AR155 s LY 11 III fill I I I P) lyll evil 111-1,1111,11mn, Hill THE GIFT OF 0 f 0 -Mf t DANA'S PRACTICAL SERIES. DAN A'S PRACTICAL HARMONY BY WILLIAM H. DANA, (President of Dana's Musical Institute, Warren, Ohio.) - AUTHOR OF --- DANA'S PRACTICAL THOROUGH-BASE, AMATEUR'S GUIDE IN ORCHESTRATION, AMATEUR'S GUIDE IN ARRANGING FOR MILITARY BANDS, ETC. PUBLISHED BY DANA'S MUSICAL INSTITUTE, WARREN, 0. COPYRIGHT, 1883, BY WILLIAM H. DANA, PR E FAC E. To the musical theorist, the question might arise regarding the needs of anothei text-book on harmony, but an examination of most works on the subject finds them deficient in points that would make them more acceptable as text-books for the class-room. In some, theories are presented, but it has been left for the teacher to prepare exercises to test the student's understanding. In others, a lack of classification has brought the pupil in contact with a rule having so many exceptions, that the necessity for it is questioned. Others lack exercises in constant repetition, presenting the cold fact without accompanying exercises to impress it upon the mind. This work is presented to the public, hoping that its contents have overcome the criticisms referred to. No originality is claimed, as the contents of the work are drawn largely from the writings of Sir G. A. McFarren, coupled with notes and criticisms taken in the class-room while a pupil at the Royal Academy of Music, London, Eng. The pupil should provide himself with a ruled slate on which to write the lesson, and a blank music-book in which to copy it after the corrections are made. The work is interleaved, that suggestions or remarks of the teacher may be noted, or better still, that in the study of other works on harmony, a comparison may be noted of the subject under consideration. Do not be satisfied with a knowledge of this work alone, but make yourself familiar with many works and theories. Strive to be rich in knowledge. A man gets more than the value of whatever he gives in exchange for learning. Experience in examinations and conversations on the subject of harmony have developed the fact that at least two-thirds of those who profess to have studied it seem to talk intelligently, but when pencil and paper are placed in their hands to illustrate what they seem to know, they are entirely at a loss how to proceed. It is urged upon any into whose hands this work may fall, that they will not only be " readers of the word," but that each subject and exercise will receive the attention necessary to become perfectly familiar with it, and by this means a practical knowledge of the theory obtained. As a matter of recapitulation, the student is advised on having finished the volume to turn back to the beginning and play each exercise from the figured bass, naming the root of each chord and adding the parts, giving proper progression to them and following out every principle under consideration. Nothing so adds to the treasures of the mind and increases its power as thinking. Learn to think for yourself. WILLIAM H. DANA. July 8th, 1884. DANA' S PRACTICAL HARMONY. CHAPTE R I. INTER VTALS. 1. An interval is the distance from one tone to another, and is reckoned upward on the staff unless the contrary is expressed. 2. An interval receives its name from the number of degrees of the staff it covers. 3. A degree is a line or space of the staff. 4. An interval may be modified by the addition of a sharp, flat, or natural. n -, -a — I A-. t-__ l_ I- 14 --- -f-~l= As the notes do not alter their position upon the staff, but are changed in pitch by the added character, it is to be seen that a variety of characteristics may be given to an interval through such alteration. Intervals so changed are distinguished by the terms Major and ~ Minor, Diminished, and Augmented. Perfect 5. The smallest practical interval on which harmony is based, is the semi-tone; on the piano or organ it would be the interval from any key to the next one above or below it. 6. A semi-tone is diatonic when the notes between which it z ~-~z --- lies are on different degrees of the staff. 7. A semi-tone is chromatic when the notes between which it __ lies are on the same degree of the staff, but modified by a sharp, fiat, or natural. 8. A tone includes two semi-tones. Note.-Some authors use the terms half-step and step, instead of semi-tone and tone. 9. A minor second is an interval con- E - - -I _taining one semi-tone,and covers two degrees Jz_______= — of the staff. I (3) 4L x AsV A IQ 'PT? \ PTTO ATTT ARtXTN' JC TV x _ X, 1 W _.A. k^~ lt l. JL_-1L..LJ X J, CTlJl.JL 1 * [ l' 1. 10. Write minor seconds above the tones in the following illustration. 11. A major second is an interval con- __ -l- - - taining two semi-tones, and covers two - i- 0 ---- degrees of the staff. i Write major seconds above the tones in the illustration, Section 10. 12. A minor third is an interval con- -_ -_ —~ taining three semi-tones, and covers three _-_ ' degrees of the staff. I Write minor thirds above the tones in the illustration, Section 10. 13. A major third is an interval con-. taining four semi-tones, and covers three - _degrees of the staff. Write major thirds above the tones in the illustration, Section 10. 14. A. perfect fourth is an interval containing _ five semi-tones,.and covers four degrees of the Bzzr _LEE_ 4_EBz _ staff.. L =i, Write perfect fourths above the tones in the illustration, Section 10. 15. A perfect fifth is an interval containing seven iF semi-tones, and covers five degrees of the staff. ___ -_L Write perfect fifths above the tones in the illustration, Section 10. 16. A minor sixth is an interval containing eight ~-~-~~-z~~:_-~? semi-tones, and covers six degrees of the stair. E- -E-If- E Write minor sixths above the tones in the illustration, Section 10. 17. A major sixth is an interval containing nine -~~ --- —F ~ — ~- - - semi-tones, and covers six degrees of the staff. -Z --- - - E-$2 — Z[ Write major sixths above the tones in the illustration, Section 10. 18. A minor seventh is an interval containinog ten -;semi-tones, and covers seven degrees of the staff. Write minor sevenths above the tones in the illustration, Section 10. 19. A major seventh is an interval containing- --— _-_ eleven semi-tones, and covers seven degrees of the: -_ - __ staff. Write major sevenths above the tones in the illustration, Section 10. twelve semi-tones, and covers eight degrees of the ---- - = - staff. h - Write perfect octaves above the tones in the illustration, Section 19. 21. There are other intervals besides those already namedL Any interval more than perfect or major is called augmented, and those less than perfect or minor are called diminished. REMARKS. REMARKS. CHAP. I DANA'S PRACTICAL HARMONY. 5 22. Intervals within the compass of an octave are called simple intervals, and are seconds, thirds, fourths, fifths, sixths, sevenths and the octave. 23. Intervals exceeding the octave are called compound intervals, and are the ninth, eleventh and thirteenth. See chapter on Discords. 24. For all practical purposes an interval is I 1: regarded as being simple, though it include one or - -- _ more octaves beyond the real notes defined by -- -- these numbers. The following intervals would I each stand as the same in name. Major Major Major Major Third. Third. Third. Third. 25. Intervals are divided into two classes-Consonant and Dissonant. The Consonant intervals are: Thirds, major and minor. Sixths, major and minor. Fifths, perfect. Octaves, perfect. Fourths, perfect. The Dissonant intervals are: Fifths, diminished. Seconds, major and miner. Fifths, augmented. Fourths, in suspension. Sevenths, major and minor. Fourths, augmented. 26. The intervals of the ninth, eleventh and thirteenth are entirely distinct in treatment from the second, fourth and sixth, which are the same notes, and they are used in different combinations. 27. Intervals are inverted when the lowest note becomes the highest, and the highest becomes the lowest. Inverted. Inverted. Inverted. Inverted. The result of inversion is that Major intervals inverted become minor intervals. Minor intervals inverted become major intervals. Perfect intervals inverted remain perfect intervals. Augmented intervals ir 7erted become diminished intervals. Diminished intervals inverted become augmented intervals. A second inverted becomes a seventh. A third " " sixth. A fourth " fifth. A fifth " fourth. A sixth " third. A seventh " second. An octave " " unison. The number of any interval added to its inversion makes nine. By subtracting an interval from nine will give its inversion. 28. In referring to the fourth, fifth and octave, the student has noticed the absence of the expression " major," and that the term " perfect " has been used. These intervals are called perfect because they cannot be increased or lessened by sharps and flats without changing them from concords (Section 25) into discords, while the intervals of'the third and sixth remain concordant under such change, and 6 DANA'S PRACTICAL HARMONY. [CHAP. 1. the second and seventh, which are discordant, remain discords. Again, the fact that major intervals inverted become minor, etc. (Section 28), wvould be contradicted if the perfect intervals were termed major. 29. In the following exercises name the interval between the bass and the part written above it. No. 1. No. 2. /V No. 3. ---.-, No. 4. ) ---- - +-r —4- r — F --- F ---4 —' — No. 5. n I tY 4-= ).1 a _ * _. 4 - No. 6. n I. I.. / i — -f-^-^ \ - - I- I REMARKS. REMARKS. CHAPTE R II. SCALES AND KEYS. 1. A scale is a succession of notes arranged as regards their intervals according to an established rule. 2. There are major, minor and chromatic scales, and they receive their names from the order of tones and semi-tones. 3. A major diatonic scale consists of eight notes, arranged in the following order of tones and semi-tones: 1 2 3 4 5 6 7 8...... ~ ---~ ---- -~, ---~ — - -e — - IC) O C C O 1 2 4 5M a4a a or the following intervals from a given tone called the keynote: ___ _ — _ _-^ ^_ — 7^z^-z Keynote. Major Second. | Major Third. Perfect Fourth. Perfect Fifth. Major Sixth. Major Seventh. Perfect Octave. In the major scale the order of intervals is the same ascending and descending. 4. The student will observe that the diatonic scale consists of major and perfect intervals. 5. Write a major scale founded on each of the tones in the illustration, Chap. I, Section 10. 6. Melody is notes in succession. Harmony is notes in combination. MINOR SCALES. 7. There are two minor scales-the Harmonic (minor diatonic scale) and the Melodic. 8. The Harmonic minor scale is so called because each tone of the scale can appear as a harmony note. (See definition of Harmony.) The Harmonic minor scale consists of eight notes arranged in the following order of tones and semi-tones: (7) 8 DANA S PRACTICAL, HARMONY. [CHA. It 1 2 3 4 5 6 7 8..... — = —. i - I Q n 0 0 0 0 A o E - ~? E.,, CO * - or the following intervals from a given tone called the keynote: ISO— _ — _ 4 ---_ --- ~-J - Keynote. Major Second. Minor Third. Perfect Fourth. Perfect Fifth. Minor Sixth. Major Seventh. Perfect Octave. In the Harmonic minor scale the order of intervals is the same ascending and descending. 9. The student will observe that the difference between the Harmonic minor scale and the major or Diatonic scale is in the third and sixth. *: / -: Major. 4-n - — = — 4-0 * * q = ^ = — = —= —E =- -1 I, --- I h o Minor.,' eJ.~. = v10. Write a Harmonic minor scale founded on each of the tones in the illustration, Chap. I, Section 10. 11. The Melodic minor scale is so called because under certain conditions some of its tones appear only in melody (see definition of Melody) and cannot be used as harmony notes (see Chap. on Passing Notes). It consists of eight notes, arranged in the following order of tones and semi-tones, ascending and descending12. From a given tone, called the keynote, the melodic minor scale contains ascending the same intervals as the major scale with the exception of the third which is minor; in descending the seventh, sixth and third are minor. 13. Write a Melodic minor scale, ascending and descending, founded on each of the tones in the illustration, Chap, Section 10. 14. A key is a scale arranged with reference to any one note, which is called the keynote, and from which the key is named, R E M AR KS. REMARKS. DANA'S PRACTICAL HARMONY. 9 CHAP. II.] 15,. The following-are the harmonic names of the intervals from the keynote in both major and minor keys: 1 2 3 4 5 6 2 8 0 0 Ca a 0 0 0 - S C$ - rJ2 -4 S Ca S.0 iS VI2 0 z1 bo rS C3 0 16. Name the letter in each of the following exercises: as, the Tonic in the key of C, is C; the Dominant in the key of G, is D; a key is supposed to be major unless the contrary is stated. The Tonic in the key of G is 4 4 4 4 C 4 9 (.4 ( 4 ( 9 ( 4 '(4 ( 4 t 4 4 4 4 4 C 4 4 C 4 4 4 C4 t 4 ( 4 9 4. 4 (i 4t C 4 4 4 cc C 4 ct C 4 4 44 ' 6 C 4 I ofninant Super-Tonic ".- '' Mediant Tonic Dominant Sub-Mediant Dominant Sub-Dominant Mediant Dominant Super-Tonic Sub-Dominant Sub-Mediant Leading Note Tonic Mediant Sub-Dominant Leading Note Sub-.Mediant Sub-Dominant Super-Tonic Leading Note Sub-Mediant Tonic Leading Note Tonic Dominant Sub-Mediant Mediant Dominant Tonic Mediant Super-Tonic Dominant I I "A flat is E is"E flat is " Bis - "D fiatis " G3 is - - "B fiat is " G4 3fl a ti s - "D is C sharp isD sharp is" G4 i i s "F is " G flat is - Osharp is - "A flat is " 'Dis - "E is 43 sharp is "A flatis"G43is. "B flat is "E is "D flatisC sharp is " Dis - "E flat is " F sharp is "C isF sharp is"D flat is "A is A sharp isCisB is 10 DANA'S PRACTICAL HARMONY. [CHAP. 1i The Sub-Mediant Leading Note Super-Tonic "Sub-Dominant " Tonic "Mediant " Dominant Leading Note *'Super-Tonic Mediant Dominant Super-Tonic " Mediant " Sub-Dominant "Dominant " Sub-Mediant Leading Note " Sub-Mediant " Dominant Sub-Dominant " Mediant Super-Tonic "Tonic "Super-Tonic " Mediant ' Sub-Dominant " Dominant Sub-Mediant Leading Note Sub-Mediant "Dominant "Sub-Dominant " Mediant Super-Tonic " Tonic "Super-Tonic " Mediant Sub-Dominant Dominant "Sub-Mediant Leading Note "Sub-Mediant " Dominant "Sub-Dominant " Mediant Super-Tonic "Tonic 'Super-Tonic " Mediant in the key of E flat is -- " "D sharp is r" " D flat is " Cis" EE is" F is " " G sharp is - " " F is " G is '; '; Cis " E is " "F sharp is - " G is " A flat is " A is F is " '" B is " D is " " E flat is " " G sharp is " " D flat is " G sharp is "" E is " " D is " G flat is ^ " "B is'" " C sharp is -- " " A is " "E flat is "n " C sharp is — " D is "" E flat is" G sharp is - " A isB flat is " D is " E flat is ' " F sharp is - " " B flat is " " G is " A is - " " G sharp is - F is " " D flat is" A flat is "B is - " G flat is " " F is - -"E is - REMARKS. REMARKS. CHAP. II.]DANA'S PRACTICAL HARMONY. 11 17. The Tonic "Super-Tonic " Mediant "Sub-Dominant "Dominant "Mediant Leading Note " Sub-Mediant "Dominant " Sub-Dominant "Mediant Super-Tonic " Tonic Super-Tonic "Mediant "Sub-Dominant " Dominant "Sub-Mediant " Leading Note " Sub-Mediant "Dominant "Sub-Dominant " Mediant Super-Tonic "Tonic Super-Tonic "Mediant "Sub-Dominant " Dominant "Sub-Mediant Leading Note "Sub-Mediant " Dominant "Sub-Dominant "Mediant Super-Tonic "Tonic Super-Tonic "Mediant "Sub-Dominant " Dominant "Sub-Mediant Leading Note " Sub-Mediant " Dominant "Sub-Dominant " Mediant Super-Tonic "Tonic in the Harmonic minor key of G is - ". D flat is - E is. F sharp is -- A flat is B is - C isC sharp is D is E flat is G isA is D sharp is - F isG sharp is - B flat is - D is E is G flat is F is G is E is - F sharp is A flat is E flat is - D is C sharp is C isD is - G is B flat is A is F is G flat is E flat is G sharp is F is - G isB is D is -- B is - F sharp is - G isB flat is E is -- A flat is - A is - G is C is, 12 DANA'S PRACTICAL HARMONY.HA [CHAP. I, The Mediant " Sub-Dominant " Dominant " Sub-Mediant " Leading Note " Sub-Mediant " Dominant " Sub-Dominant " Mediant " Super-Tonic " Tonic " Leading Note " Mediant Super-Tonic " Mediant " Sub-Dominant in the Harmonic minor key of C is -- r' '- _ " F is " " " G flat is " " " A flat is " "" E is " " " " D is - " " "r A is "' 0"- G is "" " D is " " " " 0 C sharp is " "" B is " " " F sharp is" "i D is " E " "B is t" 0- r G is " " " i " E flat is 18. The Chromatic scale consists of twelve notes, and contains the same order of intervals in both major and minor keys. The arrangement with reference to the keynote is as definite as that of the major and minor scales. Its order of intervals from a given tone called the keynote, is as follows:.- j _ -------------- ----- Keynote. Minor Second. Major Second. Minor Third. Major Third. Perfect Fourth. Augmented Fourth. Perfect Fifth. Minor Sixth. Major Sixth. Minor Seventh. Major Seventh. Perfect Octave. Every interval that can be major or minor is so, and the 4th is the only perfect interval that is changed. Whatever difference of opinion occurs in the notation of the chromatic- scale, all writers agree in writing the augmented 4th (not the diminished 5th) and the minor 7th from the keynote (not the augmented 6th). 19. Write chromatic scales, taking each of the tones as a keynote found in the illustration, Chap. I, Section 10. REMARKS.,A REMARKS. CHAPTER III. CHORDS. 1. A common chord is a bass note (1st letter or root) with its major or minor third, and perfect fifth. 2. Chords receive their modifying terms, major and minor, from the third of the chord; and augmented and diminished from the fifth of the chord. 3. A major common chord is one consisting of a root, major third, and perfect fifth. 4. A minor common chord is one consisting of a root, minor third, and perfect fifth. 5. A diminished chord is one consisting of a root, minor third, and diminished fifth. (See chap. on the Dominant 7th.) 6. An augmented chord is one consisting of a -root, major third, and augmented fifth. The letters in the chord of A major are - " B flat major are - " " i" G sharp major are ': is Ad" " C major are -t A flat major are - " B major are -- " C sharp major are" " " i major are" " E flat major are " " " G miajor are - D flat major are " " " G flat major are - " D sharp major are - " " E major are " F major are " F sharp major are The letters in the chord of A minor are " " " C " " ___ ss " t" B " " c; " ____E " " " " ________, F ' ________ " C sharp minor are " F " " _______" " " " 3 " "' " D "i '' " ___I__ 3) " " ___" (13) 14 - DANA'S PRACTICAL HARMONY. The letters in the chord of A sharp minor are - 4 4 4 i" D flat " " ___ [CHAP. III cc 4 C 4 4 4 4 4 4 &4 The letters 4 C 4 4 i 4 - 66 69 4 6 46 C 4 4 C. 4 4 9 6 4 4 46, 9 4 4 4 4 4 4. 44 6 6 i4 46 -4 C C 4 cc 64 4 4 cc 6 6 44 64 49 44 4 C 9 4 44 46 94 64 44 9 & C C C 4 C ___ _ CC CC A. C C CC CC _ _ _ _ _ in the diminished chord on A are CC CC CC I ) CC C C C C C C C ' ' _ _ _ _ _ CC CC C F i' C C C C C B C C _ _ _ _ _ CC CC CC E CC _ 94 44 " C sharp are - CCC C A CC C C C CC C C l C4 CC CC C CC F CC CC C C C C B CC C _ _ _ _ CC 4 CC A flat CC CC CC 4C C3 CC C4 C C CC C C B C C 4 C _ _ _ _ _ CC CC CC IE CC CC 44 augmented "4 C are - CC C F "4 CC CC CC B CC __ __ _ C C C C C C IE C C _ _ _ _ _ " A CC __ A __ CC CC CC 4G 4C __ __ 4~ 44A sharp are - CC CC C D CC C4 CC i t CC G CC CC _ _ _ _ _ CC CC C C CC 4i CC CC C F CC C '' B " C CCC, C E CC CC cc CC C CI flat ' C __ _ C C ~ C CC B CC C CC C' C CC C CC CC CC A " CC ~ C C CC D CC CC ' CC G REMARKS. REMARKS. - ~ r j ~r1 ~. - ~ T __.~ 1 I CHAP. IM.] DAJA b r IlAUli'UAL HAIMUUN X. 1I; 8. The following are the tones and order of intervals in a major diatonic scale: By ---- # — ~ '-a — If each one of the notes in this scale is taken as the root of a chord, and to it are added notes taken fiom the scale standing at the intervals of a third and fifth, the following will be the result: _ —1 ---_b= =. S S g g g g " b a a -0? at.3 a The above illustration has developed Three major chords-the Tonic, Sub-Dominant and Dominant. Three minor chords-the Super-Tonic, Mediant and Sub-Mediant. One diminished chord-the Leading Note. 9. The following are the intervals in the Iarmonic minor scale: — =^ ---= —eIf each one of the notes in this scale is taken as the root of a chord, and to it the intervals of a third and fifth are added from the notes in the scale, the following will be the result: W~i —9 ----0W. ~ The above illustration has developed Two minor chords-the Tonic and Sub-Dominant. Two major chords-the Dominaht and Sub-Mediant. Two diminished chords-the Super-Tonic and Leading Note. One augmented chord-the Mediant. 10. Chords built upon the intervals of the scale are named from them. A chord built upon the first tone of a scale (the Tonic) is called " The chord of the Tonic;" on the Dominant, "The chord of the Dominant." 11. In reading the following exercises state whether the chord is major, minor, diminished or augmented, as: The chord of the Tonic in the key of G is the chord of G majorThe chord of the Sub-Dominant in the key of C is " Mediant " ' D " " " Sub-Dominant " " F ". " Dominant " " A " _ " Sub-Mediant " G " - Leading Note " " A " G " Tonic " " E ". - 16 DANA'S PRACTICAL HARMONY. [CAP. II The chord of the Leading Note in the key of D is -- " Sub-Mediant " " B " " Dominant " " E " " Sub-Dominant " " B " M" Mediant " " G 0 " Super-Tonic " " C -- " Tonic" '" B " Super-Tonic " " D" " i Mediant " " F "" Sub-Dominant " " A " -- " Dominant " C " -- " Mediant " " E" - ' Leading Note " " G - " " Tonic " D Leading Note " " F " - " Sub-Mediant " " A " " Dominant " " D " " Sub-Dominant " " G " " " Mediant " " E " - " Super-Tonic " " A " " Tonic " " " " Super-Tonic " " E" " ' Mediant " " B " - " Sub-Dominant " " D " " Dominant "G -" " Sub-Mediant " " D " Super-Tonic " " F" - " " Leading Note " " C - " Sub-Dominant " " E" - M" ediant " " A" " Dominant " " F " Leading Note " " E '; " Super-Tonic " " B - " Dominant " " B " " " Mediant " " C Leading Note " " B - " Super-Tonic " " G " Sub-Mediant " " C " " Tonic " " A "" " Sub-Mediant " " F " " " Tonic - " G sharp minor is - " Dominant " " C " " 'i Super-Tonic " " F ' " - " Mediant " " G " " " Dominant " " F " " " Sub-Mediant " C " " " Leading Note " '" G - "" " Sub-Mediant " " F " " " Dominant " " REMARKS. REMARKS., CHAr. III.] DANA'S PRACTICAL HARMONY. The chord of the Sub-Dominant in the key of C sharp minor is 17 4 4 9 & 4 4 4 4 i 4 4 6 4 6 4 L L 4 4 4 6; 4 4 4 4 44 4 4 4 I 4 4 I.I 44 4 4 44 4 4 1 4 4 4 1 4 4 4 4 4 4 1 6 4 4 4 & L 4 4 4 4 44 4 4 i 4 & 4 " Mediant ' Super-Tonic " " Tonic " " Super-Tonic " " Mediant " " Sub-Dominant " Leading Note " Sub-Mediant " " Super-Tonic " " Leading Note " " Sub-Dominant " " Tonic " Tonic" " Super-Tonic " " Mediant " " Sub-Dominant " " Dominanti " Sub-Meliant ' Leading Note " " Tonic " Leading Note " Sub-Mediant " Dominant " " Sub-Dominant M" ediant " Super-Tonic ' Tonic " Super-Tonic ' " Mediant " Sub-Dominant " " Dominant " Sub-Mediant " " Mediant " " Mediant " Leading Note " " Sub-Mediant " " Super-Tonic " Sub-Dominant " Dominant " " G " "4 G "4 _ _ "4 0 " ~ g1 "4 F? "44 "~ 0 " _ _ _ "4 G "4 "~ F "L 4 D flat minor i3 " A " B " E " D L A " B " E "A B ' E " D " B ' E; E D " - E " B " A ( D " A E D B A B tr 12. Asa common chord is composed of three letters (1st, 3d, and 5th), under certain conditions any one of them may become the bass note to the chord. M; - I - -- I I 1 _- i _ W_. __I F t- Tird..