity in the choice of chords. - Continue original analysis until the following offer no obstacle: * * (1) The source of the chord and its impulse in the placé it appears. - (2) Chord position. (3) Preparation and resolution of dissonances. (4) Identity of cadences. - IOI (5) Presence and purpose of passing tones. (6) Modulations. (7) Explanation of all apparently irregular progressions. If the student has provided himself with a copy of the Choralbuch, by . August Haupt, he should copy the melody of several chorals in major, and harmonize them without reference to the originals. Then compare chord for chord. Review the chapter on the ninth chord in Part I of this text. This five-voiced chord must, in these exercises, be employed as a four-voiced chord only. The ninth must be prepared and resolved. • Of the exercises that follow, No. 1 should also be harmon- ized in F minor; and No. 4, in D minor: 1–1 | ſ I ––0- - I Hääz-fif:Hº-HEEEEEEEEEEE|| a J. w- H- vº Vo V7 V7 3. •. 2 - º º _f - | * #EEEEEEEEEEEEEEEE U =====E====2–H–E*EEEE Vo Vo IV 3 ;t; i NT———I-T- -N-T NH- T ==== -- VI IIT Wr 9 3. 7 3 —ſh 1- a * sº •=ºs. [TWILVIº D TT eº LE” a.” I I T D] º Tø #2 [Taº L | —f- 2TILº A2-. T] | 65; b; [. T lº- | =T. LT ſ I Liſt- T] JT | I - | r- | | I "I T! Vo Vo II? Ež fº-z-Tris H } ſº- s—--- =H T I *~Tºy Vo V7 Vo * * - - ANALYSIS A. MARMonteL 103 I. 3. . Where are secondary sevenths employed? . What key enters in measure 13? 4. 5 6. 7 8 Add Roman, numerals, two to each measure indicating roots; add Arabic signs indicating position. 2. Distinguish carefully between fundamental chords and inversions. * - How many ninth chords are employed? Does the Ab in measure 22 create a new key? . At what measure is the first phrase repeated? . What cadences are employed? & IOA. J. G. ALBRECHTSBERGER J. G. ALBRECHTSBERGER * These two quotations from J. G. Albrechtsberger's Musical Composition should be analyzed, chord by chord. Note particularly: g (1) The use of the ninth chords. (2) The preparation and resolution of dissonances. (3) The use of suspensions. (4) The use of modulation. r Each chord should be marked with its Roman and Arabic figuration, each new key being indicated by letter at the point of its entrance. - • IoS GENERAL REVIEW I. In what measures of the C major excerpt by Albrechts- berger, do the parts cross? 2. What voices are included in this? 3. Write the dominant ninth chord on B, and resolve it in four parts to a minor triad. - 4. What is the key of the second Albrechtsberger selec- tion, above? - 5. How do you explain the D major triad, in the final measure? ** 6. What influence, on the cadence, is produced by the Ab in measure twenty-two of the Marmontel selection? to 6 CHAPTER XIX' THE LEADING—TONE TRIAD AND SEVENTH CHORD The vLI” and VII? are an integral part of the dominant harmony. The VII°, is to be regarded as V, with root omitted; the VII? as Vo with root omitted. Hence, in the use of these two chords, it is essential to keep the influence of the dominant in mind. ; - Of the following, transpose No. 1 to B minor; No. 2, to F major, 9. I * • nº *===s_ assº- =º, -- & Y 2 * ET arº II ºn TI —l T] #: Cº. 2- I e.2 { Lº E- erº T-I | T] QY EarTL. | LTI E” 23 L → º I | SP. TIZ'ſ H | I LTD. | C*TL ºr acº | - VIIO VII? *- & * º —— | L– F#H=HEHE - T] zº | | F- gº [2-n gº I ..º. | \SL | n | U I | 6 VII VII 4. # –- • * ~ – - - rt – | > I In T. TNTUTIZ wº | M : | | I al) *= a H-r- VII? VII 3. V7 * 4 2-, 2-, –0 l- | –– | A A Z_ [TVII/ | | | | 2 AT = TIT-7 º *Tº Aft FášEEEEEEEEiff=#H#H | SP. T I- L | L —- - I g VII VII? - N-> V7 VII? VII? VIIT VII? Harmonize the above exercises twice. The first time disregard the suggested chords and use simple connections, The second time introduce the chords indicated by the Roman numerals. Every given soprano, unlike a bass with chord figuration, admits of many possible harmonizations. It is, consequently, of the greatest importance to use a given subject repeatedly, elaborating the harmonic structure from a simple basis. Io8 The following sequential passage from Albrechtsberger shows the use of the VII?. The VII? in minor: - The VII° in major: Io9 ANALYSIS . Where is the Deceptive cadence employed? . What keys are suggested and introduced? In what position is the VII° used? What secondary seventh chords are used? . Mark all instances of the Suspension. . Mark all