_ UARL FISCHER'S REVISED AND AMENDED EDITION LOGIER’S SYSTEM OF AND SELF INSTRUCTOR IN THE SCIENCH OF MUSIC HARMONY, AND PRACTICAL COMPOSITION COM FEET &.. TOGHTHER WiTH BERLOIZg THE ORCHESTRAL CONDUCTOR NEW “YORK PuRLISHED sy CARL FISCHER, 6,8 anp 10 Pourtu Avi..t : Copyright, 1889, by Cann Kiser MT CORNELL 24 UNIVERSITY L$% LIBRARY 194 GIFT OF the Estrete of Verne S, Swan Class of 1921 MUSIC | Cornell University Library MT 24.L83 1889 “WIN TNA 3 1924 022 478 675 ns CARL FISCHER'S REVISED AND AMENDED EDITION. LOGIER’S SYSTEM OF AND SELF INSTRUCTOR IN THE SCIENCE OF MUSIC HARMONY, AND PRACTICAL COMPOSITION COMPLETE. TOGETHER WITH BERLOIZ: THE ORCHESTRAL CONDUCTOR NEW YORK 2 PUBLISHED BY CARL FISCHER, 6,8 anp 10 FourtH AVENUE Copyright, 1889, by CARL FIscHER CONTENTS. RUDIMENTS OF MUSIC BY ARTHUR A. CLAPPE. PAGE. PAGE, Sound... ‘ > 2 . 5 | Speed (Metronome) . ie Ot ae ee PA Music. . ...... +. 5 | Modifications (Terms) fe ie eet tgs MAG Pitch .. . 5 : . « 5 | Style (Terms) . . tte te ae Sak Staff .. . ah arc SG Embellishments | . eat ip AD) Clefs .. ere - » » - 6 | Rules for playing the Tum .. . 16 Added Lines. | . |... . . 6] Abbreviations. . ser ca LE Duration. . . 2... « - - 6 | Expression Mechanical) | Sjen Sr dS Bar Lines. . . . . «© «© «© » «© J | Expression ee oe we a TS Time Signatures . ..... . T{| Tone . es ae A oe 1B Ties, or Dots . ...... . 8 | Taking Bresthy. 50 = as =e 18 Scales... 6 + ow 2 & 8 Time 6. we es ee we we we @ dB Keys BS Sah se) ay ae - 9 | Tune - 19 Accidentals . . . oer - 9 | How to ‘tune band Instruments . . 19 Descending Minor Seales. . . . 10 | Musical Library .. 19 Chords. . . »« « « e e « » 11 | Terms applied to Musical Composi- Intervals. 2. 2. 2 6 se eo 11 tions. . bree ae 220 Harmony. «2.» + + © «© « 11 | Schools, or Methods, ete. . ss. Ql Melody ... : . . . . 12] Transposition. ...... 21 Accent. a » « « « . 13 | Tonal System .. 22 Articulation. . ... .. . . 18 | Chart showing compass ‘of Dynamics . . eee « 18 allInstruments . . 23 LOGIER’S SYSTEM OF THE SCIENCE AND PRACTICE OF MUSIC. Construction of the Common Chord 25 secutive Fifths and Eighths . . 41 Its Bass . . oe « « « « 26 | Fundamental Seventh in Harmony Its Three Positions . . 26, 27 of four parts. : ‘ 43 Melody and Harmony Defined | .’ 27 | Second Rule of Harmonizing. sons, Discovery of the Fundamental Themes for Exercises . . . . . 46 Basses . . . . . 28 | Third Rule of Harmonizing. . . 47 First Rule of Harmonizing ot ey 2B |) PROMOS! sk ese ee Re se ee TAD The Signature . . 80 | Fourth Rule. .. eee!) Fundamental Basses to Melodies . 31 | The Four Rules Combined. | 2 - 50 Harmonization of Melodies . . 31, 32 | Themes .. 51 Themes for Exercise . 82°] Peculiar Character "of - the four Consecutive Fifths and Eighths. 34, 35 parts in Harmony. ..... 52 Diversification of the Common Concise Retrospect . 54 Chord . 35, 36 | Precautionary Hints respecting the Observations on the “Chord of | the’ Employment of the Four Rules. 55 Dominant Seventh. . . . 37 | Hints respecting the Employment Figuring the Bass. . . . 88 of the Fourth Rule . . . 55, 56 Principles of Thorough Bass. | . 38 Major and Minor Chords . . . . 56 Chord of the Fundamental Seventh Sharps or Flats in Minor Keys . . 57 and its Resolutions . . . . 38, 39 | Relative Major and Minor Keys. . 57 ‘Harmony in four parts. . 41 | Specimens of Variation leadiug to Second Method of preventing Con- Extemporaneous Performances . 59 AN ESSAY ON MODULATION. Harmonics . » » « 60 | Intervals of the three Fundamental Scale of Three Sounds . 8 - « 60 basses selected as Dominants. . 68 Its Fundamental sak . - .« 61 The 8th of the Tonic. . . . . . 68 Harmonized. . come «6b 8rd Tonic. . . . .. 69 Scale of Six Sounds . 62 “ Sth “ Dominant. . .. 70 Natural Succession of. Scales” of “ 8rd “ Dominant. . . . Tl Three Sounds ...... . 62 * 8th “ Sub-dominant .. 71 Progression. . . » «+ «+ + + 62, 63 “ 8rd ‘“ Sub-dominant . . 72 Modulation. . 64 | Extraneous Keys. ...... 78 Relationship of Keys by “Modula- aa Practical Exercises . .... . 78 tion . . 6 6 eo © © eo 0 OO, : CONTENTS. AN ESSAY ON INVERTED BASSES. What are inverted Basses? . . . 81 Effects produced . 81 First Inversion of the Chord of the Dominant Seventh. wah $8 Figuring the Bass 82 Second Inversion . e . . 84 AN ESSAY ON A Dissonance, Suspension of a Consonance - 101 Discord, Chord with 2 Dissonance. 102 Preparation and Resolution . . . 108 The Fourth resolved into the Third 104 The Ninth resolved into the Eighth 107 The Fourth prepared by the Funda- mental Seventh. . 109 ee Dissonances. of the 4, 3, an ‘i ‘ ‘ EXTENDED HARMONY AND THE MINOR SCALE. Compressed and Extended Har- mony compared 123 Minor Scale —its Construction and Harmonies Minor Melody Harmonized : 129 Chord of the Minor Ninth. 181 Modulation through all the Relative Minor Keys by Fundamental Basses 133 Inversions of the Minor Ninth . . 133 Third Inversion . . ea 85 Examination and Exercises . | 86 Inversions of the Common Chord. 90 Inversions in Warmonized Melodies 91 Rules and Exercises. . . .. . 92 DISSONANCES. The Sixth prepared by the Third . 112 All the Dissonances Combined . . 113 Accented parts of a Bar . 114 Strict and Free Styles » . 115 Figuring Dissonances . 115, 116 Cadences. . ~ 117 Chord of the added Sixth | . . 118 Figuring Inverted Dissonances 118, 119 Comprehensive Exercises. . . 120 Chord of the Diminished poe 135 Chord of the Sharp Second . . 187 Fifth Rule of Harmonizing. . : 187 Minor Ninth in Melodies . . . . 138 Major Melodies changed to Minor. 139 Minor Scales arising from ee Notes . . 3 - 140 Practical Exercises . . 141 Arrangement for the Piano-forte . 142 MODULATION IN MELODIES BY THE INTRODUCTION OF ACCIDENTALS. Modulation by accidentals occur- ringina Melody . Modulation by Intervals ‘ofa Melody aa Rule 1, ascending a Half Tone . . 148 «Embellished 192 “cc oe “i with 4, and 6, 5. ‘ 192, 198 Chord of the Thirteenth 194 Rule 2, descending a Half Tone . 150 “* of the Sharp Sixth. . 195 Rule 3, descending a Whole Tone . 152 ‘“* of the Compound Sharp Rule 4, ascending a Whole Tone . 153 Sixth .. 193 Rule 5, successively repeated. . 155 | Cadences, continued from page 117. 200 Rule 6, ascending a Fourth . 159 | Irregular Cadences » 200 New Melodies extracted from Hon Imperfect Cadences . . 203 monies . . . . 162 | False Cadences . 204 Free Motions in Harmony. » 166 Interrupted or Broken Cadences ; 206 Hidden Fifths and Eighths . 167 | Irregular False Cadences . - 206 ‘Notes of Embellishment . . 167 | Suspended Cadences. . 206 Passing Notes . . 168 | Great Cadences “Us « 207 Passing Notes converted into Notes Equivocal Modulation . - « 207 of Modulation . « « »« 169 | Deceptive Modulation . . . . . 214 Auxilliary Notes . . 171 | Protracted Modulation . ‘i - 216 Extended Passing and Auxilliary Modulation through Ascending and Notes 2 174 Descending Chromatic Scale . . 218 ‘ Secondary Harmony . . » «178 | Inversion of Minor Ninth. . 218, 219 Passages for Imitation. . . . »1%3 | Modified Basses ee oe ae we 220 Writing for the Piano-forte - 181.| Sequences of Sevenths. . . , . 224 Writing Variations . . ._. 182 | Bass Melody with Sequences. « 229 Recapitulation . r 184-186 Sequences of Sevenths and Domi- Retardation, or ascending | Disso- nants. - 230 nances ? Sequences of. Sixths, 6, 5, and 7, 6. 232 Chord of, the Eleventh, . . . . 190 | Three Motions in Harmony + 6 « 285 “ Prepared . 191 | Consecutive Fifths and Eighths. . 236 “ “ ‘“ Unprepared. 191 | Hidden Fifths and Eighths . . . 287 COMPOSITION, Construction of Melodies . . 239 | Composition . i we oe . 254 Accent and Rhythm. . . . . . 239 | Strict and Free Styles a ee - 263 Periods . « ». 244 | Analyzation. . . » « 264 How to Construct ‘Melodies . . . 249 | Concluding Observations ; oo © © 280 RUDIMENTS OF MUSIC. By Artuur A. Cuapps, M. M. C, M., Editor of Taz MEeTRoNoME, SOUND. 1. Everything we hear is termed Sounp. 2. Sound is the product of aerial disturbances communicated to the tympanum of the ear, in intermittent shocks of such extreme rapidity of recurrence, as to produce the effect of a continuous tone. 3. When the area of disturbance is large, the sound at point of generation is loud; but when small, is soft, proportionately with the modified degree of commotion. 4, Sound radiates from a given centre in two manners; that is, one originating body may throw off regular shocks, or vibrations, while in another they may be of a conflicting or complex nature, owing to the differing structure of the two. 5. Complex vibrations produce Notsn, regular vibrations result in Music. MUSIC. 6. Music is at once a ScrzeNcz and an ArT. A science, as teaching the origin, properties and combination of musical sounds; an art, as appealing to our emo- tions and the inherent love of the beautiful in nature. PITCH. 7. The variation in the altitude of sound is called Prrcu. 8. When the aerial vibrations are very rapid they produce high sounds; when slow, low sounds ure the result, while the mean between the two creates medium sounds, 9. The pitch of musical sounds is expressed on paper by means of a series of parallel lines and spaces, eleven lines and ten spaces, each of which is named by a letter of the alphabet, the first seven of which are used, viz., A, B, O, D, E, F, G. 6 RUDIMENTS OF MUSIC. STAFF. 10. The parallel lines and spaces are termed the Great Starr, and are named as follows, viz. : , LINES, SPACES, fc D— E B-— Cc G-— 7A a D A—— B F 5 G D— E B__ . Cc 7 cG— A 11. For band or orchestra instruments and voice, also for greater conven- icnce in reading, the Great Staff is divided into three parts. The bottom section, representing low or Bass sounds; middle section, medium or TENoR sounds; top section, high or TREBLE sounds, +CLEFS, 12. To show definitely which division of sounds it isintended to employ, char- acters termed CLEFS are used. , 18. There are three clefs in general use, viz.: e F, or Bass Clef ; a ©, TEXoR, or ALTO CLEF ; 6 G, TREBLE, or SOPRANO Clef. 14. The clefs are assigned as follows, five lines to each division: 15. Each division is termed a Starr, ADDED (ledger) LINES. 16. Frequently it becomes necessary to extend the limits of the staff. In such cases, short lines termed Lepozr -(Fr., legeré) lines are added, which, with the intervening spaces, are named in progressive order similarly with the staff. ~ A.B. 2G: , c 2 © Bg —————————— | Ae: = fe=- = a Eye F DURATION. 17. Duration of musical sounds is computed by Brats. 18. Beats are those movements of the hand, foot, or mechanism, which, like the oscillations of a pendulum of a clock, mark the passage of time. 19. Duration of sound is expressed by characters termed NoTES, each of which is equal to one or more beats, or to the fractional part thereof. 20. The unit of Time is d one beat, and termed a QUARTER NOTE 21. A note double the value is _| two beats, termed a HALF NOTE. 22. The simple note of longest duration in modern music is = four beats, termed a WHOLE NOTE. RUDIMENTS OF MUSIC. q 23. Fractional parts of the unit of time, or single beat, are, ZS da heagunecndene eemags two EIGHTH Norzs. -e-=asct eee four SIXTEENTH NOTES, 2: = a 5S eight THIRTY-sECOND NOTES. 24, Occasionally irregular quantities, uneven numbers of notes, are employed in beats or measures. When such is the case, these uneven groups are denoted by figures written above or below. pL ee | Termed a TRIPLET. QUINTUPLET. SEXTUPLET, S=PTUPLET. Playedin | \ time of Wd 2 P : 25. Cessation of sound in music for definite periods, is indicated by REsTs, or silences, as follows: viz.: ezefeasgl[rsd[ rb fla Rl a= Si BAR LINES. 26. Bars are short lines drawn vertically across the == and, are used to define quantity or recurring stress of accent in music. 27. The DOUBLE BAR == denotes a complete idea, or close; in other words, a full period in music. TIME SIGNATURES. 28. To assist the eye in calculating at a glance the exact quantity of time, or beats, included between two or more bar lines, fractional figures are usuaily written after the clef at the beginning of a piece of music: = 29. The upper of the two figures expresses simply quantity; the lower, quality. 30. The lower figures, or denominators, generally employed are 2, 4 and 8, though occasionally others are used, as 1, 16 and 32. 81. 2, as the denominator, means J half notes; 4, be 6 “ ‘“ P| quarter notes; 8, éc “ “c 6 a eighth notes. 82. The upper figure or enumerator, tells exactly how many half-quarters or eighth notes are used in each bar or measure of the music. 22S IL I omy om ames: x= auqu: *lusvald OY} UT v” ealoAg= *QINSBIUL JY} UT - aa2q3— “adnseeul 343 UT # “aINseoul 90) Ul i “oINSBIUI ON} UT *9.0S80TH ST} UT i *oINSvell O44 UT fr 8 RUDIMENTS OF MUSIC. 33. The character C equals . and is termed common time, while ( equals 3 and is termed aLLA BREVE (ail lah bray'vay). 34. The foregoing figures are termed the TIME SIGNATURE. ~ 85. Time signatures are said to be duple when expressing two beats to the measure; triple when three, and guadruple when four. 86. They are again simple and compound, as per EX. : é Duple. Triple. Quadruple. : *328\|82 2 \)8 2 4 i 2262/28 &| BER TIES, OR DOTS. 37. At times it is necessary to increase the value of a certain sound beyond the duration of the simple note. There are two methods of effecting this: first, by a __. termed éie, J_ 8, which binds the two notes together; second, by the addi- tion of a dot, ae J. — JN. , SCALES, 38. The distance from one sound to the next immediately above or below, is termed a TONE, 39. There are two kinds of tone steps; viz.: Whole Tones and Half Tones. 40. Two whole-tone steps and one half-tone form a TETRACHORD (Gr., four strings). Two tetrachords in following, joined by a uniting tone, making in all five whole-tones and two half-tones, form a DraTonic (Gr., through the tones) Scauz. (ITau., Scala, a ladder). Vide ex.: 43. 41, There are two forms of the diatonic scale, viz.: Mason and Minor. 42. When the half-tones occur between the 3d and 4th, and 7th and 8th, the scale is Mason, but when between the 2d and 3d, and 7th and 8th, the scale is Minor. 43. Another kind of scale is the Caromatic (Gr., chroma, color). This scale consists entirely of semitones. SCALE. | Diatonic. ~4 Masor. MINor, CHROMATIC. Ascending or Ascending form. Ascending or descending form. descending form. le z half tone” [3 _| hait'tone”""""*” & Maisussmenust cis Saws eistee: vee'y Z 2 oneees GC..ccee 3 a uniting 6 s tone. half tone ae cee Qeacece all half tones, 1st tetrachord seeveedssceee RUDIMENTS OF MUSIC. 9 44, The normal scale commences on the c position of the staff. KEYS. 45. It is frequently necessary to change'the position of the scale, and begin on some other sound than c; when such is the case, in order to preserve the above order of full-tones and half-tones, certain characters termed Suarps and Fiats are used, and, which placed in the signature, retain their influence throughout the composition, unless a contradiction intervene. 46. A sharp, raises the pitch of a line or space, on which written, a half tone. On the contrary, a flat, 2, lowers the line or space a half tone. 47. The following table will show the number of sharps or flats necessary for each scale alteration of pitch, either Major or Minor: T 2 3 q 5 7 Fe r |rec Iroc |pcoe | rac IFGG |f,0.6,D, E &G D Dea |U,Ae A, E&B E . & o—# 2. # ff a» f ft +t» + t a et |-F4 ee Heng Ha: bap tat Fra Se ite So naan coe Be er her: mM o 5 . a as == == SS a —_ ~ +. ¥——|—-_ — 2 G A E B Ft Ce 8 pe | Malor, [ese fecseee feceeee se | ceeceeee a RIES. iaiete ae Saree a.s ea n o or or or or or or or SM E B Ft Ct Gt Dg At es MDINOLs [onicecs. isso Meas nasac-cheendiy Aaadtumestnas | [ietieancn htee =| CI z Ab g ab y | Dp & Gy | Db, Go & Ch Dy » Ch, ze OQ by Ip. ‘ fee A or, 3 ((@2= 2S SS eS = 3 Ss i=] 9° |e =. hb . cis ss SS 3) Sp PS BS SS F Bb Eh Ab , Ch DO AJOL) nels becasue ol cue oll aitiand wtevateie | levtesjara Sage rlgidia o statoi sian! | Giakdranasl or or or or or or or G C ¥ Bh Ep, Ab D MOINOL.|., ey eeeefersytytyar] veces socclenevaseerel y gypaqyaefeses ers Name of Scale or Key. 48. C major and A minor have neither sharps nor flits in the signature. Major keys are said to be related to minor keys in the above order. 49. The first note of a scale is termed the KEY NOTE, and gives its name to the scale. ACCIDENTALS. 50. In order to preserve the proper order of half-tones in the minor scale, the fifth and sixth degrees must be raised; to do this accidentals are employed, that is, signs other than in the signature. 51. For this purpose are used (1) the sharp, #, (2) double sharp, x, (3) natural, contradiction, or restorer, h. 52. The double sharp raisesthe pitch of line or space a full tone higher. 53, The } restores a line or space whereon a flat or sharp has been used to its normal pitch, (1), by contradicting within the limit of a bar, or measure, only 16 RUDIMENTS OF MUSIC. the sharp or flat in a signature; (2), by contradicting accidentals previously employed in a measure. 54, The double flat, 2), is occasionally used, and lowers a line or space a full- tone. 55. When it is required to contradict a xor pp, the q must be used double G f) where the sound is to be restored to its normal pitch, as in the key of C; but if the restoration involve only a half-tone, then the 4 must be accompanied by a sharp or flat, as the case may be. Ex. [ge=2S See See Dz becomes Dg. Dz becomes Dg. Bbb becomes BY. Bbb becomes Bp. 56. An accidental has infiuence, (1), in the measure where it appears; (2), when written before the last note of one measure it controls the first note only of the next, providing such note be on the same line or space (degree) of the staff. » (Gey 57. ‘The first note in the second measure, unless contradicted, would infer the sound of DE; but the second D, and without contradiction, would be DB. DESCENDING MINOR SCALES. 58. The scale patterns given after paragraph 43 show the major and chromatic scales to have the same form—that is, the same relation of whole-tones and haif- tones in both ascending and descending forms, while the pattern of the minor scale shows simply the ascending form, inferring that a difference exists between that and the descending form. 59. Such difference really exists, and in two forms common to modern prac- tice, the first of which we may term the consuncT and the second the pissunct, or harmonic form. 60. The consunct form of the descending minor scale is controlled by the key signature, and has five whole-tones and two-half-tones; but the pisyuNcT form has three whole-tones, two half-tones and one step of a whole-tone and half. Descending Minor Scale. Conjunct form. Dijunct form. ae » Ay | n at Gel 8 q ] ‘| ee i 1 stone | 7 Dnitin tone. = = oo ~ ov mM K a & § “HI WW Poe te ti: Se all ‘p1OYOBII94 IST. : RUDIMENTS OF MUSIC. 11 CHORDS. 61. A common cHoRD is composed of several sounds selected from the scale, which, when played or sung in unison, will produce a pleasing effect upon -the ear, 62. The sounds or tones selected are 1, 3, 5 and 8. 63. Common chords are (1) major, when the sounds are selected from the major scale; (2) minor, when drawn from the minor scale. 64. A combination of 1, 3 and 5 only is termed a TRIAD. INTERVALS, 65. The distance from one sound to another is termed an INTERVAL. 66. Intervals may be (1) major, (2) minor, (8) augmented, (4) diminished. The terms perfect and imperfect are at times applied to4ths and 5ths. 2d. 8d. 4th, 5th. 6th. "th. 8th, or octave Fé Se el ° E i ee aie c cc oo oe Ss o- -o- -S- -o- -o- HARMONY, 67, The combination of two or more sounds in a pleasing manner constitutes the first principle of HARMONY. 68. Harmony is that branch of music which treats of the grammatical arrangement and progression of chords. 69. Chords are either concoRDs orDiscorDs. Concords when composed of 1, major, or minor 3d, perfect 5th, and octave. Discords when other than the fore- going intervals are used, as : Concord. Discord. —— ee a= 70. The two principal chords are : (1) common chord, based.on the keynote and termed the CHORD OF THE TONIC; (2) the chord based on the 5th of the scale, composed of the intervals 1, 3, 5, minor 7 and 8, named the cHorD or THE DOMINANT. 5 " 8 Dominant. i 3 coon Jed fp pe —7 Ee == SSS SFE Diese i] Fi 4 9 1011 12 “Tonic. or oror or 6 823 4 6 71. The chord next in importance is that built on the 4th degree of the scale and named the sus-pominant. In the key of C, for instance, the chord of the sub- dominant would be, F, A, C and F, 72. Each degree of the scale has a specific technical name for purposes of harmony, as follows: Wat GOBTCC . . ose sc aieine vieietaie s ciareleld aieieie sab eaieiee Howe « LONG, Od Weare’ «secs ss wares. eee x coed ose ea SRO S Super Tonic. BO GORE oi isiais srocesa anos ee ous s vane doen eke Mepianr. Ath, Gepree ss css ss aincts saraae siete Seats RAGS ek Gees SuB-DOMINANT. Bth degree.............0000e 5 SEOsa at hats Ba, Sie bd 9, Bass 8 Dominant. Gth: degrees hic ccceveein viene enn obi Owsley SuB-MEDIANT. Tth Gepree sss ours. ques ore eat Agee ew Gaseenss Leapine Note. 12 RUDIMENTS OF MUSIC. 73. A combination of three sounds, each at the interval of a 34 from ‘he other, is termed a TrraD. 74. Triads may be formed on each degree of tke scale, major or minor, giving rise to major, minor, augmented and diminished triads, as per example: C Major, TRIADS OF THE MAJoR SCALE. Tonic. Supertonic. Mediant. Subdominant. Dominant. Submediant. Leading note. ——=—- a =3 = S34 =4]j=—s=-| Major. Minor. Minor. Major Major. Minor. Diminished. ¢@ Minor. TRIADS OF THE MINOR SCALE. . Oh 7 = — a, = ——— ewe eS SS —— = = = = Minor. Diminished. Augmented. Minor. Major. Major. Diminished. 75. All chords are numbered from their base. 76. Motion of parts in harmony are: (1) contrary, (2) oblique, (8) similar. Contrary, where the notesin one part ascend, while in another they descend ; oblique, where one part maintains or reiterates the same note, while the other moves up or down; similar, where all parts move in the same direction. 77. CaDENCE is a term applied to the close of a phrase or period, including the two final chords. 78. There are four kinds of cadences: (1) AUTHENTIC, (2) Puaaau, (3) ImM- PERFECT, (4) DEcEPTIVE. The authentic cadence is a fiial close or progression from dominant to tonic harmony; the plagal cadence forms also a final close, and is a progression of subdominant to tonic. This cadence is used chiefly for sacred compositions, and is very effective. The Imperfect cadence is constructed so as to form a half close, leading the ear to expect something to follow. It is the close of the antecedent, and requires a consequent to lead to finish. The DECEPTIVE cadence is formed of any unexpected following of chords which occur at the end of phrase or period. 79. Mopouxation is the regular transition by grammatical flow from one key to another. 80. Modulation is of four kinds: (1) Natura, (2) GrapuaL, (8) ScpDEN, (4) EXTRANEOUS. {N. B.—Harmony will be discussed exhaustively in a succeeding portion of this work. It is, there- fore, treated most briefly here.] MELODY. 81. Sounds so arranged in order of following as to present a complete musical idea and be at the same time interesting, form a MELODY. 82. The grammar of melody is (1) the Morive : (erie suonos fife iee| (3) PHRASE geass less ee Sentence ' Phrase. hei (4) SENTENCE. Gators ies = (ear scot on, mmc pines motive, nee motive, mole, casera motive, motive. = ae Section. Section. Section, RUDIMENTS OF MUSIC. 138 83. Quantity in music may be composed of sound interspersed with silence, or rest, and still the continuity of the idea b2 uninterrupted. 84. If a melody commence with one or more preliminary notes, 7. ¢., a part of a measure, the value of such must be subtracted from the final measure of the sentence or subject (complete melody). ACCENT. 85. The leading or primary accent in a melody is on the note immedi- ately following the bar line. Duple time has primary and secondary accents. hes Quadruple time has also primary and secondary arcs 2 3 a | accents. Triple time has primary, secondary godddt and tertiary accents. ‘Ae gedal 86. Irregularities of accent are common in music. They are produced by antici- pating or retarding the regular accent and thus throwing on to otherwise sub- ordinate beats the stress properly belonging to those usually more important. jee age Ex. Anticipated. Z id dele sz | UN } of ee) Retarded. gteeltecd |p ee Ieee? 7 Such irregularities of accent are termed SYNCOPATION. ARTICULATION. 87. ARTICULATION is a8 important ‘n music as in elocution. The signs of articulation are (1) the legato, (lay-gah-to) connected, flowing ; ~~ ~ (2) semi-lega- to, <7 . 2; staccato, (sta-kah-to)+ + + + detached, short ; (4) puntato, (pun-tah-toh) '' ' ' very pointed. pH a2 ea —\ + —— A © eg = Legato. Semi-legato. Staccato. Puntato. 88. When none of above signs are employed, the notes must be played smoothly, neither too Jong 1or too short. DYNAMICS. 89. Diminution, force or stress is expressed by the following signs and words: DK CONULO, ca seeecccceccecccececeee (AY-000-'tON),......00e to hold. D> CENPIOSTVE LONE, . cee cccaccensennenecccreeneeeens ereeeeees sudden attack, slightly diminishing: —___ eres, or crescendo, .... --(cray-schen-‘doh,) ...... gradually increasing. = dim. or diminuendo, ... ..