__ _T. F__ First. Third. Fifth. lirst. Third, Fifth. 18 DANA'S PRACTICAL HARIGOCNY. [CHAP. Ili 13. When the first letter of a chord is the bass note, the chord is in the direct form, or direct. ( -i -— ~ -I-L — First. First. First. 14. When the third letter of a chord is the bass note, the chord is in the first inversion. __ j- -~ -1 \ - L L _L_ _L Third. Third. Third. 15. When the fifth letter of a chord is the bass note, the chord is in the second inversion. 9- - -— r --- ---- Fifth. Fifth. FYifch. 16. A system of figuring is used to indicate the inversions of a chord. A chord is in the first inversion when the figure 6 stands under or over a bass note. E If it-#6-1 —? —? —1 -6 6 6 6 6 A chord is in the second inversion when the figures 6 stand under or over a bass note. Q- d --— A-=: P -^ ~ --- —i^ ----^ ---- -— j6 6 6 4 4 4 5 The absence of figures, 3 or any combination of these figures, indicates the direct 8 form of a chord. 5 5 5 3 3 3 8 Name the chords and inversions in the following exercise: 6 60 6 6 6' 6 6 6 6 6 6 6 4 4 4 3 4:~' ---i ---t --- — --- -t — - - -—? --- —-'-. ---- --— ~ -,- --— + --- —------ t --- —-~i~~ ~ _ —_ - - _ + ---_ ei_: --- —----- --- -— _ 6 6 4 06 6 6 6 66 8 6 4 4 4 6 6 6 4 8 REM ARKS. REMARKS. CHAP. 111.] DANASS PRACTICAL HARMONY. 19 17. Position is that part of the study of chords that relates to the highest letter that appears in a chord. There are three positions of a common chord, founded on the three letters that compose it. 18. A chord is in the first position when the first letter of the chord is the highest note. First. First. First. /I rn I I. k IE2- -— 100- -- -17=:f — A chord is in the second position when the third letter of the chord is the highest note. Third. Third. Third. ~-D- -H — - --- A chord is in the third position when the fifth letter of the chord is the highest note. Fifth. Fifth. Fifth. L — 4 (J _- t —=g --- (1z - 19. When a sharp, flat or natural stands alone, under or over a bass note, the third from the bass note should be made sharp, fiat or natural. w-E;- -| - - L — H — b # 0 When a sharp, flat or natural stands beside a figure, under or over a bass note, it shows that the letter the distance of the interval denoted by the figure is sharp, fiat or natural. h 7 76 #8 t6 f7 1 5 -<-g~3 CHAPTER IV. PROGRESSIONV OF PARTS. A part in harmony is a succession of notes that may be performed by one voice, or by an instrument capable of sounding but one note at a time. 1. A part should not proceed by an augmented interval. A part may proceed by a diminished interval, but it must immediately return to some note within the interval, and not proceed in the same direction. ______l /, —,-D: —__-_-_-r__. -: After the leap of an interval larger than a 5th, it is recommended to return to some note within the leap. z. z j t _ _* 1I*:fc=- j=:^r i ---:^~=rr~^,2. By motion is meant the changing of pitch of a voice or instrument-the movement of tones up and down the staff in a part, is said to be its motion. When two parts rise or descend together, they are said to proceed by similar motion. I1 I ^r-1 ----iJ_-____ I. _ When one part rises and the other descends, they are said to proceed by contrary motion. _., I _ _ _ _ _ _ _ __.. - __ —___-i — -. —~-a___________ ___ Cj5 — __~" -" r -I ____1 When one part remains stationary, retaining or repeating the note, and the other moves, they are said to proceed in oblique motion. -J-n= — =-E-,Fi (20 --- (20) REMARKS. REMARKS. CHAP. IV.] DANA'S PRACTICAL HARMONY. 21 3. No two parts may proceed in perfect fifths with each other. Except fifths in the extreme parts by contrary or similar motion between the Tonic and Dominant, and between the Tonic and Sub-Dominant. ___ _ _ __ -i 4-f No two parts may proceed in octaves with each other. Except octaves, in the extreme parts proceeding by contrary motion between Tonic and Dominant and between Tonic and Sub-Dominant. No two parts may proceed in unisons with each other. Note.-The student will observe that the bad progressions in fifths, octaves and unisons, must be between the same parts. A fifth between bass and alto followed by a fifth between tenor and soprano would not be incorrect. 4. Outer voices are those that sing the highest and lowest parts; as bass and soprano in a quartette for mixed voices. They are the highest and lowest parts whether the composition be a duet, trio or quartette. 5. Outer voices may not proceed by similar motion to a perfect fifth from another interval. - 1 Except the 5th of the Dominant approached from the harmony of the Tonic, and the 5th of the Tonic approached from the harmony of the Sub-Dominant; provided in both cases the top part move a 2d. I n-= 3 Cnl r A XT A as 1 T AT~ t- A 1 TT A Tf> r/-,-r JJ^iUAINt o rl-jnA~iluA~i iu2\ i. [CHAP. IV And except the same chord in moving to its different positions. ' i 6. Outer voices may not proceed by similar motion to an octave. I I Except the octave of the keynote if approached from the harmony of the Dominant, and the octave of the Sub-Dominant if approached from the harmony of the keynote; provided in both cases the top part move a 2d, and such octave is the root of a chord. 7. Outer voices may not proceed by similar motion to a unison. 8. No part may proceed in fourths with the bass, except when the second fourth is a portion of a fundamental discord. 6 4 4 2 The progression of fourths between two upper parts against a moving bass is not objected to. 9. In harmony of two parts a 3d may not be followed by a 5th when both parts move a 2d. The bad effect ceases when a third part is added. 10. The Leading Note must rise. There is no restriction as to the interval by which it must rise, except in a full close (Chap. VI, Section 5), when the Leading Note must rise to the keynote. REMARKS. REMARKS. DANA S PRACTICAL HARMONY., 23 CHAP. IV ] EXCEPTIONS. Except when the bass descends by degrees from the keynote to the 6th of'the key when the Leading Note may bear the first inversion of a concord. I nI! WA 6 Except when all the parts proceed by degrees in a succession of first inversions. ) - J,I 6 6 6 6 6 Except in changing from one to another position or inversion of the same chord, n I I "zzt'zzz 1 I.i -1 ai t 11. As a passing note the Leading Note is free to rise or to fall., I, 12. As a suspension (Chap. XII, Sec. 2) the Leading Note falls in its resolution. 6 4 3 13. As a diatonic seventh (Chap. XIV, Sec. 15) the Leading Note descends. ) * I _.1_ _ _. __,_ 14. The Leading Note should not be doubled (appear twice in the same chord). 24 ^ DANA'S PRACTICAL HARMONY. [CHAP. IV. 15. When a bass note is the major third of a chord, it may not be doubled, except the parts move in contrary motion, and the thirds are approached and left by the step of a 2d. 6 6 6 Illustrations are given where the Leading Note is doubled under the preceding exception to the doubling of a major third. ( W ---— I _. * * I — i -- — L —__ [ 6 6 6 16. The chord of the Super-Tonic may not be followed by the chord of the Tonic, except when both chords are in the first inversion, and when the chord of the Tonic is in the second inversion. __ ~_ __ '- $' (I - H+ — F 6 6 6 6 6 4 4 17. The progressions, chord of the Dominant in the direct form, followed by the chord of the Sub-Dominant in the direct form, should be used sparingly; also the second inversion of the Tonic followed by the direct form of the Sub-Dominant. 6 _ - 4 18. No two notes next to each other in alphliabeical order may proceed by oblique motion to an octave or unison. REMARKS. REMARKS. CHAPTER V. 1. In a previous chapter the idea was advanced that under certain conditions the direct form and inversions of the common chords in a major key could be used. 2. There are five common chords in the direct form in a major key that are practical: Tonic, Super-Tonic, Dominant, Sub-Dominant, and Sub-Mediant. _ E__ _ ___5 5 5 5 5 3 3 3 3 3 3. The chord on the Leading Note is a diminished chord,:P_ — F and therefore a discord. 4. The common chord on the Mediant is so unsatisfactory in its relation to the other chords of the scale, that it is classed among the discords. It is not a discord in its construction, but in its association, or rather relationship. 5. The chords on the Leading Note and Mediant are only discordant when the 5th is between the bass and an upper part. These chords are no longer discordant when the interval of the 5th is changed from the bass and an upper part. Both of these chords can then be used in their first inversion. 9_Zi —ZKI — _ 6 6 6. Every note in a major scale can appear as the first inversion of a concord. 6 6 6 6 6 6 6 7. There are but three notes in a major key on which a second inversion can be made: Tonic, Super-Tonic, and Dominant. - ----- ------- 6 6 6 4 4 4 8. The following diagram will give the direct form and inversions on the notes of a major scale. (25) 26 DANA'S PRACTICAL, HARMONY. [CHAP. V. - ---- I5 — 3 3 3 3 3 6 6 6 6 6 6 6 6! 6 | s6 4 | 4,, | That is, the Chord of the Tonic can be used in the direct form, 1st and 2d inversions. " " Super-Tonic " " i direct form and 1st inversion. " " Mediant " " i 1st inversion only. ' " Sub-Dominant " " " direct form, 1st and 2d inversions. " "u Dominant " " " direct form, 1st and 2d inversions. " " Sub-Mediant " * " direct form and 1st inversion. " Leading Note i" " " 1st inversion only. 9. The second inversion of a chord can not be approached by leap from the inversion of another chord, but may by the step of a second from the inversion of another chord. 6 6 6 6 4 4 10. It may be approached by leap from an inversion of the same chord. 6 6 4 11. Also by leap or step of a second from the direct form of another, or the same chord. 6 6 4 4 12. A second inversion must be followed by some other chord on the same bass note, or else by some chord on the note next above or below it, diatonic or chromatic. '- ' [ ' - -I — ____:__ 6 5 6 5 6 6 6 6 6 4 3 4 3 4 4 4 13. So long as the harmony of a second inversion continues, the bass note may proceed to another letter of the chord, or proceed by a succession of passing notes to it, provided when the harmony changes to a chord having another root, the bass return to the note that was the second inversion, or to the note next above or below it, whichever it might have taken had there been no digression. REMARKS. REMARKS. CHAP.V.] DANA'S PRACTICAL HARMONY. 2._______, -u. v 6 ' 6 "^- ait-_o-L --- —l-t-q — -- - = —E --- — =t -- F-='sti —t ----3==9 -~ -0 — zz — zi ---z ---I- zzi- Ldzzr ~ —9 —~L~ I * O=W==A=[ -13- ~ —| ---= --- —-m-L —;=-t -t 6 - 6 --- 6 6 6 4 4 4 4 14. A second inversion, if followed by a chord on the '; same bass note, must appear on a more strongly accented ~ 5 part of the measure than the chord which follows it. 4 3 15. If the second inversion has been preceded by another chord on the same bass note, it may be taken at any part of the measure. 9 ' --- —- - - ----------- 6 5 6 5 4 3 4 3 16. If the second inversion is followed by a chord upon the bass note next above or below, it may be taken at any part of the measure. i)' —.== —, —F' —i-r ----= ----.... —F-t=:=-7 ------- F ---~ ----, ---=~o — -, --- — '_ _.__ _ _-' ---O — 6 6 6 6 6 6 6 6 6 6 6 6 6 4 4 4 4 4 17. There is the single case in which one second inversion may follow another: The second inversion of the chord of the -_ Dominant, followed by the second inversion of the chord of 6 6 the Sub-Dominant. 4 4 18. Exemplify the principles in this chapter by figuring the following: No. 1. _ - ' ~-~ #-t — ' ---~ —r ~-~ --- t ' --- -~-~ ~ ---t — ~-~ ~ ' --- —: — No. 2. '.- - -e-~ -^-~__ —F — -— t —l-*- ^-' — ^ ---^- -H-. 5 eD 3 No. 3. 3 No. 4. -— _ ----. ---___- _ _ No. 5.: -l~ > ~ -- '-~ —~-........-1 —~-_ ^ -, _ T'-o —r-o.... 8 No. 6. ----- - -- - — r ----o — - -_ _ _ _ _X_ _r_ _r _ _ 28 DANA'S PRACTICAL HARMONY. [CRAP. V. 19. Harmony has a richer, fuller effect when the parts'stand at nearly equal distances from one another. If there is a separation between any two parts, let it be between the bass and the part next above it, 20. Let the upper parts skip as little as possible, and where a note is common to two or more chords, retain it in the same part. 21. When several first inversions occur in succession, it is expedient to place the first letter of the chord in the upper part, and thus avoid consecutive fifths which would occur if the fifth letter of the chord was in the upper part. 6 6 6 6 6 6 6 6 22. When two chords in the direct form move a second, it is expedient to have the fifth and octave of the first chord move in contrary motion to the bass. 40-4-4___ _ _ I* *I l, --- —-~ ~~ t ___9 - 23. A lower part should not proceed to a higher note in one chord than the note assigned to a higher part in the previous chord, nor should a higher part proceed to a lower note in one chord than that assigned to a lower part in the previous chord. i=:- -==_=-9-t_ IV i I Y _-1 ---6 6 {1 =1_ i 7. It a ___1 I 91-=-=s --- r --- - 24. Also in. ordinary choral writing a lower part should not be given a note higher than a note in the part above it in the same chord. * - I -RE MARKS. REMARKS. aP. V.] DANA S PRACTICAL HARMONY. 25. In the following exercises add an alto and tenor. No. 1. 29 ~~ - - - - - - -___ -__ -+ 6 It I I ' - I — 6 6 6 66 4 -— 7 -4- --......4 —t -- 6'6 - - -I - - ~ I' 6 - ~ __ __ B - _9 - -Uf Ia — - -_ B_._____ _L-_ -— L — -_ -7- - __- -- 6 6 6 6 - 6 -- I — I -----— i - _: -_ 1 — _=-__.___ _ - _ - _ - - _ -t — -p -I___ig_4 6 6 6 ____ ___ - —. w - U --- _ 6 -I 6 - 6 — 6r-r 6 --- —--- 6 5 C HAP T E R VI. COMPASS OF PARTS. 1. In choral writing for four voices the following may be considered the average compass of the parts. Bass. O_- _ -0* Tenor. - -_ -- _ Alto. *S Treble. ~ --- ) -g__ E 2. Before proceeding farther the student should make himself perfectly familiar with every principle in Chapters IV and V. 3. Add a Treble, Alto and, Tenor to the following figured basses, etc.:No. 1. 6 6 6 6 6 6 6 6 5 4 4 4 4 3 -No. 2. __irt-, — ~..... ~_~ ~.i- - 6 6 65 6 6 6 65 6 6 6 6 43 4 43 -i —ZE__- ' ' --— _-_ --. — '.[ __ __ __ __ __ ~- '__ _ _r 6 6 5 6 6 6 65 65 6 6 6 6 5 4 3 4 43 43 4 4 3 No. 3. _ __ - -'.... ~- _ --- 65 6- 6 656 6 66 43 43 No. 4..9r —r — -F_-__. _ _r?-_ _ — __ ----'-_ _L-r_^ —g.. __~-c zj_:_ _~_ ~ q_~-F_ 9IV 6 6 65 65 6 6 6 6 6 5 43 43 4 3 NTo. 5. -- -- O --- —— ~-L -~ ~~ - - 6 6 6 6 6 6 6 6 6 6 6 4 4 4 No. 6. L~j -- _ — 66 6 6 6- 6 6 6 6 6 6 66 6 6 4 4 4 No. 7. REMARKS. REMARKS. C(AP'. l.] DANA S PRACTICAL HARMONY. 31 No. 8. ---— [= — ------ T -- ~~rL --- 66 6 6 6 6 No. 9. ": I *: i 1 —,-X-o L 16- -a -- _ _ --- —_- _ —t --- - 6 No. 10. _ --- - -— I.... ~ ~~ — "-~. __. __ ---— __ -. —. 6 6 6 6 6 65 43 CADENCE OR CL OSE. 4. The end of a musical phrase is called a cadence or close, and the term is generally applied to the last two chords of the phrase. The principal closes are the Full close, Half close, Plagal close and Interrupted close. 5. A full close is where the chord of the Tonic in its direct form, is preceded by the harmony of the Dominant. '' -,1 __ __,__ ____ __ f_ z z. _ —_- _ —_ --- --— H-_ — ' —_ _ 6 6 4 6. A half close is where the final chord is the Dominant in the direct form.: — ~* ----E --- 7. A plagal close is where the chord of the Tonic in its direct form, is preceded by the chord of the Sub-Dominant, which is either major or minor. /I_-_n- -=..............I 6 4 6 4 8. An interrupted close is where the harmony of the Dominant is followed by a chord other than the chord of the keynote. -a - -- 4- a 32 DANA' S PRA':CTICAL HARMONY. [CHAP. VI. 9. Write Full closes in various keys. a Half " " " Plagal " " Interrupted " 10. Most of America's composers are writers of church music (chorals), and their writing of other styles of composition has been reached through their knowledge acquired in writing the simpler forms of church service. The same course will be pursued throughout this work, and as theoretical knowledge is acquired, it will be made practical in writing chorals, and the more elaborate forms of vocal writings. 11. Where music is wedded to words one principle controls the union, and that is accent. Accented words or syllables must fall on accented parts of a measure. 12. Measure is the rhythmical division of melody, and what is termed " time" is the inner division of measure. 13. A measure may be divided into two units as its conftents, the accent coming on the first unit, and the time is indicated by the figures 2, 2, 2. __ 71 -1 - -— 8-= = -- A A A Also three units in a measure, the accent coming on the first unit, and the time being indicated by the figures, 47 8. And four units in a measure, the accent coming on the first and third units, the time being indicated by the figures 4, 4, 4. 2i7 4J7 81 A A A A A A 14. Compound time is the placing in one measure, two, three or four measures of three units in a measure, and the accent falls as it would if the simple measure of three units stood alone, except that it is more strongly marka3 upon the first unit than in other parts of the measure. ^==^ ___=_dx=: i;~_~:_ — _-__ - ~ —~ —~ --- — ~_ _ __ *m-s -i —__ E AA A A D-I-_ —_ -- __ ' -- -,te —, --- —i ----.-I ---, ---, —j-.- -_ --— _-~ —_~ — ^-~-... -_L_ __ ___ — ___ __ A A A A A A A A 15. Metre is the arrangement of the syllables of verse. 16. Verse is measured by the number of lines, the number of syllables in the respective lines, and the regular recurrence of accented syllables. 17. As there are accented syllables in verse and accented notes in music, a proper union of the two is essential when poetry and music are combined. The accent in prose is equally applicable. REMARKS& R5EMARKS. CHAr. iV] DANA'S PRACTICAL IiARIMONY. 33 18. In wedding music to words the first step to be taken is to scan the words for accent, and then decide as -to the time. If the following verse is read slowly, the syllables in italics will have received particular emphasis:When, gra-cious Lord, when shall it be, That I shall find my all in Thee; The ful-ness of the prom-ise prove, The seal of Thine e-ter-nal love. The above can be written in any kind of time, provided the accented syllables appear on the accented parts of the measure; but there are many things to be taken into consideration, as the character of the time, length of line in measure, etc., etc. Writing the first line of the verse in the different kinds of time, will best illustrate the principles advalnced. NTo. 1. When, gra - cious Lord, when shall it be. or, ~....F --- iH --- —--- - When, gra - cious Lord, when shall it be. TNo. 2. 'When, gra - cious Lord, when shall it be. or, -t7 ---------— '-0 --- —S --- —# ---#- — L --- —--— L- -= ----B — When, gra - cious Lord, when shall it be. No. 3. When, gra - cious Lord, when shall it be. No. 4. ~/ —i_ ----_ ----~ ----_.... --- —6 --- —_ —t ----~...... When, gra - cious Lord, when shall it be. A moment's examination of the above illustrations will probably result in No. 1 or No. 3 being selected as the most. suitable; 3 time, being flowing in style, is quite acceptable. When, gra. cious Lord, when shall it be. 19 In order to exemplify the principles found in the various chapters to this point, and to develop the knowledge acquired, it is recommended that the student write chorals, using the common chords and first and -second inversions. - 34 DANA'S PRACTICAL HARMONY. [CHAP. VL The first verse to a number, of hymns will be given requiring musical setting. At the end of each line a cadence of some kind should be introduced, unless the continuity of thought is such that punctuation does not occur at the end of the line. A full close should appear at the end of the last line. It is urged upon the student to study the effect of chords in their inversions, and in their relation to one another. There are many progressions that are theoretically correct, but unsatisfactory to the ear. As to the direct form and inversions of chords the listener will observe that the direct form is satisfactory in its effect (this accounts for the advice regarding the use of the direct form in the closing chord of a cadence); the first inversion is indefinite in its effect; and the second inversion is discordant. No. 1. Brother, thou art gone to rest, We will not weep for thee, For thou art now where oft on earth Thy spirit longed to be. No. 2. Jesus, and shall it ever be, A mortal man ashamed of Thee! Ashamed of Thee whom angels praise, Whose glories shine through endless days. No. 3. With all my powers of heart and tongue I'll praise my Maker in my song. Angels shall hear the notes I raise, Approve the song, and join the praise. No. 4. 0, happy is the man who hears Religion's warning voice, And who, celestial wisdom, makes His early, only choice. o No. 5. How gentle God's commands, How kind His precepts are; Come, cast your burden on the Lord And trust His constant care. No. 6. See how the morning sun Pursues his shining way, And wide proclaims his Maker's praise With every brightening ray. No. 7. Asleep in Jesus! blessed sleep From which none ever wake to weep. A calm and undisturbed repose, Unbroken by the last of foes, Unbroken by the last of foes. No. 8. There is a calm for those who weep, A rest for weary pilgrims found; They softly lie and sweetly sleep Low in the ground, Low in the ground. UNIS ON PASSAGES. 20. A unison passage is where voices or instruments sing or play the same melody. The interval of one or more octaves may intervene. (l9T ---0 kV. | I - I I 21. A double unison is where the voices or instruments sing or play two parts, which are divided between the voices or instruments. s, Write an original composition, introducing unison passages. REMARKS. REMARKS.. CHIAPTER VII. FALSE RELATION. 1. False Relation is when one part has a natural note, and another part has a sharp or flat of the same name; either when both notes are sounded in the same chord, or when the two notes are sounded in two successive chords; 14z1 1<< or when the two notes are sounded in two chords with a chord intervening. * *, _______, ---8-7-, --- 2. Seeming violations of the rule regarding false relation are to be found in cases of incorrect notation (see chromatic scale, Chap. II, Section 18), to which of course the rule does not apply. 