Passing tones. . Are any non-modulatory chromatics introduced? . When is it necessary to employ close position? :i FELIX MENDELssoHN-BARTHoldy III: I. Explain the use of all unisons between any two adja- cent parts. - - 2. Mark all Passing tones. - . Name the cadence at each Phrase ending. . Where do Suspensions occur? . In what key is the third Phrase (sixth measure)?' . What other modulations enter? . What is the relation of each modulation to the tonic? - . Mark each seventh chord, noting preparation and resolution of the seventh. <> * 9. Where is close position used? Why? i , CHAPTER XX THE CHORD ON THE MEDIANT, IN MAJOR Of the following exercises, Nos. 4 and 5 introduce Sequences (fundamental chord forms). Each exercise should be worked out, in a simple form of harmonization. Then again, intro- ducing the chords indicated by the Roman numerals. Re- view in Part I, the chapter on the Mediant Triad: | C–TZ; O FHTTTTTTT––. U I- ſ cº-º-H V, v1.17 Vr III A | I I Éh * * UTTTI H–H–— I H #Ef==E=#EEEEEEEEE III V, III 2. gº | T He - º º zºº ſº- —l 2-3 —l I II [ E- zºº | wº ſºn a º tº a' I tº aw ET |- | | £2— | SP-2, I | I [... | III VII? L. A. } I TI E --> º II EZºš e 23 | I ſ P-4—2 # H– T. º aw . I 6 -H II3 - T-- - IV II V III V, vi IV,V V., I, 3 V, 3 v11.7 VI III III V7 3 The Triad of III moving to VI: The Triad of III moving to IV: II4 y The Triad on III (six chord) in a modulation: The Triad on III (3 chord) in modulation: CHAPTER XXI MODULATION Of the exercises to be harmonized, in this chapter, Nos. I to 5 present modulations to next-related keys; Nos. 6 to Io to next-related and to remote keys. Each key entrance is indicated, and essential chords are shown in Roman num- erals. - It is only by extending the study of analytical harmony that the pupil can become thoroughly familiar with the influence of chromatics introduced into music. Many com- positions contain tones foreign to the key that do not even infer a modulation; again, chromatic tones may be intro- duced, and a related or a remote key may be clearly sug- gested but not established; still again, a new key may be made clear without the use of chromatic tones. The most definite and satisfactory manner of establishing a new key is to introduce its dominant chord (V or V.). Between the starting point (say, C major) and the desired end point (E minor, for example) there must be a gradual merging of tonalities, becoming definitely established when the V., (of E minor) enters. It is necessary to introduce a chord, or a series of chords, before the new V, enters that are common to both keys. For exãmple, in passing from C major to E minor, the triad on A is a valuable bridge chord because it is found both in C major, as ví, and in E minor, as IV. Furthermore, the root of this triad is the seventh of the V, of E minor, which again establishes an intimate relationship. * II6 This intimate relationship is the one fact that gives smooth- ness and naturalness to the entrance of the new key. * By the merging of the starting point key, through chords common to both keys, modulations may be made to sound as natural when remote keys are sought as when the nearly related keys are concerned. Thus, in passing from C major to F# (see Appendix), it is only necessary to prepare and connect the key of F# through the influence of the tones of C major (E+-F and B), and the tone-blending is entirely free of any abruptness. As a general rule, it may be said that a nearly related key may be reached by immediately introducing its V, chord, while a remote key may be reached by connecting a triad within the first key with the V, of the new key. The two preceding examples illustrate this statement. Modulations that merely suggest the new key, but do not fully establish it, are called transient. 