(dim-in-00-en-d0,) .. .... gradually decreasing. FO CLESLENAO C AUNINUENGO,. .ccec eer cceetenevece teen ene cae increasing and diminishing. Sfe, or sforzando..... 6, Bik Seioisiole ....8fort-sahn-doh.......... sudden attack, forced. Dy PIANO. ...00006 wee -»P’yah-no ....... ...eee softly. DD PIANi8BIMO. occ ceee cvarene eveeee peeah-nis‘see-mo. ...... very softly. Mf, MEZZLO-FLOTLE....sevees ...-Med'z0-for-tay.. ....... medium loud, F JOM saictieanibeelsiienaue esses fOr-1AY.....005 wee ees loud. 14 RUDIMENTS OF MUSIC. SPEED. 90. Relative speed or time in music 1s indicated by (1) Italian terms, (2) by an instrument called a ‘‘ Metronome,” ( Met-ro-nome, time measure). 91. The metronome is a mechanical instrument of somewhat pyramidal shape, used to indicate the relative duration of musical sounds. The contrivance con- tains within works resembling those of a clock, having on its exterior front a graded scale similar to that of athermometer. In front of which, but attached to the inner works, is an upright balance rod—pendulum—notched to correspond with the marks and numerals on the body of tke instrument carrying a movable regulator—nut—which may be set opposite any number of the scale. The pendu- lum being set in motion sways to and fro at the rate per minute indicated by such number, making in its passage a ticking noise resembling that of the clock. 92. John Maelzel, born 1792, who brought the instrument into public notice, based his scale on the division of time into minutes, dividing it into 168 degrees, taking 40, to represent the slowest, and 208, the quickest movement. Thus, when the speed of a piece of music requires an average rate of sixty quarter-notes per minute, the regulator is set to 60 on the graduated scale, thereby causing the pendulum to make that number of strokes in the above time. 98. When reference is made to the metronome to determine speed, it is usual to write above the staff, at the commencement of a composition, some such form as the following: M.M. .J= 80 — meaning Maelzel’s Metronome, 80 quarters to the minute. 94, This plan of marking speed, presenting, as it does, a concrete idea, is most definite and satisfactory; since it determines the rate with a mathematical accuracy and precision, to which words or phrases, however carefully selected, cannot possibly attain. 95. The following table will show the approximation of the leading speed terms to the metronomic scale; the quarter note being considered the unit: TERMS. PRONUNCIATION. MEANING. VARYING FROM To Largo. Larr-go. Very slow. 40 60 Adagio. Ah-dah’jo. Slow. 50 60 Larghetto. Larr-get-toh. Not so slow. 60 92 Andante. Abn-dahn’tay. Slow. 72 84 Andantino. Abn-dahn-tee-’no, Not so ‘slow. 84 100 Allegretto. Ahl-lay-gret-’toh. Moderately fast. 100 120 Allegro. Ahl-lay-’groh. Quick. 120 156 Presto. Prays’toh. Very quick. 156 180 Prestissimo Prays’tis-see-moh. Extremely quick, 180 208 MODIFICATIONS. 96. MA NON TKOPPO........- mah-non-trop'po........00+ VN ‘ ot too much so. Ma NON TANTO........- mah non-tohn'toh.......0.. § MOLTO. 6c cea ieccies 6 MOMVtOW ooo ce ceccveneeenes Much extremely. STRINGENDO..........- streen-jen doh... .....0000+ t G : radually quicker, ACCELERANDO..... ...- aht-chay-lay rahn’do...... vq RUDIMENTS OF MUSIC, 15 CALLANDO, or cal....... hah-lahn’ do... cscs eeceeees Gradually Josing MORENDO.......4.+0005 mo-ren'doh.. .ssecernee with respect to SMORZANDO............ smort-sahn'do .... cee aeees tone and time. PrERDENDOSI........... pair-den-do’seé....... 10008 J Dying away. RaLLENTANDO, or rall . .rahl-len-tahn’do............-.Gradually slower. Ap uiptrum (Latin)... 0.0.0... eee e eee ee eee e ees A PIACERE... 5.220.000 peeah-chay’Tay....6..s.ees ; At pleasure, STYLE, 97. The following terms are added to speed terms to indicate the sTyLE in which a composition is to be played: AFFETUOSO.... cece eee eee Ahf-fet-tW0’ 80... 6 eee ce eeee Soft in expression. MGIPATO oss accsreidien cya eewes ah-jee-tah'toh. . 2.0.06. .ceees Passion and fire. AMOROSO....... Lore RG ria vortions AR~MO-70" 80 0 vr eesccceaee Lovingly, tenderly. CANTABILE. .......-05 oie acer hahn-tah’be-lay ...... se eeee Singing style. CON BRIOvsws Sec ee sics se eae Hon D760’ 0.. cece cere sv ecaceee With brilliancy. CON GIUSTO.......6. 02 eee Kron joo’ stoh. 2.0... scene cane In just time. FURIOSO 6.206055 0a ee eee ease OO-P COW’ 80... eevee ceevecee Spiritedly, furiously. PASTORALE.........----+- -pah-sto-rah’lay..........+..-..Simply. SOSTENUTO.. ccs eee cee cee so-stay-noo’toh.....2..e.ceeee Well sustained. SCHERZANDO....e.0e02+ee00 shairt-sahn’ doh... ..eeceees Very lightly, playfully. VIGOROSO.. 6. eee e cece eens VEE-JO-T0" 80. vs cavees ceeeee .-Force and vigor. EMBELLISHMENTS. 98. Composers have from time to time resorted to the aid of ausiliary notes to embellish their melodies; such notes are known under the general term of Gracgs, or GRACE NoTEs. 99. All such graces must be played in the smoothest possible manner, and should be considered as analogous to those ornaments in architecture which, non-essential to the strength of the fabric, are still of great importance in lending beauty to the structure. 100. The leading graces are as follows, viz. : (1) APPOGGIATURA..........Ap-p0j-jee-@h 00-7. ....++- To lean, or dwell on, (2) AcclacaTURA ........ Ak-hee-ah-ha-too-rah....... To crush down on. (8) Double do............6.6% wae eens adurare State eae a8 es (4) GRUPETTO.......0..06+ Groo-pay-t0...eccecsceeves A group of notes, (5) Monpenve...........- Mor-daunt..........+++... Lightly. (B) LRN, A oie sacsiee asa iedaw sae eda ctovena a nian SESS Round the essential note. (7) SHARE wcsieistciee spec ceciog sales a4 aie bsaieasewielecareienes acorn ns Rapidly alternating notes. (8) Passina Saake...... agiewiatend slcsvggisea orapuaearetaes sae ss fs fs (9) CHAIN OF SHAKES ..... wc. cece evneee a ditaeceerstacs os a ae 16 RUDIMENTS OF MUSIC. EXAMPLES, { APPOGGIATURA. On the dotted note. 4s written. As played. ACCIACATURA. Double Accrac ATURA, GRUPETTO. A. —— } a = Hf -. 3 ee ———— Se ee — ~~ === S| 2 5 aa ae el oP: pe = ee eee Serge Se MORDENTE. TURN, () a) SHAKE. p 7 Ec — [a —— = 6== == pe | t r Sa ae Ds aa aE EET ACRE , 5 ows 2s a 22 ee | =e = P. CHAIN OF SHAKES, RULES FOR PLAYING THE TURN. 101. (@) When the note succeeding the turn note is one degree higher, the turn is dérect and composed of four notes, é. ¢., the note higher, original note, note lower and, again, original note, passing thence to note fol- lowing the turn. @) Similar to a, only resting longer on first note for dot. (c) When the turn note is dotted, rest on that note 3-16 of its value, turn- ing three notes; 1. ¢., upper, original and lower, returning to original note, giving it the value of the dot before proceeding. (@ When the note following the turn note is one degree or more below, RUDIMENTS OF MUSIC. 1% the turn is inverted. Begin turn one degree lower, original note one degree higher, returning to original note before proceeding. (f) A , or ,, written above the turn indicates that the upper note of the turn must be played sharp or flat; when written below, the effect is on lowest note. ABBREVIATIONS. 102. Abbreviations are a kind of musical shorthand, employed to express... briefly some note or passage previously written. Inf. sho, soe +clcce. sas /Todsd--e le Te I) | (a) | (0) (cc) (aq) | ce) | | Abbreviated. a t ni t x t 108. RePEaTs are a species of abbreviation employed to save re-writing one or more measures, section, or even a whole melody. 104. One measure to be ré-written may briefly be expressed by an oblique stroke and two dots, thus: _. , a half-measure, the oblique stroke without the dots. JTL. =| 105. Two or more measures to be re-written may be conveniently expressed by a repeat, thus: ai 2 Jeg ey 106. Should the last measure, or more, of a phrase, section or subject vary in its second ending, the abbreviating repeat may still be used by employing prone parentheses over the differing measures. In the first case, the words Prima Vouta (ist time) abbrev. Ima volta; in the second, Seconpa Vorra (2d time), abbrev: 2d voléa, are used to indicate that the measures included under ist volta are to be ommitted on reaching them the second time, and that those marked 2d volta are to be substituted therefor, thus: 1st volta I 2d volta l { o { a JTF I tt T 1¢7. The Pavsz sign @ (Ital., pausa, pah-oo-sah), has two significations: (1) if written over a note or rest, such may be protracted at pleasure; (2) if written over a double bar, jf, it signifies the point of finish. 108. The words Da Capo (dah kah-po), or D. C., signify a repeat, and mean from the beginning. 109. When the words al jine (ail fee-nay, to the end), are added to the fore- going, D. C. al fine, the whole phrase means, return to the commencement and play to the sign ~ there finish : 2 is é \ i ‘i ae Finé. "TT Fone 110. The sign % is used at any point; but if it be required to return to that sign instead of to the beginning, the words Dat Szano (dahl say-no, from the sign); or, D. 8. are used. Al fine has the same application as in section 96: pT, APT pT Ty rm 18 RUDIMENTS OF MUSIC. EXPRESSION. 111. Expression in music is of two kinds: (1) Mzcnanrcat, (2) ARTISTIC. 112. Mechanical Hopression demands the most rigorous attention to all the details entering into the construction of, or form in a melody: as motive, section, phrase, sentence, subject, articulation, accentuation and the dynamical effects of P, pp, F, ff, ete.—all of which come under the head of Purastne. Yet, with all this, the performance may be unsatisfactory. It is cold and stiff; displays intelli- gence but no feeling, It has the perfection of a beautiful statue, but no life. 113. Artistic Expression is the vivifying influence which, breathing on music, wakens it into life. The possessor of this attribute has genius. Refine- ment of taste is natural to him; he has innate the faculty of imbuing the conven- tionalities of music with an illuminating intelligence, the radiations of which reach deeply into the sympathies of his listeners. In point of fact, he identifies himself with the music, his soul absorbs it; it permeates his being, his technical skill becomes merely the vehicle by which what he feels is communicated to his hearers. Artistic expression, includes mechanical accuracy, but idealizes and lifts it from the region of the mortal inte the sphere of the divine. Vulgar mannerism is the opposite of artistic expression and should be neither encouraged nor applauded. TONE. 114. The power to produce a good tone lies much in the hands ef the per- former on any wind instrument. To acquire such demands, (1) a good instrument wherein all the essentials exist, as perfect tone, flexible, resonant, brilliant and sympathetic tone and ease of blowing; (2) a carefully critical method of practice, slow sounds, scales and intervals, subordinating agility for the time being to the task of building up the embouchure (lips aid muscles thereof); (8) cultivation of the aural faculties to a high degree, without which there can be no correct intonation; (4) a proper method of inspiration and respiration, breathing freely by direct lung action and bringing the whole of those members into play, not confining the breathing to the upper part only. TAKING ‘BREATH, 115, The lungs should be well inflated with air before commencing to play. The expenditure should be economical, and the production of the best possible result from the smallest amount of exertion always the effort, Do not breathe more than is necessary. On the other hand, itis wrong to continue playing until the lungs are thoroughly exhausted. Take breath noise- lessly at convenient points in the performance, numbers of which present them- selves, if the laws of phrasing be properly attended to. Fuld breath should inva- riably be taken during a long silence, or rest; half breath on short rests, and quarter breath, if necessary, after motives, sections, phrases, etc. (See par. 82). TIME. 116. Playin time! On all occasions when practicing, the greatest care should - be taken to conform to a certain standard of time. Scales and exercises should be practiced in strict time throughout, at slow gait until the fingers become RUDIMENTS OF MUSIC. 19 accustomed to.their work and the physique be formed, more rapidly as the diffi- culties are overcome, but always in time, with due regard to evenness and accent. Time is a perception that must be cultivated, and which can only be brought to perfection by most rigid care. Form the habit of playing in time. The metro- nome is a useful guide, TUNE. 117. The perception of tune cannot be too sedulously cultivated. Without tune all other efforts are futile. Time, tone and tune are the leading essentials of all musical efforts, but the greatest is tune. Form the habit of judging intervals mentally correct, then you can produce them on an instrument; but not otherwise. The mind must be educated through the eye and the ear through both. Never’ play with another performer who habitually plays out of tune; his faults may affect you and vitiate your powers of aural discrimination. HOW TO TUNE BAND INSTRUMENTS. 118. Band instruments, to obtain perfect balance or equality of tune, should be tuned on a similar-method with that adopted by the piano tuner; ¢. ¢., by a- series, or cycle of 5ths, thus: ms 3 - 3} 3 313 8 3° } G53 3S —-R— FS fe-te ——] —.—s eo. ry ae t (g: T o & crt =—| E - a 5 = a 4 = i j oF} C =) C r 5 t > | ' z | 3 2 1 oh - The different ways of fingering should be tested, or compared one with the other, and no effort spared to insure the most accurate intonation throughout the: whole band, The mere effort must undoubtedly have a good effect. MUSICAL LIBRARY. 119. All grades and qualities of music are now published so cheaply that there can possibly be no excuse for a band having a poor repertoire. It is a fallacy, which interested publishers and men of vitiated taste, rampant under the much abused titles of composers and arrangers, have an object in perpetuating, to sup- pose that no music is good unless difficult, or that music written down to the capacity of the youngest band must necessarily be of inferior musical worth. On the contrary, there is much difficult music which is simply atrocious, while at the same time many simple melodies are perfect specimens of musicianly writing, and truly enchanting. Band music should be selected for its educating, esthetic and entertaining qualities. It cannot be educative unless it be well written, conforming in all particulars to the grammar of music, neither esthetic unless the composer be a man of profound feeling and refined susceptibilities, nor entertaining unless the pedantic rules, fully availed of, be made by the genius of the writer to subserve his purpose of producing music whose. parts shall be interesting to all. So called popular music is not all bad, though undoubtedly true art would have advanced more rapidly had much of it never been written, neither are the 20 RUDIMENTS OF MUSIC. works of the old school of writers uniformly good. There have been good and bad at all times, and the present is no exception; but the object should be to select the best from all epochs. Gcod music, old or new always wears well; it will bear repetition; while the poor, vulgar variety show twaddle, hashed up into fantasies, not only becomes wearisome but is’positively deleterious. Therefore, select only music which will refine the mind and ennoble the feelings, irrespective of its age, or nationality, and shun that which administers only to the depraved taste of the lower and enervated order of amusement-seekers, Cultivate a taste for what is pure ard good in art. Do not trust to the representations or remarks on a piece of music in any publisher’s catalogue; but rather examine for your- selves whether this piece or that, really answers your purpose in being good and adaptable to the capacity of the band at large. To do this it is absolutely neces- sary to examine the piece in detail and as a whole. Sample parts can give you no idea, or at least a very feeb!e one, of the arrangement, for as every intelligent musician knows the finest compositions may be utterly ruined by an incompetent transcrib r, while an indifferent theme may be made quite interesting at the hands of an efficient arranger. 120 TERMS APPLIED TO MUSICAL COMPOSITIONS, AIR Arta (ah-ree'ah). Bravura (brah-voo’rah). A composition of a vigorous and brilliant character. Canon. An imitative composition in which a theme proposed aud continued by one is followed by other voices or instruments in stated intervals or periods. Cantata (kahn-tah’tah). A vocal composition, dramatic in character, of several movements. Cavatina (kah.vah-tee'nah). An operatic air occasionally preceded by a recitative. Concerto (kon-chair'toh), A composition for‘asolo instrument with accompaniment. Concertino (kon chair-tee‘noh). Diminutive of concerto. Counterpornt. Literally point against point. The art of adding one or more parts to a given melody (canto fermo). Duo, DUET, or DUETTO. Composition in two parts, with or without accompaniment. Fueus, fuga (foo’gah). A flight. Highest style of canonical writing. A subject pro- posed in one part an‘l answered in others according to set rules. Fantasia (fan-tay--zee’ah). A work in which the composer gives full liberty to his ideas. CpERa (0-peh'rah), A musical drama for stage representation. Operetta (0-peh-ray'tah). Diminutive of opera. Oratorio (or-ah-toh-ree’oh). A sacred music-drama usually on Scriptural subject. ‘Overture. A composition of prescribed style, prefixed to opera or oratorio, ‘Quar7ET. A composition in four parts. Quinter. A composition in five parts. Soto. A composition for one voice or instrument with or without accompaniment. Sonata (sch-nah’tah), A composition of three or four movements in which must be exhibited a unity of idea. SympHony. (1) Avshort introduction or interlude. (2) A grand composition ideal, but cohesive in nature, consisting of several contrasting movements. Trio (tree’oh). In three parts; or, the third part, as in a march. { A short melody, ‘with or without words. RUDIMENTS OF MUSIC. 21 SCHOOLS, OR METHODS FOR EVERY INSTRUMENT. 121. For the convenience of those who have the laudable ambition of studying their instruments from the stage of the embryo to that of the artist, the following list of very excellent methods and schools has been prepared : Cornet.—Langey, Caussinus, St. Jacome, Kosleck, Arban, Bonnisseau. Es Atto.—Langey. Frenca Horn.—Langey, Franz, Hoffmann, Klotz. Suipe Trompont.—Langey, Dieppo, Wirth, Bonnisseau. Baritone or TENoR.—Langey, Hoffman, Wirth. Tupa.—Langey, Hoffman. EvurxHonion.—Langey, Hamilton (Eb, Bb or C), Bonnisseau. Fuiure and Piccoto.—Langey, Daverges, Chapman, Devinnes, Koehler, Papp, Kummer, Furstenau. . Oxsoz.—Langey, Barret, Garnier, Wieprecht, Schubert. CLARIONET.—Langey, Klose, Lazarus, Baermann (the finest work ever written). Bassoon.—Langey, Jancourt and Bordogny. SaxopHonE.—Hoffman. The ‘‘Langey” series of methods contain excellent material for the first two years’ study. They embody a fine collection of progressive studies. TRANSPOSITION. 122. The original, or pattern scale is that of C, in major, or A, in minor. All other scales, higher or lower, are simply transpositions, each bearing the same proportion in its component parts and with respect to the key-note, as is the case in the normal scales. Now, it follows from this, that if a scale may be placed at a different pitch without injury to the sequence of its tones, so may a melody or an entire composition. Transposition is necessary, where a composition goes be- yond the compass of voice or instrument which it is intended shall perform it. The orthodox method of effecting transposition is by use of the various clefs, and really, in reading a score containing a number of parts in many keys, is the only practical method of rendering the same instantaneously comprehensible to the eye. But ordinarily the simpler method is by uumbers. This method, necessarily, im- plies a knowledge of all key signatures, and of course, the construction of the scale. The first thing to be done is to decide the signature of the key into which it is intended to transpose the music under consideration; next, to remember the numerical relation of each tone in the scale to the new key note. For instance, the scale of C major, without sharps or flats, transposed to the key of, say F major, with one flat, would present the following appearance, viz: mM I C. D. E. F. G. A. B. C. 1. 2. 3. 4. 5. 6. 7. 8. F G. A. B(flat) C. D. E. F ey —_— It will be noticed that the figures are the same for each scale, and also, that the semi-tones, indicated by ~— , occur.at similar points in each. From this it will be evident, that in transposition of melodies, care must be taken to preserve 22 RUDIMENTS OF MUSIC. the same relation of sounds to the key note in the new key, as appeared in the original. In other words, an accidental sharp, flat, or natural in one key, must find its equivalent in the other, and the natural order of key tones must coincide ‘in the copy with those of the model. The following transpositions of ‘‘The Last Rose of Summer” will serve to show this method of transposition and make the subject clear. Transposition Sac Sas a a toe 1234567 8 The subjoined table shows the note, whic on transposing treble clef instru- ments, equals C, concert pitch. D, Dp “By 4g Ab 2 G, F. Eh, T as the Horn, as the Horn, asthe Clar4 asthe fasthe Cornet as the asthe fas theClar’net, Trumpet, or [frumpet,&mis4 ionet, Cor- | Clarion-| Clarionet, | Horn or | orn or ‘Traropety Clarionet. |catied Eh Picco-| net or Tenor et or Oor-| Horn, or |Trumpet.)Trumpet.| “sniscalled to in 8ve. in 8ve. net. Trumpet. F Elo Flute. a L ~ =! t=: o== —4 ri wee, % i : Norma Prrcg. as the Oboe, Flute, Clarionet, or Horn. THE TONAL SYSTEM. 123. The entire range of sounds covered by the instruments of band or orchestra may be stated at from six to seven octaves. In six octaves the names of sounds will repeat themselves six times, and so on. For convenience of reference it is usual to name the octaves commencing from the lowest, as Double Great, Great, small, once lined, twice lined, three lined, etc., etc. This system was introduced in Germany daring the sixteenth century. (See table.) CHART, SHOWING COMPASS OF INSTRUMENTS IN COMMOQN USE. 124, The instruments in use in Band and Orchestra may be divided into three classes, (1) StRiNe, (2), THosz WITH DOUBLE REED, as oboe and basson. (8), THOSE WITHOUT REEDS, as flute, (4), THOSE MADR (2) Winn, (3) Pegcussion. OF BRASS, WITH CUP MUUTHPIKCE, as the cornet, alto, tenor, etc. Stringed instruments aro subdivided into, (1), THOSE PLAYED WITH a BOW, as violin, viola, violoncello and Percussion instruments may be divided into, (1), THOSE WITH DEFINABLE TONES, as tympani, bells, eto. bass. (2), THOSE PLUCKED OR STRUCK WITH FINGERS OR PLECTRUM, as harp, guitar, mandoline and piano. (2), THOSE WITH INDEFINABLE TONES, as snare dtum, bass drum, cymbals, etc, Wind instrume:ts are subdivided into (1), THosE WITH SINGLE BEEDs, as clarionet and saxv, one. The accompauying table gives the name aud compass of instruments commonly in use: ONCE LINED OcravVeE. INNED OcTavE. GuEaT OCTAVE. SMALL Octave. DoUuBLte GREAT OCTAVE. STRING INSTKUMENTS, | WIND INSTRUMENTS, | PERCUSSION INSTRUMEN/8, Compass. Compass. Compass... ompass. Played with bow.|________j______| Played with |_.. = »__ REED. Without Reed. |——-—— | —-—— | With Mouthpiece. ——_ ,;—_ —_ Definite Com- | Indefinite Nominal.) Actual fingers. Nominal.| Actual. Nominal.| Actual. Nominal.| Actual. || Masical Tones.| pass. tones. SSS meas | eee S| ince Compass. aa Compass. = oe yen aa Ti ee pe ile, | ouble, fo | - Nominal.| Actual. Nominal | Actual. Flate, Grand. |b orc foe b orstos | Cornet Ep. F3 We. ato & ines dto a: Snaredrum = a —— e a * = Ficcolo o. ani dtob | dtob, |]i “ By # © | eto bp bet of Bells, {tor | Bass « , Clarlonet A. | e tog. 0 e. boe. btof, || (Often calle Bay Nee Np a =" (Chromatic 8c.) = PvViolin. gtoc. | Plano. COitoa: eee £ ele = || Piccolo Ep. | atob | cptoe “A “ «a toab |) Cuckoo. ¢ to eb| Triangle ‘ C. os . De fi assoon. BBh to_bb ||(Correct naine Dp = = = = t Viola etoc. | Harp. EF tod - : we isnt | Gk ce, Cree nom 1S | oe * Alto Ep. “ "| atoey || Tympani, higi ¢ tof. | cympais : 7 . 0. e tog. “ Contra. 0 £.1B 0 f ||(Correct name Eh) E|- = = ip. UCelle. Cto.g.. || -Mandoline gto e Sell oa Pe mien eee | “ F “ “| Btor “_ low.| F to c. [Sleigh bells : 7 0. g .|Sarrusophone, of. atoe —__—___" = ——————————SSSS——_—_— t Bass 3 strings.; Gio g. | GG tog. |f Guitar. eto be E toa, = P b z = The pitch of the so-called Eb Pic- || Baritone Bh. Bees 2| Eto bb No definite pitch can be stated ¢ Pass 4atrings.| Etog. (EE te g. “ Alto Eb. do. | Gtobh| “ Alto Fy] do | dtoa || colo is one semitone only above C. ||'_ (3 valves) ease ~" || for Glockenspiel. or Bells. They : f 2 = The instrume: t should therefore be || PuPvonion * abe p& |BBhtobp|| are made in many ditferent kers : ee, “ Bass Eb. do. D to f. “ Tenor bh do. Atof ‘ (4 valves) art but usually with a compass of two called the Dp Piccolo. The fact of ‘Trouxbone Alto Boog Atoc, octaves. { The compass of string instruments, markedt, fs susceptible of Rarorbone. btoeh| atod.