3. False relation does not exist between two successive chords, when the third letter of the first chord is the root of the second; 6 and when the third letter of the first chord is the fifth of the second chord. ) -— A ----C6 ('as-) 36 DANA'S PRACTICAL IARMONY. [CHAr. VII. 4. False relation does not exist between two chords with a chord intervening when the former of the two chords is a first inversion on the minor seventh in the melodic minor scale (see Chap. VIII, Section 3). * * = — M ---t — 6 6 5. False relation does not exist between two chords with a chord intervening, when the chromatic note forms part of a fundamental discord (see Chap.>&1_ Section t ); ---— g ---~ '- i _ e et Zi~Z (''$ and also when the first chord is a Dominant or a Tonic, and the third chord (having its root a minor third below that of the first chord), is the Dominant of another key, but in this case the intervening chord must contain the note which is a minor second above the root of the third chord. I ---. I [ - _ _ __ ___ i ___- ~- II 6. When the chromatic chord of the minor second of the key (Chap. XVI, Section 6) and the chord of the Dominalt are either of them the first, and the other the third chord in a progression, there is no false relation between tb~ fifh of the one and the root of the other.. --- —--- __ _,4N..7 - 6 6 7. When the first chord is the Dominant of a minor key, and the third choi'd has its root a minor third above it, being either the Dominant of the minor third RE M A R K S. REMARKS. DANA S PRACTICAL HARMONY. CHAP. VII. ] above the original keynote, or being the Super-Tonic of the minor sixth of the original keynote, there is no false relation. 8. Either of the two notes may be doubled (sounded in two parts at once) and the duplicate note in one part stands in no false relation with the note that is chromatically altered in another part. -* --- —-U - - - 9. Chromatic passing notes (Chap. XI, Sections 15 to 28) induce no false relation, if all the rules for their treatment be observed. CHAPTER VIII. MINOR KEY. 1. There are four common chords in the direct form in the minor key (Chap. II, Section 9), founded on.the Tonic, Sub-Dominant, Dominant and Sub-Medialt. The chords on the Super-Tonic and Leading Note are diminished chords, and the one on the Mediant is an augmented chord. -'d?- - — J ---J — I IV V VI 2. There are six first inversions in the minor. _ -— _t-r key, appearing in all the tones in the scale except - i - r r the Dominant. The chord on the Mediant, being 6 6 6 6 6 6 augmented, is a discord in the first inversion, which accounts for the absence of a first inversion on the Dominant. 3. There is also a first inversion on the.:-_- w --- ——, — -r minor seventh of the scale when the bass - - = descends by degrees from the keynote to the 6 6 6 minor sixth. 4. The interval of a sixth may be taken on the Dominant of __ _ -[ the minor key, bearing the figuring 8, in which case both notes may be doubled. 86 5. There are three second inversions in the minor key upon the same notes as in the major key. _:'- __A__ ^-^ 6 6 6 4 4 4 6. The following diagram will give a recapitulation of the principles in this chapter preceding it. I 3 3 3. ______ __ 6 ]6 6 6 6 6 6 6 - -6 __ _ _ That is- 4 _____ ____ _ ___ The chord of the Tonic can be used direct, 1st and 2d inversions. Super-Tonic " " in the 1st inversion. " " Sub-Dominant " " direct, 1st and 2d inversions. "- " " Dominant " " direct, 1st and 2d inversions. Sub-Mediant i " direct, and 1st inversion. " " Leading Note " " in the -1st inversion. (38) RE MARKS. REMARKS. CHAP. VIII] DANA'S PRACTICAL HARMONY. 39 An 8 chord on the Dominant, and a first inversion on the minor seventh. A major common chord is sometimes used as the concluding chord in the minor key. 7. Exemplify the principles in the chapter by figuring the following: ITo. 1. -;- zzCiz=rn y __ ____ - - -- No. 2. ~; -__-_-._.-.F - G-__ — _- - - -__ t-u-74-Z - -- — 1- ----- --- No. 3. L........ * 4sf —r ---....-r --- —~ —r —~ —r~ ---~ E" —..-I ---i --- —-— h-"-!;-'.-: _ --- _, -- __r__ No. 4. 2:.. --- — -~' ---I ---- r — No. 5..... _ --- ~_: —~ -_-:_ ~ —_ — r __L:~ e_._%_ —~_ --- No. 6. -- - -- ___I __ ____ = _ __-_ __ _ ___ I _= *- ---- -- — ~_..... --- —- -f-12 F --- '-e —: ---- -- > ----' ---F -. ---iXT --- —i 1:_.... _-' — _ --— _ — No. 7. -6o —L OThe student's attention is called to Chap. IV, Section 1 8. Add a tenor and alto to the following exercises: No. 1.,.i: _._ __ -- - -EF=_________.-. *-_-r _ — - — __ E- -- - ~~- m — i — __............ (',__ _ —I.. —'_ - - __ t___Z__L[, L (~___ 6 6 6 6 -- 6 6:6: — 6 4 No. 2. /| -In~-,_ — -.. — --- -.-. __~ _ __._~ __ __ __ ___ _~___.F.z___,;._,_____ _.. _.__ _6.... 6. 6 6 - --.... 646 6 6: ~ 6 6 66 6. 6 -- 6 6: # 6 6 4 4 4 40 -No. 3. /l DANA'S PRACTICAL HARMONY. [CHAP. VIII. Ifix I T I i --- —- -D -- -I -__- - -i - - IT — ' - _ _ _ _ _ _ 66 6 6 6 65 6 6 6 ~6 6 65 No. 4. _ _ _ _ _ _ _ _ _ _ _ _ _-_ _ _ ---— 0 —*- _______ __ -_ _ __ _ __-_ No.52. 66 6t 6 6 6 6 6 5 No. 44 No. 6. ___ ___ ~ p4 5L__ Az zz5 4_ _ 4 _ 4 _ _ _ _ _ ~ _ _ _- H REMARKS. REMARKS. CHAP. VIII.] DANA S PRACTICAL HARMONY. 41 No. 7. _,_ _ -__ __ — 7a._ I - L- - - 1 - 6 t6 6 No. 8. _ -_ -_ __L — _-_ -__ __ _g__ — A.. -.. - _:.____ -.... u~ I -— r-~~-t3-O- --- # s 6 -- - --- -- - --— I - --- --- - -~ ----- 6 6 6 # 6 6 No. 9.:- - --- - - -- - ---- - -_ --- — -- 6 6 5 6 6 $ 6 6 6 6 6 6. 65 4 3 4 4 44; -- - -i- -- - - _ - 6 6 6 6 6 6 4 -' -- - -O - - - 6 6 6 4 No. 10. $F — 6 6 - 6 6 6 5.4; No. 11.......= --- —& — - ' ~ *- --..-.- -— a ---- --.-t- -. i.t __- -F --- ---- -X No. 12. F --- ------- -—.6 6 5 XX 6 X6 6 6 X6 X — 6 6 5 4 X 4 X Write music in the minor key to the following words, observing the uses of the common chords and their inversions: No. 1. Thy chastening wrath, 0 Lord, restrain, Though I deserve it all; Nor let on me the heavy storm Of Thy displeasure fall. No. 2. How oft, alas! this wretched heart Has wandered from the Lord! How oft my roving thoughts depart, Forgetful of His word! No 3. With broken heart and contrite sigh, A trembling sinner, Lord, I cry; Thy pardoning grace is rich and free; O God, be merciful to me. No. 4. God of my life, to Thee I call; Afflicted at Thy feet I fall! When the great water-floods prevail, Leave not my trembling heart to fail. No. 5. O sacred Head, nuw wounded, With grief and shame bowed down, How scornfully surrounded With thorns, Thine only crown. O sacred Head, what glory, What bliss till now was Thine! Yet, though despised and gory, I joy to call Thee mine. No. 6. O Thou from whom all goodness flows, I lift my heart to Thee; In all my sorrows, conflicts, woes, Dear Lord remember me. When on my aching, burdened heart, My sins lie heavily, Thy pardon grant, the peace impart; In love remember me. No. 7. Lead, kindly Light, amid the circling gloom, Lead Thou me on; The night is dark, and I am far from home, Lead Thou me on. Keep Thou my feet, I do not ask to see The distant scene; one step enough for me. No 8. Is there a lone and dreary hour, When worldly pleasures lose their power? My Father, let me turn to Thee, And set each thought of darkness free. C HAPTE R IX. PEDALS. 1. A pedal is a bass note, sustained through a succession of chords, of which chords the pedal note may or may not form an essential portion. 2. The Tonic and Dominan t of a key are the only notes that may be employed as pedals: Either or both of these may be sustained through any passage, either diatonic or chromatic, that does not modulate; were modulation to take place the pedal note would lose its relation as keynote or Dominant. 3. When the pedal note does not appear as a -harmony note, the part next above it should form a good bass (that is, it should not have any notes unallowable as bass notes-Chap. V, Section 8, and Chap. VIII, Section 6-or proceed by leaps that are unallowable in the bass-Chap. V, Section 12-or in fourths-Chap. IV, Section 8). I ___ ____:-_-_-i — ' _ __-__\____ __ -_ I- -= The errors in the above are to be seen in the first measure where consecutive fourths appear; anal in the measure that follows a 6 chord leaps to the inversion of another chord. When the pedal is a harmony note, the part next above it, if the fifth letter of a chord, is not to be regarded as bearing a second inversion. 4. A pedal generally commences. with a harmony of which the pedal note is tlie root, but it may, however, commence with any harmony of which it is essential or i jt. [ etc. 5. A pedal note can only be quitted when it is a harmony note; if this be the fifth of a chord (6), the rules for quitting the same must be observed, and if a discord requiring resolution, the rules for the treatment of the same must be enforced. e - - - X. m=-==4- t~-_,-~-.. =.=. 4 —4 —4-A= - ~-=~-1 --- —------ y ---- --— l ---'-9-1 — _ _1 1 1 i i; ) __ I_ I J J _:_ _ ---__ ________ _ - _ __ -e -__ — _='_ _ _ = -9 - _.-_6_ _ * -1-6- - - (42) REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. CHAr. IX.] 43 6,. A pedal note m.ay be continued during the progression of the other parts, or it may be reiterated. a V.0 - w.*...*. U or ~9I~ - -.*6 -.9. - 7. The following0 exercises contain but three parts-tenor, alto anid treble-to which. a bass should be added introducing: -pedals on the keynote and Dominant. No. 1. i a -~ 4.4 t=ii i CdO U gf ll I I a At A 40. 4.9 -.9. I No. 2. n L.1 i. i I I i I i i 7' _ F _ I - h - - - F - - 4I No. 3. I _ _d - 46 H - I'* — t - - 9.- i [-dLo _ _ ____- — ~ — ---- ~~ -4- -i ---— 1~~ t ___ No. 4. 1,!. I i i I I &J a1 U la la la ao Isa A a aM 4. 19 a -9. a 4.42 a 9A - I ~ — it I - - a D D 9 -- :4' DANA'S PRACTICAL HARMONY. [CHAr. IX. 8. A pedal may close with a modulation, provided no change of key take place until the last chord upon the pedal. q 4zz~zz z z-4 z ~-i I --- —-E - __ -' — _ — -— _ —._-= A/, — ~.-,-^- —, --- —~. --- 9. One series of harmonies inducing a transient modulation is allowable upbn a pedal; this is the major common chord on the Sub-Mediant of the major key, and the fundamental discords derived from the same root, any of which may be used upon a Dominant pedal, provided it be followed by some chord of which the perfect fourth of the keynote (the seventh of the Dominant) is a portion: *__ *I* * \ ^- -^-jC10. In modern music the pedal is frequently inverted, an upper part sustaining tie note through a series of chords. All the rules of the bass pedal apply to the iinverted pedal, unless it should be the.one regarding the progression of the bass. The inverted pedal in no way affects the bass so long as this remains in the key of which the peldal note is Tonic or Dominant. 11. Sometimes the bass pedal is doubled in an upper part, in which case all the rules for its treatment apply without exception. d __ ( — Gar= - '-= I —T --- -: — -— FT! -'''~'-1- --- - - q_~ --- —--- I:-_. -. - - -C t --- — ( i_- t _ _ _ \,..., — - _ — - - -- - - _ _ _ REMARKS. R E M A R K S. C HAPTE R X. SEQ UENGES. 1. A sequence is the repetition of a harmonic progression, or melodic figure, at a different pitch to that in which it was first given, all the parts proceeding by degrees in each repetition as in the original strain or figure. 2. In a sequence the name of the interval, and not its quality, as major, minor, etc., is preserved in the repetition. Figure ---------- yV 3. An augmented interval may appear as one of the repetitions of what was a perfect interval. Figure ------- -- -V 4 4. In the following sequence the bass rises a fourth, the top part falls a second, the part next to the top rises a second, and the part next to the bass falls a third. 5. In the repetitions of a sequence the Leading Note may be doubled; also the discords on the third and seventh of the major key (Chap. V, Sections 3 and 4), and on the second, third and seventh of the minor key (Chap. VIII, Section 1), may be employed. 6. Write sequences to the following bass, harmonizing the figure and having the parts progress as in the illustration of Section 4. 7. The second inversion of concords is unavailable in sequences. 8. A sequence may consist of but two chords, or more than two. Perhaps one of the best known illustrations of harmonic and melodic sequences is to be found in the Hallelujah chorus of the Messiah. (45) 46 DANA S PRACTICAL HIARMONY. [CHAP. X. Figure - —. --- —..... --- —------------ ------------ ------ -—.... --- —-....................... --- —- ---------------------..... -- - -------------------- ---------------- ---- -- ) si..-,~.SK K-,, b -) I -- -- -- — __ T d_ ---- O -- I --...... -- — _Q__- _. _....._- ~,_C...:- -—: ----W-0t --- -" — -....F. -— = — -- -r- -.-.... - 5 __-.:- i ~_ _" '_ —' ---- ' ~ — a sei o i sq s e e _ foi figures: /f_ =r -zfLJ, A ----_ - /5- -— 5-P -i _ol: No. -— _..:: -,. -. I._ _ Q__ —$ ---_=-5 =I —g —|: /-J —^-i= ----^._- _ (t~~- -d ---, ---~-~-~_-:~ ---,_,= ---~ ~~~— ai-~-I Io. 5. No.6. ) l 9. Vrite a series of diatonnc sequen ces ascending from the followin g figures: No. 2. No. 3. No. 4. ( Et —= / — C-t-~-aEE^E,-F / |aE^EE_-tEE- F 9-;- -W-__ — = —jb ---1i -— c - -E —1-i- -— e — =:f ---"-r: — ~~~~~~~~~~~-. --- —- - 8 --- —---- -- _ ----. --- _e i~f-..__ —_: ---. --- —- - L~iP Ie B --- -— ~- -47 — 2-,To. _;._ r No. 5. -— No. -—. No. 7. 10Write a series of diatonic sequences descontaining faom the following figures: No. 1. ( No. 2. No.3. No. 4. with them; or prepa-red discords. ll Aseuecema cnIsofcnrd ny orI passignsmyapa -il hm rc --- preare dicod REMARKS. REMARKS. CHAPTER XI. PASSING NOTES. 1. A passing note is a note that does not belong to a chord. 2. Passing notes may appear in one or more parts, and resolve upon the note or notes of the chord in which they appear;.. _h I _* _ _ ___ - -4_-s ---_ - - --- - -------- -D N I N,S- -- - --- — ____g pg = FSYE or resolve upon a note of another chord. (W=4' n -l-an __ __ _ 3. A passing note may proceed by oblique motion to an octave, but should not to a unison. — tS DIATONIC PASSING NOTES, 01 STRICT STYLE. 4. In the strict or diatonic style, a passing note must be approached and quitted by the interval of a second, and it must be at a less accented part of the measure than the harmony note which precedes it. A passing note approached in this manner may either rise or fall to the next note. (47\ 48 DANA'S PRACTICAL HARMONY. [CHAP. XL 5. Two passing notes may appear in a chord. 6. Where two passing notes appear in a chord they must proceed in the same direction in which they are moving until they reach a harmony note, the second passing note not returning to the note that appeared as the first passing note. - - -- ^ --- -*- - ^- -I — I-r- _ 7. The single exception to the rule regarding the approach and quitting of a passing note by the interval of a second is, that a passing note, instead of proceeding to the harmony note next t6 it, leaps a third to the note on the other side of such harmony note, and then returns to the harmony note it would have resolved upon had the skip not been made. L7 '= -----. --- -~ Z - 8. Two or more parts may proceed by passing notes, in which case the parts which move while other parts are sustained, must proceed in such progressions with each other as would make pure harmony, independently of the sustained parts. \iZ __ __ ---- --- -—. i v _= - -. = --- —- -,__' --- =E___ __ __ _=X= -___=_% --- i I - 9. Cure should be taken when passing notes appear above parts that are sustained, that consecutive fourths are not written.,'-n --- —^ ---<i-r-aL-ft-r -. —~ —r~ ---r G —f.... —r -........ \ ---_ v —'- S_". --- — — E__ —$In the second measure the two upper parts move in fourths, and as the lower voices do not move, the lower of the upper parts must be considered as a bass to it (Chap. IV, Section 8). REMARKS. REMARKS. ur. XL] DANA S PRACTICAL IAIRMONY.' 49 Add soprano, alto and tenor to the following exercises containing passing notes. Others should be introduced in the larts when they can be properly treated. A line over or under several notes, signifies that the chord belonging to the first of such notes is to be retained or repeated so long as the line continues. A line from a figure implies the same principle. No. 1. 4-_ _ _ ____ _ [ _ 6- 6- 6 -- __ 6 -obsving all ideas -- h h -- -— c — r s t — s e --— tye o wtiTo ilta t i s desired a choral will be given, and passing notes introduced. - 5 - - - 6 6 6 6 4 3 4 3 No. 2. ______ _f —. --- -. — -__ -___ -- -6 - 990S F= _XE_-1_ -_ _ _ _ -------— F..._ _ — * ------ L- tu t[-_ — - ___t t _Zt 6 6 6 6 - r 6 5 — 4 3 —3 10. Introduce passing notes in the vrarious parts of the followinrg ch orals, observing all ideas referring to their use in the diatonic or strict style of writing. To illustrate what is desired a choral will be given, and passing notes introduced. \ P i^ ____ _ l 1 -- -- -- -------- ----— * --- — --- ------------- -— 7-F (1rry z _ — zf=9 _=I R _ __ _ ^i;* _ I. I ~ I.1 i II I__ __ _ __ -- - - - - 4 - -I L I^ I I'l J dt ---d _ ---C --- -r_-t-= --- - - - - _i i6 A ---.- -.-_ _ __ -L- — _ — _ — _ I. --- -_ _-I --- — --— _ — --------- I _ --- I '-* ---- — F --- -- -_ —Er --- —--- -- --- *-____ -_ __ _ -r — 6 —, --- - _ _ _ iz __ ', -- -....J __ - _:_ _ _ _ --— 4 —. —_ --- —- -:__ —=_ —i I: —I —?5 —:: — -_~ —t? ~bz —L-....... /. -_ -L- -- — L[ __ ---'.....'- - ~.P. - -h -.i_- -I, 7' I r r,, l I I. I-.... r_ __ _ - — I_ - __ __i__ - _t j_ _ -5- -- _.-6- -..,-t- __ _ __ ___1 _t ___ __ ___ IE' --- ' _ — E-z.-..... i', P-L~=~ -— ~ —' --- -. - - -~-~ 50 DANA; P 'ACT:CAL IARMONY. [CHAr. XI. No. 1. i —..... - _ — -- - ',_ _.^- 5 ~___ __ __ —. __ _'_. _ _-_ _ __ 7_-: --- —w —,-r —{-..... — ~- w-k, -— e-~-k-.. ___-=-r — -t --— ~- t --- — ----- -- \_ ----_-_ — -_ — - i_ —1-Ll _^: --- — _~ —_ — No. 2. [ e!I-z g --- h I -Ii- 'I I i| -— =_'.... 1I —t- 1- - r —. -- - ~ l= ~ 4 - - -- - No. 3. ' _E__ ____ ____ _ /~~SX tt ~-~:-<-.-_,-F. —=8 —~-< —e-<-rz-~-4-F~ —F~-, —=-jF~ --- ) - I -- I - --- - - __ — _ 9 _ __ --- — _-_- -1 --- —-— __ -- _ ---- — _-____ —__ I --- -- -. --- - _- _ _ _ No. 4.. _-^-.-J-;- -F -,-.^ ~.g-F --- - - --— ^;: - — ^ -. - _ _ ___ __ __ " — [-i —~-.-g- i ---i:- |-*-~ - -n-i — P- - ~ | ----. — -~ —~- ~ —,~-:^ z ---- ~F'-~- ~ —F.... Write original compositions exemplifying diatonic passingnotes in the major key. Review the melodic minor scale, Chap. II, Section 11. 11. The major sixth of the melodic minor scale may appear as a passing note ascending and descending, when the fifth and major seventh of the key are harmony notes. * * * * r- p REMARKS. REMARKS. CHAP. XI.] DANA'S PRACTICAL HIARMONY.. 51 12. The minor seventh from the keynote of the melodic minor scale may appear as a passing note ascending or descending, when the minor sixth and keynote are harmony notes.!(a:_ " -i-A 13. The minor seventh and minor sixth of the melodic minor scale may appear as passing notes descending, when the keynote and the fifth of the key are harmony notes. _Z --- —— ____ --- —-- -. -- Q —~ — 14. The major sixth and major seventh of the melodic minor scale may appear as passing notes ascending, when the fifth of the key and the keynote are harmony notes. -# I Add soprano, alto and tenor to the following exercise containing passing notes, observing the suggestions in the preceding exercise (Chap. XI, Section 10)..... ___.... - _- K —IL_ 6 - 6 - 6 _ -6 6.....:......-s-,-... —, _. — __ --— __ _ —__ is4 ---- -~-m- — * ---1 iII 6 --------- 6 -- 6 — 6- 6 6 6 t4 5 Introduce passing notes in the various parts of the following chorals (see Chap. XI, Section 10, for an illustration). NTo. 1. __ _ -..L.... ---r.-. _..i - -—..-L. _. - __ __-......... --- —--- ---- —.. — — ~ —._ —_ T [ I I- A_ I — I__ - t -_ -- 52 DANA'S PRACTICAL HARMONY. [Cr. x1 J2-!- --- a_ __ _ __ _ __ o__ =t= -— '" — k- -— ~-_ — -- -'- '= --- -— " — = =:- -- _ ---=4- -0 -No. 2. — r — -— I — =a- i__ --- -- --- i ' __- _ _ (jS z S"| — -- 1- =S tf=\~.. --- —— E ___ ~..?.- r - -' - - r t- I n 0 _0L 42 i-.'_-t- - - — +- —, — — ' —9 — -- -- -----—: — I --- I ( — '.... ' — r-=-f _NO. 4. --- _-: --.. - 0 — Write original compositions exemplifying diato'ic passing notes in the minor FREE OR CHROMATIC STYLE. 15. In tUie Free or Chromatic Style, a passing note may be approached by the stcp of a second, as in the strict style, and it may also be approached by leap. — _.i -___ REMARKS. REMARKS. CHAP. XI.] DANA'S PRACTICAL HARMONY. 53 16. An augmented interval is allowable by leap to a passing note. _AFI __ ___-_ --- ll=|=EE-l —E-E.' - - 17. If a passing note that is approached by leap resolve upon a harmony note below it, the passing note may be at the interval of a tone or semi-tone from it, according to the diatonic scale. -- r 18. If a passing note approached by leap resolve upon a harmony note above it, and such harmony note is the first, fifth or seventh letter of a chord, the passing note must be at the interval of a semi-tone. * — = — _ __ -_i- -i~~ ---- -' --- * I*L * - -* ' 1-~" (l-:_,::L~ -~ —.-~.. —' —..~ ---... - -...19. When it resolves on the third letter of a chord it may be at the interval of a tone or semi-tone. is-~ —' rF::: -~== — 20. Where a passing note leaps a third to the note beyond the note of resolution (Chap. XI, Section 7), and the note of resolution is the first, fifth or seventh of a chord, the passing note below must be at the interval of a semi-tone. DANA'S PRACTICAL HARMONY. [(:rP. x 21. A passing note approached by the step of a descending second from the first or fifth letter of a chodil, and returning upwards to the same note, must be at the interval of a semi-tone. By some authors, passing notes with this characteristic are termed changing notes. 22. If two parts proceed togethvr as passing notes, when one steps a semi-tone that belongs to the diatonic scale of the key, the other may step either a semi-tone or a tone. I-' _ j 'A, Ir -F EhI W _ F ~ ) -I, 11 -w-,i 'f -, ---- ---- - I I -a -. a -~.o ____ --- When one steps a chromatic semi-tone, the other must step a semi-tone also. [f,^ -— v 23. When two parts proceed by the intervals of thirds or sixths, the need does not hold for the note below a first, fifth or seventh letter of a chord to be at the interval of a semi-tone. - -_ --- ----- i - H — -- -- '_ __ __ __ __ 24. The harmonic minor scale may be employed for a succession of passing notes upon the Dominant harmony in the minor key, in which case the interval of the augmented second between the sixth and seventh degrees is not objectionable.* row- — _^- _.___.. — ^ -- -.- _ --- ——.,_ — __* —..____________ _-lm,,-[__ ( ) _ — - c-.......... -O__t 25. The major sixth and minor seventh of the melodic minor scale are available as in the strict style. 26. The note a semi-tone below any letter of a chord may be taken by leap as a passing note if it be resolved upwards. * It is also employed, but less frequently, for a succession of passing notes upon other harmonies in the minor key. REMARKS. REMARKS. CHAP. XI.] DANA'S PRACTICAL HARMONY. 55 - ---- ~ — H - (6 6 - -—, ----.-~ --- See Chap. II, Section 18, for the proper notation of the preceding, which produces no false relation with the harmony note on which it resolves (Chap. VII, Section 9). ---- --- I ~D --- — - -- 27. The note a semi-tone above any interval may be taken by descent of a semitone, if it be resolved downwards, without producing false relation with the harnmony note on which it resolves. a T:- -_ t:___-g -- A=I-....