117 Modulations may be chromatic or enharmonic. The former embrace those that are brought about by the smooth and satisfactory entrance of the tones of the new key. En- harmonic modulations effect the same purpose but retain a pitch while changing its name. (See the above modulations from C major to F# major.) g The following modulations from Albrechtsberger should be analyzed. Note the close connection from chord to chord, and the entire naturalness of the voice progressions. C major to G major: C major to F minor: t _-J - C major to Eb major: I 18 C major to A major: C minor to Dh majcr: ExERCISES TO BE HARMONIZED Capital letters indicate major keys ; Small letters, minor keys. - (/1 *:::: f Vº Ry a * Teº Aº I | I T Eſºx{#–E–C–F–F–EEEA-FCEſ-CEEE L \SUV. | I I | |. | I [[ | | tº * J y - T I I- ſ I s C G 4. —ſ). * - I zºº E ºf i } T] |CU a ſ ) LE- 2 4 º' I arº T I Hº-HEEECEECEFEEEEEEE2-EH IVLATſ. A wº TETI | I ſ I I | I | | | II9 VA ^ - Aº [ _ L Tººl/º E, H • &\ L VLVT2 Tº TUT O. 1- ſº | TV, V Bb Eb VI Vg b A E f{ f; VII'ſ VII? º F- —H----- VII —l |- &T's I- TII e VII? I2 I I R= ab VII? （2–2–H L II | II RE o VIIT Wºr Sequence * l | Sequence Ep zº-i-T ſº III || L- ºn { \SUTZ'ſ Hºs [ \SLJ 2- =# # ~ # - *º-H-------H Sequence «3 Þ> EGBETEH- I22 . APPENDIX I TABLE OF SIMPLE CHORD PROGRESSIONS, IN MAJOR Triad on: May proceed to: I IV V VI II V VI III I IV VI IV I II V V I II III VI VI II III IV V VIIo (To be used fundamentally in sequences) TABLE OF SIMPLE CHORD PROGRESSIONS, IN MINOR . Triad on: . May proceed to: I rv *. IIo V * III+ I V VI IV I IIo V VI V I III+ IV VI VI I II° III+ IV vnº (See VII° under major scale triads) The student should review the rules and models in each chapter of “FIRST YEAR HARMONY” (omitting the chap- ter on Melody Writing), and construct original basses for har- monization in four parts, close position. This should be followed by a review of the same material written in open position. - - I23 The chords to be taken up in this original writing of basses (and later of the soprano part) are: I. Fundamental triads in major. . Fundamental triads in minor. . The six chord (in major and minor). . The four-six chord (in major and minor). * . The V” fundamentally. - . The inversions of the V" (3 # # tº 7. The various sevenths in the order in which they are presented in Part I of this book. * For the first attempt in writing original basses, use only the four measure phrase form. For final cadence, both the Authentic and Plagal forms should be introduced. : MODULATIONS (See Chapter XXI): I. Original modulations, at first as brief in extent as possible, should be made at the keyboard. - 2. For the first effort, let the modulation take place from C major, as a starting point, and proceed to every other major key. Thus: C to DB, C to D, C to Eb, C to E, etc. 3. Such brief modulations may be limited to three or four chords. Thus, from C major to F# major. The first-chord is C major, the last chord will be F# major, the penultimate chord will be the V" of F# major. A connecting chord between C major and the V" of F# major is required for smoothness. In all cases the connecting chord must con- tain one or more tones in common with the V” chord of the new key. Thus: I24 C V, F#V, 4. Many brief modulations require but three chords. . In such cases it will be found that the V” chord of the new key is intimately related or connected with the first chord. Thus: C maj. I FV, I maj. 5. These brief modulations should be first worked out at the keyboard, and then written in correct four-part, open position, harmony. - - 6. Once this simple mechanism is mastered, the modu- lation should be carried out over a greater number of meas- ures, preferably in the four-measure phrase form. I25 APPENDIX II EXAMINATION PAPERS A. THE NEW YORK STATE EDUCATION DEPARTMENT - HARMONY Candidates are required to answer six questions from this group. * - I. Figure and resolve each of the following chords: pe. 'º. * 2. Write in four measures a modulation for four voices, from G major to D major. 3. Harmonize the following for four voices, open score: t #4. - a * Fi cº tº F z T- 4E====E r— I-– =–H 4. Harmonize the following bass for four voices, close posi- tion: - 126 5. Resolve each of the following chords in two ways, giving in each case the name of the resolution and the key: $ 6. Add soprano, alto and tenor to the following unfigured bass; any chords or inversions may be used: ÉÉÉÉÉ######## 7. Harmonize melodies a and b for four voices, in short SCOre: *... 127 8. Illustrate with three chords, the following suspensions: 4-3 9–8 7–6 9–8 9-8 4-3 7–6 B. ASSOCIATE EXAMINATION PAPER SET BY THE AMERICAN CoLLEGE OF MUSICIANS . 1. Write in four voices and resolve a diminished triad and an augmented triad. 