| “ Baritone Fy} do. | Dtog || tts lowest sound giving concert Fh |]/ manor j 282 wine chesee era tps f) 7 aes 2 oprano Bp. = = = has o joned th ; ing. ||| ““ Tenor B ae nor third. The instrument to extension by the use of HARMONICS. ‘ Nataral harmonics are those || (5 ‘Alto Ey| btof | dtoa.| « Cass B,.| do. | Aatoe TeriECe ae ee. eae ae bk is Zi | B to bb represent the voice of this bird bas produced by touching certain points of open strings.” “ Artificial = = = y dae + |) Bass G. C§tog || achromatic slide, by which it can harmonics are :o be obtained very distinctly throughout the extent || ‘‘ TenorEh.| do. | Atof.| ‘ Contra vase Btof | DDtof. i as ans Seminor oe pee um any key . heehee 5 = hy. = ~|| higher than the ¢, or concert Fiute, ||: Bass ‘The Tympani tunes by single of the gamut, by meuns of the first finger; which, firmly pressed up- || « paritoneEy.| do. | Dtoa.| cor. Anglais F) btof | eto b>]! shonid ve called the Eh Flate. tts ||, (3 wiih AA to gb ea notes; increased or decreased ten- on the string, while the other fingers touch it, serves for 9 movable = = = os Ep Flute. ; ' GGh to by|| Sion of the heads of the two drums rest.""—Berlioz. ‘« Bass Eb. bto eb. | AA to db. lowest cound, however, giving con- ||| (4 valves) EE} to | “|| admitting of one octave, as the ‘ cert_f hasled tothe mistaken name. ||! Rass BB EE to bp|| limitation of compass. Seen ee ees reer a aero ee * The compass, nominal and actual, here given for Alto, applies also te French Horn, with the exception the following keys : Bh low, C, D, Eb, Et, F, Gj Ab, AY, Behigh, and C high. Tram ets 7 that the ‘‘ Pedal” tones of all valves on the latter are more or less accessible, many of them being used con- ing in keys ever iors varied than those of the (French Ham having procs and slides for ao aieenae stantly for orchestral effects. French Horns have a series of crooks, by which they may be pitched in any of | semitone, from Ak low up to Ab high, The Eb Trumpet is pitched one octave lower than Eh Cornet. | A Copyright, 1887, by Car. Fiscuzr, New York. A COURSE OF HARMONY AND COMPOSITION SPECIALLY DESIGNED FOR SELF-INSTRUCTION. Bv Joan Bernagp Loaisr. THE COMMON CHORD. The Musica ScaLz may be compared to an Alphabet, and a CHorp may there- fore be ccnsidered as a worD in the language of music. A combination of letters selected from the alphabet forms a word; a combination of sounds selected from the scale forms a chord. Thus, if we select the ist, 3d and 5th from any scale und write them over each other (as in the following example) the combination of these sounds will form a chord, usually called a common chord.* If this chord’be played so that the sounds are heard simultaneously, the effect upon the ear, with respect to music, will be very like that produced, with respect to language, by pronouncing a word after having spelled it; thus, M a n, Man. The Common Chord extracted from the Scale. Q. Ex. ». SS SSS SSS = = — i = a es & 6 7 8 oe Whatever Common Chord we propose to write, let us (in order that it may be clearly understood) first write the scale of the kev note of that chord with the necessary sharps or flats; and then selecting the 1st, 8d and 5th sounds, place them each over the other, as above. The Common Chord of A extracted from the Scale. “4 2 te. a Ex, 2, te = = = bead 1 2 3 a 5 6 7 8 To the combination shown in the preceding exampie may at any time be added the 8th (or octave), it being merely a repetition of the 1st, thus: Common Chord of F. on pag Ex. 3. =F fo eae = = ff 1 2 3 4 5 6 7 s These examples (it will be understood) are only specimens of Common Chords, showing the manner of their construction; itis not expected that the pupil should rest eatiefied with these alone as practice; on the contrary, he should write the scales with single and double sharps and flats through all the keys, and extract the chords according to the rule. * This is the combination most commonly met with. See aleo Ex. 48, where this combination (as consisting of the harmonics) is shown to be common to every musical sound. 26 HARMONY AND COMPOSITION. Whilst proceeding with these exercises let the pupil audibly* pronounce each chord, commencing always with the lowest note; then the 3d, and after that the 5th; thus: the chord of C is C, E, and G. Let him not say C, G, and E; for by so doing he will inevitably frustrate a very important object here contemplated, and which in due time shall be explained. L-t the common chord, therefore, at all times, without any exception whatever, be pronounced in this manner, laying a peculiar emphasis on the word and, preceding the last note. Having attained sufficient facility in extracting the common chord from the scale, the pupil may write the chord from reflection only; thus, instance, if the chord of E be required, let him write E, and then at once add the 3d and 5th to it as they arise: E, G, and B (as at I). Il. A L : a ee ee But as the key of E requires four sharps, it follows, of course, that the @ in that chord must have a sharp placed before it (as at 1I.); thus the chord of E is not E, G aud B, but E, ag and B. The same rule must be observed with respect to all eommon chords. BASS OF THE COMMON CHORD. Every chord is supposed to have a bass, called the fundamental bass, upon which it is founded, and which is always the same as the first note of the scale from which the chord is extracted. Thus the bass to the chord of CisC. The bass to the chord of Dis D, etc., ete. Henceforth the bass notes of the chords shall be written on a separate staff, thus: 7 x Y r2% (é re —————— e tek Hn ut It has already been shown that the 8th sound of the scale is but a repetition of the 1st; and, as the bass may now be considered as representing 1, we shall ir future figure the chord 8, 3, 5, as exhibited in the preceding example.> It will be of very great advantage to the pupil, in the progress of his future studies, that he should be able to write correctly and without hesitation any common chord proposed to him; and he is str ogly recommended to make himself perfectly master of this by frequently writing common chords on basses which he may propose to himself; in pronouncing them, let him be careful to follow the instructions already given for that purpose, remembering the word ‘“‘and"’ before the /asé note of the chord. The Three Positions of the. Common Chord. This chord consists of three sounds beside the bass, viz., 8, 3,5. These three sounds are written over each other, and may change their situations in such a manner tnat each may alternately appear in the upper, wer or middle part of the chord. * This makes a forcible impression on the memory. + Should it be asked why we do not figure the several notes of the chord according to their rea, distance from the bass, viz , 8, 10, 12, asin Ex. 5, ¥?- Answer. As the 8th is a repetition of the Ist, ao the 10th is a repetition of the 3d, and the 12th a repetition df the Sth, etc., etc. HARMONY AND COMPOSITION. 27 Heretofore the 5th has always appeared in the wpper part; and when this is .he case, we say the chord is in the 2d position. When the 8th is in the upper part, the chord is in the 8d position; aud when the 8d is in the upper part, it is in the 1st position.* 2d position. &d position. Ist position. 2d position. 8d positicn. 1st position, ¥ Tt a tT —— u— | Having shown the construction of the common chord as exuacted from the Diatonic Scale, and also its three positions, we shall proceed to point out the method of employing it in composition. First, let us explain the distinction between Metopy and Harmony. Although both owe their origin to the same source, and are inseparably united, yet they 1equire to be clearly distinguished. Melody is a succession of single sounds, ascending or descending, thus}: re» Eee I ee Harmony is a succession of combined sounds or chords, ascending or descending, as in the following example, which exhibits a portion of the preceding melody harmonized: | HY iW (a.) (2.) A scale has been compared to an Alphabet, a chord to « word; and if ve pursue this analogy a little further we may compare a succession of chords to a sentence. Now, between the various words which compose a sentence there must necessarily subsist some connection, in order to produce sense; so it is with a succession of chords; there should subsist some connection in order to produce a proper effect. The connection required is, that in an immediate succession of any two chords there shall be found one sound that is common to them both. In the preceding Example, at a, we perceive, by the curved lines, the links which constitute the chain of harmony. In order that the pupil may frm a just estimate of the necessity of this connection in a progression of chords, the same melody 1s exhibited at 5, accompanied by chords indeed, but without any of the connecting links above mentioned. Let the pupil play these two exercises and compare the different effects. It shall now be shown how a melody may be harmonized so that this necessary connection of the chords shall be effected, and that each note of tue melody shall have its proper chord and the whole its appropriate harmony. * How thie arrangement has arisen will be seen at Ex. 48. + The whole of the Diatonic Scale is a melody, and as such {t will be trerted when we begin to harmonize. ¢ There are, however, exceptions to this general rule, which shall be explained in the proper place 28 HARMONY AND COMPOSITION. The first step towards this object is to discover the proper fundamental basses; but how is this to be done? The melody itself shall point out the way, and the basses being thus found they, in return, shall furnish the harmony with which that melody shall be accompanied. DISCOVERY OF THE FUNDAMENTAL BASSES. Let us take the scale-as a theme to be harmonized; and, in order to find the ‘fundamental basses, let us write over the notes the figures 8, 5, 8, as in the following example :* 3 Ae 2 eS & & 2. & 23 —_ | — e-— FR L r = T T Ee a 5 [ [ iL [ sail 1 L L + ee } [ Te tL { a I { i. i C ID ' Ex. 9. ) rs. T C c c C . C —1n = | 1 i t io 1 = + \t i E —£ E a E E sy The figure 8, placed over the first note, points out the bass to be an octave, or eight notes below; the 5 over D discovers the bass of this note to be a fifth below; and so on with the rest, which, when completed, will appear thus}: 3 3 & 0 5 5 a 2 2 -&- —. = eee i. ra T ‘2 i ees f -F— E E f ah 5 C t t E c t f TH 2 c 15 C EC. Co t L au Ex. to. : ee S. f eS L f c., iC Fe = L (= | | | _—— \ Coed |b [ = [ ee if E: f —~ - i} C C - = i L {n the preceding example it will be perceived that thére are only three bass notes; C is employed four times, G twice, and F twice. Each of these three fundamental basses has its peculiar name. The first is called the Tonic, which is always the same as the tone which gives the name to the scale; for instance, the preceding example isin the scale or key cf C, there- fore the tonic is C. . The second fundamental bass is called the Dominant. It is the same as the fifth sound in the ascending scale, and may easily be found by repeating the chord of the Tonic, as the last note of that chord (viz., the fifth) is always the Dominant. Thus the chord of Cis C, E, ‘ann’? G. Gis therefore the Dominant to C. Again, the chord of Dis D, F¢, ‘‘anp” A. Q. What is the Dominant to D?—A! Q. Why?—Because A is the last (or 5th) note of the chord of D. And thus may be found the Dominant to any key. The third fundamental bass is called the Sub-Dominant; it is the fourth note of the ascending scale, and may easily be discovered and recollected, as being a whole tone under the Dominant. If the Dominant be G, what is the Sub-Dominant?—F. Why?—Because F is a whole tone below G the Dominant. By way of exercise, the basses to other scales should now be found according to the same method as in Ex. 23, * A reason for this arrangement will be seen in the introduction to Modulation; Ex. 49 and 50. + The simplicity of this method, and the ease and certainty with which the Pupil is thus enabled at once to discover the true basses to the scale, and the harmony subsequently arising from them will be still better appreciated when he arrives at the harmonization of melodies. t The pupil will now see the motive for urging the necessity of pronouncing the chord as stated Ex. 16, and cf emphasising the word and; for, had the common chord been pronounced in any other way, this result could not have been attained. HARMONY AND COMPOSITION, 29 The pupil having been thus shown how to tind the proper fundamental basses to the scale, he shall now be taught which of the intervals of the scale are accompanied by the Tonic, which by the Dominant, and which by the Sub-Dominant.. First let him write a scale and add the fundamental basses as already directed; then let him remove the figures 8, 5, 8, and write in their places the figures from 1 to 8 over the different inte, vals of the scale, thus: —P- 3 T 2s - & a > 2. = 7h Ex. 1. oo Tonic. Dominant. Tonic. Sub-Dominant.Tonic.Sub-dominant. Dominant. Tonic, E SS SS hes as Having done so, he will discover The first rule of Harmonizing. The 1s¢, 8d, 5th and 8th of the seats are oncaminignted by the Tonic. The 2d and “ith, by the Dominant. The 4th and 6th, es as by the Sub-Duminant. To show the mode of exercising upon this rule, let us take, for instance, the scale of A. Our first inquiry must be: What are the names of the three fundamental basses accvmpanying this scale? The key being A, the Tonic must be the same A. The chord of A is A, CH and #; the Dominant therefore is E. A whole tone below E ia D; the Sub-Dominant therefore is D. Having written the scale of A, we proceed to write the basses according to tke above rule, reasoning thus: A the first of the scale, is eecompanied by the Tonic A. B thesecond ‘“ by the Dominant E. Ce the third cs « by the Tonic A. D the fourth se ss by the Sub-Dominant D. E the fifth se a by the Tonic A. Fe = the sixth a sf by the Sub-Dominant D. G$ theseventh ee by the Dominant E. A theeighth ‘“ as by the Tonic A. By this process we have tound the proper basses to the scale of A. LL. AZ =e rc = eS EE Ea t ‘ E -—e 5) T t [ = Ex. 12. ———— Tonic, Sisainaat Tonic. Sub-dominant. Tonic. Sub-dominant. Dominant. Tonic. —— ——— =e XC I r foe: LL L ad. c C c ia 1 Le mae Pursuing this method, the pupil may find the fundamental basses to all the scales as far as six sharps and six flats, making use in future of what is called The Signature. This is the sign by which the key is known, 4. ¢., the number of flats or sharps 30 . HARMONY AND COMPOSITION. belonging to it being placed at the commencement of each staff, instead of being written before each note. a 5 i ay _——_— Ese oa c 1 it A It will be admitted that without a certain degree of ready practice it is in vain to expect much advancement. Unless the student of arithmetic have the multiplication table at his fingers’ end, he will make no great progress; so it is precisely with respect to portions of the subject on which we have been treating. for instance, the common chord of any note, with the sharps or flats necessarily belonging to it, should be pro- nounced with as much readiness as a schoolboy would answer the question how many are four times four? How easy it is for him to impress upon his memory the sharps and flats, so as at all times, quickly and unhesitatingly, to declare their number and order in any key! He needs but to extend his hand and he will behold the whole system; afterwards to forget them is utterly impossible. More of this by andby. We shall here endeavor to bring to the recollection of the pupil what he has already learned, and suggest the following mode of proposing questions which he is supposed to answer without hesitation. Q. Of how many sounds consists the Diatonic Scale?—Seven, besides the 8th, which is a repeti- tion of the ist. Where are the half tones found?—Dcetween the 3d and 4th and between the 7th and 8th. How many sharps in the key of A?—Three. What notes are sharp?—F#, C# and.G#. What is the chord of E?—E, Gf and B. THiow many fundamental basses are there!— What are their names?— Tell me the Tonic, Dominant and Sab-Dominant in the key of Af—The Tonic is A, the Dominant E and the Sub-Dominant D. : Q. What notes of the scale are accompanied by the Tonic?—The 1st, 38d, 5th and 8th, Q. What by the Dominant?—The 2d and 7th. Q. What by the Sub-Dominant?—The 4th and 6th. &L0LL00 The above form of question and answer tends chiefly to exercise the memory. The following mode brings into action the reflective faculties; it introduces a mental exercise which will be found highly interesting and useful in after life for other purposes than the mere advancement in the science of music; it is calculated to stimu- late the reasoning powers, compelling, as it were, the mind, before it arrives at a satisfactory conclusion, to pass through certain evolutions and reflections, Supposing the key to be F, what is the bass to E?” (Reflection of the pupil).—In the key of F,—E is the 7th of the scale.—The 7th of the scale is accompanicd by the Dominant —The Dominant in the key of F is——. Here mentally repeat the chord of F, thus, F, A, “‘and'’’C. The last note of the chord ia the Dominant, therefore C is the bass ty Z. “his process should be observed at all times when the Dominant is to be discovered. Suppose the key is Eb—what is the bass to C? (Reflection of the pupil).—In the key_of--Rb—€ is the 6th of the scale.—The 6th of the scale is accompanied by the Sub-Dominant.—The Sub-Lominant is Ab—therefore Ab is the bass to C. Suppose the key is B, what is the bass to C$? (Refiection of the pupil). The key is B—C¥ is the second of the scale—the second of the scale 138 accompanied by the Dominant—the Dominant in the key of B is F{—therefore Ff is the bass to C$. But what will be the bass to that C¥ if we change the key to DP—A Q. Why ?——-—_—. “ * — Supppose we change the key to G, what then will be the basa to Cf{?—No bass can then be found y to Cf, because C¢ is not one of the notes of thescale of G. The pleasing and attractive form in which the pure elementary principles of har- HARMONY AND COMPOSITION. 31 mory and composition are thus conveyed to the pupil is calculated not only to accom. plish the object proposed but also to materially improve the understanding. To Find the Fundamental Basses to Melodies. Hitherto we have taken only the ascending scale as a Theme or Melody, to which we have added the fundamental basses; we will now depart from the rigid observance of that plan and select such intervals of a scale as shall, in their progression, form a pleasing and effective melody. ' Let us suppose that the pupil is required to find the proper basses to the fol- lowing: Ex.13 = = A. } {— 1 1 c T _— cS t Lt t va t I t t t + - set] In order to accomplish this it will be-necessary to-enter upon the following reflections: ‘“«The melody is in the key of C, and as E, the first note in the melody, is the 8d of the scale, I shall write the figure 8 over that note.” As Dis the 2d of the scale, I shall write the figure 2 over that note; and so with all the rest, thus Ex. 13. B. The next step will be to call tu mind the three fundamental basses of that key; thus: The key is C, therefore « The Tonic is C, which accompanies the 1st, 8d, 5th and 8th of the scale. The Dominant is G, ss ss 2d and 7th of the scale, The Sub-Dominant is F, as as 4th and 6th. Let the pupil now write the fundamental basses according to this rule (as laid down in Ex. 11), and the melody thus accompanied will appear as in the following example: =e ee Ex. 14. ; : DT, iD. T Sub-D, D oT Q. Why is D (the 2d note) accompanied by @ ?—Because the 2d of the scale is accompanied by the Dominant, and the Dominant is G. Q@ Why is C (the 3d note) accompanied by O ?—Becanse the first of the scale is accompanied by the Tonic, and the Tonic is C. Q. Why is A (the 10th note in the Melody) accompanied by F f—Because A is the 6th of the scale, and the 6th is accompanied by the Sub-Dominant. Q. Why is F (the 11th note) accompanied by F ?—Because F is the 4th of the scale, and the 4th is accompanied by the Sub-Dominant, After having acquired, by sufficient practice, a readiness in distinguishing what interval of the scale each note is, the pupil may dispense with writing the figures over them, and at once write the bass under each note as he proceeds with the examination; as thus, with the following Ex. We perceive this melody is in the key of F: by the signature—one flat. The first note, F’, is the 8th of the scale, and requires the Tonic F. 32 HARMONY AND COMPOSITION. The following note, G, is the 2nd of the scale, and requires the Dominant ©, The next note, F, is the 8th of the scale, and requires the Tonic F.. 3 is the 7th of the scale, and requires the Dominant C. That the pupil may become perfectly familiar with this subject, and attain the atmost facility in writing the fundamental basses to any given melody, he is here pre- sented with a variety of themes in different keys, which, having first served as exer- cises similar to the above, may afterwards be fully harmonized, when he has been made acquainted with the mode of adding the chords. Themes for Haercise on the First Rule of Harmonizing. No. & No. a, Fra pe ee SS Sees ry m7, — E A he toy ce © Progression of the melody from the 6th to the 7th of the ecale, to be referred to tm @ future Exerciee. HARMONY AND COMPOSITION, 33 After having employed all the above themes, should the pupil be desirous of further practice, it is only necessary to change the signature of any one, by which the intervals of the scale will be changed, whilst the notes themselves remain unchanged: and thus a new Exercise is produced. Ex. 16. IL Ex. 16. Til. At II the theme is in the key of C. Let us suppose the pupil to have already accompanied it by its proper fundamental basses, viz.,C, Gand F. If he afterwards changes the signature as at IH, the key will then be A; the fundamental basses of which are A, E, and D. The signature being thus changed, the same melody will require other fundamen- tal basses; for instance, the note Hat II is the third of the scale of C; C (the Tonic) is therefore its proper bass. The same note E, however, at III, is the fifth of the scale of A, and requires A (the Tonic) as its bass. Q. How is F (in the 4th bar) at Il accompanied?—A. BYE the Sub-Dominant. Q. Why?—A. Because F is the 4th of the scale of C. Q. How is F in the 4th bar at III accompanted?—A. By the Sub Dominant D. Q. Why?—A. Becauee F in this example is the 6th of the scale of A A farther variety of melodies, on this and and all the subsequent rules, may be found, if desired, in a small work, “Themes for Exercise in Harmony,” by the Author. It has been stated, previously, that the melody, by means of the figures 8, 5, 3,: points out the way by which we discover the fundamental basses, and that, in return, the fundamental basses will point out the harmony to the melody. To-exemplify this, we shall again resume the Diatonic Scale, as it exhibits, in a prominent degree, the harmony in a connected and combined form. The scale having been written with its fundamental basses (asin Ex. 11), let the pupil add the remaining intervals of the chords which are indicated ue those ethic Ex. 17. ™m = = Eat }} The first bass note is C; the chord of Cis C, Hand G. Here C the 8th (one of the intervals of the chord) is already in the melody; we have therefore only to add the 8rd and 5th; these intervals should be written immediately under the note of the mel- ody, and thus the chord will be complete; always taking care that the note which be- longs to the melody be the highest note, and to write the other notes of the chord un- derneath as near to it as possible. To proceed; let the pupil point to the second bass G, and (having pronounced the chord G, B and D) write first the note G, then B, and (as the D is already in the mel- ody) merely point to the note and say ‘‘D.” By a close observance of this method, all mistakes will be avoided. If we examine the above Ex. 17, we shall perceive that, by adding to the melody the chords pointed out by the fundamental basses a progression of chords is produced:. 34 HARMONY AND COMPOSITION. ' as each of these chords consists of four notes, four rows of notes are thus produced: and, as each row forms a distinct melody, four melodies appear, each different in its pro- gression, but all uniting together, forming a pleasing combination of harmony. Thus:— , Soprano or Treble, a =o as poet L — ee eee rh +— t t ¢ } HH - = t ; t E Hi Alto, Counter Tenor, or Second Treble. ® s— 3 : rN a — = =< se es n - ——: E iH Ex. 18. _—"s : x. im - J + es 1 | mL Se iW —. T T = = = z ah WV. rt =H In the foregoing Ex. the four distinct melodies, being written each upon a separate staff, iscalled @ harmony in four parts, The dots, as they appear in the upper staff at I, mark the place from which the potes composing the other parts at II and III have been taken.