=- — H 28. If in a succession of passing notes a chromatic note be taken, the passage must proceed by semi-tones until a harmony note is reached. or I i~ _- -rz _ _ —__ - =S [ -=qu_ _ —_-_ ___ - — _t ---S-0_>= —o$<,< _ to-i-# h-t.._.s ----.- -....... For the following exercise read Sections 20 and 21 of this Chapter. Add a tenor, alto and soprano, introducing passing notes. =;6~^ - - | ~'. --- - i --- —— 6 - -5 ---- ------- ' _ P ---_- ---- - _ -6 --- _ — 6- -- 9_ --- —- — __a__ 6 6 ---- 6 — 6 6 --- — 6 ---- ' - 5 --- 4 4 8 -_- -6 —_ ---___~ 6- - -— _ _ 4l - 6 ---3 -& --- ---- 8 — ~ =-:i2 '~"~~ ---~-....-~ —~ o... —,-~-, —~- 6 6-~ —~ ---,5 —~ --- —n ~~4 --- —-- 8~ --- Write a number of exercises exemplifying the principles in the free or chromatic style of passing notes. (See last page of the work for Appoggiaturas.) CHAPTER XII. SUSPENSIONS. 1. Notes that do not belong to a chord are unessential to it, that is, the chord or its name is not affected by their appearance; the discordant tones that appear in this manner are passing notes and suspensions, and are called Unessential Discords. 2. A suspension is the retaining of a note of one chord into the chord that follows, of which chord this note forms no portion, and to a note of which it resolves. 3. Three conditions are essential to a suspension, namely: Preparation-The sounding of the note in the first chord. Suspension-Its retention and appearance as a discord. Resolution-Its progression to a note of the chord in which it was a discord. *. o o ~ k o F 0 0a 0a ".* Ca M W m o 0 ~ o 0 o p4 4 0 1 2 I I ____-_ d_ ___ = - ~- ~ --- +- w- - -+- — i - - (_ ______ ___ P.#t —I-=t ---__] 5 f L8 --- —--- 9:- j.iL__i ~-4 a A=+ _-F ----=T- lk -H -+ - 1 9 8 4 3 5 6 The preparation and suspension must be in the same part. 4. An essential to a suspension is the retaining or holding of the note from the first into the second chord. If the note were newly sounded in the second chord, there would be no suspension. ~9 — - 8 -_ A Suspension. Not a Suspension. 5. The suspension should be no longer than the-preparation and is sometimes shorter. 6. The suspension appears at the accented part of the measure. Sometimes one or more of the parts may move from one to another interval of the chord in which the suspension appears. O-.._9 6 9 — (56) 9 9 8 REMARKS. REMARKS. CHAP. XII.] DANA S PRACTICAL HARMONY. 57 7. The only intervals that appear in suspension are the ninth and the fourth from any root, and the dissonant fifths in the chords on the third and seventh degrees of the minor and major scales (see Chap. I, Section 23; Chap. IV, Sections 3 and 4). 8. The ninth in suspension resolves upon the root of the chord. 9. The fourth in suspension resolves upon the third letter of the chord. 10. The dissonant fifth in suspension resolves upwards to the root of the chord. 11. A suspension is always one degree from the note on which it resolves. In case of the ninth and fourth one degree above, and of the dissonant fifths one degree below. 12. A suspended discord always stands in the place of the note upon which it resolves, and any progression that would be forbidden is not relieved by the use of the suspension. No. 1. No. 2. 8 8 5 5 8 8 5 5 The forbidden progressions in No. 1 are equally bad in No. 2. A suspended discord is accompanied exactly as it would be were there no suspension, subject only to the conditions stated in Section 14 of this Chapter. N.INTH IN SUSPENSION. 13. The ninth in suspension resolves upon the root. 14. The note upon which the suspension resolves should not be sounded together with the suspension, except the suspended ninth with the root in the bass; _O_ and except the suspended ninth with the root in an upper part, in whiep cast the root must be at the interval of an octave, and approached by the step of a second. * * 15. The last exception, though admissible, is undesirable, and should be employed with the most careful discretion. 16. The following is the figuring of the direct form and three inversions of the ninth in suspension. 58 DANA'S PRACTICAL HARMONY. [CHAP. XIL In the direct form (the first letter of, the chord as the bass note), it is figured 9 8. — 9 8 --- 9 8 In the first inversion (the third letter of the chord as the bass note), it is figured 7 6..1 -! / 14: — - F 6 7 6 In the second inversion (the fifth letter of the chord as the bass note), it is figured 6 4. 6 -5 4 In the third inversion (the ninth appearing in the bass), it is figured 4-. - \ --- --— 2 6 t17. As the suspended ninth resolves upon the root of a chord, the last inversion of it must be upon such a note as in its resolution would leave the direct form of a common chord. SUSPENDED NINTH IN THE MAJOR KEY. 18. As a suspension is no part of a chord, it can appear in the direct form and inversions on such notes of the major scale as bear the direct form and inversions of common chords (Chap. V, Section 8). 19. There is no suspension of the ninth in the third inversion on one and four of the major key, as the resolution of the suspension Would be upon seven and three of the scale which do not bear a common chord. 20. The following diagram will give the direct form and inversions of the suspended ninth on the notes of a major scale. _ 5. i. 9 8 9 8 9 8 9 8 9 8 7 6- 7 6- 76. 76 76- 76 [76 6 -g [_ _ ___I --- _.T __............................................... i...... __ REMA RKS. REMARKS. DANA'S PRACTICAL HlARMONY. 59 CHAP. XII.] 21. In the first inversion of the suspended ninth, when the bass is a major third, Chap. IV, Section 1S, should be observed. Double the fifth letter of the chord. n I I _I _- 5_ OL _ -— ' - -- -- — 5- - --- /_ ---- ] -_-5.. ---— r- - I 1 / I I --- i _-f__ — _ ---_ _. _' _, _ to 1 7 b 6 7 t 7 6 6 76 4 I - J n 6 ( — tE _ 6 7 6 6 7 6 6 7 6 22. Add a treble, alto and tenor to the following figured exercises: No. 1. 98 98- 6 6 98 6 98 98 98 6 98 No. 2. - 98 6 98 98 98 6 6 4 98 98 98 6 98 98 No. 3. 0_ _ 76 76 76 6 i —=~i - 6 98 76 76 No. 4. 76 76 76 6 98 76 76 6 — 6 6 98 6 76 6 76 -6 76 6 76 6 76 6 76 98 6 5 4 3 5 —=5 —E 6 76 6 4 No. 5. 6 76 76 76 6 6 5 4 3 76 76 6- 6 54 6 6 -54 98 76 65 43 6 6- 6 6 -54 54 6 6- 5 6 54 3 6 5 98 4 3 60 DANA S PRACTICAL HARMONY. [CHAP. XI1 -No. 6. _ ____ _,_- __ ~ __ -_ 7 t _6 4 --- 76 98 6 6 4- - 76 98 6 76 6 6 6 6 6 2- 2 -98 6 98 6 98 6 4- 6 6 4-6 6 4- 6 2- 2 ---- 2 ----- E-_-__- t l: _ - __ 9 8 7 6 98 7 6 98 76 6 98 6 6. 7 6 Write original compositions in a major key, introducing the ninth in suspension. SUSPENDED NINTH IN THE MINOR KEY. 23. The suspended ninth can appear in the direct form and inversions on such notes of the diatonic minor key as bear the direct form and inversions of a common chord-Chap. VIII, Section 6-provided the resolution of the suspension is not by forbidden progressions. 24. There is no direct form of a ninth in suspension on the Sub-Mediant of the minor key, as the resolution is by an augmented interval. 9 8 25. There is no first inversion on the Tonic, as the progression is by an augmented interval. 7 6 26. There is no third inversion on the Leading Note, as the progression is by an augmented interval. as 6 = 27. As there is a first inversion on the minor seventh in a minor key (Chap. VIII, Sec. 3), there can be a first inversion of the suspended ninth on the same degree. - - -- - - 6 76 6 REM ARKS. REMARKS. DANA'S PRACTICAL HARMONY. 61 CHAP. XII.] There is also a last inversion of the suspended ninth on the minor seventh. e} _0t _ 6 4- 6 2 - 4 28. The following diagram will give the direct form suspended ninth on the notes of a diatonic minor scale: and inversions of the 9 8 9 8 9 8 7S6 76 7 6 7 6 17 6 6- ~6 — 6-| 4 5 4 1 I 5 4 I./~= I I I t!~ = I 7 6 — 1 I- I I:::I] 29. Add a treble, alto and tenor to the following figured illustrations: No. 1. _,,......,,. - 98 6 6 65 f 6 98 f 4 4f 6 98 6 5 98 l6 6 4 98 f No. 2. I V 7t6 6 6 6 5 6 4 4 76 76 7 6 7t6 6 98 6 5 4 1 6 76 6 98 - - 98 6 6 - 6 — 6 98 4 6 98 6 6 6 6 4 5 98 -4f No. 3. 6 6- 5 6 6- 5 54 3 54; No. 4. 6 t — 6 76 6 6 6 s6- 6 6 - 6 54 4 54 54 76 4 — 2 - 56 6- 4- 65 76 4 -3 54 2- 4 2 --- 76. 7$6 6 -5 4 6- 6 5 4 98 7`6 6 76 6- 6 6 54 4 # Write original compositions in the minor key, introducing the ninth in suspension. CHAPTER XIII. THE FO URRTH IN S USPENSTON. 1. The fourth in suspension resolves upon the third of the chord. 4 3 2. The note upon which the suspension resolves should not be sounded together with the suspension; except the fourth together with the third in the bass (first inversion), or an upper part, in which case it must be approached by the step of an ascending second, and the interval of an octave intervening from the note of resolution. 3. The following is the figuring for the direct form and three inversions of the fourth in suspension: 4. In the direct form (first letter of the chord as the bass note) it is figured 4 3. 4 3 5. In the first inversion (third letter of the chord as the bass note) it is figured 9 8, and the bass is approached from the second below. _ —}g^j — 6 9 8 6 --- 6. In the second inversion (fifth letter of the chord as the bass note) it is figured \ B. (62) REMARKS. REMARKS. CHAr. XIII.] DANA S PRACTICAL HARMONY. 63 7. In the third inversion (the suspended fourth in the bass) it is figured 2-. SUSPENDED FO URTH IN THE MAJOR KEY. 8. As the fourth in suspension is no part of a chord, it can appear in the direct form and inversions on such notes of the major scale as bear the direct form and inversions of common chords (Chap. V, Section 8). 9. There is no first inversion of the fourth in suspension on the Leading Note, as the resolution of the suspension would double that note (Chap. IV, Section 12). 10. As the resolution of the fourth is upon the third of a chord, the last inversion of this suspension can appear on every note of a major scale. 11. The following diagram will give the direct form and inversions of the fourth in suspension: -4 — - - -4 -42 - 4- 2 2 4 2 12. Add a treble, alto and tenor to the following figured exercises: No. 1. 6 43 6 43 76 98.43 6- 43 65 76 43 6 6 6 43 No. 2.... _ --- -- - -- — tt —' - r I-t -- -— = ---'-= -T —~ —[t ' —! _1 ---. ---L 98 6 6 43 43 76 43 6 76 6 4 43 98 — 6 6 76 6 43 6 6 4 No. 3. - 6 98 6 5 98 76 43 6 76 - 6 98 -- 6 76 6- 4 3 6- 6 -_-_-_ --- —— _-I- _ ----- - -t —E --- 43 76 6- 43 6 43 6 98 76 6 98 6 6 54 6-. 6 - 64 DANA'S PRACTICAL HARMONY. [CAP. XJII. - [CHAP. Xnl., No. 4. I.- ' 76 6 6 76 5- 6 6-5- 6 43 6 98 6 98 76 6 6 98 4- 4- -3 54 -3 6-4 -No. 5. 5- 65- 6 5- 5 — 676 6 6 676 5- 6 65 2- 2- 2- 2- 2 — 43 Write original compositions in the major key, introducing the fourth in suspension. SUSPENDED FOURTH IN THE MINOR KEY. 13. The fourth in suspension can appear in the direct form and inversions on such notes of the minor key as bear the direct form and inversions of common chords (Chap. VIII, Section 6), provided the resolution is not by forbidden progressions. 14. There is no direct form of the fourth in suspension on the Sub-Dominant, because of the augmented interval. 43 15. There is no first inversion of the fourth in suspension on the minor sixth of the scale, because of the augmented interval. * 9J9 7 --- —. —~ 6 -16. There is no first inversion of the fourth in suspension on the Leading Note, because of the doubling of that note (Chap. IV, Section 12). _ ___ -_ 6 9 8 6 -17. There is no second inversion of the fourth in suspension on the Tonic, because of the augmented interval. 7 6 4 -— (-+1 (-, —1 R E MAR KS. REMARKS. CHAP. XII.]. DANA'S PRACTICAL HARMONY. 18. As there is no first inversion of a common chord on the Dominant of a minor key, there is no third inversion of a fourth in suspension on the minor sixth of the key. 19. There is no third inversion of the fourth in suspension on the Leading Note, because of the augmented interval. 6. ---2 — 20. The following diagram will give the direct form suspended fourth on the notes of a diatonic minor scale: and inversions of the he 4 3 4 3 g6 8 8 68 I S 8 I - - ------------ _ —i 47' a I -__ - I I _ 6 1 1 _ _ _ I' I _ -= B= B IR 1 -- I ' L, L _ i2. I see no reason why the minor (Chap. VIII, Section 3). seventh should not be used in suspension 6 6 — 22. Add a treble, alto and tenor to the following figured illustrations: No. 1. 6 44 6 6 6 98 6 4 - 98 65 76 43 S6 6 6 No. 2. ~~~~~~~~~~~ --- —-~-=-H - r ~ - D ~ - i r ~ - - - - r - - -_ d6 98 98 98 76; 6 98 76 98 - 76 98 76 6 6 6 4t - 6- F- - 4 6 -No. 3. 6 6 4$ - 6 — -- TT...... a.. __ I - 1-F-' — -— 1 ---- _ ---- __ --- _ — ~-_ _-_ _... ---- 6, --- —- --... - 4z 6., fj 7:6 6 -4 - G_ _ 4::s It --- 66 DANA S PRACTICAL HARMONY. _-., _ [CHAr. XIII. No. 4. I — F ---I —t - -;. I -H~-. - - i _ J ---1-. -r --- 5 — 6 25 — 6 5- - 5- 6 7t6 2- 2- 2- 2 - 6 $ 6 676 5- 6 65 4 2- 4 23. Write original compositions in the minor key, introducing the fourth in suspension. DISSONANT FIFTHS IN SUSPENSION. The dissonant fifths in the chords on the third and seventh degrees of both major and minor keys, can appear in suspension. 24. This suspension appears only in the direct form, the fifth rising to the sixth from the bass note, and is figured 5 6; the resolution resulting in the first inversion of a common chord. 25. The letter that the fifth resolves upon must not appear in any of the other parts. -n, I -- - I I --- -Or r -O - 95 6 T 56 5 6 26. Add a treble, alto and tenor to the following figured illustrations: No. 1. Z2 =- - — r= -#1__ i __ = _ =, __ - __ F.6 -56 6 56 98 ---- 6 98 4 No. 2. 6 56 6 56 98 56 98 43 No. 3.. -.9 - 6 — ------ 6, - K_ -_ _ —_ - _ ---_ -=-_ -_- -- '- ' -:_ _-_ --- —_ _ — 76 56 6 98 56- 5. 6 4 2 -' — i ---_-~_-_ ____=- --— i —[ ---.- ___ 6 56 6 6 5 43 5- 6 76 - 6 56 2-. 6 56 6 6 5 4' 3 Write original compositions in both major and minor keys, introducing the dissonant fifth in suspension. 27. Any suspension may, previous to its resolution, proceed to a consonant note of the same chord, either by leap or step of a second, but must return to the note of resolution before the harmony changes. The return to the note of resol-ution may be by leap from a consonant note or by passing notes. 28. The following illustrations of suspensions, strictly written and then floridly ornamented by leap to other letters of the chord, and the introduction of passing-notes, will give the student an understanding of the principle: R E MARKS. REMARKS. DANA'S PRACTICAL HARMONY. 61 CHAP. XIII.] No. 1. 43 56 76 76 76 29. Add suspensions in the florid style of writing, to the following figured illustrations: No. 1. No. 2. 76 76 76 56 6 76 43 98 76 6 43 No. 3. No. 4. 6 98 56 $6 #:56 7~6 7 6 $56 6 56 6 7 6 # No. 5..., _ _ - -.4 -a --. —,5 -2 --- — No. 6. _ __ _-_ -- - - - -- _ -- 6 4- 5 -: 6 2- 2-.-.... 4I " ZZiZ=- I IF r-i ---Ie I =! —i — -.::~ ' F- - -{::. ~,:.:J I: I 1,-~ - _ -- 'r~: -- =LC -_-; _ -— I --- — - — I — T- T — I t -T z li - i=_A i_ i_ i t _ -— t. 6 4 6 4- 4 6 5- 6 2- 2- 2 2 Write original compositions in major and minor keys, illustrating the florid use of suspensions. 68 DANA'S PRACTICAL HARMONY. [CHAP. XIII DO UBLE SUSPENSIONS. 30. The ninth and fourth may be suspended together in the direct form and inversions of a chord. 31. The treatment of each discord is the same as if it stood alone. 32. The dissonant fifth in the chords on the third and seventh degrees of both major and minor -keys, may be accompanied by the first inversion of the ninth in suspension. No.. /1+ _ 'r _ -07 -. r', — _- - I 76 76 56 56 No. 3. _ 4 ~)_-E_ i____, ---~ ____ 6 98 6 98 76 76 66 t 56 33. The dissonant fifth in the chord on the third degree of a major or minor key, may be accompanied by the first inversion of the fourth in suspension. I.. -- -.- -" I-'_ 6 98 m6 98 56 56 34. In a double suspension of the ninth and fourth, where the ninth is in the bass, the chord is figured 4 3. _ L 4-. 8 3 REMARKS. REMARKS. "HAr. XII.] DANA S PRACTICAL HARMONY. 69 35. In a double suspension of the ninth and fourth, where the fourth is in the bass, the chord is figured 2 6., —~ —t -w~* (,r r2 6 6 6 2 -36. The following diagram will give the direct suspensions in a major key:,. form and inversions of double -.__ —_ - -- -L —L 98 [981 8 98 F 9 8 98 76 76 76 6 7 76 I 7 6 76 5 6 7 6 7 6 7 6 75 4 5 6 1 5 4. I __- -----— 4 --- —----— I 4- 4 —+ --- —_Q_ IQ _ _ __ K _ _ 0~~K- KY'-T.4K'7:4. I ' U ' I ' ' I I o _ I, I f26 1 6 6 6 66 66 6 6 37. Add a treble, alto and tenor to the following figured illustrations: No. 1. 98 76 6 6 6 76 56 76 66 2 — 4 43 9 8- _ 76 56:No. 2. 98 6 - 6 6 6 6 2~ 76 76 43 54 6 43 98 98 43 No. 3. 1* 98 98 -6 43 43 6 666 2 - 4- 6 3 3 6 6 2 - 6 76 6 6 65- 76 6 65 98 6 98 6 76 6 6 6 6- 5 56 4 43 — 56 4 43 76 76 56 54 3 56 Write original compositions in the major key, illustrating the use of double suspensions. 38. The following diagram will give the direct form and inversions of double suspensions in a minor key:, ------- HHH --- —------ -------------------— _ --- —r __ F 7 6 __ __6 I: 76 1 56 __"' L 5' L L I _-.I..1 1 1 -- - I_-_ - __ t -I-I I -- t- I - _6 '1 ~6 166 ~ 6 r L., - - I 70 DANA 'S PRACTICAL HARMONY. [CHAP. XII. 39. Add a treble, alto and tenor to the following figured illustrations: No. 1..__. ' L- - 1 —: - -- -....... - -.__- _ _.. —0 — _ —o ---- _ —_ -_: -_. 6 76 98 76 98 6:- 76 98 56 56 $56 4: No. 2. 6 6 6 76 6 6 6 6- 6- 6 2 — - 2 --- 54 6 9 8 6 4 - 76 9 8 76 76 6 B 5 — 6 44 6 5 76 3: 56 t5 6 2- 4 4: 5 6 Write original compositions in the minor key, illustrating the use of double suspensions. SUSPENSION OF COMPLETE CHORDS. 40. A chord may be suspended over the bass (whether the root or third) of a following chord, provided the root of the second chord is a fourth above the first one. There being suspended sufficient notes to define the chord that prepares them, they are regarded not with reference to the bass over which they are suspended, but proceed just as they would were there no suspension, except that no discordant note move more than a second. This rule applies not only to concords, but to all the discords hereafter described. Lines drawn from a note or figuring signify the suspension of the complete chord, and the figures that follow, the resolution of the chord. I e9-:~- I _ - 5 ---- ------- 5 5 3 3- - 3 —.- 3 41. Add a treble, alto and tenor to the following figured illustrations: No. 1. 5 98 — 5 6 --- 6 6 - 6 3 4 ---- 3 5 - 6- 6- _ N --- 6 - 6 5 — 5 56 46 35 —3 No. 2. 9 ___: "_ _...._ — __ _._ _.:-'.___.. 6 - 6 —. — - 0 B 6 6 - REM ARKS. R EM MAR K S. CHAP. XIII.] DANA 'S PRACTICAL HARMONY. t5- _ -. 71 b - I t t h - Iw -7- * I r6 6 6 6 -- 4 -- 8 r ----- 6 6 6 6 6 --- 4 — 8 6 -Write original compositions in both major and minor pensions of complete chords. 42. A suspension can be prepared by a discord. 1 1 ---- I 4 3 keys, introducing sus );t -— _- -~ --- — 76 4 -43. A fundamental discord (Chap. XVII, Sec. 1) and suspended in another; ( --- —-5 3. may be prepared in one part or any notes derived from the same root may be introduced in the suspension which did not appear in the chord that prepared it. I ---- 5 ---5 3 -5 3./ I i I= 4* HVU 5 3 44. Other intervals-as the thirteenth-are often treated. the same as suspensions, and are termed intervals of retardation. "PROVE ALL THINGS." It is desired that the student examine the works of Handel, especially his Suites, Vols. I, II and III; also, the writings of Bach, among which might be mentioned his Mass in B minor. These authors' writings contain illustrations of the principles advanced in preceding chapters regarding suspensions, that to the earnest student will afford much pleasure in their examination. 72 DANA'S PRACTICAL HARMONY. [CHAP. XIII, The following diagram- will give a recapitulation of all figuring on common chords, to the close of suspensions. IMAJOR KEY. MI-NOR KEF' Chords and theix Inversions. r I 5 5 3 3 5 3 5 3 S 3 6 6 4 6 6 4 6 6 6 6 4 6 6 --- ~ZI__ I I -------. --- — i I 6 4 4 I 6 4 - tia7-:j I~ 5 5 5 5 3 3 I 3 3 I-I.6 146 6 6 8 6 6 I 6 _ _ _ _ _ _ ____6 _ _ I I 1 u 98 76 98 76 98 76 98 76 98 76 98 1 98 98 I Ninth In Suspension and its Inversions. 16 6 -54 6 -54 6 -54 7 6 76 7677676 6- V6- 6 -54 54 54 4- 4 -2- 2 - 4- 4- 4 -2- 2- 2 - 4 -2 - j 4 -2 - 4 -t~ - 1 4 -2-:: _ _ _ -:- _ _ _ _ _ _ 4 3 3 4 4 33 4 34 Fourth 98 93 98 98 98 98 98 98 98 98 in Sus- 6- 6- 6- 6- 6- 6- 6- 46- 6- 6 pension- - andits 76 76 76 706 7 6 Inver- 4- 4- 4- 4- 4 -sions. ___ — ___-_________ ____ __ __ 2- 2-2-2-2-2-2- 2-22 --- 2-2-2 -Dissonant 5th 56 56 in Suspension. 43 43 43 43 43 43 44 98 98 98 9-8 98 98 98 98 98 98 98 98 98 76 98 98 98 76 56 76 76 767 76 76 76 56 7t6 7 6 7 56 Double Suspen- 7 6 76 76 7 6! 7 6 sions. 54 5 4 54 S45 4- 4- 4- 4- 4- 4- 4 33 33 33 33 33 33 3 66 66 66 6 6 66 6 6 6 6 6 6 6 6 6 6 6 6 2- 2- 2- 2- 2- 2- 2- 2- 2- 2- 2 - I Suspension of complete Chords. 8 -5 -3 - 8 -5 -3 - 8- 8 -56-* 56 3- 3 - 8 -3 - 8 -5 -3 - 8- 8- 8 -i-* 5- 56.* 3- i 3- 3 - I I I I I * This chord is only practical when it resolves upon the first inversion of a chord whose root is a fourth above. REMARKS. REMARKS. CHAPTER XIV. ESSENTIAL DISCORDS. NOTE.-Passing notes and suspensions being no part of a harmony, are inessential to it, and are termed inessential discords. 1. Essential Discords are those that enter into the harmony, and are a part of the combination. 2. Such discords are the Dissonant Fifths in the " chord on the mediant," in both major and minor keys. Chords of the Seventh. 7 Chords of the Ninth. - etc., etc. 9 7 DIATONIC DISCORDS. 3. A diatonic discord is one consisting of notes according to the signature of the key. When modulation occurs, the accidentals that denote the change of key are to be regarded as belonging to the signature of the new key, and are diatonic in the key to which the modulation is made. The leading note of the minor key, though indicated by an accidental, sharp or natural, is diatonic; so also are the major sixth and minor seventh of the melodic minor scale. 4. A diatonic discord resolves upon a chord whose root is a fourth above the root of the discord. 7 5 (73) 74 DANA S PRACTICAL HARMONY. [CHAP. XIV 5. Two conditions are essential to a diatonic discord, i. e.: Preparation.-The sounding of the tone in the chord before the one in which it appears as a discord. Resolution.-Its progression to a tone of the following chord. ~4A 4 0 A i* I X_ _ '77 _.__ 6. No two parts may proceed in seconds or sevenths with each other. CHORD OF THE DISSONANT FIFTH. MAJOR KEY. 7. The dissonant fifth in the " Chord of the mediant," in a major key (Chap.V, Section 4), may be taken as an essential discord, resolving when the entire chord changes. 8. The chord of the mediant is resolved upon the chord of the sub-mediant (Chap. XIV, Section 4). The fifth, appearing as the discord, must be prepared, and as it is the leading note, resolves upward to the third of the following chord. o 4-) 9. The chord of the mediant, in its first inversion, is not a discord, being available as a concord (Chap. V, Section 5). 