2. Classify, figure and resolve the following: { 3. Progress by good voice-leading, from the following chord (triad of F major) directly (i.e., without intervening chord) into the dominant seventh chord, which will resolve primarily into the triads of: (a) G. flat major; (b) D minor; (c) B flat major; (d) C minor. Work this test similar to the following illustration. Any position of the Dominant seventh is available. « » - I 28 4. Modulate from G major to E flat major by means of triads only. Finish with complete cadence. Modulate back to G major in the same manner. Finish with complete cadence. - 5. Illustrate suspensions. Give rules therefor. Figure your examples. 6. Give example of diminished seventh chord. Resolve it. * * 7. Mention any other kind of chord that is not included in the foregoing example. , - 8. Harmonize in four voices the following Cantus. Em- ploy sufficient embellishments, passing notes, etc., to secure smooth movement. C. FELLOWSHIP ExAMINATION PAPER: AMERICAN CoILEGE OF MUSICIANS 1. Harmonize following bass in four parts. The letters represent the roots of chords to be used. Roots, however, do not always appear in the bass. Capitals represent major chords, small letters minor chords. I29 2. And the following melody in four parts. Additional parts may be embellished. F g F C F d a Bb F , d g c F d Bº – g c F C F 3. Harmonize the following bass in four parts. Additional parts may be embellished. - - 4. And the following melody in four parts. Additional voices may be embellished (imitation, etc.). {}-h's - –––. º F; | —º == fi t- - & tº. *-* tº. —3– CEA-Eº-CEEEEEC-EECEGEECEEEE L TT [. LIT I Dº I IT TI L I T L -º 2 º, immi *TL *-T LIT L = I-T- l * º f - l A- Ef . _l I * Tl I H- Hºlſ. Tº w k I ſº r— u Eºr- f) - L. m g i– #EE=#EEEEEEEEEfe EFEEE § #FE P-- 5. Take same melody and write free piano accompani- ment. I3o 6. Write and harmonize in four parts an original melody of eight or more measures. 7. Give some general principles which you would carry out in teaching modulation. 8. Resolve each of the following two or more ways. In- dicate keys and give explanations. D. GENERAL HARMONY TEST. No. I. I. Harmonize the following chord-scheme. Key of C minor: #. * v|1–nº att, V-VI att |Ivatt VI att, I, v' I | 2. Harmonize the following melody, using as few chords as possible and some non-harmonic effects. 3. Complete the following 4-measure cadence-group in two different ways; (a) by a modulation into a minor key; (b) by a modulation, effected by means of a hinge-chord which shall be chromatic in both keys. I31 Harmonize this melody in two ways, completing the exercise with a modulation. Notate all chords. fº TIZIP. l -l bº--- –E–F E. — ===HE ––H– — 4===================== e al | Tººl (a) Harmonize the melody in a minor key. Consider the last note (a) as part of a hinge-chord that is chromatic in the first key and diatonic in the second. - (b) Harmonize the melody in a major key. Consider the last note (a) as the root of a diminished seventh chord, then by changing this chord enharmonically, make a modulation. Write three exercises using these chords and notate all the material. - . . . . . -] —I- TUI # # ſº == # | I32 (a) Introduce attendant chords to any four of these chords. (b) Introduce passing notes, and one or more suspensions and appoggiaturas. (c) Introduce a pedal point and one major-minor effect. E. GENERAL HARMONY TEST. No. 2. 1. Define: (a) Note, (b) Staff, (c) Sharp and (d) give the rule for II to I3 ; (e) rule for V to VI in minor. Illustrate (d) and (e) with examples. 2. Write and name the twenty-three used intervals from F#. - º - 3. Write a major, minor, diminished and augmented triad on EP and the table of all the keys in which they are found. (In this and all the remaining questions the proper contrast in size of the chord numerals, etc., is imperative.) 4. Harmonize and letter fully. - F-I-D- I L– D. I —I Lºlºl QTLVICI ſ —] l Lº | —1 [Tº l – H wº I Ébé-ºf-4CEEE--—EE-53–ºf– Tºy - Tºy 3 6 | 6 | 6 6 - —l— _- - - Tº º: º T -. - I Lº | —l FE * > H —º - ÉÉE ==#EE:#EEEG E==: 6 6 £5 6 6 6 4. t 4. t - + + + —a —l —l l #E ======E====== ILTT _ –D– LT- º Tºy ~ º l w—-a-Z-E- 5. Harmonize with I, IV and V only, and at + show the four different ways of using a 3 chord correctly. I33 (a) -** <º- gº à L. i- a. E* Lll i _º-º assº Lº zº- I Fº [. º *— |--|- tº- | || Tº tºº Tl | I n L I I [ _ E. | | T L. T2- r— l– I | || I TL. Tº —I- z-z. 3 6 6 6 6 - - f 4. (3) cº- e •eº- É= DI |Tºº- tº TE- t T –I. g | 2- º LITE- *— Tº ſº L E. Lis- i l Hºl g I I — L–F- ! | | || g L. [- 8 6 6 6 6 6 6 (a) (8) Ç | e L º I #2 º T- É 3–5–E He E- E-z- —Her—H l F–F n I- T g ITI F-1 |U| - 5 e a. I We t 7. - (c) Fº —ſ-- I – [- T |ſ L–l –º 2- I 6-2 —ſ | Ll 2- ſº tº [. i I | Zºr-E-L-E- _l illº-P - -eº- § fº 6 6 ? # F. TEST IN CHORD CONSTRUCTION I. Construct the diminished seventh chord on C#, and resolve in two ways. 2. Construct an augmented # on Eb, and resolve in two ways. & 3. Write as a four-voiced chord the Vo of G major, E minor, B major, and resolve. 