* CONSECUTIVE FIFTHS AND EIGHTHS, Let us return to Bx. 17, and particularly examine the chain of connection between the chords as marked by the curved lines. It will be perceived that the G in the first chord forms a part of the second, and that the same note forms a part of the third chord also. The C in the third chord iz the connecting link with the fourth, fifth and sixth; but no connecting link is found between the sixth and seventh. Here thea (according to what has been observed concerning the necessary connection of chords) the sense of the séntence is, as it were, interrupted; and, on being played, the passage will produce a corresponding effect upon the ear. That such a progression of harmony is éncorrect and ought to be avoided, has been already noticed in the observations following Ex. 8. At the 6th note of the scale in Ex. 18, we find (in the alto) an F which is marked with an 8, as being the eighth, or octave, to the bass note; and in the same part (the alto) the note immediately following is also an octave to the bass note. These are consecutive octaves. At the 6th note of the scale, also, we find (in the tenor) a C, which is a fifth to the bass note; and in the same part, immediately following is also a fifth to the bass note, These are consecutive fifths. * Supposing four persons to sing or play this progression of harmony: The first person would aing all the Aighest notes of the chord (which, in this example, form the scale of C.) This we cali the Aret part. The second voice would take the range of notes next underneath, The third voice would take the range of notes next above the basa, And the fourth voice would take the bass, or lowest row. The alfo and éenor parta, a8 written in this example, are not intended to represent the real pitch of those voices; to do this, would require a different arrangement, calculated, at present, only te puzzle the learner and obscure the subject. For the eame reason also, their peculiar clefs are nov {mtroduced. If these two parts be played an octave lower, all will be right. ¢ Aga matter of course, an 8th and a 5th may be used in every chord; but the same interval eaght not to appear twice in the same part in immediate succession. HARMONY AND COMPOSITION, 35 TO PREVENT CONSECUTIVE OCTAVES, In Ex. 19, at I, are consecutive cctaves. Let the note which is an octave in the first chord be continued in the second chord, as at 11, and that note will then become a Tub: thus consecutive octaves are avoided. Why the 7b may cous he allowed to be heard in the second chord at II, shall be explained presently. eae "2°32, eT eee ee ee feocisifroioetfoue IL III. IV. Vv. VI. ee 1 r= E 4]. t a ae it} T fe L = | i (or baer Ex. 19. TO PREVENT CONSECUTIVE FIFTHS, Observe this simple rule—whenever the fundamental bass ascends one degree, the 6th of that bass must not be allowed to ascend to the 5th of the following bass, as at III; but must descend one degree, as at IV. Thus the OC, being the 5th of the bass F, having descended on the bass G (with which it now forms a 3d), the consecutive Bths are prevented; but as we have already a 3d in the principal melody, it becomes necessary that we should ascend again to the nearest note of the chord, viz., the 5th, as at V. Consecutive 5ths and 8ths* are both avoided at VI, where the harmony proceeds to a close;.the 7th descends to the 3d of the last chord (the Tonic), whilst the 6th descends to the 8th. On this subject we will say no more at present; indeed, it would be rather injurious than otherwise to enter more minutely into it here. The student is recommended to reflect upon what has hitherto been said; and, by exercising himself on subjects in which consecutive 5ths and 8ths arise, he will not only impress this matter upon his mind, but require a facility in writing which will be found exceedingly useful in his future studies. The three last notes of any scale will answer this purpose, as the fundamental bass there ascends one degree, Let him here add the alto and tenor (asin Ex. 19) to the themes which he has accompanied with fundamental basses only, and prevent the consecutive 5ths and 8ths, as direcied above. To dwell a little longer upon the delightful simplicity of the first steps in this science we will, for a little while, postpone the subject of the Dominant 7th, to point out the diversified effects to be produced by different methods of playing the same chord, which, if occasionally introduced in subsequent exercises, will render them more amusing, as well as instructive. DIVERSIFICATION OF THE COMMON CHORD. In a word of three syllables, each syllable is separately pronounced; yet it is still only one word. In a similar manner each of the three notes of a common chord may be separately sounded without in the least altering the nature of the chord. ® Tt may be observed, that these objectionable progressions will occur wherever the funda- mental bass and princips! melody ascend together one degree. 86 HARMONY AND COMPOSITION. ‘As the common chord eonsists of three intervals it may be varied or diversified in siz different groups, by employing the figures which represent the notes, in this order: 8, 5, 8,8, 5. : To form the first group, take the first three figures, commencing at 8 (as below at a). For the second group, take the three figures commencing at 5 (as at 0). And for the third group, take the last three figures, commencing at 3 (as at ec) a, 8 5 8 b 5 3 8 6 8 8 5 For the next three groups, reverse the above order, beginning at the last figure (5), and proceeding from right to left; then commencing at the 8. and lastly at the 3, In this manner we will proceed to diversify the chord of C, writing, on aa under staff, the fundamental bass, and, on the upper staff, the six diversifications, the same process serving for each of the three poxitiens. Ss q y J = tf rz a =i When a scale, or any other meivey, bas been harmonized, the che.us may ve thus diversified, selecting some one variation or group of notes as a model, and coutinuing the same through all the chords of the exercise.f The following is a melody in four parts, to which is added an accompaniment, taking for the model of diversification the Icwest, the middle, aud then the higiest note of each chord. 4 — Z. —) rok J. o- ic. 1 aie. 2 Ee oe C =| 0 +r coz t e fa aca ¢ This will be found to be a very usefnl exere're for young pianoforte nlayera. © Thies is a mark of abbreviation, denoting that the preceding gruup of notes mast be repeated. @ Consecutive 5tbe and &ths avoided, HARMONY AND COMPOSITION. 87 The harmonized scale of C, employing the different diversifications, as in Ex. 22. Ex. 88, SS See Se eee ee eee 5 ¥ co oe —— = } ee ee ee ee | Xa. eee = =I — = c a teal ated bp aloe + + (tee ee = ae Other scales and melodies may now be taken to extend this practice, oy which the student will thus early acquire ideas, as well as a facility in varying his exercises, Preliminary Observations on the Chord of the Dominant Seventh. Let it be observed that our harmonies at first consisted entirely of Conimona Chords, #. ¢., chords composed only of the intervals of the 34, 5th and 8th; until (in avoiding consecutive octaves) we introduced a new interval, viz., the 7th; which, as its name implies, is the 7th note above the bass.* This 7th we call the Dominant 7th; because whenever it is introduced into a chord, that chord immediately becomes a Dominant Chord, and leads the ear to expect the Tonic ¢ It is also called the fusdamental 7th, for a reason which will be explained here- after ¢ Ir is likewise called the added Tih; because it may be added to any common cho § For instance, in Ex. 19, VI, to the chord G we huve added the fundamental th, F, which 7th is a whole tone below the 8th. This common chord of G, by the addition of this %7th, becomes a Dominant Chord, and proceeds to the chord of its Tonic. C. N. B —It is in this progression of the chord of the Dominant fo its Tonie, that each interval has its particular course appointed, which is called its resvlution: & salise factory explanation of which will be afforded in its proper place. It is stated above that the interval of the fundamental 7th may be added to any common chord; whenever this addition is made it is usual to place the figure 7 over or under the bass cf that chord (See Ex 24 a), and this is called figuring the basa. Every bass note is supposed to be always accompanied by its common chord, according to the signature; therefore it is not necessary to figure the bass, except when ® Observe. thia 7th 1: not the 7th of the ecale, it 18 a whole tone below the 8ve of {te bass. + See philozoph'cal explanation, Ex. 48. ¢ See Ex. 52, bar 1, last chord. It is sometimes called the flat 7th, in contra. distinction to the 7th of the scale, which is a sharp 7th. See Ex 249. § To the Preceptor.—A Major chord, of course. 88 HARMONY AND COMPOSITION. some addition is made to that chord, or some alteration is required, such as any interval of the chord requiring a sharp, flat or oatural: Thus at Ex. 24 a, because the fundamental 7th to C is Bb, we have placed a flat before the 7; and in the same Ex. at 6, because the 5th requires to be made flat, we place the figure 5 over the bass, with a flat before it. But when the 4d of the ebord requires a flat, then a flat alone, without a figure, is sufficient; it being understood among musicians that « flat, sharp or natural (without a figure) placed over a bass note shall aiways be considered as applying to the third of the chord. (See the sharp alone in Ex. 25.) : When any other interval of 9 chord requires s sharp, then in figuring the bass we spare the trouble of writing a sharp. and merely make a slight dash through the head of the figure which represents ‘ne interval, as the & in the following Ex.: =ST == teas 7 | Ex. 25. Ct 8 It may be asked, ‘‘ Why is a bass figured at all?’? The answer is, “‘ That a figured bass represents, in an abbreviated form, those chords which constitute a musical composition.” This is, in fact, THoRoveH Bass. The thorough bass player is required to play the chords thus represented by figures, as if they were actually printed, as they are in the above Example, from which, if the pupil will remove the treble staff and play the chords from the figures alone, he will be a thorough bass player. Perhaps he may wonder at this, so little having been said upon the subject; yet the little that has already been said may be considered as containing all the ele mentary principles of ez ze, 2 i rim Hd ty Nites rryT 1 | rity TT THOROUGH BASS! It has been shown (Ex. 24 and 25) that the interval of the Fundamental 7th may be added to any common chord. When this addition is made, the chord becomes a Dominant Chord, and a power is communicated to it, by the addition of that interval, which irresistibly propels the harmony towards the Tonic. This impulse towards the Tonic arises principally, if not altogether, from the effect produced by the 31 and the 7th of the Dominant Chord when heard together; the former (viz., the 3d) having tendency to ascend a half tone to the 8ve of its Tonic; while the latter (the 7th) has a tendency to descend a half * tone to the 3d of its Tonie. ® We will not anticipate an observation which may be made at Ex. 53, b; and 51, ete., which ts explained at Ex, 145. HARMONY AND COMPOSITION. 3y Resolution of the 8rd and tth of the Dominant. v . a Ex. 26. by br These two intervals exercising so powerful an influence over its progression, the Cherd of the Dominant or Fundamental Tth may justly be viewed as the main-spring of the who'e machinery of harmony—it governs and directs all—the name of Dominant is, therefore, given to it with great propriety. After what has been said, it may be considered as @ law, that the several interval of this Chord, which is called the Resolution of the Dominant Th, should proceed thus:* ‘ The bass... .... to ascend a Ath, or descend a 5th to its Tonic. The 8rd of the Chord to ascend a half tone ..... - to the 8h of its Tonic. (2) Teh (Ft The 8ve —~ to remain in its place, and thus become the 5th of its Tonic. (¢) The 5th —— to descend one degree. ..... tothe 8th of the Tonic. (d) The 6th may, however, be allowed sometimes to ascend to the 8rd of its Tonic. (()) Hach interval resolved. a oy Oy Dees Oe ” (é peat == peel Ex. 27. " br by by br br eS ee ee | Allowing, then, the intervals of the Chord of the Dominant to proceed as it ppears itself to dictate, we shall find the succeeding chord will always be its Tonic, as fin the preceding Ex.}t Resolution of the Chord of the Dominant 7th in its various portions. i == ———— 2 Ee} Ex. 28. | br br br Ca. F —n t Ty t mi L mtg 22 ma) TTT? = at 1 = c TTT] =o In resolving the Dominant Chord, let the pupil first dispose of its 8rd, which must ascend a half tone, and keep in mind that the note to which this 3rd proceeds will be the 8ve of the Tonic ; then resolve the 7th, next the 8ve, and, last of all, the 5th. As it is of essential importance that he should be very well exercised in the use of this Fundamental 7th and its Resolution, we will commence a course of exercises caleus lated to bring into practical operation what has been said in explanation of Ex. 27, * The pupil is requested particularly to attend to what is here said, as very frequent reference will be made to it. ¢% To the Preceptor.—When the key is Major, of course. 4 To the Preceptor.—See Exception, Ex. 267. 40 HARMONY AND COMPOSITION, We shall begin with the chord of C, at bar 1, Ex. 29. That Chord, when heard (being merely a-common chord), produces no desire te proceed to any particular chord; we may proceed, if we please, to the chord of G (as at 2), or to any other chord, and return again to C (as at 8); the ear seems perfectly indifferent upon the subject. The case, however, is greatly altered, when to that chord of C we atid the 7th, Bb (as at 4). Then an immediate desire manifests itself to proceed to the chord of the Tonic F. By these two important intervals of the Dominant Chord (the 7th and the 8rd) we are now, as it were, compelled to allow the harmony to proceed to the Tonic at 5. The 8rd being determined to ascend a half tone, and the 7th to descend, whilst the 8th and the 5th of the chord are passively carried along to the place of their destination. At 5, we see that the chord of the Tonic F arises, as it were, spontaneously out of the resolution of the chord of the Fundamental 7th at 4. At 5, the ear would have come to a perfect state of rest; we might have ended the exercise there, but the 7th (E2) having been added to the chord (at 8), it becomes a Dominant, and the ear requires-the harmony to proceed to the Tonic Bz (as at 7), and thus we may extend the exercise by continuing this process through all the keys with single and double flats. However difficult the above exercise may seem to the eye of the young student, let him rest assured that it is only so in appearance, and not in reality. The process is - exceedingly simple, especially to one who has made himself acquainted with the flats and sharps by the method shown at page 9. If the pupil writes a similar exercise (as in the following Ex. 80), commencing with BE, it will carry him through all the keys with single and double sharps and flats, ending in D2?, This he is strongly recommended to do, as it will be found au excellent introduction to exercises in modulation. HARMONY AND COMPOSITION. 41 In coneluding the subject of the resolution of the Fundamental 7th, we shall make the followi: g additional remarks. By the introduction of this %th the progression of harmony acquires a more decided character, and produces, in effect, a certain degree of light and shade, of which a progre-sion of mere common chords is incapable; thus, the necessity of per- fectly under tanding how to employ that chord to advantage cannot be too strongly enforced. To multiply examples is unnecessary; but it is strongly recommended to the pupil frequently to play the preceding exercise with and without the 7th, by which means the ear will be early accustomed to compare and judge of the difference of effect. HARMONY IN FOUR PARTS. An instance of this has already appeared in Ex. 18, which is generally called writing in score. Hach part being vritten upon a separate staff its progression is more clearly distinguishable than when all the harmonies are compressed into two staves, as they are always written for the pianoforte. In our remarks on Ex. 18, we partially entered upon the subject of writing in four parts, taking the scale as athem». The pupil was afterwards directed to add the alto and tenor to those themes which he had accompanied with fundamental basses, and to present the consecutive 5ths and’ 8ths as shown in Ex. 19. We will now proceed to harmonize a melody, in four parts, in order to make him acquainted with another method of preventing consecutive 5ihs and 8ths, Soprano. * Alto. Ex. 31. Tenor. Bass. The consecutive 5ths and 8th appear in the above Example, in the 7th bar, where the note Eh in the alto (instead of being changed into a 7th, by the ascending of the Fundament»] bass) descends to the 5th of the succeeding Dominant Chord; whilst, at the same time, the 5th (Bb) in the tenor ascends to the 7th. Thus, the alto and tenor cross each other, or, in other words, interchange places; and therule, that ‘‘the same interval ought not to appear again in the same part in immediate succession,”’ has been observed. This, as well as the preceding method of preventing consecutive 5ths and 8ths may be employed at pleasure. The pupil may now, by way of exercise, re-harmonize in Score some of the themes already given; not forgetting to mark each interval of every chord with its proper figure; let him especially keep in mind, that the harmony which has been employed to accompany these themes has, up to the present time, consisted of common chords, only except at the 7th of the Scale, to prevent consecutive 8ves, As the importance of the chord of the Dominant 7th, together with its decided character, and the vast influence it exerts in guiding the harmony, dispensing light, 42 HARMONY AND COMPOSITION. shade and energy through the whole, have already been fully explained, it shall now be shown how and where this new and powerful auxiliary may be introduced in aharmony of four parts. The question first naturally arises, to which of the chords of the three fandamenta basses may we add it? and where shall we find room for this new interval? Answer —We can introduce it in any chord, provided the chord immediately following be its Tonic. Thus then arises the rule, “* When the bass proceeds from Dominant to Tonic, we may introduce the ith upon the Dominant. Let us now examine by this rule Ex. 81, and discover which of the basses will admit of a 7th. é Q. Can we introduce a 7th on the first note, Bb !—A. No; because Bb is not the Dominant toF which immediately follows it. Q. Canfwe introduce a 7th onthe second note, F ?—A. Yes; because F is Dominant to the note, Bb which follows ? Q Can we have a 7th on Bb, the third note —A. Yes; because Bb is Dominant to Eb, the follow- ing note.* Thus let the pupil proceed through the whcle example, writing the figure 7 over such basses as will admit of a seventh being added. Let us now inquire in which of the four parts must the 7th be written ? Ans. ‘ In that part where its resolution is found.” As the Dominant 7th resolves into the 8rd of the Tonic which immediately follows, we have only to look forward to that chord, and ‘‘ wherever in the four parts its 8rd is written, in that same part write the 7th.’’ Thus, in the following Example, 32 (bar 3), the 7th 1s written in the tenor part.—Why? Because the 8rd of the following chord is there. In the last bar but one, the 7th has been introduced inthe tenor. Why ?—Because the 3rd of the following chord is there. ee 3 1 C 3 s - 4 -: 5 Cc a &. oe 17 ee t r r Soprano. (Gxt a -—— i aH a t L i IL Lt nt Rete i. L ig af ails 1 f E t t t +r 7 t Tr t t t et = Tt [ ale SS ee Lam . * Ex. 32. vax pe. + 3 Pa 2 | EF E 5 Pee tt +—t 7 Tenor. t E F FE E >— a : Ui 7 tr ? tr Bais f z | f T +r F —— = a’ (eS Set = eH In adding the 7th to any chord, it is necessary to remark, that, as the harmony consists of only four parts, one of the parts must be expunged to make room for the %th. Thus, in the above example (bar 3, tenor), the 5th has been expunged, as marked by a dot, the 7th, F#, being introduced in its place. It will, therefore, appear that whatever interval happens to be found immediately preceding the 3d of the Tonic chord, must be taken away to make room for the 7th. Q. Upon the bass D (bar 2) can we have a 7th ?—Yes. Q. Why ?—Because D is the Dominant to the note G, which follows it. . © We are not here speaking of the Dominant belonging to the key only; but the Dominant of any ang. HARMONY AND COMPOSITION. 43 Q. In which part should this 7th be introduced ?—In the soprano. Q. Why ?—Because the 8rd of the following chord is there. This ‘s true; but if we were to introduce the 7th there, we should be obliged (in conformity with the rule just given) to expunge the note A (which occupies that part) and write C, the 7th, in its place; and in doing so, we should alter the original progression of the scale or meledy given as an exercise. Let us suppose that we are not permitted to do this. In such a case, we are necessitated to omit the 7th altogether; although from the pro- gression of the bass, it might be admitted. In bar 5, a similar circumstance occurs; the 8rd (E) of the following chord (bar 6) being in the principal melody, we cannot introduce the 7th. The pupil should now exercise upon scales in other keys, avoiding consecutive Bths and 8ths by the two different methods, and always introducing the 7th wherever the progression of the bass and the melody will admit of it. Melodies which have already been harmonized with common chords only may now answer this purpose, the Pupil proceeding always according to the routine already pointed out—thus:— 1st. Write the basses. 2d. The common chords, 8rd. Prevent consecutive 5ths and 8ths, 4th. Discover the Dominants proceeding to their Tonics, and mark them with a 7%. 5th. Introduce the 7th. Keample of a@ Melody harmonized in four Parts, with the Fundamental Sevenths introduced. s. apne Bh et eS eee aig _. a 6 Rh a a SSeS ae al 3 5_-—* 3, ¥_* 4, 5 _7t#— 1 —y = oy po tee ee el ? 7 ? q = The pupil is recommended carefully to examine the above example; first, to make his own remarks on what has taken place at every bar, and afterwards to compare them with the following observations, Bar 1.—Though the first Bass note is the Dominant to the second, still the 7th is not intreduced, because the 8rd of the following chord is in the principal melody. Moreover, it is not usual to commence with the chord of the 7th, although there is no absolute law against it.* In this first bar, also, where the Bass ascends one degree, the consecutive Gths and 8ths are prevented by the second method, that is, by the crossing of the parts. Bar 2.—In the alto, appear two 8ths in immediate succession. How can this be allowed? Because that part (the Alto) and the Bass proceed by contrary motion.t ® See Ex. 87. + This may be considered as a general role, ‘‘ When one part ascends, while another descends, they proceed by contrary motion.” “4 HARMONY AND COMPOSITION. Bar 5.—There appear to be two chords over one bass note; but these are merely the same chord in two positions. Bar 7.—The figure 7 is placed over the jirst note only of the Bass. It must be understood that a line drawn from any figure and extended over other bass notes, sig- nifies that the interval which that figure represents shal] be continued in all the chorda over which the line is extended. Now, let the pupil pause and reflect on the progress which he has hitherto made and on the effect he was able to produce by the application of the materials with which he has already been furnished; and as this will be productive of the best effects, and cannot be too early or too frequently put into practice, let us take a retrospective view, commencing with Ex.4%7—8, where Melody and harmony having been described and illustrated, we proceeded to the discovery of the Fondamental Basses (Examples 9 and 10), by which we found that, in Example 11, - The 8d, 5th and 8th of the Scale were seiirainsaite by the Tonic, The 2d and 7th......... eae . .by the Dominant, The 4th and 6th.......... by the Sub-dominant, which we called “the first rule of harmonizing.” By this rule we were enabled to write the Funda- mental Basses to a scale or melody (Ex. 14,15). The chord were then added (Ex. 17), producing « tarmony of four parts, subsequently appearing in score in Ex 18. In preventing consecutive 8ths we were intrcduced to a new interval (the Fundamental 7th, Ex. 19 which was afterwards interwoven, and variously employed in producing new effects and in avoiding the monotony which, from a too frequent succession of common churds, would eventually arise. Having now availed ourselves of all the variations of effects resulting from ‘he application of the three Fundamental Busses, according to first rule, let us see whether we cannot produce a still greater variety, by some change in their application. We shall find that an oppertunity presents itself, arising fromt the introduction of the Fundamental 7th (as in Ex. 33). On examination, it will/be perceived that the 4th of a Scale is, in fact, the Funda- metal 7th of the D minant of that Scale; consequently we may accompany the fourth of the Scale by the Dominant, as its bass, provided that the fourth, on this occasion, in its progression, descends one degree.