10. The figuring used to indicate the dissonant fifth in a major key, will be the figure 5 placed under or over the bass note on the third degree of the key. Add a tenor, alto and soprano to the following figured exercise:...-.r X._.__- --. — r_ ^ — —. - 6 6 5 6 5 6 6 5 76 6 REMARKS. REMARKS. CHIAP. XIV.] DANA' S PRACTICAL HARMONY. Th 6 66 66 6 6 6 6 66 6 5 6 6 4 3 CHORD OF THE DISSONANT FIFTH. MINOR KEY. ii. The dissonant fifth in the chord of the medianit,in aminor key (Chap. VIII, Section 1), may be taken as an essential discord, resolving when the entire chord changes. The preparation of the chord and resolution is the same as in the major key. o4 12. The figure 5, with a ' or # ~before it, standing alone under a bass note, signifies the essential discord of the augmented fifth. Add soprano, alto -and tenor to -the following figured exercise: -7 -r- 6d- -i - 1. 60' I __ i -p- I %'; 0 I -019 —7 -__ - — *- I 1. I 9:5 6 6 g 6 r,6 Z'6 ~;5 6 4 1 13. The first inversion of the chord of the miediant, in a minor key, is also discordant (Chap. VIHi 7 Section 2), and the dissonant fifth requires the same treatment as in the direct form. Cd 0 - C) 0 6 14. The figure 6 or 6, over or under the dominant, in a mninor key, indicates the first inversion of the dissonant fifth. Add soprano, alto anid tenor to the following figured exercise: — _ _ _ 0 1= - 7 —. — I.= = —. - - - - - - - - 9_ _ _ _ _ _ _ _ _ _ 4 3 4.J s - 6 6 5 9.8 a 4;)~ W 43 4 46 6 # DANA'S PRACTICAL HARMONY. [CHAP. XIV. DIATONIC CHORDS OF THE SEVENTH. 15. A chord of the seventh is a common chord with a seventh from its root added. 16. A seventh letter may be added to dissonant combinations; as the chord on the mediant, in both major and minor keys, the diminished chord on the second degree of a minor key, etc. 17. As there are four letters in a chord of the seventh (and under certain conditions any one of these can appear as a bass note), there will be the direct form and three inversions of the chord. The direct form, first and second inversions, are founded on the same tones as in the common chord (Chap. II, Sections 13, 14 and 15), and the third inversion is when the seventh letter of the chord is the bass note. o o o 18. A system of figuring is used to indicate the direct form and inversions of a chord of the seventh. A chord of the seventh is in the direct form when the figure 7 stands under or over a bass note. 7 A chord of the seventh is in the first inversion when the figures 6 stand under or over a bass notes REMARKS. REMARKS. CHAP. XIY. DANA'S PRACTICAL HARMONY. 77 A chord of the seventh is in the second inversion when the figures 4 stand under or over a bass note. 4 3 -A chord of the seventh is in the third inversion when the figures 4 stand under or over a bass note. 4 2 NOTE.-The figures under or over a bass note show the intervals from the bass note; for the present they will be used to show the derivation of the chord, but it cannot be said too often that the figures under a bass note are only intended to describe the intervals from it, and not to show it8 derivation. Perhaps the following will illustrate the principle: ~7 The figuring indicates a chord of the seventh, on B, in the direct form, but as B is not a common chord with a seventh from its root added (Chap. XIV, Section 15), then the figuring does not describe the derivation. 19. A diatonic chord of the seventh must be resolved upon a chord, the root of which is a fourth above the root of the discord, and this second chord may be a concord or another prepared discord. 20. The seventh is the discordant tone which must be prepared, etc. (Chap. XIV, Section 5), and resolves upon the third of the following chord: _ _ _ l_ 4 _ The resolution may be delayed by its being suspended as a fourth., _4-3,7 43 78 DANTa S PRACTICAL HARMONY. [CHAP. XIV. 2.1. A seventh may be; added to the chord on the mediant, in a major key, when both the seventh and the fifth have the same treatment as either would have without the other. The figuring of the combination is 7. O.I: --- — -- ~ ---- I 7 22. In the first inversion on the mediant, in a major key, the fifth is not discordant (Chap.V, Section 5), and if the seventh is added, it is the only tone requiring preparation. ( ---- == 6 5 23. As there is no common chord upon the leading note, there can be no chord of the seventh upon the sub-dominant (except in the-last inversion), as the resolution of the chord. would be upon the leading note (Chap. XIV, Section 19), which is not a common chord. In one of the repetitions of a sequence it is available (Chap. X, Section 5). The last inversion of a chord of the seventh upon the sub-dominant may be taken, as the resolution of the discord is upon the first inversion of the chord upon th" leading note, which is a concord. (Chap. V, Section 5). - -'T- _ __ ----_ 6 4 6 2 24. As there is no common chord& upon the mediant, there can be no chord of the seventh upon the leading note (except in the last inversion), as the resolution of the chord would be upon the mediant (Chap. XIV, Section 19), which is not a common chord. In one of' the repetitions of a sequence it is available (Chap. X, Section 5). The last inversion of a chord- of the seventh upon the leading note REMARKS. REMARKS. CAr. XIV.] DANA S PRACTICAL HARMONY. 79 may be taken, as the resolution of the discord is upon the first inversion of the mediant which is a concord (Chap. X, Section.5). K — " — tH= -- -_ 6 4 6 2 25. The second inversion of a diatonic chord of the seventh is unavailable. 26. The following diagram will give the direct form and inversions of di.tonLd chords of the seventh, and the dissonant fifth, in a major key. -: 9: _ 10i== o-=. -_-~_~ _C; —:- -- i. 7 7 71 5* - I_ _ 6 6 6 5 i 5 5 There is no second inver4 1 4 4 4 2 2 1 2 j 2 7 6 5 sion of 4 2 7 diatonic 4 2 6 7ths. 4 2 * In the use of this chord of the seventh the fifth may be omitted, and the chord is figured 7-. Add a soprano, alto and tenor to the following figured exercises: No. 1.!- a= FitF -Q- 0- -F-> _ Fad __ __ 9__ __ _ s — - e — 7 7 7 6 7 43 6 7- 7 5 No. 2. - 4 6 7 -5 6 4 6 5- 6 4 6 4 66 76 743 2 3 2 2- 2 2 No. 3. D1C9. -.- —.__ 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 555 5 N1o. 4. 7 7 6 7 7 6 6 46 46 6 6 6 6 5 5 5 2 2 5 1No. 5. 6 4 6 _ _ 5 4 6 6 6 6 4 6 6 4 6 4i 6 6i5 6465 46 6 6646 646 4665 2 3 2 2 2 2 43 80 DANA' S PRACTICAL HARMONY. [CHAP. XIV. No. 6.,L ^-s^- -- — 9^ —Q ----1 - =- T ---i ---i -—, ^-rb61 4.- —,,-; — ---- ~~ 7 6 6 6 6 6 6 4 6 6 7 6 5 5 5 4 5 2 5 No. 7.. ----—. -u- -=e:-.6 6 66 6 6 436 6 6 76 6 6 -5 5 5 5 5 4 5 5 5 54 No. 8. -~_7 56 6- 437 6 7 6 6 4 6 43 6 4 6 6 5 3 5 2 2 5 Write original compositions in a major key, introducing diatonic chords of the seventh..DIATONIC CHORDS OF THE SEVENTH MINOR KEY. 2T. A seventh may be added to the diminished chord on the super-tonic in a minor key (Chap. XIV, Section 16), in which case the fifth and seventh both require preparation. This chord is only used when accompanied by the seventh. The fifth resolves upon the root of the following chord. a 0~ 6 7 5 In the inversions of this chord the fifth is not a discord (Chap. VIII, Section 2), and the seventh only requires preparation. 6 6 4 6 5 2 28. A seventh may be added to the augmented chord on the mediant of a minor key (Chap. VIII, Section 1), when both the seventh and fifth have the same treatment as either would have without the other. -.W - REMARKS. REMARKS. CHAP XIV.] DANA'S PRACTICAL HARMONY. 81 In the inversions of this chord the fifth is a discord and requires preparation 6 4 6 2 29. There is no direct form of a-chord of the seventh on the tonic in a minor key, as the resolution of the seventh would be by an augmented interval. f7 30. There is no first inversion of a chord of the seventh on the mediant in a minor key, as the resolution of the discord is by an augmented interval. t —1- - 31. There is no third inversion of a chord of the seventh on the leading note in a minor key, as the resolution is by an augmented interval. ih ---ii —~-fi4 6 32. As the leading note does not bear a common chord, there is no chord of the seventh on the sub-dominant. The last inversion of a chord of the seventh of the sub-dominant is admissible, as its resolution is upon a first inversion. 4 46 82 DANA'S PRACTICAL HARMONY. [CHAP. XIV: 33. As there is no common chord on the mediant, there can be no chord of the seventh on the leading note. 34. As there is no common chord on the super-tonic in a minor key, there can be no chord of the seventh on the sub-mediant. The last inversion of this chord is admissible, as its resolution is upon a first inversion. 4 6 2 NOTE.-A seventh in the direct form may be taken on the sub-mediant, provided its resolution is upon a seventh on the super-tonic. 35. As there is a first inversion on the minor seventh of a minor key (Chap. VIII, Section 3), the last inversion of chord of the seventh can appear on this interval-and resolve on a first inversion. 6 4 6 2 36. The following diagram will give the direct form and inversions of chords of the seventh in a minor key. k ~-; ' 7 ----* --- --- 7 7 7 7 5 6 6 _6 5 5 There is no second inver- sion of tonic 7ths. 4 4 4 4 t4 2 j 2 2- 2 2 * The fifth can be omitted in this combination when the seventh alone requires treatment. 37. Add a soprano, alto and tenor to the following figured exercises:No. 1. 67 - — t6 6 76 7 7 ~ _ -_:- -E m. fl5 ' 41 RE MARKS.. REMARKS. DANA'S PRACTICAL HARMONY. 83 CHAP. XIV.] No. 2...... -H — O-D-~ - -- -... _ i- -- - -— L ------ Z ~ -T --- --— __* --- —------- ~ --- —-— L --- —. 6f h6e 6 -6 6t643 6 l 6 6 4 5 5 5 5 No. 3. 6 4 6 6. 4 6 4$ _5 6. 5 5-.5 6 6 -- 6 6 6 6 2 2 -No. 4. 0 --- —-- ----- __ I,__ $ 7 4# 6 - - 66 6 4 6 $6 $6:5 5 5 4 # 2 i — + 6 6 7 6 98 98 — - f6 6 4 6 6 -- 6 # --- —4 2 No. 5. -— io _ ' -?-E --- -+_ _L -1 --- ___ 7 $ 6 7 $ 3D6 6 $ 7 4 6 7 6 6 6 — 6 — 6 4$ 5 5 5 No. 6. - 7 6 4 6 43 6 4 f6 6 6 6 6 4 #6 6 98 4 S5 & 2 2 4 2 2 N-o. 7..n ----—,6 6 6 -4 4 -AN EXCEPTION. 38. There is an exception regarding the preparation and resolution of diatonic discords. 39. The chord of the seventh of the dominant may be used without preparation. 40. There is a second inversion of this discord, and its progression is the same as the second inversion of a concord (Chap. V, Sections 9 to 18). 41. When the second inversion of the dominant seventh is followed by a first inversion, the bass rising one degree, the seventh may rise to the fifth of the following chord. 2 r — z — r12 ~t79 I? __ _ 4 6 3 t6 6 4 3 42. In the use of the second inversion of the dominant seventh, the root may be omitted and the seventh doubled; in which case one seventh observes the rule, and the other is free to rise by step of a second to the fifth of the following chord, or leap to the root. 84 DANA S PRACTICAL HARMONY. (CHkpr XIS. 6 6 46 43. When the seventh appears as the bass note, it may be approached by leap from below, but not from above. It can be approached by the step of a second from above or below. 4 4 6 4 ~ 4 8 1,4 6 4 2 2 2 2 6 2 2 44. There are also exceptional progressions of the seventh on the dominant. Besides being resolved according to the rule for diatonic discords (Chap. XIV, Section 4), it canA resolve upon a chord whose root is the sixth degree of the keythe leading note and seventh both observing the rule regarding their progressions of rising a second and falling a second. 7 7 - Add a soprano, alto and tenor to the following figured exercises: No. 1. 4 6 6 6 4 6 4 4 6 4 6 76 7 a 5 4 4 2 3 2 3 4 4 NO. 2. 4 566 667 46 6 64 6 4 6 6 7 3 4 3 3 4 2 4 No. 3. 4 66 4 64 4 6 6 ~ 6 4 6 66 6 7 2 4 2 3 2 4 2 4 4 No. 4. 6 t6 6 7 6 66 6~ f6 6 6 - 6 6 4 4 4 4 4 33 3 No.t 5. oiia opsto, lutaigdaoi cod ftesvnh REMARKS. REMARKS. CHAPTER XV. DIA TONIC CHORD S OF TIIE NINTH. 1. A chord of the ninth is a chord of the seventh with the ninth added. ir: 2. A diatonic chord of the ninth resolves upon a chord.whose root is a fourth above the root of the discord. 3. The root of a chord of the ninth can only be sounded in the bass, and consequently it is omitted in all the inversions. 4. In the inversions of a chord of the ninth, the notes bear the same treatment as in a chord of the seventh. In a chord of the ninth, when the fifth appears below the ninth, care should be taken that in its progression it rises to the third or fifth of the following chord, and thus avoid consecutive fifths. ls — ^-4=~5. When the root of a chord of the ninth is omitted, the seventh is not discordant, except when it appears in a first inversion on the mediant, leading note, etc., in which case the rules for its preparation and resolution must be observed. — =S — -7- I --- 6 7 7 6. This chord consists of four notes when the root is omitted, and has therefore four inversions. The last inversion (ninth in the bass) is unavailable. The first, second and third inversions of the ninth contain the same intervals as a chord of the seventh, and the figuring and treatment of the chord are the same, excepting that its root is decided by the resolution. 7. The figuring for the inversions of this chord is the same as for the direct form and inversions of a chord of the seventh. The direct form of a chord of the ninth is figured 9. first inversion " " "( " " 7. " second " ( " " 6. " third " " " " " " 4 (85) 86 DANA'S PRACTICAL HARMONY. [CHAP. XV. 8. The following diagram will give the direct form and inversions in a major key. 7 7 7 7 6 1 6 6 1 6 6 6 5 5 1 5 1 5 5 5 4 4 4 4 4 3 1 3 i 3 3. I_ I Add soprano, alto and tenor to the following figured exercises: No. 1. L — t __ _ _ __ -T- ----- v - --- 9 7 6 7 43 66 6 6 7 43 4 6 4 6 4 6 798 7 5 5 5 3 3 3 43 No. 2. 9- -_J -- __-_L r___ -- _ 7 76 66 66 6 9 6 4 6.69 5- 5 — 6 5 6 5 4 7 3 7 2 — 2 — 4 3 5 _ - -— _ -- --.. ---. 4- 4 --- — - -- - - — _ ---= ---". - -= — - -= ---- i-E-L 4' 6 6 6 4 6 6- 6- 6 6 98 4 6 76 98 6 6 43 ~ 3 5 3 56 Write an original composition, illustrating diatonic chords of the ninth in a major key. 9. The following diagram will give the direct form and inversions of the ninth in a minor key. 9 9 91 _ - 7 1 7 7 I 7 6 7 55 I | j 7 1 7 i! _, 5 _ _ _ _ I - 5 _! 4 4! I 4 _ _ 3 3 3 3 I j 3 Add soprano, alto and tenor to the following figured exercise: - - -... 4- __... 6 9 6 6 67 6 6 -- - 6 6 --- 4 7 5 5 3 6 6 - 4 6 -- 6 ~6 6 7 98 4t 52 5 7 - 5 Write an original composition, illustrating diatonic chords of the ninth in a minor key. .REMARKS. REMARKS. OAP. xv.] DANA S PRACTICAL HARMONY. 87 10. The exemplification of diatonic discords will close with this chapter. In the use of these discords the observation is made that the root of discordant combinations is known by the resolution. The following discord __. __ 6 5 uas two resolutions that are quite common. No. 1. NTo. 2. _~ (I _ _ _ and _ * 6 6 6 6 u 4 The rule has been given that a diatonic discord must resolve upon a chord whose root is a fourth above the root of the discord (Chap. XIV, Section 4). In illustration No. 1, the discord is followed by a chord whose root is G, and this root being a fourth above the root of the discord, then the root of the discord is D, and the chord is the seventh of D in the first inversion. In illustration No. 2, the discord is followed by a chord whose root is C, and this root being a fourth above the root of the discord, then the root of the discord is G, and the combination is the seventh, ninth and eleventh of G, the seventh appearing in the bass. For the exceptional progressions of the discords, see Chap. XIV, Sections 38 to 44, and fundamental discords on the dominant in following chapters. In a combination of discords, as the seventh, ninth and eleventh, there is an omission of some of the letters of the common chord; the ninth causes the first to be omitted in an upper part, and the eleventh the third, leaving the fifth as the only letter of the common chord. When the seventh appears in the bass, as in illustra. tion No. 2, it is not discordant against any of the tones represented, and is therefore free in its progression. CHAPTER XVI. CHROMATIC CONCORDS. 1. The student should review the chromatic scale (Chap. II, Section 18). 2. A chromatic chord is one that contains a chromatic tone, or tones taken from the chromatic scale of the key represented, and that does not induce modulation. MINOR KEY. 3. The tones appearing as quarter notes are the chromatic tones in the scale. 4. A major common chord may be taken on the super-tonic of the minor key, of which the third and fifth are chromatic tones.. The third letter of this chromatic chord may never be doubled, and in its progression to the following chord must rise a second or fall a chromatic semi-tone. The chromatic chord on the super-tonic must be followed by some chord containing the diatonic fourth of the scale, or by some form of the key-note. tJ '' 6 6 - 6 ) 5. The first inversion of the chromatic super-tonic can be used following the same progressions as in the direct form., (88) R E M A R K S. REMARKS. DANA'S PRACTICAL HARMONY. 89 CHaP. XVI.] Add soprano, alto and tenor to the following figured exercises containing chromatic super-tonic harmonies. 6o 6 6 5 6 7 # f 6 6 - 6 6 6 5 f 4- 4 6- 6 t 6 m6 6 4 6 5 fl 7 6 6 2 4 6 -- 6 f5 6 4 v f 6 a6 -f 6. A major common chord may be taken on the minor second of a minor key, the root appearing as the chromatic tone. There is no restriction as to what chord in the key must follow this chromatic chord. 7. The first inversion of the chromatic chord on the minor second can be used. In this inversion it is often referred to as the " Neapolitan Sixth." [ i-c I I ^j I I I I * be6 6 v _ __L_. L e 6 6 5 4 3! a1 *I I i l Pi. ___ __ 6 1,6 s6 I6 t5 fl NOTE.-There are instances where this chord is used in the second inversion, but they are very rare. Add a soprano, alto and tenor to the following figured exercise: 6 6 tf6 6 f 4 3 6 b6 7 4 t5 3 t o6 6 6 5 6 4 6 4 4 e6 6 5 4 j 90 - DANA'S PRACTICAL HARMONY. [CAr. XVI. The following diagram will give the chromatic chords and their inversions in a minor key. As a recapitulation of chromatic chords and their inversions in a minor key, add soprano, alto and tenor to the following figured exercises: No. 1.:_L::-_r:l- - ~ —.~t-_-0: ---g- - --— =- +i:- i —:x: ---- ~t-t-_ -- 6 6 6 6 - 6 667 ---- 6 6 6 4 5 4: 4.... _-_ _ t- = — = ___ _3 f5 h 65 6 6 b 6 t6 o 6 5 65 6 6 6 67 No. 2. -- -OE - - - [.... 6 5 6 6 6;6 6:5- 6 6 t6 5 6- 6 — 6- 6 6- 6- 6 -4 4 44- I3 4 -3 3 — _ ~- -~- -t -r- — ~-;-! - -:~ -— t-~....-= —.:~ ---1 r —r-:r-t~-~-t ---~-r ---: — ----- 4-6 6 6 6 6 ~6 p6 6;6 6 6 6 6 7 2- 4 $4 ' 4 - 3 4; 3 2 3 Write an original composition, illustrating chromatic chords in a minor key. MAJOR KEY. - ________ —_ ---__-_; ---__-_, —_ —I-j —= _ _._... _ - 8. The tones appearing as quarter notes are the chromatic tones in the scale. 9. A major chord may be taken on the super-tonic of the major key of which the third is a chromatic tone. The third letter of this chromatic chord may never be doubled, and in its progression to the following chord must rise a second or fall a chromatic semi-tone. This chord can appear in its first inversion. 10. The progressions of the chromatic super-tonic are the same as in the minor key (Chap. XVI, Sections 4 and 5). Add soprano, alto and tenor to the following figured exercise: 6 --- 6 6 5 - 6 6 4 6 4 3.4 2 ____9_ -- ^=__- - -- -_- = _^ - -— _,_ _ _ __ ___ —. F-_ r --— t - _- _t -.__ ----, _'r _ tF ~_-_ _ _: 4 6 6 6 7 6 6 - $ 7 3 4. 4 REMARKS. REMARKS. CrAP. XVI.] DANA'S PRACTICAL HARMONY. 91 11. A major common chord may be taken on the minor second of a major key, the root and fifth appearing as the chromatic tones. The uses of this chromatic chord and its progressions are the same as in the minor key (Chap. XVI, Sections 6 and T. A'dd a soprano, alto and tenor to the following figured exercise: ----- ------ ' — -.-. -- 6 i 5 6 7 43 6 6 t5 6 4 4 7 al, IX<__I ----L 98 5 6 6 --- 56 76 56 6 i6 t5 5 7 12. A major common chord may be taken on the minor sixth of a major key, the root and fifth appearing as the chromatic tones. There is no restriction as to what chord in the key must follow this chromatic chord. 6 '( —_3- _ --- -- - ___ —_ ---_r ---( 1 ( aY '....( —_ ----_ -----— '... —. --- -— _ -H13. The first inversion of the chromatic chord on the minor sixth of a major key may also be taken. Add soprano, alto and tenor to the following figured exercise: 6 6 6 - I5 — 5 6 6 6.6 5 6 I --- ---- - _-_. - _ _ h5 g6 7 6 6 6 65 4 4 4 3 93 DANA'S PRACTICAL HARMONY. [CHAP. XVI. 14. A minor common chord may be taken on the sub-dominant of a major key, the third appearing as the chromatic tone. There are no restrictions regarding the progression of this chromatic chord. c_ z rGW E e I -- -- i — i* I I:.l- - _, i I r; 15. The first and second inversions of sub-dominant can be taken. the chromatic minor chord on the I I F r Add soprano, alto and tenor to the following figured exercise: 4 6 S -0. Z --- 4 6 6 6 4 6 2 4 2 4 6 3 -e6 5 4 3 4 6 3 6 t6 4 4 16. The first inversion of a diminished chord (Chap. III, Section 5) may be taken on the sub-dominant, the fifth appearing as the chromatic tone. There are no restrictions regarding the progression of this chromatic chord. S6 l 1 i 9 -—, ---' —! Add soprano, alto and tenor to the following figured exercise: 6 6 5 6 4- 3 6 6 6 6 6 5 6 6 6 7 i $ 43 B 4 b5 6 6 5 3 E 4 3 REMARKS. REMARKS. DANA'S PRACTICAL IARMONY. 93 CHA. XVI.] The following diagram will give the chromatic chords and their inversions in a major key. As a recapitulation of chromatic chords and their inversions in a major key, add soprano, alto and tenor to the following figured exercises: No. 1. -- - _- _ - - --- -4 — - +F --------- ------ 4 6 t 6 6 65- 6 4 ]6 6 6 6 5 6 5 '5 3 4 4 3- 3 4 i 43 y5 6 6 --- 8 ---- f6 5 6=- 5 — t5 6 4 f 5 —, 4- 3 — 3 3 3 3 3 6- 5 — 6 7 6 6 6 6 6 166 4 6 4 6 6 7 4- 3 — | 4 2 |4 No. 2. _ T __ __ -- — _- __ - - 6 65 4 6 665 6 b6 5 6 674 6,6 5 b 43 2 43 4 2 *. tIfj J b5 -- 5 4 6 3 b b 4 3 L5 4 3 6 — 6 6 67 -4 Write an original composition? illustrating the use of chromatic common chords in a major key. CHAPTER XVII. FUNDAMENTAL DISCORDS. 1. When a tone is sounded, a series of harmonics arises in the following order: * * _ etc., etc. THis series of tones, containing a major third and a minor seventh, will suffice for the present purpose. In the use of diatonic discords, the rule that every discord must be prepared (Chap. XIV, Section 5) was presented,but from the above illustration the discord enters the combination without having previously been heard, and is therefore not prepared. There are but three tones in every major and minor key which can appear as generators or roots of chords containing unprepared discords, and they are the Dominant, Super-Tonic and Tonic. As the third springing from the root sounded is a major third, then the chords built on the three tones named would be major chords in both major and minor keys, and would appear as diatonic or chromatic chords according to the keys in which they appeared. In a major key the Dominant chord would be diatonic. In a major key the Super-Tonic chord would be chromatic. In a major key the Tonic would be diatonic. (94) REMARKS. REMA RKS. CrP. XVII.] DANA'S PRACTICAL HARMONY. 