4. Illustrate the preparation and resolution of the follow- ing chords in Eb major: IT IV.1. 5. Write a melody embodying the chord progression V VI, 134 6. Write a melody illustrating the resolution of the II, chord. 7. Use the V; chord in E minor resolving otherwise than to the tonic. 8. Write in four parts, the chord succession I Vo V, I. 9. Illustrate the use of the 3 as the passing chord. Io. Resolve the V7 of any major key so that the seventh (which should be placed in the soprano) will proceed as follows: * (a) Up an augmented prime. (b) Up a major second. (c) Remain stationary. - II. Resolve the Wr (as in No. 10) in any minor key. 12. Construct the following on D5 and resolve at least in two ways: Augmented six-four-three, Augmented six- five-three, Augmented six-three. • * 135 APPENDIX III HARMONIC ANALYSIS The real, but often apparent freedom of many modern composers seems to present chord formations that lie en- tirely aside from the recognized successions of the Classical and Early Modern Schools. - r The following excerpts will illustrate some of the freer instances of tone distribution all of which are, however, re- solvable into clearly recognized chord-formations and suc- cessions. - * { * * Scriabine : Feuillet d'Album, Op. 45, No. 1 The key is Eb major. These final (cadence) measures establish the cadence on BP in the fourth measure, the left hand chord of Eb carrying to the end. The Cb serves to add two colors: (1) that of the flat six of the tonic minor, (2) and impressing the final Bº – dom- inant of the key—as Ve. - º Exercise : (1) Write the Vo in various keys, resolving it. Note the emphasis that the ninth itself places upon the dominant of the key, which, in turn, places equal emphasis upon the tonic. The following illustration shows the use of an unusual meter with anticipation tones (the first F#, for example). 136 REBIkoff : Ruff, Op. 13, No. 8 (6) () () Exercise: Locate each chord, up from the Bass, checking in the right hand part the chord tones only. The first F# (right hand) is a chromatic leading (or leaning) tone, the purpose of which is to make the following G emphatic. Two chords result, (a) (b) D minor II°, then F major W. What is the key location of the third chord (c)? of the fourth (d)? - - - The prevailing key is, throughout the composition, D minor. The final cadence takes this form, however. - REBIkoff : In the Caucasus, Op. 13, No. 2 Alemto I37 The Bass which continues unchanged for twelve measures is composed of the two chords in B minor, V., II?. The F# of the first measure (right hand) belongs to the V, chord. Although it follows the II? its purpose is to emphasize the following E which also continues as a drone tone for twelve measures. All other tones (the triplet, for example, in meas- ure 3) merely play around the E. The twelve measures con- stitute a repeated six measure phrase and not a twelve measure period. - The succeeding section of eleven measures is based upon the pedal point (B and F#). Note the relation of the upper tones to the bass. ... tº Piłł wiza Y- The final cadence makes the following “unfinished ” suc- cession. The effect, of course, justifies the color. Analyze each of the following four-measure phrases, ac- counting for the chromatic tones. They either serve as passing tones or as bringing about the suggestion of a for- eign chord (for passing effect) or they produce a definite I38 modulation. The work laid out in the chapters of this text- book will enable the student to explain the purpose of each chromatic without presenting any special difficulty. HUBER: Intermezzo, Op. 94, No. 4 The E4 (first measure) is equivalent to FB as chromatic tone emphasizing the continuing tone EP which with the Bass Ab creates the drone effect. Note the formation of each chromatic in relation to the continuing chord of Ab major. - . Where a modulation