* This we shall call The Second Rule of Harmonizing. “When the 4th of the scale descends one degree, it may be accompanied by the Dominant.+” ? AZ 2 = iF = e rH ae (@) ® ; SS SSS SF At a, the 4th is accompanied by the Sub-Dominant, as heretofore; at b, by the Dominant. Here we see that, by anew application of one of these fundamental bases (viz., tle Dominant), a new effect is produced, not only as it respects the interval of the 4th itself, when heard in conjunction with the intervals of the D»minant Chord, but also ¢ Why this proviso 1s necessary, will be evident when we consider the progression of the 7th, which, in ite resolution, is required to descend one degree. ¢ Instead of the Snb-Dominant. HARMONY .AND COMPOSITION. 45 as regards the new progression of the Alto and Tenor. Compare I. with IV. in the following Example: The Second Rule Illustrated in Four Parts, At I, the 4th of the Scale (F) descends one degree to EH, and we have accompanied it by the Dominant, G. When the 4th of the Scale in descending is thus accompanied, -let the 8rd of that chord (the Dominant) be written in the Alto, and the 8ve in the Tenor, as at I; otherwise the 8rd of the chord will be excluded at II, or the concludiug ehord will want its 5th, as at III. In both these cases one of the chords would be in- complete, which should be avoided. It need scarcely be stated that, when the 4th of the Scale ascends, if cannot be accompanied by the Dominant, because its progression would be contrary to the resolution of the 7th*. Observations. Although the primary object in introducing the second rule is to produce variety, and open a more extensive field for the employment of one of the Fundamental Basses, yet another and important object is also attained by the employment of that rule. It is a general principle in harmonizing an air, that the key of that air should be established and impressed upon the ear as soon as possible; this can be effected only by the introduction of the Dominant. The second rule affords us this opportunity. See Ex. 86 a, where, the fourth of the scale descending, we have accompanied it by the Dominant, by which the key becomes established; but at b, where the 4th again descends, we have accompanied it by the Sub-dominant; the necessity of establishing the key here no longer exists, and it would have exhibited a want of taste as well a judgment, had we again accompanied it by the Dominant, as will be evident if we examine the harmony at a, and compare it with that at b. These fw observations, if carefully attended to, will suffice for the present to show how the pupi. may emplov the second rule with propriety and effect. ascent Se b& a + — ; = = ES t | f ————— QO } x + 4 al jaa Ty r = = er tH £ FE £ br 3 ' 3 - — rE 7H : ———— tH br ma ot = — ——— — Hy When the fourth of the scale is repeated and then descends, it is good to employ © An apparent exception to this rule shal) be stplained hereafter. 36 HARMONY AND COMPOSITION. both the fundamental basses—firat the sub-dominant, and then the dominant. (See the following Ex. @.) But let the pupil be careful he does nct employ the dominant first, and then the sub-dominant; for in that case the fundamental seventh couid not be tesolved. (See 5.) Pe se a oa = —, a. a G < fb ——t —. | <7 — TH 5 — ft tf E rf Z Zz = ee — }—= [os i at c 1H 7 a = ce Vt Z a: TT HH. \ an. ——, J. Ba — 1 fs — | —F 1H {om d Cea Li. it t To of ao Ex. 37. ; — pb +. T. 7}. T ae aL iz + [ iH) Hi H — f Ht = —— 5 t = C i at U: py =I I a1] a o ao Co ao => So = br ' . = {ez tee = sh Se iL 5% i 1. TT. NC Ee hn eee ae iO: fj th i ae ole aD It is not usual to commence a composition with the chord of the seventh (although there is no absolute law against it) Should we, however, be inclined at any time to introduce the fundamental seventh upc the first chord of a melody, it will be better to let the chord be first heard us a common chord, and introduce the seventh only on the latter part of it (as in the tenor at ¢). In order clearly to ascertain the variety which has been produced simply by the introduction of the second rule, the pupil should harmonize the fourth of the scale descending by both rules alternately, noticing particul rly the change which takes place in the inner parts. Themes for Exercises on the Second Rule*. ot a a 2 = Ro ats ed No. 2. : =e a Sees os cee oes cee ge eel os ae oe fe pee ee + v No. 3. 3 1 2 2 + = s5—e—f eee co (aan 2 dock F=é — T t f-2-8— = E No. 4. - pee? pF 2 T ei Ge — 7. Lire. TL 1 1 ad =, [ [ Cy t - LT EF t ze pt + Da iL | f E p= =F = co t t No. 5. 7 i a ee co y. £ 1 ae 7 Ts = = a a eee + No. 6. e é ae: mene Pe ea P eee as = —, —| — E+ Pet Et —_o eee tse ean oe ) i t i it 1 z: ——-- T = i ii * The figures placed over the notes point out the rales to be empl >yed; 1-2, thus placed over a mote, denotes that both rales are to be employe? + See Ex. 42 and Remarks; also, page 45 ¢¢ seg. See Ex. 97 (a). HARMONY AND COMPOSITION. 4 The intelligent student must, ere this, have observed that when only the first rule of harmonizing was employed, no judgment was necessary in selecting the fundamental basses, and finding the harmonies: the question was simply—‘‘ what part of the scale is such a note, and what is its fundameutal bass ?”’ But, by the introduction of the second rule, the case is very different; because, as the fourth of the scale in descending has now the advantage of being accompanied by two bases, and as a choice is thus presented in selecting either one or the other, the judgment of the pupil is required to be exercised in this selection. Hitherto, as far as regards harmonizing airs, he has been, as it were, in leading strings; now he is beginning, it may be said, to walk alone; and as this is the very first step toward the cultivation of his judgment, let him exercise it in harmonizing the pre- eeding melodies—remembering that, even when the fourth of the scale does descend one degree, he is not obliged to accompany it by the Dominant; this is left entirely to his own judgmert: but when it ascends, he is obliged to accompany it by the Sub-Dom- inant only. We are now to suppose the pupil to have harmonized the preceding melodies according to the second rule—that he has played them, examined the different effects— and attained a certain degree of facility in judging correctly and readily as to the best mode of employing the three fundamental basses. Thus prepared, we shall proceed to show him how, by a new and varied application of another of the three fundamental basses, the harmony may bestill more enriched and improved, and a greater variety of effect produced. In the preceding examples, the fourth of the scale came under consideration; in the following, the eighth of the scale shall be our object. We are aware that, accord- ing to the jirst rule, the eighth of the scale is accompanied by the Tonic; but it shall now be shown how ¢hat interval (under certain circumstances) may be accompanied by the Sub-D-minant instead of the Tonic. This we shall call The Third Rule of Harmonizing. ‘* When the eighth of the scale is repeated, it may be accompanied by the Sub-Dominant instead of the Tonic).” At a,in the above example, the chord of C being repeated five times, a very monotonous effect is produced by the application of the first rule only. This, however, is avoided by the employment of the first and third rule alternately, (as at 0 c.) 48 HARMONY AND COMPOSITION. Although this rule has reference particularly to the eighth of the sesle when repeated, yet it may occasionally be employed where that interval is not repeated (as at d aud ¢); but, as the effect produced at d is rather harsh and unsatisfactory, the rule should, on such occasions, be used sparingly. The effect, however. at ¢ is good. What was stated respecting the effect produced upon the alto and tenor hy the application of the second rule (see Ex. 85), may be applied here also to the third rule: by the latter, it will be perceived, we are enabled still more frequently and effectively to avail ourselves of the powerful influence of the Fundamental Seventh, by which the whole texture of the harmony becomes more firmly connected and amalgamated, and also, (as has been stated before) the inner parts become, in their progression, moie flowing and melodious. All this will be evident, if the Pupil play and then carefully examine the preceding Example, comparing the monvtonous effect produced by the first rule. st a. with the Giversity of effect which arises out of the employment of the third rule at bande. : However, he must not rest here; let him also carefully examine and compare the varcety of effect produced in the progression of the melodies of the alto and tenor by the di erent application of the third rule at } and ¢. The Pupil is most particularly recommended not only to notice well what has been said, but also (in order that the value of these rules may be still more permanently impressed upon his mind and thus practicall established) to harmonize a melody by the first rule only (see Ex. 39, I), and then harmouizs the seme melody by the three rules (as in Ex. 39, II); and, if he carefully examine atid compare them, he will be surprised to find, that all the variety of effect hitherto produced has arisen solely out of the different application of two of the three fundamental basses only. Melody harmonized a-cording to the First Rule only. to be compared with Ex. 39 II. Nothing, perhaps, is better ealculated to impress upon the mind of the pupil the value and importance of these rules than the preceding examples, which he is strongly Same Melody harmonized according to the three Rules, i 2 3 + 5. 6. 7. & » HARMONY AND COMPOSITION, 49 recommended to examine and investigate with respect to the effects which they pros duce. In o.der that he may derive all the advantages which the examples thus afford, let him not pass through this examination hastily; on the contrary, let him compare the two, bar for bar. For instance; let him take the first bar of I and compare it with the first bar at II. Play each of these bars, and mark the difference of effect pro- duced, Having done so, let him play and compare the alto and tenor of each example, observing the effect of each. The advantage resulting to the pupil from this process is incalculable, because it will (even at this early stage) uake him acquainted with the practical part of that harmony, without which all his theoretical knowledge is useless. * We shall now proceed to explain Ex. 89, LI. In bar 1, the seventh is introduced iu the alto. Why? Because its resolution is in that part, and it is thus introduced only on the latter part of the chord, in order that the harmony may commence with the common chord of the tonic. + In bar two, the seventh is introduced in the tenor. Why ? Chr 60 iessicindicwedacscavecsseeveeseewisuiceasess's’s SOPTANC. FOUL. cc cceccccscccccee cocscccsecscscs se cece tENOle AVG s 6:5 sis cassis yasscososeiaoncaeseumsease one ve witty SIX: dasiiniassewisaviareisaiideeis ees setae aeiteiees eae CONOKs N. B. Where one Dominant Chord is immediately succeeded by another, the third of the jirst D minant needs not ascend, but may descend and become the seventh of the following Dominant Chord, as in bars 4 and 6 alto. This may be considered as a general rule. ¢ The following melodies, although written expressly as exercises for the third rale, are so constructed that the second rule can be introduced with equal advantage. Trey should be harmonized by the pupil in a variety of ways; and, in doing so, he mav he considered as having entered upon the second step in the improvement of bis judg- meut with respect to effect. Themes for Exercise on the Third Rule. No. 1. See Retrospect, pages 54 to 56. i See also Ex. ‘7c, and remarks 46. ¢ Obeerve how a similar progression is treated, Ex. 41, bar. 5 where the 3d of the Dominant the ie has ascended first to the octave, and afterward descended on the same bass to the 7th; alsq bar 10 in the tenor, same Ex. § See consecutive 6th and Sth, Ex. 81. 50 HARMONY AND VCOMPOSITION. We shall now explain The Fourth Rule of Harmonizing. “ The Fifth of the Scale may be accompanied by the Dominant.” Hitherto the fifth of the scale has been accompanied by the Tonic only; but, as by the fourth rule (as shall be shown presently) we are enabled to accompany that interval with two basses, a still greater variety will be thus introduced into the har- mony; chiefly su, when the fifth of the scale is frequently repeated, or heard in notes of long duration. In the following example, at bar 1, the fifth (D) being four times repeated, wae have, upon the second D, introduced the fourth rule ;-and thus the monotony, which by the employment of the first rule only would have been unavoidable, is here pre- vented; a great similarity appears to exist, in this particular, between the third rule (Ex. 38) and the fourth; as will be perceived, if we compare bar 1 in the present example with bar 3; in which latter, the octave being five times repeated, the third rule has been opportunely introduced to prevent monotony, similar to the fourth rule at bar 1, : At 5, is shown how the fourth rule may be employed, although the fifth is not repeated. Py z = ra 8. 6. 7. 8. tv Let the Pupil now carefully examine the following ex+icise, in which ths preveding four rules will be found combined; and, in order that he may discover, without any d:fiiculty, how and where each rule has been introduce’, figures are placed cver the notes (as in the Themes), pointing out the particular rule that has been employed.’ The Four Rules combined. 4 5, 6 8 1,3 Ex. 41. HARMONY AND COMPOSITION. 51 At bars 1, 9, and 10, Eb (the fifth) being a note of long duration, we have employed the first and fourth rules alternately; thus monotony is prevented and variety introduced. N.B. When the fourth or the third rule is employed, the seventh will be found in the alto. Observe the progression of the inner parts, arising out of the application of this rule. At bar 3, the fourth of the scale (Db), in descending, is enriched by both the Sub- Dominant and Dominant harmonies. Had that interval been accompanied by the first rule alone, we should have deprived ourselves, not only of these harmonies, but also of that very important interval, the Fundamental Seventh. In bar 5, the eighth, being repeated, has been accompanied alternately by the first and third rule. By the employment of the latter, the seventh appears in the alto. Examine bars 6 and 7, and observe the different effects produced by the same progres- sion of intervals—by the first rule at 6 and by the second rule at %. Which of these would the pupil prefer? !! It will be exceedingly improving to follow up what has been here said, by har- monizing the above (or any other medley) in a variety of ways. For instance: let it be harmonized first by the first rule only; and at that stage compare the progression of the harmony (especially of the inner parts) with the aboveexample.* Afterwards, har- monizing it again by the second rule, comparing that harmony with the former. Then by the ¢hird rule, and, lastly, by the fourth rule; the pupil still continuing his observa- tions and remarks as he proceeds. Then, and perhaps not until then, WILL HE HAVE LEARNED WHAT THESE FEW SIMPLE RULES ARE CAPABLE OF ACCOMPLISHINGt!! 1 Themes for Hzercise on the Fourth Rule. No. 1. pet — 5 = ee aT + : a a {E a 1 SS A ee et [ yew * See specimens, Ex. 89, I, I. t See Retrospect, pages 54 to 56, and Ex. 48, B, C, D. * See consecutive 5th and 8th, Ex. 81. How prevented, HARMONY AND COMPOSITION. Enough has now been said upon this subject to guide the choize on all future ocea- sions: we shall only add, that, in harmonizing a medley, each interval should be care- fully examined, in order to discover whether it admits of two basses; and, if so, whick of them will be most effective. The following specimen may probably suffice to show the process of reasoning in the selection of the basses: aaaaa— e—~ 2 i. SS ee >i 2 — Ex. 42. 2 — + re - f = t t T it t _ Let as suppose that, in the course of a medley, the fourth of the scale were to appear as in the above example. How ought we to accompany it ? The jirst F (bar 1) we would accompany by the second rule (the Dominant), because the second F (bar 2) ascends, and therefore we are compelled to accompany it by the Sub-Dominant, it is evident, therefore, that had we accompanied the first F by the Sxb-Dominant, we should have deprived our- selves of the variety produced by the harmony of the Dominant, which would have been an error ig Judgment, inasmach as neither of the basses are absolutely wrong. Would it be permitted to accompany the descending fourth at a by the firet rule ? No! because it wonld produce consecutive eighthe with the preceding chord; therefore the fourth can here be accompanied only according to the second rule; viz., by the Dominant. CHARACTER OF THE FOUR PARTS IN HARMONY. This will show us that, whilst only the first rule for harmonizing a melody was known, little reflection was necessary to accomplish that end; but now we are led ta consider the consequences of every step we take: the melody must be carefully examined; a certain degree of foresight and circumspection employed in forming the pian for the succession of the several basses; and, finally, the judgment is called on for the selection of those which are calculated to produce the best effect. One reflection is here very satisfactory; viz. that, though it is possible we may err in mere matters of taste, we are sure, by attending to the rules, to be always gram- matically correct, and that a moderate share of care in the application of those rules already given will produce results which could be little anticipated by those who have studied harmony by any other process. Definition of the peculiar Character of the four Melodies in a Progression of Harmony. In order clearly to comprehend this subject, it is necessary again strongly to impress upon the mind of the Pupil the importance of the chord of the Fundamental Seventh, and the almost irresistible influence which it exercises over the whole body of harmony. That chord not only invigorates and gives life to the whole, but each interval of the chord, having its own peculiar progression*, communicates to the melody of which it forms a part, a character also peculiarly its own. The soprano progression is produced, and distinguished from the rest, by the two intervals of the Dominant Chord which proceed direct to the octave of the succeeding Tonic; viz., the third ascending half a tone, or the fifth descending. (Hx. 43, a,) The alto progression is distinguished by the interval which remains in its place and becomes a fifth in the succeeding Tonic chord. @.) The tenor progression is distinguished by the interval which proceeds direct to the the third of the Tonic, whether descending from the seventh, or ascending from the fifth. (e.) e an deviation or departare from theestablished and settled progression of each of its intervals ean only be considered as a licence, employed to produce some pecuiiar effect. See false cadences— suspended cadences—equivocal modulation—-and deceptive modulation. HARMONY AND COMPOSITION. 53 The bass* progression is that interval which ascends a fourth. or descends a fifth; or, in other words, that which proceeds directly from Dominant to Tonic. (d.) m Soprano. ALTO. TENOR. = eee ae £ Hf i +H Ei LL _ TT - tt i Ti 1. + i 51) == 3: i Es Ty e/ — 2) a. Ex. 43. a & 6 Bass, a. > — x TV T —_— r V2 ™m .- 4. LI. | Ws i. A i cE TH 4 2 4¥ 1 ik es = tT i= ion, Wi x at it ; i. 1 8 Ir 5 RICE To The Pupil is here assured, that however unimportant the preceding matter may appear, it is nevertheless of very great importance. Let him keep in mind, therefore, what has been just said, and he will be enabled to enter still more fully into the nature and spirit of the preceding rules, aud the principle on which they are founded. With some of the advantages resulting from their application in harmony he is already familiar; but how comprehensive they are in their object, and how productive (when judiciously applied) in effect, can only be discovered and appreciated by those who will carefully study and practice them! ! It will be found that, in harmonizing a melody by the first rule, each of the four parts retains its peculiar character throughout. (See Ex. 48, where the seventh is always found in the tenor.) From this it is evident that, had we continued to harmonize by the first rule only, monotony must have been the result.¢ By the application of the other rules, however, a variety of effect is produced by an interchange of character among the four parts. This peculiar interchange of character may, perhaps, be more clearly distinguished by directing the attention especially to that part wherein the seventh of the Dominant is found. . In Ex. 50 I, The tenor character (the seventh descending into the third of the Tonic) is in the soprano part. The soprano character (the third ascending into the octave) is in the alto part. The alto character (the eighth remaining in its place) is in the tenor part. The ass retains its own character. N.B. The above interchange of the parts has been effected by the second rule. We may hereafter have occasion to observe more at large on this characteristic distinction of the four parts; at present, we shall content’ ourselves by giving the following table, to show the various interchanges which are effected by the application of the four rules. When harmonizing by the First Rule, the an will be in the tenor. Brd oe eeeeeeeeee- SOprann, Sth. s+. sesceeee alto. (Ex. 47, 48.) When harmonizing by the Second Rule, mie will be in the Bepranos TU. eavceccece eallO. Bth........ . ....tenor. (Ex. 51.) When harmonizing by the Third Rule, the 7th will be in tha alto. 18.h...... eeeoes SOprano, Brd.....05 eo... -tenor, (Ex. 54, II.) When harmonizing by the Fourth Rule, the 7th will be in the alto. 8th..............Soprano. Brd.....eeeeee--- tenor. (Hx. 56.) ® The fundamental bags, of course. + It is true that by inversion this monotony might be obviated; but we are not advanced yet 80 far. +t This admits of a slight exception ; see Ex. 82, bar 2, where, the 5th being in the soprano, the 8rd is in the alto. See also Ex, 43, bar 1, where consecutive 6the and Sthe have been prevented. 54 HARMONY AND COMPOSITION. From all that has been said upon this subject, it is quite evident that, without the aid of the Fundamental Seventh, we should have been without any light to guide us on our way through the mazes of harmony. Without the aid of the four rules for harmonizing, we should have remained ignorant of the variety which has been produced through their instrumentality; for, let it be remembered, withow. a single addition to the three original fundamental basses, and without having changed a single note of the melody, we have (merely by attending to the rules ) been enabled to effect not only new combinations in harmony, but likewise new progressions in the alto and tenor, which ( when we arrive at Inversions ) shall be introduced into the bass also. A concise Retrospect of all the Four Rules in harmonizing, with a few precautionary hints for preventing improper Progressions, which might occur by an injudicious and indiscriminate introduction of those Rules on some occasions. It has been stated elsewhere,* that, when only the first rule of harmonizing was employed, no judgment was necessary in selecting the fundamental basses: the Pupil, at that stage, was (it may be said ) not a free agent; for every note in the melody, according to that rule, had its specific bass appointed; from which he was not allowed to deviate in the slightest degree. By the introduction of the second rule, however, his sphere of action became in some degree enlargedt: two basses, under certain circumstances, might then be employed to accompany the same interval of the melody; and as a choice was thus presented to him, he had to make a selection; and as the proper selection depended on his own judgment, so the employment of the second rule was the first step towards forming that judgment. In illustration of this, we shall suppose the Pupil—in his first effort to harmonize by these rules—to reason thus: — ‘‘Here is the 4th of the scale (for instance), the fundamental bass of which is the Sub-Dominant ¢’’— He would then carefully examine the progression of that interval,— whether it ascended or descended one degree. If it ascended, then only one bass—no choice; but if it descended one degree— two basses — viz. Sub-Dominant and Dominant §. —‘‘Which of these shall I employ?’’ — (For let it be remembered that, although the fourth may descend one degree, he is not compelled to employ the Dominant; that would counteract the very object contemplated. ) Suppose that the melody at I in the following example were presented to him to be harmonized. ‘Probably he would reason thus, and say —( pointing at bar I) — ‘‘ Here is the 4th of the scale; it descends one degree; I will accompany it by the second rule” —(the Dominant.) (See II. bar 1.) Ex. 43. (Pointing at 2, he would say)— ‘‘Here the 4th descends again; but I will now accompany it for the sake of variety by the first rule (the Sub-Dominant ) ; and at 3 by both basses.” * See page 47. + See pages 45 to 46., + Referring to the jirst rule, which must constantly be kept in mind because the others emanate from it, See first rule of harmonizing, page 29. § See second Tule, page 44, ; HARMONY AND COMPOSITION. 