95' In a minor key the Dominant chord would be diatonic. In a minor key the Super-Tonic chord would be chromatic. In a minor key the Tonic chord would be chromatic. These three chords constitute what are termed Fundamental Chords, and to them may be added without preparation the discords that spring from their roots as generators, and are termed Fundamental Discords. They are not prepared, and have various resolutions. 2. The discords are the minor seventh on the Dominant in both major and minor keys. r I-10 1,00, 0 I i 91t7_ P I __ __ L. The minor seventh on the chromatic Super-Tonic in both major and minor keys. The minor seventh on the Tonic in both major and minor keys. (19=^=l=^ 96 DANA'S PRACTICAL HARMONY, [CHAP. XVII. The minor ninth on the Dominant in both major and minor keys. -----— ~~L~ ~ — 4~The minor ninth on the chromatic Super-Tonic in both major and minor keys. he minor ninth on the Tonic in both major and minor keys.The minor ninth on the Tonic in both major and minor keys. _ szzizL The major ninth on the Dominant in a major key only. The major ninth on the chromatic Super-Tonic in a major key only.! ---~ ---The major ninth on the Tonic in both major and minor keys. The eleventh on the Dominant in both major and minor keys. ------ REMARKS. REMARKS. DANA S PRACTICAL HARMONY. CHAP. XVII.] The minor thirteenth on the Dominant in both major and minor keys. ' _ The minor thirteenth on the chromatic Super-Tonic in both major and minor keys. The minor thirteenth on the Tonic in both major and minor keys. The major thirteenth on the Dominant in a major key only. The major thirteenth on the Tonic in a major key only. 3. Every unprepared discord whose root is the Dominant, Super-Tonic or Tonic, may, like the leading note (Chap. IV, see exceptions), be transferred from one part to another, but must resolve in the part in-which it last appears. 98 DANA'S PRACTICAL HARMONY. [CHAP. XVII. 4. Fundamental discords are founded on major common chords. DOMINANT SEVEN TH. 5. The chord of the Dominant seventh is the major chord on the Dominant in either major or minor keys, with the minor seventh from its root added. ---- u 7 — -^-r q- ** — 6. Some of the characteristics of this discord are to be found in Chap. XIV, from Section 38 to the end of the chapter. 7. There are two progressions of the Dominant seventh-to the chord of the Tonic and chord of the Sub-Mediant in both major and minor keys. In neither of these progressions does the leading note or discord violate the rule regarding their progression. The third in the chord of the Dominant seventh rises a second, and the seventh falls a second. 7. 7 8. The Dominant seventh also resolves upon the chromatic chord on the minor sixth in the major key (Chap. XVI, Section 12). 7 ' ----:. ~ ---~'9. The Dominant seventh may resolve upon an inversion of the Sub-Dominant in both major and minor keys, the seventh remaining to be a letter of the following chord. - -_ --- ---- -.. —j —V- — t- _ —~__ - -m-___ -- ___ t - - i - r- --- ":i 7 6 7 6 7 6 7 6 4 4 f 4 REMARKS. REMARKS. CHr VI]DANA'S PRACTICAL HARMONY. 99 10. The Dominant seventh also resolves' upon the inversions of the chromatic chord on -the Sub-Dominant in a major key (Chap. XVI, Section 14). \ — I PEI a74-.1 = --- rzz 7 6 7 h,6 4 1I1. The Dominant seventh also resolves npon the chromatic chord of the seventh on the Tonic (Chap. XVII, Section 21) and its inversions, in both major and minor keys. - - — ~ --- —~ —g VP *o * _7_4 6 6 _ _ _ _ _ _ _ _ _ _ _ 5 -4 _ -t —67-E__ 7I 6 -_6 -4 4 b5 3 _4 6 4 4 12. There is a characteristic' peculiar to the Dominant seventh, the effect of which is not to be felt from any other discord, i. e., as the closing chord to a rhythmical period, or having a hold written over it. 6 5 __-~-__ - ___ P_ -e. I 2!.-!R; 7~ 7- -2 m.-40- - -~:_ -9. 4' 7 -100 DANA S PRACTICAL HARMONY. [CHAP. XVII. 13. The diminished chord on the seventh degree of both major and minor keys (Chap. V, Section 3-Chap. VIII. Section 1) is the chord of the Dominant seventh, with the root omitted. V d db Add soprano, alto and tenor to the following figured exercises: No. 1. 5il-h-_i=- -I-=_-_ -? — m — f —:-Z-E- _ 7 6 67 6 6 4 66 6 6 4 4 6 4 3 4 3 2 4 ~.: — r-r-+-~ It- - ' — --- - ---- 766 66. 6 4 6 f6 6 6 7 4 3 5 4!=- - 1_ -H --- I-: ___=. _ t-5 -7.e s5 47 6 5 t6 5 7 be f6 5 4 3 4 3 4- _ 6 _ 7 6- 7 6 6- 6 6 6 4 4 6 6 65 6 4 6 4 6 6 7 4 43 5 3 3 43 2 3 No. 3. t66 6 6 - 6 t6 6 t4 6 7 6 6 6 7 4 4 5 2 4 4 3 3 No. 4. ____- _ -- - _-_-__,_ -l ---: - _.___. 6 7 6 5 6 16 7 6 7 5 4-.- 4.. 3 CH-R OMA TIC SZUPER-TONVIC SE VEN2TH.. 14. A minor seventh can be added to the chromatic chord on the Super-Tonic in both major and minor keys (Chap. XVI, Sections 4 and 9) without preparation. ~ ----~ — 7 6 7 X7 5 REMARKS. REMARKS. CHAP. XVII.] DANA S PRACTICAL HARMONY. 101 15. The progression of this chord and the treatment of third are the same as in the chromatic common chord on the same tone of the scale (Chap. XVI, Sections 4 and 9). 16. The seventh in this chord must fall a second, or remain to be a letter of the following chord: 6 17. It is used in the direct form and the three inversions. - 6 t7 B6 6 r4 5 4 5 2 3 18. When the seventh in this chromatic chord remains to be a letter in the following chord, it can be doubled (appear in two parts), and one part is free to leap as a concord. _ _ _ I _ _ Op_ - 7 6 6 t6 6 4 4 4 3 19. The seventh can also leap without being doubled when the fifth in the chord of the seventh goes in the following chord to the letter that was the seventh in the chromatic chord.: 1 --- 20. In the second inversion of the chord of the chromatic seventh on the Super-Tonic, the root may be omitted and the seventh may be doubled. ( --- —-- ---- — _ ---~-1~BE 102 DANA'S PRACTICAL HARMONY. [CHAP. XVIL MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key: No. 1. -- -- _ ----* —_ —_ —_ 6 7 7- 6 6 2 6 4 4 6 6- 6 66 5 3 2 --.. _, -~ — --— ~ --- -:. —~ t-t_ — -- ____ 6 5 7 7 6 4 6 6 6 7 6 4 6 6 6 6 7 i6 6 7 4 3 3 t4 t 4 5 2 5 4 5 4 4 2 3 3 Ito. 2. ). --- —Ho-~ —___ - _- __ __..__ 4 6 7 6. 6 65 -- 66 6 4 6 7 6 7 3 5 5 43 4 5 2 4 - '6 65 6 6 t6 6 65:4 6 7 6 7 4 43 5 4 4 t5 43 2 t5 $ 4 NTo. 3. _', ---_o — z__-L ^Z__o. - E-Z": --—. --- —_ ^'FF -- - C^ ^ = ^ - ^ 4 6 6 7 t4 6 6 6 6 6 7 6 6 6 7 4 6 4 3 4 2 L5 5 4 4 5 2 3 76 6 7 4 Write an original composition in a major key, introducing the chromatic chord of the seventh on the Super-Tonic. MINOR KEY. N"o. 1. _ q; --- _ ------- ------ --- --- -- -- 6 7 6 6 - 6 5 7 6 5 - 4; 4 - - 3 6 -46 6 5 -- 6 6 — 7 4 --- 2 -4 4 t4 $ 3 2 NTo. 2. 9@ — -t- ---... _- ___ — _ F _ —s — _ -E ---F -— ___-~ _ - - — F _-: —=:z_ -_' —' — -= —. -~ -'- --— ~- 1 - - 6 $ 7 7 6 7 6 6 4 6 5 6- 6 66 5 -- 5 4 5 4 4 5 33 3 6 5 7 7 6 6 6 6 t6 7 4 5 $ 4 $4 5 4 t3 2 3 6 t4 6 2 6 6 6 t7 46 6 4 5 4 4 f 3 7 ~ Write an original composition in a minor key, introducing the chromatic chord of the seventh on the Super-Tonic. REMARKS. R EM A RKS. CHAP. XVII.] DANA'S PRACTICAL HARMONY. 103 CHiROMATIC TONIC SEVENTH. 21. A minor seventh may be added to a major chord on the Tonic jn both major and minor keys. In a major key the seventh is a chromatic tone, and in a minor key the third is the chromatic tone. -i -- 22. In order that this chord shall not induce modulation it must be followed by a Dominant discord or a Super-Tonic discord. 23. The third in this chord cannot be doubled, and in its progression must either rise a second or fall a chromatic semi-tone. I -'I:-:- -1- rnr -- I "- F W- -__JrW_~ i __ -Fiz -i t- I ~ ~'z[ 1 __ I b7 t6 L7 7 7 9 4 3 24. The seventh in this chord must either rise a chromatic semi-tone (to the third letter in the Dominant discord), ( 7 4 b7 t6 3 4 3 or fall a second (to the fifth letter in the chromatic Super-Tonic discord). b7 7 7 104 DANA S PRACTICAL HARMONY. rCHAP. XVII. 25. This chord can appear in the direct form and -three inversions in both 'major and minor keys. g* * * e * 7 6 4 4.5 b 2 26. In the second inversion the root may be omitted, but the seventh cannot be doubled, as in the Dominant seventh (Chap. XIV, Section 42) and chromatic Super-Tonic seventh (Chap. XVII, Section 18). MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key: No. 1. 6 6.6 6 6 6 6 6 56, 6 7 - 6 B 7 4 4 4 3 4 h4 E5 5 - -r-2 ----.. --- —-, --- —----— _ ___'-_ _ __ 4 - - 6 6 4 6 6 6 4 6 4 6 6 6 6 6 7 2 - - 4 4 2 4 2 25 2 4 3 -No. 2. 7 p6 6 65 6 t7 7 65 6 f4 6 6 6 6 4 7 4 43 ~ 43;5 --- 2 t5 ---- 5 4 t3 g 3 4 t6 6 4 6- - 4 6 7 6 6 6 ~6 6 6 6 7 - 2 4 4 2 2 5 t5 5 4 t5 4 g 3 3 Write an original composition in a major key, introducing the chromatic chord of the seventh on the Tonic. MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key: No. 1.:__ --.. -F- -: - _- -- _, 6 6 6 6 7 6 6 5 7 - 6 6 6 6 7 4 4 5t5 4 - 4 4 5 5 '~-2z! ----. ---- -: ---,' --- L —r- -..^.....I -—.- -T-t4 - - 6 t4 6 P 4 4.6 T 6 7 2 - - 4 4 1,2 - - 5 4, 3. 2 I2 REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. 105 CHAP. XVII.] NTo. 2. __ ___ ______ * -~ ----[-E 7 7 6 6 6 7 6 6 66-6 6 6 s 4 - 5 54- 4 4 - 6 ~6 6 6 f4- - - - 6 7 4 4 4 2 ---. - 4 4 3 Write an original composition in a minor key, introducing the chromatic chord of the seventh on the Tonic. 27. The following diagrams will give the fundamental chord of the seventh in both major andI ininor key1-s on the Dominant, Chromatic Super-Tonic and Tonic. MAJOR KEY. Dominant 7tI Chromatic Super-Tonic 7th Chromatic Tunic 7th. ~-7iIy r 4 4 7 6 3 2 5 476 ~r 2 5 5 4 MINOR KEY. _ _ — H -I - -— _ 7th. 4 2 7 6 325 CHAP T E XVIII. THE D OMINANT MINOR NINTH. 1. A minor ninth may be added to the chord of the Dominant seventh (Chaps XIT!, Section 5) in both major and minor keys without preparation. 2. In a minor key the ninth is a diatonic tone, _* __ I and in a major key it is chromatic. 3. There are two resolutions of the ninth. 1st. It may resolve while the rest of the chord remains. a. To the root of the chord of which it is the minor ninth.,._n___.-__. _ fix - ff, -- d b. To the third of the chord of which it is the minor ninth. __ j -_ _- '.:~:= --- - e —t j _L4 f- $- ff '^.. gi =E?=E-i= EEEE~^ 1i _.L ___ L bg 3 bi 3 7- 7 2d. It may resolve to a chord having another root. i — 1 r --- ]REMARK..-There are other resolutions of the minor ninth which may be considered excep. tionfal, as the minor ninth rising to the major ninth, etc. (106) IR IE M A RK S. REMARKS. CHAr. XVIII.] DANA'S PRACTICAL IARMONY. 1 7 4. If the ninth resolves upon the root (Section 3, a) the root may be sounded in the bass with it, but should not be sounded in any other part; consequently the root is omitted in all the inversions of this chord. 5. There are the direct form and four inversions of this chord. Resolving on the root of the same chord. * - =a- I —=- i —x- --— ~- - ' ---_ 2 - -- 9LLA" — __ — _ b -" 6 — 6 — e 29 8 b7 6 6- 6- 6 -7- 5- 5 4 4- 4 --- 3- '3 2 2 -Resolving on a chord of another root. - __ _ _. __ _- ~ _ t9 b7 6 - 4 6 7 5 t5 b3 2 3 3 3 Resolving on the third of the same chord. - ' - -_ _ — p9 3 35 6 3 4 7 -7- 4- 2- 6 --- 3- 4 -The above is the figuring for the minor ninth in its various inversions. The absence of the character of depression (t or t) before the nine would give the figuring of a major ninth. MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing the resolution of the minor ninth upon the root of the chord. No. 1. 4 6 b9 8 7 6 6 6 5 6 4 6 b7 6 3 7 - 5- 4 3 3 5- 5 ___._.-? — -_i",- 2 — -____._ __ -- 65 -- 6 6 -- 6 4 6 - 6 7 6 -- 6;7 43:5 5 4 - 3 4 4 4 3- 2 3 No. 2. 6 t9 8 t7 6 --- - 6 4 6- 6 4 6- 4 6 4 6 -7- 5 54 3 4- 3 2 3 4 -3- 3 2 2 — 108 DANA'S PRACTICAL HARMONY. [CHaP. XVIII MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key, containing the resolution of the minor ninth upon the root of the chord. No. 1.._ __ _ -_-3_9 ' ------ — '- - - -.- - D- o - 6 - 6 - 67 f 98 6 --- 6 -— 4 6 6 — t2 - 4 7- 4 2 — 3 A3 3 d3 -.. T __ -' -3 —: —D —3-D-'4D — W7 6 7 t4 6- 6 --- 6 6 --- 6 4 --- 6 6 --- 5- f 32 54 4 2 — 5 2 -3- 3 6- 6 6 -4- 6 46 6 --- 4 6 6 ---- 67 4 2- - - 2 4 2 4 2 ---- 4 3- 3 'Io.. 2. 98 6 6 6 6 --- 6 6- 4 -7- 5- 54 32 $- 3 -4 32 4 43 4- 4 - 3 $2 - 6. If the ninth resolves upon the third (Section 3. b) letter of the same chord, the third must not be sounded in any of the parts together with the ninth. 7. With this resolution of the ninth there is no first inversion of the chord, and it is rarely used in any but the direct form. 8. When the ninth resolves upon the third of the same chord, the seventh may be omitted and the root doubled; but when the ninth resolves upon the third, the root must proceed to the seventh. Eq 3 ~ q 3 8 7 8 7 9. The resolution of the minor ninth is made -by rising an augmented second (Chap. IV, Section 1) or falling a diminished seventh. MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing the resolution of the minor ninth upon the third of the chord. REMARK S. REMARKS. CHAP. XVIII.] DANA S PRACTICAL HARMONY. 109 No. 1. 693 6,5 6 665 6 t3 4 6 7- 6 6 -4- 43 2- 6- 4 3- 4- 2 No. 2. t9 3 6 b5 6 65 b34 6 6 65 b6 6 7- 6 6 6 6 6 - 7- 4- 43 2- 4 43 4 6 4 4 4 - 3- 4 3 2 -MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key, containing the resolution of the minor ninth upon the third. - -— _ _-_-_ —_ _ _ 5 6 6 6 6 # 6 6 '6 6 3 f4 6 4- 2 -3 — OL 6 6 t 6 6 7 7 4 6- # 4 10. When the minor ninth resolves to a chord having another root, the entire chord changing (Section 3 \, the progression is to a chord whose root is a fourth above; namely, the chord of the Tonic. The minor ninth then resolves upon the fifth letter of the Tonic. REMARKt.-There are exceptional progressions of the resolution of the entire chord. The chord of the Dominant minor ninth can resolve upon a chromatic Super-Tonic discord, the ninth and seventh each rising a chromatic half step, 6 7 6 3 T irxipon.a ehron~~afc qtonic discardl. 110 DANA'S PRACTICAL HARMONY. [CHAP. XVII 11. In the third inversion of the minor ninth, where resolving upon the Tonic chord, care should be taken in its resolution to avoid consecutive fourths (Chap. IV, Section 8). Let the fifth letter of the Dominant rise to the third or fifth of the Tonic. '. =7_I (19 6 4 2 6 4 MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing the resolution of the ninth to a chord having another root. No. 1. 6 6 6 6 b9 7 6 9 6:6 I7 4 4 7 5 4 7 4 4 b3 3 " 3, - -- ---— _ __ 6 6 4 6 6.6 6 7 4 h3 2 4 No. 2. 4 64 -=_- -r — 6 6 6 6 4 6 6 6 6 6 6 7 b3. 73 743 43 4 MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key, containing the resolution of the ninth to a chord having another root. No. 1. __ _"_ _ __ '....-s - 7 1 6 - 1 - 6 t6 1 - 5 5 3 7;6.65 66 6 - - t4 6 6 7 ~4 6 6 9 t2 4f 5 a 4 4 3 7 3 1 No. 2. t 7 7 65 $. 6 6 - 7 6 5 43 REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. CHAP. XVIII.] 111 - _-rnFY - E__E -_o7[ r6 6 3 6 6 r4 6:2 4 3 6 6 6 7 - 8 4 5 - 5 9 ---- - 3 Add soprano, alto and tenor to the followingS figured exercise, containing the reIsolution of the root to the seventh, while the ninth proceeds to the third (Chap. XVIII, Section 8). _ _ _a - - - _ Ta r =,-_F. -r;.,-# 7#_ h9 3 6 5 6 b5 6 87 43 43 4 - 6 6 h9 4 6 4 - 6 r9 &. 5 8 7 Write orig.na. compositions in both major and minor keys, illustrating the uses of the minor ninth on the Dominant. MAJOR NINTHY ON 71TUE D OHIJNANT. 12. A major ninth may bc addcd to the Dominant seventh without preparation, btit in a major key only. REINARK.-In 1he harmonic minor scale the sixth interval is minor (Chap. III, Section 9> and oniy as such can appear as a member of a chord; as the major sixth never appeai s in a minor diatonic scale, cxcept as a passing note (C'hap. XI, Sections 11 and 14>, consequently there can be no major n~nth on the Dominant in a minor key. 13. The resolutions of the major ninth are the same as those of the minor ninth (Chap. XVIII, Section 3). 14. The characteristics of the major ninth are the same as those of the minor ninth, with the single exception that the major ninth should not be sounded below the third, and there is, therefore, no last inversion of the chord when resolving upon the root. Add soprano, alto, and tenor to the following figured exercises,.containing the resolution of the major ninth upon the root. 6 98 6 6 6 6 6 76 4 7 6 6 7- 36-2 6 -____ —L"T__ __ _ _ _ _ _ E - Z1 6 6 6 —: 6- 6 4 54 0 - 76 6 4 4 3 4 2 6 6 7 Add soprano, alto and. tenor to the following figured exercises, containing the resolution of the majir ninth upon the third of the chord. No. L. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -~ — ---- - - _ _ _ _ _ _ _ T 6 56 6 34 6 6 7- 6 6 93 4- 2 4 6 7 -3-, 4 -No. 2. _ _ _ _ _ ~- - D D - - - ~ _ _ _- - _ _ _ 93 65 6 56 8 7 43 43 4 - 6 6 9 4 6 6 4 5- 5 9 3 8 7 112 DANA'S PRACTICAL HARMONY. [CHAP. XVIII Add soprano, alto and tenor to the following figured exercises, containing the resolution of the ninth to a chord having another root. No. 1. _ -:i -AT — _ t —< 6 6 9 7 6 6 4 6 4 6 4 7 5 5 3 2- 3 3 3 3 7 4 6 66 4 6 6 6 4 6 6,664 66 6 B 7 3 4 3 5 3 43 5 4 No. 2. a —tJ t-Ado-t- E ---O —FF — 1 --- ~ —F-T ---~ ~ —~.:?-:-'-': - F — 9 7 4 6 6 6 6 5 6 4 6 7 86. 6 ~7 7 5 2 5 43 3 5 4 3 Write original compositions, illustrating the use of the major ninth on the Dominant. SUPER-TONIC MINOR NINTH. 15. A minor ninth may be added, without preparation, to the chromatic chord of the seventh on the Super-Tonic (Chap. XVII, Section 14), in both major and minor keys. 16. In a major key the ninth is chromatic, and in a minor key diatonic. 17. The resolutions of the Super-Tonic minor ninth are two: 1st. It may resolve while the rest of the chord remains. a. To the root of the chord, of which it is the minor ninth. b. To the third of the chord, of which it is the minor ninth. REMARKS. REMARKS. o rAP. XVIII.] DANA S PRACTICAL HARMONY. 113 2d. It may resolve to a chord having another root. \l_ — — C ----r --- —f7 6 7 6 4 4 18. If the chord resolves upon one having another root, it must be followed either by a Dominant discord or an inversion of the Tonic harmony, as given in the preceding illustrations of resolutions to a chord having another root. 19. The minor ninth, in resolving upon a chord having another root, must either fall a second or rise a chromatic semitone, or remain to be a letter of the following chord. _=e' -— i.T 1 Z-' n ---I 20. All other characteristics of the Super-Tonic minor ninth are the same as those of the chord of the Dominant minor ninth (Chap. XVIII, Sections 1 to 12). MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing the resolution of the minor ninth upon the root, third, etc. No. 1. F,.__ _,_ _-_ _.... -- _ - t9 8 6 6 ~6- 6 4 3 6 --- 6 7- - t5 4 t5 7- 4-?5 3- -3 2 -— _m~ __I -i —Fi -_-_ --- —-- __ - -_. -_' t -- ________________i ___L 77 6 4 6 6 — 7 ---- 6 6 7 5- 2 4- 4 4 3-:2- 2 No. 2. __ n Lf __________ __ --— 3- --. -r — -- -— 9 -- T: —f —s —,-' - - r-E —~ - — c —, --- —=I -=-.19 t3 W6 5 6- 9 6 5 "7 6 4 6 6 $ 7- 4 43 5 4 2 4 ~5 3.. — --!" — O ~ _ _-_ - D -__-_ g6 5- 6 --- —- ~4 5 6 ---- 4 7 4 6 43 —. 3 t ----3 t5' 3 S —#-=-=p=>~ —n-~ 21S 6 6 4 6 4 6 6 6- a ' 6 6 t2 3 2 2 t5 4 97 6 9 8 - 5 4 7 -3 - 114 DANA S PRACTICAL HARMONY. MINOR KEY. [CHAP. XVIII Add soprano, alto and tenor to the following figured exercises in a minor key, containing the resolution of the minor ninth upon the root, third, etc. 6 98 67 6 9 647 6 76 6 4 7- 4`4 7 4 f 4 $F- 4 67 6 — t7 6- 6 f- 6- ~ t4 — 5 54.. 54 t5 3 2 42 —.3 -6 6 t4 6 6- 4 9 #3 6 7 3 4 b 3 1:4 ---Sf2 --- 6 ii 44 -- 4 4 SUPER-TONIC MAJOR NI2TTI. 21. A major nifth may be added with o t preparation, to the chromatic chord of the seventh on the Super-Tonic, but in the major key only. (See chapter on "False Relation," which debars its use in a minor key.) 22. The resolutions, of the major ninth are th6 same as those of the SuperTonic minor ninth (Chap. XVIII, Sections 16 and 17). 23. All other characteristics of the chromatic Super-Tonic major ninth chord -re the sarne as the major ninth on the Dominant (Chap. XVIII, Sections 12, 13 aind 14). Add sop!;ano, alto and tenor to the following figured exercises, containing-the resolution of tile major ninth upon the third, root, etc. 9 8 65 9 b7 76 65 7 6 7 6 7 43 7 3 5- 43 5 4 z~zz~ ~3 5 ~6 6 7 4- 6 4- 4 5 32 3 - 6 r4- 6 4 32[L5 7- 65 6- 43 7 6 7 5 4 TONIC MVINOR NINTH. -J 24. A minor ninth may be added, without preparation, to the chromatic chord of the seventh on the Tonic, in both major and minor keys. 25. In both major and minor keys the niith is a chromatic tone. nlkZ4hiL hoai oe REMA R IS. REMARKS. CHAP. XVIII.] DANA S PRACTICAL HARMONY. 115 26. As in the case of the minor ninth on the Dominant and Super-Tonic it can resolve cn the root or third of the same chord, or up.on a chord derived from another root. 27. If resolved on the root or third of the same chord, the minor ninth observes the same rules as in the minor ninth on the Dominant. 28. If resolved upon a chord derived fiom another root, the resolution of the chord would be the same as the chromatic chord of tlhe seventh on the Tonic (Chap. XVII, Section 22); that is, to a Dominant discord or a Super-Tonic discord. I II - I~-. 3ZZZ. rV7 - 9 7 V 1i b7 a 8 6 4 29. If the ninth falls a second, the root should not be retained as a note of the following chord. b9 h7 MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing the various resolution of the Tonic minor ninth. - 8 7- -- '6 t -- 6 — 3- -- _ ---_ —_ --- —-, ---- -F —f ---. --- — ' — — F 2__. _-,-___._ -._.-s-_ _. E:_E7 6 656 6 — 6 7 4x6 4- 43 b --- — t5 - 3 2 6 5 - 4- 6.... 6- - 6 4 - 6 6- 7 4 3 b3 — - 3 - - --- $ ^i4r=^j^-j-3 I -,.-Hi:, _ j^^^q*" I-a-' _ - I - - 9 2 — 4 8 - 7 6 6 — 6 7 -4 - - hS______ 116 DANA'S PRACTICAL HARMONY. [CHAP. XVIII. MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key, containing the various resolutions of the minor ninth. b98 7 6 9 76 65 6 7 4- 6 — I, 6- 4_ 2,h32 65 t4 d6 6 6 t4 6 6 7 44 b3 4:3 ---- 4 6 d6 6 98 7 6 7 2 4 5 4 3 TONIC MAJOR NINTH. 30. A major ninth may be added, without preparation, to the chromatic chord of the seventh on the Tonic, in both major and minor keys. 31. This chord contains all the characteristics to be found in the chromatic Tonic minor ninth chord (Chap. XVIII, Sections 24 to 30). 32. As in the case of the Dominant major ninth, the Tonic major ninth should not be sounded below the third. MINOR KEY. Add soprano, alto and tenor to the following figured exercises in a minor key, containing some of the various resolutions of the major ninth on the Tonic.,__-_-__-q_~-_ ' —_ __ —^. 0-_~__.___~-___ '_._D 98 6 7 ~4 6 6- 6 6 6 7 5- 7 -7-4 4 4 a 3 5 5 4 4 3 3 5 -5-3 3 3 3.-_ ---i-C-_ — _ ----- __ _____ _ -A_ —_ - Bi- ~ t- _ __. _ 2 6 66 6 ~6 7 t46 34 6 6 6 4 76 6- 66 7 2 2 4 2 3 4 52 5 4- 5 3 3 h 3 MAJOR KEY. Add soprano, alto and tenor to the following figured exercises in a major key, containing some of the resolutions of the major ninth on the Tonic. -.