is to be effected, the chromatic tone must be of the new V., chord. Thus—at the point marked (a) — Here the D# is not of the chromatic type as shown above. It becomes wholly of harmonic succession influence. Each chromatic tone should be explained in relation to the prevailing chord. I39 MAYKAPAR : La Flåte du Berger, Op. 15, No. 4 > While there is but one harmonic progression in the above (the V7 I of the last measure) it illustrates how melodic and harmonic successions are made servants to the intended pro- gramme. The music, entitled La flûte du Berger, by S. Maykapar, Op, 15, No. 4, brings about its effect (of flute melody) by the slightest use of harmonic support, the reason being not to overburden the melody to the point of drawing attention away from it. - Measure I, tonic (I) of Gb major. There is one foreign tone (EP) present. Measure 2, tonic (I) of Gb major. The foreign tones are Ep and Ab. - Measure 3, tonic (I) of Gb major. The A5 second beat is a passing dissonance. Measure 4, the C5 suggests the rest of the V7 chord. Why is not the V7 not used in full? Only two of its tones appear. Exercise: Experiment at the keyboard with the V7 I pro- gression and also with the Vo I, resolving the V, or Vo to I melodically. The melodic use of the Wo may be seen in the first example of this set of exercises by A. Scriabine. If the student will “experiment” at the piano with chords, using at first only two in succession, he will adventure upon many interesting combinations. Besides V7 I and VoI; use II, V, I; III, WI; VII° W., I; etc. 14o The key of the following is C major. t Chromatic inflec- tions are freely used in every measure. Note the descend- ing whole tone scale in measures one and two; again, in measures three and four. Claire de Lune, Op. 25 I. Analyze the chords (1) as independent tone groups thus C C# E, B5 E C and so on. 2. Note by what progressions the above continues through the following three measures to arrive at D9 major. The key is definitely established from the point marked (a). The Fp is emphatic of Eb in the Dominant seventh chord (Ab C. Eb Gb) of D9 which is resolved at the seventh In ea.SUIIſe. * <- From the same composition the following is quoted to show the use of the chromatic tone in melodic embellishment • On the way to a cadence point. The key of the composition is C major. From the end of measure 12 the melody pro- ceeds thus: * I41 . Chromatic tones as passing, anticipation and delayed tones are freely employed to give the melody variety and richness of color. This may be done, even to apparent complexity, without creating any uncertainty as to key- terminal. In the above illustration the Ab chord is wholly undisturbed—as to clearnéss— by the highly chromatic approach. * a * Modern music abounds in such progressions. They dif- fer from like-intentioned passages in the writings of the Classical School by their freer use and greater complexity; this, however, chiefly to the eye for the ear readily grasps — - even anticipates — the approaching tonic terminals. The relative simplicity of chromatically enriched passages is illustrated by the following: The melody is along the chord line except in measure four where (as V, to F) the B4 and D are passing tones em- phasizing C which is the root of the cadence chord to F. In the four measures that follow the same melody is va- ried (a) along the original chord line, (b) by the introduction of chromatics that suggest or emphasize chord progression. I42 Example 2 2+==============ſ==H |- H-º-º: Egº-É=EE É=############# ºf Ffºſ FF —t --- --- ſº-º- Compare each beat of Example 2 with the corresponding beat of Example I. Measure I, beats 1–2–3–4. There is rhythmical variation (PFF) with the use of one tone foreign to the chord, C. Measure 2, beats I and 2. Chord of F (V) the first BP in the measure suspending the coming A. The final note of the second beat is a passing tone be- tween C and Db of the V, chord on F. The third and fourth beats continue the V chord. The F# to G is an intimation of the Vo. Measure 3, in the theme (Ex. 1) is, beats one and two, the chord of Bb I. In Example 2, the two beats are the chord of D major. Thence, beats 3 and 4 to the seventh on D (D F AP C) leading to Eb in measure 4. In measure 4, the Bº is leading tone upward (between C and C) while the G9 falls to emphasize the rest chord on F.