55 This, it is presumed, will suffice to show what may be effected by small means, viz., the employment of the second rule. By the introduction of the third rule,* the sphere of action—already enlarged by means of the second rule—became still more extended, and formed the second step towards the improvement of his judgment. Finally, by the addition of the fourth rule,t he was altogether emancipated and set at liberty from the trammels in which he was bound by the observance of the Jirst rule. ; ; . Let the pupil, however, remember that in proportion as this liberty opens an extensive field for the exercise of his mental faculties, so, in the same proportion, will he be liable, (unless caution be observed), to fall into error: for, to be ac- quainted with rules, to know when and where they can be employed, and (we shall add) even a knowledge of the variety of their effects, is not sufficient; care also must be taken, when they are employed, that the purity of the harmony be preserved, that no improper progressions (consecutive 5ths and 8ths) be allowed to make their appearance. To preserve this purity in the harmony, observe the following Precautionary Hints respecting the employment of the Four Rules. We will commence with the third rule.t’ Let us suppose the pupil. about to harmonize the following example 48 C, I. He would reason thus, saying — ‘‘ This is the 8th; its proper fundamental bass, .according to the first rule, is the tonic,{ but as the 8th is here repeated, I can accompany it by the subdominant.§ Is it proper to do so? for, though the 8th is repeated, does it follow that I must necessarily accompany it by the subdominant ? If I do, may it not effect the purity of the harmony? How shall I know?”’ _These are questions of no small import. The answer is: Examine carefully the progression of the melody, see whether the interval immediately following the 8th will (when accompanied by its proper bass) produce either a consecutive 5th or an Sth. Should this be the case, the FIRST RULE ONLY MUST BE EMPLOYED. At I, in the following example, the 8th is repeated, and accompanied by the third rule; but, as that interval is followed immediately by E (the second of the scale, which requires to be accompanied by the dominant), the employment of the third rule is here improper, because consecutive 5ths and 8ths are thus inevitably produced. Under these circumstances, the first rule only must be employed (as at II). 3 5 8 5 5) 38 5 Ex. 43. c. At III, the 8th is repeated, and accompanied by the third rule; but this note is immediately followed by A (the 5th of the scale), and as that interval requires the tonic, consecutive 5ths and 8ths are the result; therefore, the first rule only can be employed (as at IV). Let the pupil examine and make his own observations upon V, VI, VII.—Q. May the third rule be here employed with propriety? Hints respecting the Employment of the Fourts Rutt. Looking at the following Ex. 48, DI, the pupil would say— “This is the 5th of the scale; its proper bass (by the first rule) is the tonic, but as the fifth of the * Page 47. + Page 50. $ See page 29. § Page 47. 56 HARMONY AND COMPOSITION. scale is here repeated, I may accompany it by the dominant.” (Whether we should do so, will depend upon the intervals which follow.) This fifth A is repeated; yet, in consequence of the interval which immediately follows, it would be highly im- proper to accompany it by the dominant; because as G, the 4th (which here ascends), must be accompanied by the subdominant,* consecutive 5ths and Sths would be the inevitable result. The case is very different at II, where, the 4th having descended one degree (thus admitting the introduction of the second rule), the fourth rule may be legit- imately employed upon the 5th of the scale. At III, the harmony (though similar to that at I) is correct, because it proceeds by a motion contrary to that of the bass. In conclusion, it may be well to observe, that the above hints, if carefully attended to by the pupil, will not only guard him against gross faults, into which young composers are liable to fall, but they will also add greatly to his practical knowledge as regards the introduction of these rules with the best effect: and further, the reflections and reasons which are here supposed to direct him in the choice of proper harmonies, although stated in a few words, contain the germ of many reflections which, by analogy, may be applied to other purposes besides music. , Major and Minor. It has been our object, from the commencement, to lead the mind gradually to the attainment of harmonizing a melody in four parts. We have, therefore, care- fully avoided all matter which could in the least interfere with our object, or cause the slightest embarrassment. The pupil may now be informed that every exercise in which he has hitherto been engaged was written in what is (technically) called “‘the major key,” in con- tradistinction to that called “‘minor.”” But, before we proceed to the subject of the major and minor keys, it will be proper to explain the construction of MAJOR AND MINOR CHORDS.{ These terms, major and minor, refer here to the third of the chord only, which is major or minor, as it may contain a greater or less number of semitones. All the chords hitherto written have been major, containing jive semitones in the third, commencing with the key-note, and calling that one. a. Major Chord. b. Minor Chord. ff +H a Bo vo. 4" 5 ay oe ge- ¢ Se 3 I. 2. 3 4. I. 2. 3. u Sa The minor chord contains in its third, four semitones only (b), which, as it has one semitone less than the major, is called minor. * See Example 42, and Remarks. + See Ex. 144, where the nature and origin of the minor scale are fully treated upon. At the \t wonld not be advisable to enter upon the subject. y Pp present stage, HARMONY AND COMPOSITION. 57 All chords are understood to be major, if not otherwise marked or expressed. To change a major into a minor chord, we have only to lower its third a semi- tone, and the chord becomes minor, thus: — What is the chord of C? Answer — C, E, and G. What“ “ “ = of CG minor? —_——-C, E flat, and G. What is the chord of D? Answer— D, F#, and A. What ‘6 “ “ of D minor? ———_-D, F, and A. What is the chord of Eb? Answer—Eb, G, and Bb. What‘ “ ‘ of Eb minor? —— Eb, Gb, and Bb. In order to accustom the ear to distinguish the difference of effect, a chord should be frequently played alternately major and minor. Minor. Major. Minor. Major. Minor. * EF ff = = —e = Ft —e Ht 2 — —— I. Ike III. bk b t q = TT. ae } tome iT E +h oa Ht fe Ht ci fae +H E; iT f O Anca Te Major. Minor. Major. Minor. Major Minor |e b . Bs Having now fully explained thé construction of the minor chord, we will here show, though the subject will be hereafter resumed, ite TTT! HH Fl How to find the Numbder of Sharps or Flats belonging to any MINoR Key. For this purpose, it is only necessary to ascertain the third of any minor chord, and whatever sharps or flats are required by that third (if taken as a major key- note), the same number are required for the minor. AtI, the chord of C minor is C, E b,and G; the third of this chord is E b; ; the key of E b requires three flats, therefore the key of C minor requires three flats. Atl, G minor requires two flats. Why ?— Because its third (B b) requires two flats. Why does the key of E minor require one sharp? — Because the chord of E minor is E, G, and B; G is the third, G requires one sharp, therefore E minor requires one sharp. The Relative Major and Minor Keys. It is necessary to mention that each major key stands in intimate relationship with a minor key, called its relative minor. This relative minor is always found four semitones below the key-note of its major;* and has for its signature always the same number of sharps or flats as its major. What is the relative minor to C? Answer— A mjnor. Are there any sharps or flats in A minor? Answer—No. Why?— Because the key of C major has none, What is the relative minor to F?: Answer — D minor. How many flats has D minor? Answer— One flat. ways Because F, its relative major, has one. What note is flat? Answer —B The following example exnibits a regular progression through the whole circle of major and minor keys. It commences with the key of C major and its relative minor, proceeding through the keys requiring flats, which gradually increase in * The pupil may find this minor key on the pianoforte by counting four semitones from the key-note to the left-hand, counting the key-note one. 58 HARMONY AND COMPOSITION. number until, arriving at Eb minor (six flats), that chord is changed enharmoni- cally to D ¢ minor (six sharps); after which, by sharps (which gradually decrease in number) the progression returns to the original key. freee ee =) a b - b ts b bs b OF 6 SS SS Se Se — Enh. a Se Ee bs : 4 \ tO BHC ‘ 5 ‘ & Hy — |=. | —* es || | |~¢ { | |- == F 5 — | Se | pe] = | In examining the preceding example, we perceive, from the beginning to the end, not only a beautiful symmetry and regularity pervading the whole, but also a double union of intervals — two of them always remaining undisturbed, —as show. by the curved lines.* The same union likewise subsists between the relative minor and the chord which immediately follows it; the whole progression forming a chain of harmony unequalled in any of our former exercises. The pupil is strongly recommended to practise it on the pianoforte, as it forms the groundwork on which may be constructed an almost infinite number of pas- sages and variations, serving, subsequently, as materials for more extensive exer- cise. This will in some measure appear, if we examine the specimens exhibited in the following examples, which, though few in number, are sufficient to show the extensive variety of effect which may be given, even with only simple common chords. No particular rule, as to the construction of all the variety of passages arising thus from a progression of chords must here be expected, as it would be calculated rather to cramp than to assist and expand the inventive faculty of the pupil. Let him learn to choose for himself. Ex. 47. A few Specimens of Variation which may be employed in Performance. 1 * Why this close union subsists between the chords in this progression will be better understood when we arrive at Ex, 52. HARMONY AND COMPOSITION. 59 ORIGIN OF MELODY AND HARMONY, THE DIATONIC SCALE, FUNDAMENTAL BASSES, AND MODULATION. WHEN a musical string is put into vibration, we may imagine that we hear only a single sound; but, on listening attentively, we shall discover that the prin- cipal sound, particularly if it be one of the deep tones of the pianoforte, is accom- panied, though faintly, by other sounds, called its ‘‘ harmonics.” By all sonorous bodies (a bell, for instance) the principal sound and its har- monics are produced at the same time, and are all heard at once; but by wind instruments (as the French horn, trumpet, etc.) they are produced separately, so as to be distinctly analyzed; and these prove to be exactly the same, in order and proportion, as those produced by the vibration of a musical string. Thus a tube or string, whose lowest sound is C, will introduce the following Harmonics. pol EE ov : — ot Ex. 48. 7 \e ee HH Generator. Génierator. These are the sounds in the order in which they are actually produced from the tube of the French horn, etc., etc.* The lowest sound we shall call the foundation or generator of all the rest, which are called its harmonics, and which appear to be, as it were, regular portions or fractional parts of the generator. The first note above the generator, being the octave C, may be considered as one half of the whole tube; in fact, one half of this tube would really produce, as its lowest note, this very octave C. By the same rule, G would be produced by a tube which would be only one third the size of that which produced the generator, and so on with the rest, as marked in the example. To illustrate this still further, let us extend a musical string over two bridges until its grave sound be the same as that produced by the tube C. If we then place another bridge exactly in the middle, each half will produce the octave of the whole. If we divide the same string into three equal portions, each of the three portions will produce a G; and so with all the other divisions. *In this example we see at one glance the chord of the fundamental seventh, progression, modulation, Melody, and harmony. (60) HARMONY AND COMPOSITION. 61 Referring to the scale of the harmonics in the preceding example, it will be remarked, that they are produced in a succession of gradually diminished dis- tances from each other, until they end in a progression of whole tones—a real diatonic progression, thus: — The note first appearing above its generator is the 8th. The next is a 5th above that. The distance to the next is a 4th, and the next a major 8rd, etc., etc. All the sounds, as far as E (the last note in the example), are perfect and sat- isfactory to the ear. Let us now take the three last sounds produced by the tube, as a scale or mel- ody, and endeavor to harmonize it. How are we to proceed? We must discover the fundamental basses; but by what means? Let us take, as basses, the three jirst sounds produced by the same tube, and our object is accomplished. Scale of Three Sounds with its Fundamental Basses. & 5 3 iO - fe f E +H DB: c t i 7 oe Ex. 49. : ——— Se —E EE BEE oe ee i E za FE +H] SO SSS e HH Generator... ia iat Sa LR I! GOERS Sat GB Be” sa. Be eee SaGRE vec ies se) Jor gee ses 8s a Woy UAL an Obi a The fundamental basses being discovered, we shall now add the chords. Scale of Three Sounds Harmonized. * 8 5 3 (i == | et e-—H ra ez ut S35 Ex. 50. \ , rn 3 it} | Ce. 1 TH ee ee ee ee Generator set ssi sea al CS Ge Beas ae Be eae A Referring again to example 48, 1et it be observed that amongst the harmonics of C, the 7th sound is B. This is not the seventh note of the scale of C, but the fundamental 7th, beiug a whole tone below the 8th.t When the chord of C is heard with this seventh added, it at once assumes the character of a dominant chord, and thus produces an irresistible inclination to proceed to its tonic. The ear acknowledges, in the Tth, a decided tendency to descend,t and in the 8rd, an equal tendency to ascend into the nearest sound of the . chord which immediately follows.§ Therefore, after having harmonized the scale of three sounds produced by the harmonics of the tube C (the last of which is accompanied by the chord of C), were we to bring the 7th sound prominently forward, and add it to this chord of C (as in the following example, 51, I.), we should be irresistibly forced to the chord of F (as at II.). *It will be observed that the chord of C, formed by the harmonics in Ex. 50, is nat complete until the Speer anata cy agpenin a thio e allsat it th tnd Solon oe osdy Sad wake Bae the top, the 3rd position. (See p. 26.) + See preliminary observations on the dominant 7th, page 87. +See Ex. 27 (0). § See Ex. 27 (a). 62 HARMONY «..v2 COMPOSITION. Thus, were we disposed to extend the scale further than these three sounds at I., the next sound, as here pointed out, must decidedly be F, as in the following example. Having ascertained that our next bass note can be no other than F, let us take that sound as a new generator, and treat it exactly as we did the preceding one, C. We have only to consider this new generator as a tube of smaller dimensions, and it will give us, amongst its harmonics, a melody or scale of three sounds, viz., F, G, A; to which let us write the basses, as pointed out in example 49, and we shall form a scale of six notes, properly harmonized.* Scale of Six Sounds. ; 5 ; 4 & a Se Z =] Ex. 51. L br Il. a za = rand Ht ea =H tT w TT *. Generator. =: Generator. We have now six notes, and, if we desire to extend the scale still further, to what note must we next proceed? —To Bb. Why?— To answer this question let us apply the same reasoning which guided us in discovering the second generator, F. The generator of the last scale of three sounds being F, let us add the 7th to the last chord, and the bass F, thus becoming a dominant, will lead us to Bb, and thus we gain a third scale of three sounds, viz., Bb, C, and D (as in Ex. 52, A, bar 3). Here also another 7th may be added to the last chord of this scale, which will lead us to the scale of Eb (bar 4); and thus we might continue to proceed, adding scales of three sounds ad infinitum.t Natural Succession of Scales of Three Sounds, Harmonized. 1. Le 3- Ex. 52. A. eS Generator. PROGRESSION AND MODULATION. When the harmony moves from one scale of three sounds to another, without the aid of the chord of the fundamental 7th, we shall call it simply a Progression. (Ex. 52, B, a.) When it thus moves by the aid of the chord of the fundamental 7th, we shall call it progression and modulation. (b.) be *The figures 8 5 3, 853, placed over the six notes in the above example, will explain the principle upon which the finding of the fundamental basses in Ex. 10 is established. +Itannears clear, from this examination, that no seale can naturally consist of more than three sounds, for which there are only two fundimental basses reqnired. The subdominant, which we have hitherto employed, appears uow to be really the generator or tonic of its own scale. $ HARMONY AND COMPOSITION, 63 But when it proceeds directly from the first chord of a scale to the first chord of the following scale, or, in other words, from key to key, by the aid of the chord of the fundamental seventh, we shall call it Modulation. (c). a a. 6. 1 C a Ye ~ 3ST = ae hee a ees 7 Ex. 52. B. \ bz br bz These subjects will be resumed in their proper places; meanwhile let us apply what has been already’said, in an examination of the diatonic scale, with which this work commences. I. I. ii . i! 3 = 2 —— Z FS 7H er - t fF +H Ex. 53. br 1 |e ae - : i came: i 82 th = ka ib [ sat) In the preceding example, the first three sounds, C, D, E (I.), are in the key of C. The harmony moves by progression, until it arrives at the third sound, E. Here, however, by the introduction of the fundamental ‘ith, (Bb), on the chord of C, a modulation to F takes place. (II.) When we arrive at the sixth sound (A), the ear, as far as regards the harmony, feels no natural inclination to return to the original key, as we have modulated out of that key; yet if we are determined so to do, we may return to it, but only by the same means, viz., modulation; and, as we modulated to F by C (the dominant of F), so we modulate back to C by G, (the dominant of C). (III.) It will now be perceived that, in this case, the seventh note in this scale could not be Bb, as found in example 52. It must here be Bh, because the dominant chord of G, thus introduced, requires that its third should be major, and ascend a half-tone to its tonic, C.* The pupil will now see the reason why the diatonic scale (concluding upon the note from which it set out) requires the half-tones to be between the 8rd and 4th, and 7th and 8th. Thus we complete a scale of eight sounds, commencing and ending in the same key. Had we, on the contrary, after arriving at the sixth sound (A), proceeded as in 52, A, we should have diverged still farther and farther from the key from which we set out; and, pursuing that course, we should never have been able to arrive again at the original key. It will now be evident to the pupil why it became necessary to stop the mod- ulation at the sixth sound. Here, also, he will discover the cause which produced the consecutive 5th and 8th between the sixth and seventh of the scale; for, had we continued the order of progression pointed out in Ex. 52, A, these consecutives could never have occurred. * See Ex. 27. 4 HARMONY AND COMPOSITION. MODULATION. We shall now enter more fully on the subject of modulation; it is one of great importance, and, in order that the pupil may be impressed with a correct idea of its nature and object, and of the extraordinary influence which it exercises in a well constructed composition, it is only necessary to observe, that those works which lay the strongest claim to excellence have derived it in a greater or less degree from this inexhaustible source; more especially with reference to modern compo- sitions. Here we shall observe that progression stands in strong contrast with modu- ‘lation; for, whilst the former moves and ranges amongst the chords immediately connected with the key (in other words, its generator), or such as are related to it, the latter at once carries us out of that key to another. The principle by which we are to be guided in modulation, as well as the course to be pursued on every occasion during our progress, is pointed out by Nature herself. This fact has now been so well established, that it may perhaps be superfluous to refer to it again. But let us keep our guide in view, and she will not permit us to go astray. It may be remarked, that although the modulation embraces such an impor- tant branch of harmony, and occupies a position of so much consequence, yet the principle on which it is founded is exceedingly simple. The Rule of Modulation. The dominant ofthe key to which we intend to modulate, must be introduced immediately before that key. By way of illustration, let us select the three first bars of example 61, which contain a progression through all the major and minor keys. x Zz. Progression. Modulation. : Ex. 54. cs S- br . aac TE i i Sa el ee i, Il. How shall we change the exercise of progression at X, in the above example, into one of modulation — what says the rule? Place the dominant, E (I.), before the chord of A minor, and the dominant C (IL.), before F, and thus the progression will be changed into modulation at Z.* Let us again illustrate this by the following interrogatory. Suppose we are in the key of F, and would modulate to the key of D minor; what bass must we introduce before D? Answer, A. Q. Why? Because A is dominant to D, whether that key be major or minor. Q. We are now in the key of D minor, and would modulate to Bb; what bass must we introduce before B b? Answer, F. Q. Why? Because F is dominant to B b. * When we modulate to a minor key, the 7th will descend a whole tone, instead of half atone. See puge 39. is wie us keep in mind that, whether we modulate to a major or minor key, the dominant chord must always HARMONY AND COMPOSITION. 65 In the preceding example we have shown: 1st. The nature of modulation, by placing it in contradistinction with pro- gression. 2nd. The rule by which modulation is to be effected when the key has been proposed by the preceptor. But let it be remembered that it is one thing to find the dominant when the key to which it is proper to modulate is proposed by the teacher, and quite another thing when the pupil himself is required to find the key to which he may mod- ulate. The rules by which he may accomplish this object shall now be given, and we will here again repeat what we have so frequently endeavored to impress upon the mind of the pupil, that Nature alone is our instructress; if, on a former occasion, this fact has been clearly evidenced, then the present investigation will still more clearly demonstrate that the principles of modulation emanate from the same source. ‘ It has been shown elsewhere that nature, in developing the principles of har- mony, in the vibration of sonorous bodies, etc., etc., produces certain sounds, which, in their progression, not only form melodies,* but also form a union among themselves as chords, with which thése melodies are accompanied.t These chords in their progression, thus forming harmony, participate in this unity, much in the same manner as do the sounds of which the chords are constructed.t RELATIONSHIP OF KEYS BY MODULATION. This will be rendered plain by the following diagram: — Scale a ‘i : c d e f g a fe a | 8 5 8 8 5 8 Chords . : : 5 3 8 5 38 8 3 8 5 3 8 5 Fundamental Basses c¢ g e f -c¢ 4 Generators Cc F If we examine the upper row of the horizontal figures, commencing with 8, 5, 3 (which point out the true fundamental basses),§ we shall find, by looking from C, at the figures 8, 5, 3, downwards, that they are the same figures, and express the identical intervals, or sounds, of the common chord of that note. || If we commence at D, the second note in the scale, the horizontal figures will be 5, 3.8. The last figure (8) is the first link which unites the first generator to the second. Looking downwards, the same figures express the common chord of the bass of that note. Let us commence at E (the third note in the scale). 3, 8, 5, are the horizontal figures; the two last of which, 8, 5, form two links more in uniting the first gen- erator with the second. We shall find the same figures express the intervals, or sounds of the notes of that chord by looking downwards. Here we find that the generator C is as closely interwoven with the generator F, its dominant and harmonies, as C, the former, is with its dominant and harmonies. * See Harmonies, Ex. 48, 49. + See Ex. 60. 4 See Harmony in four parts, Ex. 16, § See Ex. 49. || Ex. 50. 