__9~ _Er n z#rt _ _ -t — __. ---I_ _- _-_ -- 98 t6 6 6 q6 97 4 6 6 — 66 6 6 7 5- 76 7- 4 4 3 5 54 2 4 3 3 5 -5-3 3 3 3 -- -_ —+- -_ 4 6 f6 6 6 6 7 4 6 2 g 5 t. 4 4 2 fji 3 4 6 6 6 4 7 6 6- 6 3 4 4 5 2;5 5 4 — 5 3 -- 7 $t REMARKS. REMARKS. CHAP. XVIIIJ DANA S PRACTICAL HARMONY. CHORD OF THE DIMINISHED SEVENTH. 33. The student's attention is called to what in most works is classified as the diminished seventh chord; and also that it is built on the leading note of a minor key and consists of a minor third, diminished fifth, and diminished seventh. (N In diatonic writing there would be but the one chord of this character, and that, as already stated, appearing on the leading note in the minor key. The chord of the diminished seventh is the first inversion of a minor ninth chord (Chap. XVIII, Sections 4 and 5), and as there are three minor ninth chords in chromatic writing, there would also appear three first inversions or diminished seventh chords in both major and minor keys, namely: The first inversion of the Dominant minor ninth. The first inversion of the chromatic Super-Tonic minor ninth. The first inversion of the chromatic Tonic minor ninth. fi - v~ ---r H =^'' I -- Fundamental discords are founded on a major common chord. As the major common chord and its discordant tones are built by adding thirds from the root, there is no difficulty in deciding the derivation or root of a chromatic discord. By properly naming the chromatic tones in a key, and arranging them so that they stand at the interval of a third from one another, and then adding thirds below until a major common chord appears, it will give the derivation of a fundamental discord: To illustrate. Arranged Third-wise. Added Third below. Hi tHi' The root is A, or rather the chromatic Super-Tonic minor ninth chord in the key. In some of the inversions of the chromatic Super-Tonic minor ninth it is 18DANA S PRACTIA HRON.[CHaAP. XYIIL common to write the ninth as a sharp of- the note below, which avoids the use of an accidental to contradict.it. Properly written it should appear as follows: No. 1. No. 2. Reference to the intervals of the chromatic scale of Et, (Chap. II, Section 18) shows that there is no F#-augmented second-in it, but that, as in illustration 'No. 2, it should read GL,. The following diagrams will give the direct form and inversions of the minor niuths in both major and minor keys. MAJOR KEY. Minor 9th on theF -6 Dominant b98 6-b 6 resolving on the ~ L5 4 4- b9 8 65 -root. F~ - 2 Reso'ving on F 4 6 7 tLe 3d. 3 _ 7 Resolving on a 6 MVinor 9th on the F6- bP 8 6-62 -Chromatic Super- 6- 4 b6 Tonic resolving 4- 2- ~ -5- ~ on the root. F____ 2___ ___ _____ Resolving on V4 b ~ 6- 4-~ 4- 4 -Resolving on a F 6h chord having ~ another root. b 2 6 M~linor 9th on the C-6 Chromatic Tonic 1k9 8 h6- h~ 6 6- 6 -resolving - 7- 2- b5- ~ - ~ on thb root.~ Resolving on 9_ 3 6- 54 the 3d. ' 4- E.3- 2 -Resolving on a Fq b6 h~7 64 chord having - 7 2 5h another root. L hE2 REMARKS. REMARKS. Cr.XII]DANA'S PRACTICAL HARMONY. 119 MINOR KEY. Minor 9th on the F6 6- 9 8 6 Dominant 5 t- 2- - 7 6 resolving on the 3- 3 2 2-5 -ro o t. L_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Resolving on I43 4 9'~3 4- 6 -the 3d.2 -2- 7 -Resolving on a r 6 6 6 chord having - ~ 5 7 2 anuther root. I 3 Minor 9th on the F 6- 9 8 6- 7 6 t6 -Chromatic Super- 4-7- t4-5 4 Tonic resovn on th e root. L _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ Resolving on 69 -56 3,A - -4 -the 3d. ~ ~ 6 3 L2- t5- t4- 3 9'7 Resolving on a t6 6 chord having ~ 4 355 Minor 9th on the F _ Chromatic Tonic 7 98- b7 6 5 4 64 -resolv'ing ~5 3- I 3 2 on the root. 4 Rsling, on h ~. 2 the 3d-. P7 2-I2 Resolving on a F9 b6 ~ 7 t6 chord having 7 t2 l5 anotherroot. ~h7 Z23 A diagram of the major ninth is omitted, as the figuring is much the same as the above, there being the omission of the character of depression that made the minor ninth. The figuring of the root proceeding to the seventh (8 7) when the ninth pro. ceeds to the root, etc., is also omitted. CHAPT E R X I X. ELEVENTH ON THE D OMNANT. 1. The interval of the eleventh may be added, without preparation, to the chord of the major or minor ninth. 2. There are two resolutions of the eleventh on the Dominant. 1st. It may resolve while the rest of the chord remains. a. To the third of the chord of which it is the eleventh. I-E b. To the fifth of the chord of which it is the eleventh. 4~ --- -— ~~ —* 2d. It may resolve to a chord having another root. - --- --- --— __ _ L ~ 6 6 4 RESOLVED UPON THE THIRD. 3. If the eleventh resolves upon the third, the third should not be sounded together with the eleventh. 4. In the resolution upon the third there is the direct form of the chord and four inversions, founded on the fifth, seventh, ninti and eleventh. 1st. 5th. 7th. 9th. NOTE.-See Chap. XIX, Section 14.:ith==3 — ~z —t_ ~- -~- — f=r= lith. 1st. th. 7th. th. 1lt, (120) REMARKS. RE MAR.K S; CHAP. XIX.] DANA'S PRACTICAL HARMONY. 121 Add soprano, alto and tenor to the following figured exercises, containing the resolution of the eleventh upon the third of the same chord. No. 1. 6 4 6 65 113 - 6 b6 t6 65 7 7 2 43 498 43 t5 t5.,7- 3 3..~. _ = _ -r- --— I --- —7 t93 4 6 -- 6 6 6 7 6 6 98 t5 7- 3 5 4 4 4 5 7- &7 3 2 3 3 t3 $No. 2. _O.. — 9....W- --- 1 ---_ r-L_, ' ~ L _ L L __ ____ 6 g5 113 6 7 7 j6 6 g 6 4 9 58 5 5 4 5 3 - --- 3 ____=_-L -p- - ^- ___ __. _ _ __ __ L t-_ rz ==' __=__=-__ $ 6 4 6 6 6 6 6 6 7 5 2 4 2 4 3 3 3 RESOL VED ON THE FIFTH. 5. If the eleventh resolves upon the fifth, the fifth should not be sounded together with the eleventh, except in one instance, in which the fifth proceeds to the root when the ninth and eleventh ascend to the fifth and third. 6. It is very rare that the third is found sounded with the eleventh. 7. In the resolution upon the fifth there is the direct form and two inversions, founded on the seventh and ninth; also, when the fifth is the base (Chap. XIX, Section 5). - g__,. f. I i r-=-r I 8. It is common for the ninth to rise to the third when the eleventh rises to the fifth; in which case the third and fifth are omitted, and the root and seventh complete the harmony. (See preceding illustration.) 9. When the eleventh and ninth proceed to the fifth and third, the root may 122 DANA'S PRACTICAL HARMONY. [CHAP. XIX be doubled; one taking the place of the seventh, and proceeding to the seventh when the eleventh and ninth resolve to the fifth and third. ( t. —s2-s-X-.-e( __ 9 _ _-I — _ D-g1__ _s __ Add soprano, alto and tenor to the following figured exercises, containing the resolution of the eleventh upon the fifth of the same chord. No. 1. 6 6 6 6 - 7 115 6 6 4 6 4 5 4 - 93 4 2 7 -2- 3 3 87 No. 2. _...__ _ _ - _. _ _ _.... 1- - --,-r- L -- 9'L-~ ----........ 6 7 5 6 7 5 6 7 3 5 3 5 3 7 5 8 3 7 4 7 3 7 )~ t"~ ~ - -[.... 6 11 6 9 4 8 2 6 7 6 7 5 3 3 11 6 9 3 8 (7 6 6 7 RESOL VED ON A CHORD DERIVED FROM ANOTHER ROOT. 13. If the eleventh be resolved upon a chord derived from another root, the resolution will be upon the chord of the Tonic or a Super-Tonic discord. 11. In this form of the chord the root can only be sounded in the bass; the third is omitted, and the fifth must not descend to that note in the following chord which was the eleventh in this (i. e., no two notes next to each other, in alphabetical order, may proceed by oblique motion to an eighth or unison). 12. There is the direct form and four inversions in this resolution of the eleventh, founded on the first, fifth, seventh, minor ninth and eleventh. 1st. 5th. 7th. 9th. 11th. NOTE.-See Chap. XIX, Section 14. REMARKS. IREMARKS. CHAP. XIX.] DANA S PRACTICAL HARMONY. 123 Add soprano, alto and tenor to the following figured exercises, containing the resolution of the eleventh to a chord derived from another root. No. 1.:-,_ ---- __ ---F —....- — F ---- -D ---- -__-i,-F 9"-F —t Ei-zz~ -— L —hz _-t ---_ —... -—. ___ 11 11 7 6 6 6 6 6 6 6 6 6 59 h9 5 4 4 4 5 4 4 4 7 7 3 3 13 3 2 13 13 3 3 13 3 E3 3 I _ ___t _. _ - _, __ _. _ _ _ - I- -— ~E,_____ I_ _____ _ _ _ __ _ 6 6 6 7 657 7 — 3 6 6 6 6 4 5 3 43 5 — 8 5 4 5 2,3 3 3 — 3 b3 No. 2. -. - ---- ------ --- --- 6 F5 11 -- --- -- 6 11 7 6 -7 6 9 --- 4 9 t5 4, 7 7 7 - -— i- -- -- 7 6 6 6 65 7 7 6 7 7 6 7 6 6 5 4# 5 4g 5 5 4 6 6 6 6 6 7 6 7f4 --- —--- 6 -- 5 5 5 4 2 — 5 —7E __L_ _ _-_, ' - -_ -- — [_-_6 — 6 6 - 7 6 4 6 6 6 5 5 — 5 - 4 3 4 — 5 ~ — 6H -- 7.~ 6 ~ D.411T [ dr ---~ ---- _ 6 5 4 $6 2 t4 3 5 3 4 6 6 6 4 6 9~3 3 4 5 4 3 4 - 13. Attention is called to the inversion of the Dominant eleventh when the seventh appears in the bass. 6 6 6 6 5 5 5 5 This form of the chord, in some works, is referred to as the added sixth chord, the chord appearing as the Sub-Dominant with the interval of the sixth from its 124 DANA'S PRACTICAL HARMONY. [CHAP. XIX. root added. If the student will examine the chord in Chap. XV, Section 10, he will find the same combination of tones as in the present illustration. The characteristic of the present combination is that the discordant tone C enters without preparation, which classes it among fundamental discords. As fundamental discords are founded on a major common chord (Chap. XVII, Section 4), by applying the rule in Chap. XVIII, Section 33, the chord will have as its root G, and is the eleventh on the Dominant. 14. When the root and third are omitted in a chord of the eleventh, the seventh is not discordant, and is free in its progressions. NOTE.-The chord of the eleventh, if derived from any other root than the Dominant, cannot be satisfactorily resolved within the key. REMARKS. REMARK R S. CHAPTER XX. CHORDS OF THE THIRTEENTH. DOMINANT MINOR THIRTEENTH. 1. A minor thirteenth may be added without preparation to the Dominant eleventh (Chap. XIX, Section 13). 2. The root and third are frequently taken instead of the ninth and eleventh, and in such cases the seventh is often omitted. 3. There are two resolutions of the minor thirteenth on the Dominant. 1st. It may resolve while the rest of the chord remains. a. To the fifth letter of the chord. 1~ —?-= —~ I, b. To the seventh letter of the chord. '-r ----t-x 2d. It may resolve upon a chord having another root. 4. If resolved while the rest of the chord remains, the minor thirteenth on the Dominant can only be employed in the minor key. (125) 126 DANA S PRACTICAL HARMONY. [CHAP.XX 5. If the thirteenth resolves upon the fifth, the fifth must not be sounded together with the thirteenth. 6. If the root is doubled by the omission of the seventh, then it must proceed to the seventh when the thirteenth resolves upon the fifth. -— 1 --- —~ --- —I — L___t --- —: ____[ 7. If the root and fifth are omitted, the Dominant minor thirteentl as a chord of the seventh on the Sub-Dominant. * Add soprano, alto and tenor to the following figured exercise, containing the resolution of the Dominant minor thirteenth upon the fifth letter of the chord. _ —t: ---— D —T- -— ' —* ----+ __ 135 76 6 6 65 6- 6- 8- 7 5 $ 7- f4- 6- 5- 5- 6 5 5 ~- 2- 43 43 43 453 3 8 _ __:''-_-_ —_- __ ___ i ~'-.. ---r-~ --- L ~ --- —C-" — ~ — t--- -— ~-_ -. -......... 7 5 $ 65 5 6 5 6 b6 t6 6 6 6 135 5 t t3- # 4 3 8 4 4 4 7 -3 8 87 2 3 3.8. If the thirteenth resolves upon the seventh, the seventh must not be sounded together with the thirteenth. Add soprano, alto and tenor to the following figured exercise, containing the resolution of the thirteenth upon the seventh. 6 5 — 13 7 45 6 )6 6 4 3 -- 4 5 4 8 / -i-~ 5 ---- 13 7 t6 t6 6 6 65 6 t5- 7 3 44 4 ---- 2 3 RES OL TED O A CHORD HA VING ANOTHER ROOT. 9. The chord of the minor thirteenth on the Dominant is resolved upon the chord of the key-note in both major and minor keys. a. It may remain to be the minor third of the following chord, when the seventh may not be sounded together-with the thirteenth (Chap. IV, Section 18). REMARKS. REMARKS. T\ A "*T A " ' 'C i T-' A 1 ri^m'T- A T T A Ifii TV 1 of CHAP. XX.] J-UANA D ri n11 I LU Li li.viui i., JL I b. It may rise a chromatic semitone to the major third of the following chord. In the last illustration the minor thirteenth is often written as the augmented fifth of the first chord, which is incorrect. (See " Chromatic Scale," Chap. II, Section 18.) 10. Where the minor thirteenth resolves upon a chord having another root, it may be accompanied with the root and third alone. — 4 -11. Where the minor thirteenth appears in the bass, it may be accompanied by the root, third and fifth.!~F12. In the major key the minor thirteenth may be accompanied with the root, third and seventh, in which case the thirteenth must be sounded above the seventh (Chap. XX, Section 8). -W- - ^l^EE^IEEE Attention is called to the incorrect notation of this illustration. 128 DANA'S PRACTICAL HARMONY. [CHAP. XX. 13. The minor thirteenth may be accompanied by the minor or major ninth. 14. The minor thirteenth may leap a third to the root of the following chord, if this chord be minor. -- Add soprano, alto and tenor to the following figured exercises, containing the resolution of the minor thirteenth upon a chord having another root. MINOR KEY. No. 1. __ __-_ ___- *= e-=z ZZ^-qZ_ _= Z_ 13 6 6 6 5 7 6 t6 6 6 6 6 9 8 8 4 4, $5 4 6 6 7 -3 3 3 4 4 -- '- - ____ _._ _ — + I __ — -t ----s- -— f —U —r - -- __._- _ rzI - ___ ---.7 6 6 6 6 6 6 6 6 6. 6 6 6 6 98 5 4 4 t4 4 4 4 4 4 7 -3 3 3 2 3 - MAJOR KEY. 3No. 2. 1l3( 5) -73(5) - 6 5 6 8 7 5. 4 -3 3 3 t13(P5) 3 -6. 6 5 6L 6. 6 I6 6 4 6 5 6 h6 t6 4 4 4 3 t4 5 — 3 3 t2(g8) 2 43(:2) 3 3 3 6 ' 7 --- 6 4 5- 4 3 Write an original composition illustrating the use of the minor thirteenth. D OMINANT MAJOR THIRTEENTH. 15. A major thirteenth on the Dominant may be taken without preparation in the major key only. 16. The major thirteenth may resolve like the minor thirteenth, upon the fifth or seventh letter of the same chord, or upon a chord having another root (Chap. XX, Section 3). 17. When the major thirteepth -resolves upon the chord of the key-note, the thirteenth must leap a third to the iont of the following chord. REMARKS. REMARKS. CHAP. XIX.] DANA S PRACTICAL HARMONY 129 -— r —l Add soprano, alto and tenor to the following figured exercise, containing the resolution of the major thirteenth. 13 5 6 7 9 7- 7 3 6 7- 6 6 7 13 5 7 7 4 5 5 6 6 5- 44 4 8 7 3 3 4 3 4 4 3- 2 2 3 3 Write an original composition illustrating the use of the major thirteenth. THE SUPER-TONIC MINOR THIRTEENTH. 18. A chord of the minor thirteenth on the Super-Tonic may be taken without preparation in both the major and minor keys, and consists of the chord of the major or minor ninth, with the minor thirteenth added. 19. Any of the notes, except the thirteenth and third, may be omitted. 20. The thirteenth in this chord is rarely resolved while the rest of the chord remains. 21. The resolution of this chord is upon a Dominant discord or upon a Tonic discord. 22. If resolved upon a Dominant discord, the minor thirteenth rises a chromatic semitone to the third of the following chord, in which case the seventh must be omitted. Its resolution would double the leading-note. The fifth and ninth are not desirable in the combination. ---—;23. If the chord resolves upon a Tonic discord, the thirteenth remains to be the seventh of that chord. ---—. ---- -- ~ --.7 4 6 s3 b5 Add soprano, alto and tenor to the following figured exercise, giving the resolution of the chromatic Super-Tonic minor thirteenth. 4 3 64 ~S($$ 5 46 6: z~ 130 DANA'S PRACTICAL HARMONY. " [CHAP. XX. 4 ___ _ i-I T — -- - -: -z V5 _ -- _ __ - -__ _ _ _ _ _ _- - - d I__ _ _ _ ~ ~ _ _ _ _ 7 fl 6 6 t4 6 b13(4t5) h7 06 06 t4 6 b13(-5) E7 - 15 b5 2 3 4 2 t2 3 Write an original composition illustrating the use of the Super-Tonic minor thirteenth. THE TONIC MIINOR THIRTEENTH. 24. A chord of the minor thirteenth on the Tonic may be taken without preparation in both the major and minor keys. 25. This chord consists of the minor or major ninth, with the minor thirteenth added. 26. The thirteenth may resolve on the fifth or seventh of the same chord, as in the case of the Dominant thirteenth (Chap. XX, Sections 1 to 8). -' — -h Add soprano, alto and tenor to the following figured exercises, containing the resolution of the minor thirteenth on the Tonic to the fifth or seventh of the same chord....No. 1. _ - __...__..-. __ * __j_ - 8 --- — 13 5 t6 6 6 ---- 6 6 6 4 4 6 --- 7 5 — - 7 7 5 4 3 3 3 5 5 8 2 333 t4 4 3 3 3 # 3 3 4 3 2 2 __ ___ -E g J I ^ — E --- - ^ 7 6 13 5 -- 6 13 7 7 6 — 7 5 5 7 7 $ $3 3 T-.o. 2. 7 6.13 5.6 6 6 6 f 4 66 6 7 6 6 4 7 7 4 5 2 4 4 5 -6 6 6 -6 6 6 -13 -7 7 5- 6 6 6 5 -6 6 11 5 4 f5 4 S5 5 3 - 3$ 3 — 4 5 5 4 4 4 9 3 2 2 3 3 3 7 7 27. The minor thirteenth on the- Tonic may resolve upon a chord having anotlier root, in which case the resolution is upon a Dominant discord, or upon a Super-Tonic discord. 28. If resolved upon a Dominant discord, the thirteenth falls a second to the root of the following chord, AM, sipM-E REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. 131 CHAP. XX.] or remains as the minor ninth of the following chord, or rises a chromatic semitone to the major ninth of the following chord, provided - the seventh is not sounded together with the thirteenth (Chap. XIV, Section 6). 29. If resolved npon a Super-Tonic discord, the thirteenth must rise a chromatic semitone to the fifth of the following chord. NoTE.-The minor thirteenth is often written as the augment d fifth from the root. or _ _ — f --- —— i I-' Add soprano, alto and tenor to the following figured exercises, containing the resolutions of the minor thirteenth on the Tonic to a chord having another root. No. 1. 13 9 8 13 9 8 16 6 6 f4 4 76 7 6 6 9 7 7 4 4 3 2 ~'53 f4 5 4 - 3 4 3 3 6 6 6:5:6 7 6 f4 7 6 6 b6 7 6 p5 6 7 4 5 4 5 4 2 *5 3 4 5 4 K2 3 4 3 No. 2. f13 7 6 -13 7- 6 E13h1 — 7 6 7 3 5 5 3 5-5 3- 4 3 ~5 68 ~ 6 5 6 6 5 213 ~7:6 6 7 3 — 5 b4 4 3 1?4 4 3 3 5 5 4 3 5- h3 6 f3 6 n 3 Write an original composition illustrating the use of the minor thirteenth on the Tonic. THE TONIC MAJOR THIRTEENTH. 30. A chord of the major thirteenth on the Tonic may be taken without preparation, but in the major key only. 132 DANA'S PRACTICAL HARMONY. [CuAr.::: 31. This chord consists of the minor or major ninth, with the m:ijor thirteenth added. 32. The major thirteenth may resolve on the fifth or seventh of the same chord, as in the case of the minor thirteenth (Chap. XX, Section 25). 33. If resolved on a chord having another root, the major thirteenth resolves upon a Dominant discord. The major thirteenth may fall a second to the root of the following chord, _- q- — _ or fall a chromatic semitone to the minor ninth of the following chord, or remain to be the major ninth of the following chord. Add soprano, alto and tenor to the following figured exercises, containing the various resolutions of the major thirteenth on the Tonic. No. 1. 13 6 t6 6 6 6 65 7B 6 7 6 7 -7 7 4 E5 5 5 43 4 4 5 5 4 3 833 3 43 3 33 > r-J4-ri L - _t_ - _ _- t- __|-_ _ _ _ __r-p b6 6 t6 6 6 7 7 6 6 7 9 3 7 6 13 h7 7 5 4 4 t5 5 5 5 5 t6 6 t3 5 5 6 4 2 2 3 4 3 4 4 8 3 No. 2. 13 t6 6 6 6 t4 4 6- 6 7 b7 6 ~7 4 [5 3 2 '4 6 6 3 3 4 2 L t36 6 t6 6 6 o6 t6 6 6 9E3 t3 3 5 5 5 5 5 4 5 6667 2 3 2 3 2 3 4b5 45 5 Write an original composition illustrating the use of the major thirteenth on the Tonic. REMARKS. R E M A R K S. C HAPTE R X X I. A UGMENTED SIXTH. 1. Two augmented sixths may be taken in either a major or minor key without preparation; One on the minor sixth of the key and the other on the minor second of the key. 2. This combination, which is termed by some writers a double-root chord, consists in the case of the augmented interval on the minor sixth of the key, of the minor ninth on the Dominant, — 4 with the major third and seventh of the chromatic Super-Tonic. To this combination the root or minor ninth of the chromatic Super-Tonic may be added. I 3. The resolution of this chord is upon the common chord of the Dominant or its first inversion; *__ -1 ---1- __, -~~ —^ --- -^ ---^n —:"_^_. —:-.-r --— j—, 8 6 5 6 3 3 3 the common chord of the keynote or one of its inversions; I _ -'-I ---6-=> _ Abe+ ---- --- *-> -- -: _ _-. ~~ — =_:.-~_~:-_ = -t l, --- ~.I=-t-hee (133) 134 DANA'S PRACTICAL HARMONY. [CHAP. XXI. an inversion of the dominant minor ninth; j -—! — t ---- — ( —rt ---- - j - _o. b^i^= or upon a, Super-Tonic discord. i \~ ----4- — 4 — - -— r --- 4. The resolutions upon the Dominant or Tonic chord, are those most frequently used. 5. The two notes which form the interval of the augmented sixth must never proceed in similar motion with each other. -.....-... --- — —: ---E --- —-3 --- —I [! I I i I r / 6 t6 4 5 4 4 3 3 2 6. All the notes of this compound chord proceed according to the rules for the treatment of the two chords. The minor ninth of the Dominant, which is the lower note of the augmented interval observes all its characteristic progressions (Chap..3tI. Section,. ), and the tones in the chromatic Super-Tonic chord the rules for the treatment of that chord. 7. It is rare that the tones which form the augmented sixth are inverted. The other notes of the chord may be placed in any position, which gives the following inversions of the chord. ___ _ __ -4_: J___. _ (E1 ___ — i- -xE- -i-F — r ___ -_- t0z- -4 I _ _:____......i --- —- - ~ ---- -f* * * * Add soprano, alto and tenor to the following figured exercises containing the resolutions of the augmented sixth founded on the minor sixth of the key: Io. 1. _ _ -L —: 1-_=- - _ _:.:_. _____= 36 6 t4 6 t6 $6 4 6 q 6 t4 6 6 3 4 2 3 4 4 2 4 3 3 _ -i r- FH - -F_- 6 6 t4 6 t6 t6- 6 6 6 6 6 6 7 5 4 2 54 5 4 3 3- 3 REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. 135 CHAP. XXI.] No. 2. 6 `6 6 4 6 - - o 6 t7 3 3 43 4 4.3 33 r6 6o5 ~ 6-4 6o ~ 6t 4 6 15 4 3 4 3 2 4 1,5 4 2 3 3 ~3 3 ID010 p6 6 t7 3 43 No. 3. 4-L 6 6 7 6 6 5 6 6 7-3 6 6 6 t6 t4 4 3 -8 4 3 4 3 3 k& t~ 2 3 t 6 6 t4 6 1, 6 6 7 - 5 16 6 7 4 4 2 5 5 t2 3 - 3 - 4 t 3 33 No. 4. 1,5 6 17 o ~ -6 p6 ~ 4 5 45 4 1,5 4 2 3 $2 3 3 6 ~6 ~6 5 ~6 6 r6 5- 6 ~6 6 2 15 4 3 4 1,5 4 3 - 3 4 3 3 3 + _ _I F_ 3 8. The student's attention is called to what are termed the "4French Sixth,"7 "1Italian Sixth, 7 and "German Sixth;" also the "American Sixth," which is referred to in Palmer's Theory of Music, but which isnodifrtfomheGmaxcp that the minor ninth on th~e chromatic Super-Tonic is incorrectly written. (See "1Chromatic-Scale," Chap. II, Section 18). French sixth. Italian sixth. 4# _ 3 German sixth. (ze 1__. -__1,5 American sixth.,- __ -- 9. ' A chord of the augmented sixth may also be taken without preparation o~a the minor second of both major and minor key. 136 DANA'S PRACTICAL HARMONY. [CHAP. XXI. 10. The use of this chord is more rare than that built on the minor sixth of a key. 11. This double-root chord consists of the minor ninth on the Tonic with the third and seventh of the Dominant.. 