66 HARMONY AND COMPOSITION. The first of these generators is the dominant to the second generator, F.* Whether we view these figures horizontally, obliquely, or perpendicularly, they always form the common chord, as produced by the vibration of a string, etc. From what has been stated, would it not appear that there are certain keys, also, which stand in as immediate relationship with each other as the aforesaid chords do in their progression? And that this is the fact, shall be fully and practi- cally demonstrated as we proceed. That modulation can be effected only by the dominant ghord of the key to which we modulate, is pointed out to us by nature, and illustrated at Ex. 67 B, and 70. The discovery, therefore, of a dominant, by which we shall be enabled to mod- ulate from a given key to one of those which stand in relationship with that given key, is a matter of the first importance, and it may be said that in this consists the whole mystery of modulation. Considering the subject in this point of view, then, let us examine the chord. of the key, from which we are about to modulate, and see whether we can discover a sound in that chord, which, by being employed as a dominant, will guide us to a key with which the given key stands related; and as such dominant, when once discovered, stands in the same relation as the branch does to the tree, or a child to its parent, no doubt could exist as to the relationship subsisting between the given key and the dominant sofound. Now, that these dominants may be discovered thus, will be evident if we attend to the following simple process. We shall suppose ourselves, for example, to be in the key of C; the pupil wishes to know to what key he may modulate. Let him select the 3rd (E) of the chord C, in bar I. Write it in the bass (at 2), add the chord of the fundamental 7th, and resolve it (at 8). By this process, he is enabled to modulate to a key which stands in the closest relationship with the given key; viz., its relative minor, A. Q. Why? Baesise the 38rd of the chord of C is E, and E is dominant to A.t Observe, we are now in the key of A minor; but how shall we return to the original key of C? Does the chord, from which we selected our first dominant, furnish any note by which, as a dominant, that object may be effected? Yes; the pupil has only to select the 5th, G, of that chord, and, as G is domi- nant to C, he is enabled to modulate back again to the original key of C (at 5). From what has been shown above, the intelligent pupil may perhaps have already anticipated that — selecting the octave C (the key from which we originally modulated) as a dominant, will enable him to modulate to F, the subdominant t (at 7), and by again selecting the 5th, (G) of the original key, modulate back to C.§ * Do we not here clearly perceive the origin of the Tetrachord as well as the Hexachord of the ancients; the former ending with the fourth sound, and the latter with the sixth? See Ex. 52, A and B. And whether Guido was the discoverer of it or not, one thing is certain :—that those scales and their harmonies are as old as Creation itself. + See Ex. 59. The above modulation may be considered as the first fruits arising out of this fruitful soil. + See Ex. 58. § That the 5th of the chord cannot be employed thus at the commencement will be self evident, when we consider that that 5th is the dominant of 1'8 own key, which, while it governs the key, effectually prevents a inoi- tation ont of it. HARMONY AND COMPOSITION. 67 Thus an important and unerring principle in modulation is established, viz., vat , A major common chord contains within itself the germ of three modulations: 1st. A modulation to its relative minor, as above at bar 3. 2nd. ———————— to its subdominant, —————————- 7. 3rd. ————————- back to its own key, ————————- 59. The following general observations require to be carefully attended to by the pupil, as we shall have frequent occasion to refer to them. (m) When we select the 3rd of a major key we ought to modulate to a minor key.* Sce bar 3. (n) When we select the 3rd of a minor key we ought to modulate to a major key. See bar 5. (0) When we select the 8th of a major key we ought to modulate to a major key. Sce bar 7. ? (p) When we select the 8th of a minor key we ought to modulate to a minor key. See bar 10. I. 4. 5. 6. 8. 10. fe (2 SS eel Ex. 56. . . > = * (mn) f (n) ‘+ br (0) "+ br (Qe te t b For further illustration of what has been said, we shall now proceed to give a short practical exercise on this interesting subject — preparatory to which it will be necessary to state: ist. That we may commence our exercise with any key, and select for domi- nants any interval of the chord we please, except the 5th of the tonic. Why? — Because that interval is the dominant of the existing key, and therefore cannot, of course, carry us out of it;+ but, when we have, by either of the other two intervals, modulated out of a key, then the 5th enables us to modulate immediately back to that key. See Ex. 71, whera (at 3) we modulated to A minor, and (at 5) returned to the original key. 2nd. When a modulation out of the original key has been effected, and we desire still further to continue the modulation, then the key at which we have arrived must be treated in the same manner as if we had commenced with it. See Ex. 72, where (at 3) we modulated to A minor, and then, selecting the 8rd of that chord, modulated (at 5) to F, etc. The following exercise commences in the key of G; the first three chords pro- ceed by progression. t At 8, we have selected the octave, wd modulated to C major. (Why to C major? §) At 6, we have selected the 5th of the original key (viz., D) and modulated back to G. At 7, we have selected the major 3rd (B), which modulates (at 9) to E, the relative minor of C. (Why to a minor? ||) At 9, we have chosen the 8th, E, and modulated (at 11) to A-minor. — (Why te a minor? J) * Because it is the relative minor. t See note, bottom of p. 66. $See Progression and Mgdulation, page 61-62. § See ovservations (0) before Ex. 56, || See observation (7m), 7 See observation (p). 68 HARMONY AND COMPOSITION. Here we have selected the 3rd, C, and modulated (at 13) to F major. — (Why to a major? *) The rest of the example, it is presumed, will be understood without any explanation. nana N nT If the pupil has carefully attended to the preceding matter—studied the > examples — and reflected upon all, he must, ere this, have observed how clear, how explicit the rules are which nature unfolds for our guidance in this branch of the science; and, whether we contemplate them abstractedly as to their beauty and symmetry, or listen to the effect which they produce when played, we cannot but admire and wonder at that simple source from which all emanate. The truth of this observation will be better understood as we proceed; because, as yet, we have introduced as specimens, such modulations only as are derived from tbe intervals of a tonic chord; but as the intervals of the chords of the dominant and subdomi- nant may be employed in a similar manner, a system of modulation will be developed, . which, when thoroughly understood and carried out into practice, cannot fail to prove highly interesting and satisfactory to every lover of music. In Ex, 51, all the modulations arising from the intervals of the tonic chord were exhibited, in order that the pupil might thus be enabled at once to form a general idea of the principle upon which this system of modulation is established. In the following examples, however, the modulation arising from the 3rd and 8th of this chord shall be treated separately, as he will thus be enabled still more clearly to distinguish the peculiar effect of the modulation produced through the instrumentality of either one or the other. We shall commence our Modulation by seiecting the Octave of the Tonic as a DoMINANT. § By pursuing this process, we continue to modulate to the subdominant of the original key (or, in other words, to a key which is a 4th above|| that from which we set out), and are led through the whole of the keys which require flats, until (after having madc an enharmonic change at G-flat) we return again to C, through keys which require sharps. J * See observation (n). + See inversions of the first seven bars of this Ex., at Ex. 72, D and E. $ Except the 7th. § This is the first modulation, as pointed out to us by nature (see example 52, A). I Or 5th below, which is the same. 4 If the pupil, however, chooses to continue the exercise without making an enharmonic change (which, by way of practice, will be very useful), it will conduct him through all the keys requiring double flats, and he will arrive at D double flat. HARMONY AND COMPOSITION, 69 6. : eee br fe ee SSS ; 5 14. ese is a tt etc. te E $= 4 In the preceding example we commence in the key of C major, and select the octave C (at 1). C 1s dominant to F, therefore we modulatc to F major (at 3). Here we select the octave and modulate to B-flat major (at 5). An enharmonic change takes place (at 13) from G-flat to F-sharp, and thus, by continuing the same process, We modulate back to C. We shall now select the same interval, ‘viz., the octave from a minor key, the effect of which will be found very differcnt to that of the preceding example. In the following Ex. we commence in the key of A minor, and select the octave A. Ais dominant to D; we therefore mudulate to D minor.* ‘ The process in the following example is similar to that in the preceding, with this exception, that the modulation proceeds through minor keys, and in the for- mer through magor keys: The pupil is particularly recommended to play all these exercises, in order that he may become practically acquainted with their various effects. We shall now continue our Modulation by selecting the THIRD of the Tonic as a DoMINANT.t By pursuing this process we are enabled to modulate through all the major and minor keys. t We shall here repeat the observations made after example 41, as they are of importance. When we select a major 8rd, we ought to modulate to a minor key. When we select a minor 3rd, we ought to modulate to a major key. Ex. 59. * See Inversions of the first eight bars of the above exercise, Ex. 72, F. t This is the second modulation arising out of this principle. See e ple 40, and explanatt ¢ Soe example 46, where those keys are exhibited in progression, and compare that example with 44 20 HARMONY AND COMPOSITION. N.B. Let the pupil finish this exercise himself. It has been stated (page 68) that the intervals of the chord of the dominant and subdominant may likewise be employed as dominants. It is necessary to bear in mind what has already been stated in pages 56 and 57. From what has been there shown by several practical illustrations, it appears evident that the same connection which is found to exist between intervals forming the chord of the tonic, exists also between the three fundamantal basses — tonic, dominant, and subdominant. If this fact be kept in view, it will at once be understood how it is that those keys, which are related by MopULATION to the tonic, (as shown in the preceding example) must necessarily be related by modulation to those keys which arise out of the intervals of the dominant and subdominant also; although not in the same degree of ajfinity as those which immediately emanate‘from the chord of the tonic. With this view, we shall now proceed to select the intervals of the dominant chord, reccllecting that the jifth* and third only can be employed as dominants on this occasion. Modulation by selecting the fifth of the Dominant as a DoMINANT. t It is necessary, when modulating thus, that the dominant of the key from which we modulate be constantly kept in view; because here we have no visible intervals from which to select our dominants, as in the preceding exercise. The dots in the following example point out the dominant of the key, and also - the fifth of that dominant which is here selected as a dominant. : By this process we modulate from a given key to its dominant; for instance, from C (1) we modulate to G; from hence to D (7), and thus we may modulate through the whole circle of keys. TO THE PUPIL#$ Explain how you can modulate from C to G. At (1) Iam in the key of C, the dominant of which is G (2). The 5th of G is D (2). D is dominant to G (3), therefore I can modulate to G (4). By a similar process we have modulated to D.§ OBSERVATION. ‘When we modulate from a major key, as above, we again modulate to a major key (X). When we modulate from a minor key, we again modulate toa minor key (Y). Let the pupil pZay the above ¢zercise, and compare the effect produced at (X) with (Y). * Why cannot the 8th be thus employed? Because that interval is the dominant to the key from which we set out. + This is the third modalation arising out of this principle. + As the bass in the above modulation ascends one degree, it is necessary that the harmony proceed by con- trary motion, to prevent consecutive 5ths and 8ths. § This method of tuition will, on all occasions, be found most efficacious; it throws the studer: back upon his own resources, and compels him to reflect, HARMONY AND COMPOSITION. WW Modulation by selecting the third of the Dominant as a DoMINANT.* x. Y. a 1. 2. 3 4. 5: 6. as 8. = SS ee Ex, 61. z 3. u b 3. br bs SS SS ey j 26 C —_ f i i T —. te To N.B. By this process we modulate to the key of the third above. Explain how you modulate from C to E minor. At (1) Lam in the key of C major, the dominant of which is G (2, see dot). The 38rd of G is B (2, see dot), B is dominant to E (3); therefore, etc., ctc. N.B. When we select the third of the dominant (as in the preceding example), no connecting link is found between the key from which we modulate and the sub- sequent dominant; yet, to that very circumstance we are indebted for a beauty and effect which, when mingled with other modulations, is quite peculiar to itself; it is highly characteristic of boldness and independence. { OBSERVATION. When we are in a major key, and modulate as above, we proceed to a minor key, X. But when we are in a minor key we modulate to a major key, as at Y. N.B, In the latter case, the third thus selected must always be considered as MINOR. The following example exhibits a mixed modulation, arising from the intervals of the tonic and dominant choi Ex. 62. } At 1, has been selected the 8rd of the tonic, a major chord modulates to minor. At 3, —— the 5th of the dominant, from a minor chord, imudulates again to a minor at 5. At 5, ——-——— the 8th of the tonic, SS to a minor at 7. At 8, ————_. the 3rd of the dominant, ——~———_——__—__—_————-_ to a major at. 3. At 10, —-—_-—_ the &th of the tonic, from a major chord, to a inajor at 11, At 12, —-_—-—__—_ the 5th of dominant, to a major at 13. We shall now continue our Modulation by selecting the octave of the subdominant for a DOMINANT.§ N.B. Here, as well as in the preceding modulation, we have no visible intervals from which to make our selection; therefore the subdominant of the key from which we modulate must be carefully kept in mind. * This is the fourth modulation arising out of this principle. + When we modulate thus, iet the 5th of the chord ascend. N,B. The7th may, on this occasion, be permit ted to ascend to the 5th, the octave being omitted See Ex. 88, G. $ See Weber’s Overture to the Freyschutz. § This is the fifth modulation arising out of this principle, 12 HARMONY AND COMPOSITION. Pupil. —At X, bar 1, I am in the key of F-sharp major, the sebdominant of which is B (2). B is dominant to E, and therefore Iam enabled to moduiate from F-sharp to E (8). The subdominant of E is A (4); A 1s dom- inant to D (5); therefore, etc. OBSERVATION. When we modulate thus from a major key, we modulate again to a major key, X. (See o, p. 68). And from a minor again to a minor key, Y. (See 7, p. 68.) By this process we modulate to a key which is a whole tone below a given key; for instance, from F-sharp at 1, we modulate to E, at 3, from E to D, etc. The pupil ought to continue this process through all the major keys, as at X, and through al: the minor keys, as at Y, and by making an enharmonic change, he will return again to the original key. (See example 58, A, which bears a strong re- semblance to this.) We shall now continue our Modulation by selecting the third of the subdominant for a DoMINANT.* Ex. 64. = T 3: = f | T be: ud Ly be tC | ae f z $ ae = ee Dirteadilaacceaphdicensleiasce” Tieitnassinintnaacatee Pupil. I am in the key of C (bar 1), the subdominant of which is F (2, see dot). A, the 8rd, is dominant to D (3), therefore I modulate to D minor (4). OBSERVATION. 1st. In selecting the major third (2) of the subdominant, we modulate to a minor key (4t). We may indeed occasionally modulate to a major key (as at 10); the former, however, as being the relative minor to the subdominant, is preferable; it produces the better effect. : 2nd. It is necessary to observe that when the key is minor, the chord of the subdominant requires to be a minor chord likewise (5). And, further, that when we select the minor 3rd of the subdominant, we modulate to a major key (7).t For example, at 4, we modulated to D minor, the subdominant of which is G; and as this must be a minor chord, we have been enabled, by selecting the third, B-flat (6), as a dominant, to modulate to E-flat major (7). It has been shown that, by selecting the intervals of the chords of the three fundamental basses, dominants may -be found by. which, without the slightest apprehension or chance of a mistake, we are enabled to modulate, not only direct * This is the sixth and last modulation arising out of this principle. + See (m) page 68. $ See (n) page 68. HARMONY AND COMPOSITION. 73 to those keys which arise out of, and are immediately related to the tonic, but to those also which are derived from the dominant and subdominant. The following exercise may be viewed as an epitome of all the preceding. It contains the six modulations arising out of the intervals of the above three chords. When all these six modulations are introduced in immediate succession, the exer- cise will conclude in the same key as that from which it originally set out. I. 2 35 As 5. 6. 7,8 9. 10. In, 12 13. Ex: €5. — The preceding example begins and ends in the key of C. At 1, we have selected the 3rd of the subdominant, and modulated to D minor at 3. — 8,——_—_——_—- 5th of dominant, ———_—_-—— A minor at 5. — 56, 8th of the t. nic, ——— D minor at 7. - 7% - 3rd of the tonic, iS B-flat major at 9 — 9, —————_—__—_- 8rd of dominant (a) ———— D minor at 11. = TY, - 8th of subdominant (g) C major at 13. It matters not in what key the pupil commences the exercise, or the order in which he chooses to select his dominants; if he but carefully attend to the directions pointed out, he will assuredly be guided back to the key from which he set out. y c c iE i { eas t Te: t rE t a Tit TTT oe. TWO KEYS TO WHICH NO DIRECT MODULATION CAN BE EFFECTED. On a critical and careful review of the preceding examples, we find that, with the exception of two keys, we have been enabled to modulate direct to all the others,. whether major or minor. The first of these exceptions refers to the key which is diametrically opposite to the one in which we then find ourselves; the other is a half-tone below that key. It is curious to observe how nature has excluded these two very modulations, which would produce upon the ear an effect at once harsh and discordant. No in- terval is found among the chords of the three fundamental basses, which enables us to modulate direct to their keys. This is a remarkable fact; which, when coupled with what has been said immediately preceding, example 65, may serve as an additional proof (if it were necessary) of the unerring principles on which these modulations are established. In order to illustrate what we mean by a key diametrically opposite to another, let us draw a circle and divide it into twelve equal portions, placing C, the natural key, at the top, which, if we please, we may call|the north pole. The portions on the right, gradually approximating from the east to the south pole, may represent those keys which have sharps; and those on the left by the west, the keys which have flats. 3 Sharps. 6 Fe The pupil is recommended to play these modulations with variations, as exhibited in example 23, 74 HARMONY AND COMPOSITION. Here it is plain that, when we proceed towards the right, the key diametrically opposite to C is F-sharp; but, when to the left, the opposite key will be G-flat. If we consider this circle as representing the map of the world, then F-sharp or G-flat are the antipodes to C; G the antipodes to D-flat, etc. In order, therefore, to dis- cover the antipodes to any given key, (requiring sharps) it is only necessary to deduct the number of sharps which the key requires from six, and the remainder will point out its opposite key with flats. For example: G has one sharp; deduct one from six, and five remains;— what key requires five flats? Answer, D-flat. Then that is the opposite key. The key of B has five sharps; deduct five from siz, and one remains :— What key has one flat? Answer, F. What is the opposite key to E-flat. Answer, A. Why? Answer, E-flat has three flats — three from six, and three remains. The key of A requires three sharps, and that is the opposite key to E-flat. ~ Again, N.B. 1st. To keys which are diametrically opposite to each other, nature has forbidden us to modulate. 2nd. To the key which is found a HALF tone below a given key (the second objec- tionable key) we cannot modulate direct, because the dominant, which is required for this purpose, is that very diametrically opposite key to which we are not allowed to proceed directly either by modulation or progression. A few practical exercises, founded on the preceding rules, shall now be given; and if the pupil is desirous to make himself practically as well as theoretically ac- quainted with his subject, he ought to study and play them with variations, as in example 47, and let it be kept in mind that theory and practice must be inseparable companions. The following example exhibits a course of modulation arising from an unin- terrupted employment of the 3rd of the subdominant; and though the 3rds, selected here as dominants, are major (which would direct us to modulate to minor keys*), yet, for the sake of showing the effect thus produced, we have modulated to major keys t indifferently. Z. Enharmonic, + Ex. 66. By the above process, we continue to modulate by whole tones ascending, that is, we modulate from the key of C to the key of D, from Dto E. And although a chromatic scale is thus produced through the intervention of the dominant, yet we must not confound this chromatic progression with a modulation through the chromatic scale.§ ‘ Let the pupil continue this exercise until he arrives again at the original key. The above example, at Z, shows how a minor chord may very effectually be changed inte a major; thus not only producing variety, but preparing the ear for the modulation which follows. This will be more clearly understood in the explanation of the following example. * See observation (1), Ex. 64. +t Let the pupil himself say which of these modulations he prefers. $ See observation on Ex. 67. § See Ex. 68, HARMONY AND COMPOSITION. 75 We shall now select the octave of the subdominant. This process enables us to modulate by whole tones descending, that is, from C to B-flat, from B-flat to A-flat, etc., etc. Ex. 67. In example 66, at Z, in modulating by whole tones ascending, we changed a minor into a major chord. In this example, at Y, we have changed a major into a minor chord, because we are modulating by whole tones descending. This process of changing a major chord into a minor, or vice versa, affords an additional con- nection between the preceding tonic and succeeding dominant, prepares the ear to hear the following modulation, and softens any harshness of effect which might be produced when modulating to keys remote from the original one, called extraneous, as in the following example where we have modulated to a key within one point of that which is diametrically opposite, viz., from C to D-flat. Had the chord of C continued major, the modulation to D-flat would have been extraneous; but, by making that chord minor, the modulation to D-flat is no longer extraneous, because we modulate not from C major to D-flat, but from C minor to D-flat. If we continue this process, a modulation by ascending major semitones will be produced.