1 -To this combination the root or minor third of the Dominant may be added. --- J — (. -= L — tLL _ 12. The progression of the tones in this chord is similar to that of the corresponding tones in the augmented Sixth on the minor sixth of the key.:1 —V- I- - __ 11 in _M__'V --- -0 —, F-0 —a -! p 1~- -9 --- _- -. --- —-c 13. In the minor key the progression of the chord is not be resolved on the common chord of the key-note. progressions in a minor key. restricted, that it may The following are its I- -- _- --- a —. Add soprano, alto and tenor to the following figured exercises containing the resolutions of the augmented sixth chord on the minor second of a key. No. 1. E ZZf_ __-_.- _ — _ --- —__ 6 5 6 5 8 6 6 7 4 8 6 4 8 6 4 3 3 4 4 5 7 5 4 7 5 4 4 3 3 5 3 2 _5 3 3 3,_ _ _ — 4. _ _ ___ _ _ _ _L _: ---_ - -= --- - _____ 5 6 6 t6 8 3 5 4 fl - 3 6 t8 -6 3 4 2 5 3 8 3 3 7 6 7 4 REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. CHAP. XXI.] 137 No. 2. *-<__=r*_ _- L t_-_ -o....... Z — 3 _ -— _ -. _t- c —_ m.. m -... 6 4 7 3 $6 6 6 4 6 6 6 6 5 2 5 6 3 4 3 b4 3 6- 6 6 6 h6 6B 6 t6 6 5 4 \ 3 t4 5 4 4 3- 8 3 3:_t_- _[ t:-'=r _ _o__o_=..__ g^=r:-t- _ 6 p6 6 3 7 f6 6 6 6 6 6 -4 3 4 5 4 3 ' 4 t4 4 h5 4 S `2 2 3 3 3 - x 13 5 4 9 3 8 7 The student desiring further study in chromatic writing as exemplified in the preceding chapters, will find pleasure in examining the writings of the representatives of the Romantic School-as Mendelssohn, Schubert, Schumann, and others. The oratorios, cantatas, etc., of Spohr are especially recommended as illustrating the free or modern harmony. Analysis is very valuable, as it is the only way of comparing one's criticisms. N. B.-lst. What key? 2d. True names of notes in the chromatic' scale of that key. 3d. Which root, tonic, super-tonic or dominant of the discord? By observing these points the student will not find himself disappointed, however complex the situation. CHAPTER XXI I. MOD ULATION. 1. Modulation is the moving from one key to another; a modulation is said to have taken place when a major chord other than the Dominant (or a chord of the seventh other than the Dominant seventh) is followed by a major or minor chord whose root is a perfect fourth above; or a minor chord, whose root is a major second above-in the latter case the modulation is to the relative minor of a chord whose root is a fourth above. Modulations are referred to by some authors as one degree forward, when the new key contains one sharp more or one flat less than the previous key,.e- 1 I I T t$ '-I nf I- *-4 -1 -12H I I__ ___.- +_ <.I I and one degree backward when the new key contains one sharp less or one flat more than the previous key, ' - l —ll ~_ -1 -p - i UI;P _I 1-. F t tr two degrees forward when the new key contains two sharps more or two flats less than the previous key; and two degrees backward when the new key contains two sharps less or two flats more than the previous key. A key is said to have moved as many degrees forward or backward as there are additions to the new signature over the old. 2. A modulation may be effected by the chromatic elevation of the fourth of a key, which tone may become the leading tone of a key. * -H -'H 7 - - / (1&8) REMARKS. REMARKS. CHAP. XXII.] DANA S PRACTICAL HARMONY. 139 3. A modulation may be effected by the chromatic depression of the leading tone of a key, which tone may become the minor seventh of a Dominant harmony. '-I -- -~-1 —.-.-,= I- i r w T Write an exercise in all the keys, modulating by means of the observation in Section 2. Write an exercise in all the keys, modulating by means of the observation in Section 3. Write an exercise in all the keys, modulating by means of the observation in Section 2, and returning again to the original key by means of the observation in Section 3. Write an exercise in all the keys, modulating by means of the observation in Section 3, and returning again to the original key by means of the observation in Section 2. 4. There are three tones in a major key that may be raised a chromatic semitone and each appear as a leading tone; namely the first, fourth and fifth tones of a scale..__,I,__ It_.._, — I _01 PK —_ --- il1 Great care should be taken to avoid abruptness, and this can be effected through the use of the various inversions of a chord (Chap. VI, Section 19). 4- ~ -1 --- —q --- —— 1 — ( _ - _ _ _P I... '* — ~, ~ --- O - _ i - I_ _ I I ( d _ ZZ 1~ 6 6 6 4 Write an exercise in all the keys, making a modulation by means of the raised Tonic as referred to in Section 4. Write an exercise in all the keys, making a modulation by means of the raised Dominant as referred to in Section 4. 5. In a major key there are three major chords (Chap. III, Section 8), Tonic, Dominant, and Sub-Dominant, and three chromatic major chords-chromatic SuperTonic, chromatic minor sixth, chromatic minor second (Chap. XVI, Sections 9 to 14); any one of these chords may be considered as the Tonic, Dominant, Sub-Dominant, chromatic Super-Tonic chord (Chap. XVI, Sections 4 and 9), or a major chord on the minor sixth (Chap. XVI, Section 12). 140 DANA'S PRACTICAL HARMONY. [CHAP. XXI. The following illustrations will show the Tonic treated as a Dominant harmony: as a Sub-Dominant harmony: - -I — -...__. — -__ — -- -- - _ ~E ~- _ -, --- — _q - S - _,_...-~-....-~- — _:'-,._ — Z —~-~ - — ~ — $ — -- - I Wio _T a. ___ ____[==^-E--S==:-S-Z-:^ -: ---= ~- -5 — p -- -M -M - - as a Sub-Dominant harmony: L -___,,__ ----, --- —, —4 --- —] s.___ I- _ L - - -- t.- --- -----.._ as a chromatic Super-Tonic harmony: \__ -^ l ----1- __-^ _- — ^-_ - _-^ --- -- * - -_gi l as a chromatic chord on the minor sixth: __,__ __ __-_ __,._ _ __ _. ______ __. —....-. __ _: ___ __ ------ ------ - ~ --- as a chromatic chord on the minor second: ----- _____ -_ _- * =| ---- -- _I _. I,,. 5< z z _ __-_ ___ -__ H _, m \tl-' ---~ ---- - -- ---- - ----- Write an exercise in all the keys, treating the Tonic chord of each key as a Dominant harmony, and complete the modulation into the key in which it would be the Dominant. REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. 141 CHAP. XXII.] Write an exercise in all the keys, treating the Tonic chord of each key as a ab-Dominant harmony, and complete the modulation into the key in which it would be the Sub-Dominant. Write an exercise in all the keys, treating the Tonic chord of each key as a chromatic Super-Tonic chord, and complete the modulation into the key in which it would be the chromatic Super-Tonic.. Write an exercise in all the keys, treating the Tonic chord of each key as a major chord on the minor sixth of a key, and complete the modulation into the key in which it would be the minor sixth chord. Write an exercise in all the keys, treating the Tonic chord of each key as a major chord on the minor second of a key, and complete the modulation into the key in which it would be the minor second. Treat the Dominant chord of every key, 1st, as a Tonic chord. 2d, as a Sub-Dominant chord. 3d, as a chromatic Super-Tonic chord. 4th, as a minor sixth chord. 5th, as a minor second chord, and proceed as in the cases of the Tonic chord. Treat the Sub-Dominant chord of every key, 1st, as a Tonic chord. 2d, as a Dominant chord. 3d, as a chromatic Super-Tonic chord. 4th, as a minor sixth chord. 5th, as a minor second chord, and proceed as in the Tonic chord. Treat the chromatic Super-Tonic chord of every key, 1st, as a Tonic chord. 2d, as a Dominant chord. 3d, as a Sub-Dominant chord. 4th, as a minor sixth chord. 5th, as a minor second chord, and proceed as in the Tonic chord. Treat the chromatic chord on the minor sixth of every key, 1st, as a Tonic chord. 2d, as a Dominant chord. 3d, as a Sub-Dominant chord. 4th, as a chromatic Super-Tonic chord. 5th, as a minor second chord, and proceed as in the Tonic chord. 142 DANA'S PRACTICAL HARMONY. [CHAP. XXII. Treat the chromatic chord on the minor second of every key, 1st, as a Tonic chord. 2d, as a Dominant chord. 3d, as a Sub-Dominant chord. 4th, as a chromatic Super-Tonic chord. 5th, as a minor sixth chord, and proceed as in the Tonic chord. 6. There are two minor chords in a major key (Chap. III, Section 8), Super-Tonic and Sub-Mediant (see Chap. V, Section 4), and a chromatic minor chord on the SubDominant (Chap. XVI, Section 14). Any minor chord in a key may be treated as Super-Tonic, Sub-Mediant, or chromatic minor Sub-Dominant. The following illustrations will show Mediant: the Sub-Mediant chord treated as Sub (_ -' --- —-------. I. _.... - V - ------ --- - as Super-Tonic harmony:.E.1 0-7 -9;z I_ _l -_LS7 tr ' ai — <as chromatic Sub-Dominant harmony: Xl-$-o ---o ---....- I____ __,. _- - --. _.\- - F — ------------- -- - E-*- - -_-___- — ~ -- 1i ----i.1 5.. — -- 5 i -' *. -- I ^ - ' ii i~ Write an exercise in all the keys, and treat the Sub-Mediant chord of each key, 1st, as a Super-Tonic chord. 2d, as a chromatic Sub-Dominant chord. Write an exercise in all the keys, and treat the Super-Tonic chord of each key, 1st, as a Sub-Mediant chord. 2d, as a chromatic Sub-Dominant chord. REMARKS. REMARKS. DANA S PRACTICAL HARMONY. 143 CHAP. XXII.] Write an exercise in all the keys, and treat the chromatic Sub-Dominant chord of each key, 1st, as a Sub-Mediant chord. 2d, as a Super-Tonic chord. 7. Chords that are major may be made minor by lowering the third a chromatic half-step, and they can then be treated as Sub-Mediant, Super-Tonic, or chromatic Sub-Dominant, and progress accordingly. * _ _____ __TILjziIirnzzI ___ M 4 ] —fit9 ---i-+ —j\7rnazIz4zzzxt-I / - I____ __ yy- 0 ---= - g- -#I~~ I A__ '-_,,- t —,_*-_, — = K -lL- b- IsI| — Take the various major chords in a key-chromatic and otherwise-reduce them to minor chords, and treat each one as a Sub-Mediant, Super-Tonic or chromatic Sub-Dominant, and progress accordingly. 8. The resolutions of the fundamental discords that have been described, may proceed to some chord out of the key, and so be resolved in a different key from that in which it is approached, provided the several tones make their proper progression. The third must rise a second, or remain, or fall a chromatic semitone. _ _ _ _ _ _ _ _ _ _ _ _t ~24 0Z I The seventh must fall a second, or remain, or rise a chromatic semitone. ( - m- 1 I-t - 0- - -- I --— '-= I__ __ - -_'I z = -144 DANA S PRACTICAL HARMONY. [CAP XXI The minor ninth must fall a second, or remain, or rise a chromatic semitone. \l ~ — W ---~ ---;.-L~ — -... _ -c —C The major ninth must fall a second, or remain, or fall a chromatic semitone. ____-__ -- ---- -..i -- 4...z__z_, --- —— _ —,:,,_: — The eleventh must remain. The minor thirteenth must fall a second, or remain, or rise a chromatic semitone. - =(= =:= 'i -= --- —--: --- —~ --— t: The major thirteenth must fall a second, or remain, or fall a chromatic semitone. H__ 2_T- A-__-_ __ — _-H ---_- -------.. Write original exercises, introducing, the various fundamental discords in modulation. 9. Modulation may be made from a key with flats to9 a:key with sharps, or the reverse, by the enharmonic change'of notation. REMARKS. REMARKS. CHAr. XXIl.] DANA'S PRACTICAL HARMONY. 145 10. The inversions of the minor ninth in which the root must be omitted, may, according to the notation, belong to either of four roots. ___ — H-A --- — — - ___ * *-1- ___ ____ C __ __ __ __ ______ j2i iL 4 11. As there are three chords in a key to which minor ninths may be added, and each one of them by an enharmonic change appearing as having four different roots, we then induce a modulation to twelve different keys. 12. Each of these four roots may be considered as a Dominant, Super-Tonic or Tonic harmony, and may so belong to each of three major or minor keys. Write an exercise in every key, introducing the inversions of the minor ninth on the Dominant, with the change of roots through an enharmonic change, and have each appear, 1st, as a Dominant discord. 2d, as a Super-Tonic discord. 3d, as a Tonic discord. Write an exercise in every key, introducing the inversions of the minor ninth on the Super-Tonic, with the change of roots through enharmonic change, and have each appear, 1st, as a Dominant discord. 2d, as a Super-Tonic discord. 3d, as a Tonic discord. Write an exercise in every key, introducing the inversions of the minor ninth on the Tonic, with the change of roots through an enharmonic change, and have each appear, 1st, as a Dominant discord. 2d, as a Super-Tonic discord. 3d, as a Tonic discord. 13. By the enharmonic change of notation, a minor seventh chord may appear as an augmented sixth chord, and be treated as founded on the minor second, or minor sixth of a key (Chap. XXI, Section 1). As there are three major chords to which a minor seventh may be added (Dominant seventh, chromatic Super-Tonic seventh, and Tonic seventh), there would be an opportunity through an enharmonic change for three augmented sixth chords to be used in modulation. *i -- --- ---- -— e- *_ — _-__ — -------- 1_ 146 DANA S PRACTICAL HARMONY. [CHAP. XXII. Write an exercise in all the keys, introducing the Dominant seventh chord, and by means of the enharmonic change treat it, 1st, as an augmented sixth chord on the minor sixth of a key. 2d, as an augmented sixth chord on the minor second of a key.!Write an exercise in all the keys, introducing the chromatic Super-Tonic chord of the seventh, and by means of the enharmonic change treat it, 1st, as an augmented sixth chord on the minor sixth of a key. 2d, as an augmented sixth chord on the minor second of a key. Write anl exercise in all the keys, introducing the chromatic chor, of the seventh on the Tonic, and by means of the enharmonic change treat it, 1st, as an augmented sixth chord on the minor sixth of a key. 2d, as an augmented sixth chord on the minor second of a key. 14. Abrupt modulations are softened by introducing a unison passage, characteristic of the new key, or the repetition of a tone belonging to a chord that shall follow related to the new key. No. 1. _ e-_ —, 7 -.I. No. 2. I I.,I ' t-t'5F-( l-j ' Write an exercise introducing modulations through the use of u::ilo: passages. ' 15. If a tone in a unison passage appears in repetition, or is prolonged, it may rcrnman to be the root, third, fifth, seventh, minor ninth, major ninth, eleventh, minor thirteenth or major thirteenth of the chord that follows. I —II ~~~.. —T —E0=:=rt= — t —r-:: REMARKS. REMARKS. DANA'S PRACTICAL HARMONY. 147 CHAP. XXII.] ( -— F'M --- -- -=: -~. — Ay nte o a d t dcrd m r n t b a tr t seventh may _e ___ seventh, minor ninth, major ninth, \-___ -._- __ _,W _ ---- ---— r -m i __- __: — ---- ___ _ _ A_ _ _ __ _ _ 16. Any note of a fundamental discord may remain to be any other note of any other fundamental discord; that is, the root of an unprepared chord of the seventh may remain to be the third, fifth, sevenlh, minor ninth, major ninth, eleventh, minor thirteenth or the major thirteenth of another chord, and the same is the case with the third, fifth, seventh, etc. Write an exercise in all the keys, letting each note of the three fundamental discords remain to be the third, fifth, seventh, etc., of other fundamental discords. ] 7. Possibly many of the illustrations and suggestions regarding modulations, etc., may seem abrupt or harsh, but as they are found in the works of the present day, they are given with the hopes that.the student will, through his education, know what to accept or reject. Since the days of Wagner the following progression of chords is to be met with, and others equally effective: but by most authorities are considered objectionable or ignored entirely in their theoretical writings. -MODULATION. MINOR KEY. 18. In a minor key there are two major chords, the Dominant and SubMediant; two minor chords, the Tonic and Sub-Dominant; two diminished chords, 148 DANA'S PRACTICAL HARMONY. [CHAP. XXII. the Super-Tonic and leading note (the last two named being Dominant harmonies G::tt W. —, -..z Minor Minor 9th. 7th in inversion), and an augmented chord on the Mediant, which is an inversion of the Dominant minor thirteenth (Chap. III, Section 9). I 19. In a minor key there are three chromatic chords: the chromatic SuperTonic, chromatic Tonic, and a major common chord on the minor second of the key (Chap. XVI, Sections 4-7). 20. The Sub-Dominant chord of a minor key is a minor chord, which should not be forgotten. 21. Any major chord (diatonic or chromatic) may be made minor, and so become the Tonic or Sub-Dominant of a minor key. '22. Any major chord in a major key may be treated as the major chord on the Sub-Mediant of a minor key or a Dominant harmony. 23. Any diminished chord or minor ninth chord in inversion may be treated as the Dominant harmonies of a minor key. 24. It ismrecommended that the minor sixth of the minor key modulated to, be introduced in some chord early, as its presence helps to thoroughly establish the new key in the mind of the hearer. -342 L_ _ _* Z x z z z~ z 4 _ _ _ _ _ _ _ _ _ _ _ 1 ~ - _ _ _ -~ - *. * * _ _ _ - _ _ _ _ _ _ d REMARKS. REMARKS. CHAP. XXII.] DANA'S PRACTICAL HARMONY. 149 _ * ]1~-~-_-,z-t-.-_ '-,5-: ~ I —L-_<= —1 -—, ~' ' —~1 --- -~-~\_ _ i- - -- Write exercises in modulation from the observations in Sections 18 to 24, of this Chapter. In conclusion the student is recommended to study under a teacher, as many errors creep into progressions that an uneducated ear would not detect, and that an unmusical taste would accept. Analyze works of the greatest composers, beginning with the earlier writings, and so down through the diatonic school, with its tendencies toward a freer style, to the modern or chromatic works of the present day. It is possible for a person to become a harmonist without being able to play his exercises and other writings upon the piano or organ; but the most successful teachers of harmony are those who play from score, and are able to play their own compositions, thus discovering crudeness in progressions and errors that only the ear would detect. THE END. 150 DANA'S PRACTICAL HARMONY., APPO G GIA TURAS. Where passing notes, in the fiee style of writing, appear on the strongly accented parts of a measure, they are termed c appoggiaturas" or leaning notes. -__' \ __ ----__ --- _ L IL An appoggiatura may be preceded by a passing note as the exceptional progression in the diatonic style (Chap. XI, Section 7). __ _- - __ _ _ (1,___:^:__: ----_-_::: L_- - — ~ --- —---- - —[ 'g-~-+"-' "0*- "L i ____ __ — _ E' — - |-_ '....-::: — — F — r^ —+ ---- -F~ --- ——: 8;_ -_.- ' L- -L ___ __ - L~ --- — ~ ---mx~: Add a soprano, alto and tenor to the following figured exercises, introducing occasionally an appoggiatura. No. 1. No. 2. o 6- 5.-1-. o__-__- T- 6 o __ _ _ j — t _ t_ I- -r- Lg g --- 1>-1= ---;;-1 L JO6 6 5 6 6 6 t6 6 6 6 6 6 5 4 3 4 4 4 4 -— ____ _- __ --— l-r- ----- -- 6 6 6 6 o 6 6 6 6 f 4 4 REMARKS. REMARKS. R EM A R KS. REMARKS. REMARKS. REMARKS. C You Play Church Music? C Y L1t You Teach the Art of playing Church Music? You Teach Thorough-Base IF NOT, BUY A COPY OF DANA'S PRACTICAL THOROUGHlBASE, OR, THE Art of Playing Church Music, BY WILLIAM H. DANA, President of Dana's Musical Institute, Warren, Ohio. THE TEACHER'S HELP. In the use of language, this work can be understood by the child nine years of age; and yet it contains the theoretical uses desired by the theorist or composer. THE SCHOLAR'S GUIDE. All that has made this study blinding and confusing to the scholar has been removed by using common English terms instead of classical. A LONG FELT WANT SUPPLIED. The volume is the beginning of a series of text books for class and private teaching, suggesting itself from the following resolution offered at a teachers' meeting: "We must teach that which the pupil can understand; all the faculties of the mind must be relatively developed, so as to produce an equilibrium. To teach thoroughly, we must give one idea at a time-we must teach pupils according to '`eir ability to learn." LIBERAL DISCOUNT TO TEACHERS. Specimen Copies sent Post-Paid for $1.00, by addressing Dana's Musical Institute, WARREN, OHIO. " THE RIIGHT PIrNG ER ON TH.E RIGHT KEY." The FArt of Fin gering; OR, THE TECHNIC OF THE PIANO-FORTE. BY ALOYS BIDEZ, Professor of Piano, Dana's Musical Institute, Warren, Ohio. IN THE UNITED STATES there are not less than one hundred and fifteen thousand teachers of Piano and Organ, and out of that army of teachers there are hardly ten thousand of them who have any knowledge of the technic of the instrument; in other words, but very few of them can " finger a piece of music" from any knowledge or rules they may have, but they must sit at the instrument, and make a number of efforts at playing in order to find an easy way, which is as apt to be incorrect as it is to be right. This array of teachers gives instruction to not less than one million f5upils, who are not taught the technic or resources of the piano, but learn, generally by imitation, a number of compositions of different grades, and this constitutes their knowledge of the piano. In order that the 'scholar's instruction shall be real, that the study of the piano shall not be presented to the pupil as a mere accomplishment, but as a refreshing study, this work has been written, and is presented to the teacher and student as a guide in the study of piano-playing —containing rules and observations on fingering chords, scales, arpeggios, and all forms of melodic construction. Specimen Copy, elegantly bound in Cloth, sent post-paid for SIXTY CENTS, by addressing DANA'S MUSICAL INSTITUTE, WARRENS OXIX0. PROFESSIONAL, - ~TEACIIER, -i'~ AMATEUR, SCIIOLAR. 0 i rs4o t 0lt BY CARL. THORBAHN,. Violin Teacher and Conductor of Orchestra, Dana's Musical Institute, Warren, Ohio. In the study of the Violin one great troubl~e has been to find studies suitable for beginners, and that progressed from one degree of difficulty to another through graded technical exercises. We find the works of Spohr, Do IBeriot, Alard, Compagnoli, etc., fit studies for a professional player, rather than the amateur or scholar; that the wants of teachers and their pupils may be met, these graded studies have been offered to the public. These exercises consist of six books, and are in appearance like the various books of Ozerny's exercises for piano, and in grade of difficulty are the same. The type is clear, and cano be read with ease from a music-stand. BOOKS I ST, 2D AND 3D, Consist of primary studies, velocity exercises in the first position, and prepares the scholar for the second and third positions and their compound positions. BOOK 4rII Consists of studies and velocity exercises in the second and third positions, and their compound positions. BOOK 5TH Treats on the different styles of bowing, double stops, broken chords (ArpegbGios), and various styles of embellishment. BOOK 6rzz Consists of exercises in the fourth and fifth positions on the shake, trill harmonics, etc. Price per Book, $1.00. Set of a Books, $5.00. PUBLISHED BY Dana's Musical Institute, WARREN, OHIO.