* Wehave selected throughout the 3rd of the subdominant, and have thus modulated (at 3) to D-flat; but as the major semitone which follows D-flat is -double-flat, it becomes necessary (in order to prevent the accumulation of flats) to change D-flat enharmonically into C-sharp (4), and thus modulate to D (5) instead of E-double-flat; from hence to E-flat (6), then to F-flat (7); here, again, an enharmonic change must tuke place; F-flat, at 7, therefore, is changed to E-natural (8), from whence we modulate to F, instead of G-double-flat. N.B. We have changed the major chord (bar 1) into a minor; and this process has been observed at bars 5and7. When a note is raised or lowered a half-tone, and its position on the staff is thereby altered, it is cal’sd a major semitone, but when a note is raised or lowered a half-tone, without changing its position on the staff, it is called a minor semitone; thus, from C to D-flat 1s a major semitone; from C to C-flat is a minor semitone. The pupil should continue to pursue the same process until he arrives again at C, It is an exercise well calculated to show, net only the wse of enharmonic changes, but also how indispensable they are when inodula- ting into extraneous keys. It may have been remarked that, in selecting our dominants, we had especial regard as to whether the chord from which they were selected was major or minor. As this is a matter of importance, we shall proceed to point out those keys which are more immediately and directly related to major, and those related to minor keys. If the pupil has carefully examined examples 52 to 56, and comprehended what has been stated with reference to them, it will be clear that were we to set out from a minor key, the modulation would be different from that which would flow from a major key. See observation on Ex. 64, 16 HARMONY AND COMPOSITION, For instance :— Atl, the keyis C major, we have selected the 3rd E, and modulated to A minor. But at 4, the key is C minor }==—H¥-H+W¥_______— E-flat —————_ A-flat major. At 2, the key is major ————_______——_——_ the 8rd of subdom. A, ———_—_—. D minor, But at 5, the same key is minor, ——____-—-_—_——— the 8rd of subdom. A-flat —————--—— D-flat major. At 3, the key is major ———_—__—___—_—_—_ the 3rd of the dom. B, ———___—-—- E mninor. But at 6, the key is minor ———___————— the 3rd of the dom. B-flat —___—_-——- E- flat major. N.B. At3 and 6, the 5th of the dominant chords has (for the sake of effect) been permitted to ascend; in consequence of which, the 3rd in the tonic chord, which immediately follows, is doubled. In the above example, the 3rds only have been selected as dominants to show their influence; it has already been shown * that the octave of the tonic, the octave of the subdominant, and also the 5th of the dominant, exercise a similar influence, although not quite so decided. Instances of these are given in the following example. Atl, the key is C major, we select the 8ve of the tonic C and modulate to F major. But at 4, the key is C minor, Cc F minor. At 2, the key is major ———_———8ve of subdom. F - B-flat major. But at 5, the same key minor, F B-flat minor. At 3, the key is major —_—— 5th of dom, D —-~_______- G major. But at 6, the same key minor, 5th D G minor. The two preceding examples (69 and 70) plainly show (especially when played, and on comparing the different effects produced by I and II) how very much a modulation is influenced in its course by the key from which we set out, whether that key be major or minor. They also teach us, that were we simply to change a * See observation on Ex. 56, 60, and 63. HARMONY AND COMPOSITION. 77 major key (to which we had modulated) into a minor, the whole course of modula- tion would at once receive an entirely new impulse and direction; that.is, in the latter case (minor), we should be directed to those keys which are immediately related to the minor (IL., 4, 5, 6); and, vice versa, by changing a minor key into a major, we should modulate to those keys which stand in relation with the major (I., 1, 2, 3). We shall now suppose the pupil placed at the pianoforte, and about to pursue a practical course of modu- lation. He is already aware that he may modulate direct to any key except two; (the reason haz been shown in page ). We shall suppose him to be in the key of C; and instead of asking himself, as heretofore, ‘lo what key can I modulate?” let him at once say, “I wil? modulate to such and such a key.” — We will suppose him to have chosen F. His next inquiry would be: What is the dominant of F?— Answer, C. From whence have you derived the dominant? — Answer, from the octave of the tonic. I am now in F, and will modulate to E-flat. What is the dominant? — Answer, B-flat. From whence is that dominant derived? — Answer, it is the subdominant of F. Iam in E-flat, and will modulate to its relative minor, C. What is the dominant to C?— Answer. G. From whence is that dominant derived? — Answer, from the third of the tonic. I wil] modulate to G minor.—The dominant is D. From whence do I derive that dominant? (See Ex. 60, y.) I will modulate to B-flat —the dominant is F. From whence i is that dominant derived? (See Ex. 61, y,) Iam in b-flat.— Can I modulate to E? No; because the key of E is diametrically opposite to B-flat. (See Cirele of Keys, page 73.) And thus he may continue his exercise. If the principle on which these modulations are founded be well understood, no further illustration will be required; nor will the pupil experience the slightest difficulty or embarrassment in his exercise; that is, provided he is quick and ready at finding the tonic to any given dominant.* It must now be manifest to the student what an inexhausible variety of modu- lation may be produced by the application of the preceding simple rules; and, as they are based on an unerring law of nature, the learner can never go astray; it is impossible, nothing is left to chance—nothing to guess at. Let the pupil avail himself of the extensive power of modulation now placed within his reach, varying his selections from the different intervals according to his own taste; and, by fol- lowing his guide carefully, he must produce ever new, and only the best effects; all harsh and extraneous modulation being totally excluded by the rules themselves. The following example may serve as a specimen of the effective employment of the preceding rules of modulation; and it will be observed, that in this instance we have not confined ourselves to mere modulation, but have occasionally introduced progression.+ This intermixture of modulation and progression will greatly add to the general effect, and prevent the monotony which would otherwise occur.} It will be observed that, in writing the variations in this exercise, we have nct confined ourselves to the simple intervals of the chords, as in examples 22, 23, 47; on the contrary, we have employed them in such a manner as to form a variety of passages, to the construction of which the pupil is advised to pay particular atten- tion. Neither have we written the chords in that simple form in which they appeared in the preceding examples, but, in order to make the exercise as useful as possible, we have written the same chords in different positions; and, to add * This habit may easily be acquired, by simply recollecting that, in keys with sharps, the tonic has always one sharp Jess than the dominant; and, in keys with, flats, the tonic has one fiat more. Thus, if the dominant is D, the tonic will be G. Why?— Because D has two sharps, and G butoze. If the dominant be E, the tonic will be C-flat. Why?— Because F has one flat and B-flat has two flats. + These progressions are pointed out by the letter P. t To the professor. — It must be kept in mind that, up to the present time we have been entirely confined tc fundamental harmony; when we arrive at Inversion, our field of operation will be vastly enlarged; but how extensive will that field be when we arrive at the Inversions of the Chord of the 9th, Equivocal Modulation, ete, ete. 78 HARMONY AND COMPOSITION. still more to the general effect, some of the intervals have been doubled;* and, if they are played thus on the pianoforte, whilst another performer plays the varia- tion an octave higher, the effect will be found pleasing. To make this matter still more interesting, a few notes have been introduced into the variation, which do not form a part of the harmony, called “passing and auxiliary notes,” t into an explanation of the nature of which it is not at present necessary to enter; the subject will be fully considered hereafter. Exercise on Modulation and Progression. ee MM FS K.CUCSCSseeS ST GUE. i a RRS ee he sass TC my Ec T a 3 :. t 1 eZ io} - rt t at = ty | al Eb Te t ] k f += i t Eat ft er t 4 T r tL a a a a 38 MR ROR a or ae a ee ee * Doubling of intervals in accompaniments is permitted, and consecutive octaves arising thus, us in the present instance, are never considered as such: but we must be careful not to confound this writing accompan- tments with writing in four real parts, where every interval, we know, hasin its progressions its place distinctly pointed out. See Ex. 41, etc. + A few of these notes are pointed out by a mark, thus X. HARMONY AND COMPOSITION. 79 Pn Nore. —X, Y, W, Z, show the different ways of doubling some of the intervals of this chord. 80 HARMONY AND COMPOSITION. References to examples from which the above modulations have been selected. 1. Ex. 58 (A), 8ve of tonic.—II, Ex. 56, 3rd of tonic.—III. Ex. 60 (¥), 5th of dominant.—IV. Ex. 63, Sve. of subdominant.—V. Ex. 61(Y), 3rd of dominant.— VI. Ex. 64, 8rd of subdominant. AN ESSAY ON INVERTED BASSES. If the pupil has carefully studied and comprehended the matter contained in the preceding examples, he must have observed that the harmony employed heretofore has been deriyed from the vibration of a sonorous body:* this harmony we call fundamental; because it is the basis and foundation, the solid and primitive rock, it may be said, upon which rests the entire superstructure of musical composition. The bass of this is called the fundamental bass, in contradistinction to that which is called the inverted bass, with which the pupil shall now be made acquainted. He will have noticed the peculiarity of the fundamental bass with respect to the progression of its intervals, as compared with the progression of the intervals ~ of the rest of the harmony; for, whilst the former performed its evolutions by ex- tended distances, such as 4ths and 5ths, the latter did so by 2nds and 3rds._ This fact should be well kept in mind, and the pupil is recommended to review once again what has been said on the peculiar character of the four parts at page It is evident that, were none but fundamental basses to be employed, a great monotony would be the result; not only in the bass, but in the other parts also. By the employment of the four rules in harmonizing, without the addition of a single fundamental bass, very considerable and important changes have been effected, and variety produced, not only with regard to the harmony as a whole, but likewise as respects the individual melodies of the soprano, alto, and tenor.t However, although these rules have the power to influence the immediate progres- sion of the fundamental bass,} yet after all, they can produce ONLY common chords and chords of the fundamental 7th: all that could be effected, therefore (as far as fundamental harmony is concerned), has been effected. Our object shall now be to show how the characteristic difference, still exist- ing between the progression of the bass and that of the other parts, may be re- moved; how the bass may be incorporated with the harmony so that it shall lose (for a time at least) its individuality —that all monotony shall disappear —new effects be eliciced —and the whole harmony assume an aspect differing from any of the former, yet without altering the fundamental progression on which it is estab- lished. It has been made clear that, by the employment of the four rules, the funda- mental 7th appears sometimes in the soprano, sometimes in the tenor, sometimes in the alto, but never in the bass. If this fact be kept in mind, the pupil will almost anticipate what is now proposed for his consideration, namely, how to find a bass which shall in its progression assimilate with, and partake of the character of, the other parts of the harmony, yet without destroying, in a single instance, the foundation upon which the harmony has been constructed. An example will make this plain. * Ex, 48, t See Ex. 39, I, II. $ Bee Ex. 41, : a (81) 82 HARMONY AND COMPOSITION. We shall suppose the pupil to make a modulation from C to F, as in the follow: ing Ex. “s L Ex. 71. }GE 1 FE Inverted Bass. br ipa +} E {AS f —— —— F = Fi Fund. Bass. . ww > At Lis a modulation by fundamental basses, and no similarity of progression is perceivable between the bass (as it proceeds from tonic to dominant) and the other intervals of the harmony. But if we take E, the third of the dominant chord (as at II), and convert that interval into a bass note, a similiarity will be effected, for the bass E will then pro- ceed by one degree to the tonic F. Thus a new bass note is found; which in its progression assimilates with the rest of the parts, without changing the nature of the fundamental harmony, and also produces a new and important effect: A bass note, thus chosen, we shall call an inverted bass; and as this inverted bass occupies now the fourth or lowest part of the harmony, the fundamental bass must be expunged, as it forms no longer a portion of the four parts. The intervals, also, which are thus chosen for inverted basses (and which are pointed out by dots) must not be allowed to remain in the chords from which they are taken. As the 8rd of the chord is the jirst interval which presents itself immediately above the fundamental bass, * so when that interval is chosen as an inverted bass, we shall call it The First Inversion of the Fundamental 7th.t Let the pupil now, by way of exercise, make afew modulations, first by the fundamental bass, and then choose his inverted bass, as shown in the above ‘example: When he has written such modulations, by the first inversion as at II, played them, and formed his judgment as regards the difference of effect between fundamental and inverted basses, he may be introduced to other inverted basses; but, before we proceed, it will be necessary to enter a little more minutely into the nature of Figuring the Inverted Bass. It has been stated elsewhere ¢ that every bass is supposed to be accompanied by its common chord, and therefore requires not to be figured; but this, let it be well kept in mind, applies to fundamental basses only. With respect to inverted passes, the case is widely different; for, although the notes of the chords remain the same, yet the names of the intervals, with reference to the inverted bass, are not the same; they must now be counted from the inverted bass, and figured accord- * See construction of the common chord.-- Example 1. + Why the chord of the fundamental 7th is first selected for inversion, rather than the common chord, is, that the pupil may at once enter upon a course of practical modulation by inversion, which the latter would + have afforded. > ¢See page . HARMONY AND COMPOSITION. ingly; in fact, it is only now that the real figured bass commences, and the neces- sity of figuring the bass thus will be evident. For instance, let us suppose the fundamental basses, at II (in the preceding Ex.), together with their chords, were removed — and that we were required to play the chords to the three bass notes, C, E, and F—the performer would play three common chords; but that is not the intention of the composer; for it is intended that the inverted bass E shall repre- sent the chord of the fundamental Tth of C, and not the common chord of E. Here, then, we perceive the absolute necessity of figuring the bass, so that it shall truly represent the chord intended.* Let us now ascertain what figures are required to be placed over the bass E, in order that it may express the dominant chord of C. At I, in the following example, the inverted bass is E. From E to G is a 8rd (original 5th of the fundamental harmony). From E to B-flat — flat 5th (original flat 7th of the fundamental harmony). From E to C— 6th (original 8th of the fundamental harmony). The jirst inversion, therefore, of the dominant chord is figured thus—D§;+ no matter in what position the chord may appear. Compare I with II and IV in the following Ex. 9 rae = it ee og ey —-2 = SS SS ee SS SS : — ee Ex. 72. < 6 6 Inv. Bass. bs 3 lee: ——— i z F = =] ze ae f I T 4 N | a | a v io. { @ =k o~ o- wT Fund. Bass. = om w re ow °° At I, the 8th of the fundamental bass is in the soprano expressed by 6. AtII, the th Be At IV, the5th 3. N.B. Where any interval requires a sharp, flat, or natural, the corresponding figure must be marked so likewise, as has been already explained in page 38. The reason why we have been so circumstantial in the explanation of the first inversion is because we are now arrived at avery important branch of the practical science; and it is necessary that the pupil should, at the very outset, obtain a clear and comprehensive view, not only of tne characteristic difference which exists be- tween fundamental and inverted harmony, but also of the mode of employing them with propriety and effect. From what has been stated, it is clear, that if the 38rd of the chord can be employed as an inverted bass, the 5th of the chord may be thus employed also. * This is called playing from figured basses. +The 3rd, in figuring this chord, is generally dispensed with, except when it requires an accidental. See III, Iv. 84 HARMONY AND COMPOSITION. In the following example, at I, the dominant chord appears fundamental. At II, the 5th (G) of the dominant chord C has been selected as an inverted bass; and as the 5th of that chord is the second interval which presents itself above the fun- damental bass, we shall call it The Second Inversion of the Dominant Chord. jie I, I. _ a = = ee ee | fey Ex. 73. . Inv. Bass. 4 br se 's be ! E H = [=F y t ——— {=F H Fund. Bass. < ; = = 4 IV. g as v. eo Figuring of the Second Inversion of the Dominant Chord. At III, From the inverted bass G to B-flat tenor is a 3rd (original 7th of the funda- ‘mental chord). From the inverted bass G to C alto is a 4th (original 8th of the fundamen- tal chord). From the inverted bass G to E soprano is a 6th (original 38rd of the funda- mental chord). The second inversion, then, is always figured 3, in whatever order the inter- vals of the chord may appear. At 4 the figure 6 has a dash through the head, thus,¢; because G-sharp (the interval which this 6 represents) has a sharp placed before it. The same occur- rence takes place at 5. The pupil should now, by way of exercise, write an extensive modulation by the second inversion, and then employ both the 1st and 2nd according to his own discretion, -arefully figuring the bass, and observing to mark the sharp, or any accidental -hat may occur; he should then play the whole, marking well the dif- ference of the effect produced by the different inversions.t We shall now proceed to the explanation of the third inversion of the funda- mental 7th; it is not improbable that the intelligent pupil, if he has carefully attended to the preceding exercises, may have already anticipated the subject, reasoning thus: If we can take the 8rd and 5th of the dominant chord as an inverted bass, why not take the 7th of the chord also? In the following example, at I, we have again made a modulation from C to F, by the fundamental bass; and, by selecting the 7th at 2, as an inverted bass, have produced * See page 38, fifth line. + When the pupil is able to perform modulations with ease and facility (during the performance of which he should fix his eye as much upon the figures as on the notes), he may try to play without the notes of the treble, by covering them with a slip of paper; thus he will learn (if he desire it) to play from figured basses. Sea re marks at bottom of page HARMONY AND COMPOSITION. 85 The Third Inversion of the Dominant Chord. — I. 2. 3. IL 4. Se pci Ss oe -o- = o At a, first inversion of the dominant chord, 8, soprano progression in the bass. 6, third inversion St ————_——- tenor progression se ca re ¢, first inversion of the common chord, 6, arising from the preceding 3rd inversion of the dominant. @, second inversion of the common chord, §,--———— alto progression in the bass. e, first inversion of the common chord, 6. a J,second inversion of the dominant chord, 4 , ————-soprano progression Observation 1.— The soprano and bass, being the exteme parts of the harmony, are always the most conspicuous (that is, they are more easily distinguished than the inner parts); therefore-to them are generally given those intervals which are considered to produce the best effect, or contrary motion. See bars 8, 9, 11, 14 and let the pupil well notice the gradual descending bass in bars 9, 10, 11. Observation 2.— At f, bar 3 and 11, the 5th is in the soprano, and, according t. the first rule, the 38rd should be selected as the inverted bass; but, as that interva in its progression ascends, we have chosen the 5th for variety, by which not onl a flowing melody is procured in that part, but also contrary motion. Observation 38.—It has been shown at page 43, in what part of the harmon the fundamental 7th may be introduced; the reason was there stated, also, wh that interval could not be admitted at that time, although the progression of tha fundamental bass would permit its introduction; however, having now arrived at inversions, that interval may be very effectively employed, though its introduction can be considered only as by license; because the 7th, so introduced, will appear in a part of the harmony where the 3rd (its proper resolution) is Not found, and which in such case will necessarily be doubled. See (f), tar 11, where D-flat (the ‘ith) appears in the tenor, and resolves on C the 3rd; and as that C is found also in the soprano, the 8rd of the tonic chord is doubled. At bar 9, the licensed 7th appears in the inverted bass, and the 3rd is consequently doubled in that part and in the soprano. Observation 4.— We are aware that the chord of the 6th (first inversion of the common chord) has heretofore arisen out of the resolution of the 3rd inversion of the dominant chord*, At bar 14, however, that inversion, in order to procure a flowing and melodious progression in the bass, has been introduced unconnected with the dominant chord. Observation 5. — An inversion may be interchanged with another inversion, and thus produce a more melodious progression in the different parts: see bar 12 * See Ex. 74, bars 5, 7,9. HARMONY AND COMPOSITION. 95 where the second inversion is followed by the 3rd. Observe the interchange of intervals between the alto and bass. It would be imprudent to enter here into all the minutix of this fertile sub- ject; sufficient has been said to direct the intelligent student how to proceed; let him only harmonize and reharmonize example 88, in the variety of ways with which he is already acquainted, and then his own experience will probably teach him more than all that could be said upon the subject. Observation 6. —It has already been observed, that a strict adherence to the rules, as exhibited in example 85, may occasionally be dispensed with, when it is our object to produce variety— contrary motion — or a more effective melody in the bass; however, when we do thus depart from the observance of these rules, a slight departure from the established progression of some of the intervals of the dominant chord will also take place. This will be evident by examining the following. ee ogee ae pha eee Spears ear , 8, 8 pote 1 Li oy ho = fof. > ao CET F J. je 7 f +H eee (= ES ie Se Se eee t t o- £ t 103 i ak i ii) a. . a a TH Ex. 89. ovis Bad | +t 7: 4 1 Tf fe T cs A 7. f f Ty aH 1 it It re 1. TT 1 1. rf 1 iI 1: WW ep See eH Pee te tS teed i 6 a 6 Desi i é ERE =aE ae {l= =e a =i | eo -o -e- -~e At a, Ist rule, all is right. At b, the 5th is in the bass, and ascends. Here wehave proceeded by contrary motion; but the 3rd in the alto must, in consequence, descend on the 5th of the following tonic, to preserve the harmony complete. Atc, the 7th is in the bass, for variety. The 3rd ascends, but the alto and sorpano are doubled. Observation 7. — A word concerning the 6th of the scale descending, when it is preceded by the "th. We know that the fundamental bass of the 6th of the scale is the subdominant; now were we to accompany that interval thus in descending, after having been preceded by the 7th, consecutive 5ths and 8ths would be the immediate conse- quence (as in the above example at d); to avoid this, the fundamental bass of the 7th of the scale, instead of descending from the dominant to the subdominant, should ascend a whole tone to the relative minor of the key (as at e). The following is a ee illustration of all the Nae observations. Soprano, I. Alto. oe pb | BE aon 3 f I es eal E> c f f Ce ee er ae ee oe ea et eed v T T r v oF vtCc = Tenor. —p—p TY’ I cot 10 oe f <1 | = + f — + £ T > t hc > ca =| > = Ex. 90. Ee — Kv a iis | F 6 ieee” Bass. 4 6 bs ;- (— see aioe Fund. ee 7 bz i. = Ce Biase =e aE Lee 3 ise aS oe e eo oe 96 HARMONY AND COMPOSITION. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. oot. 1 i. 4 i is ee CC f - f cia 1 x Ti et j i L t T Th uv At. 4 7 y 4 1 } 1 Vy st Lod iz qk 1. 1 a { ee jae = ae eo pe fof il Ht. a 4. Yl T > f LC LE f£ > J_T { E% +, sti I Ss Ss a a,_t on ist J =a Sep ee ee tee eee oe I t D Hf { i i hs I rf + ae if To br 7 6 6 7 z 7 7 el Lote peat Fat Pate =r ———a 7H ee + cz. Ci L = =H a ie oe tS = a t =i At a (bar 1), the 5th in the soprano descends ; we have selected the same interval for the inverted bass (second inversion), and have made it to ascend*, producing a good effect and contrary motion. Compare this with bars 11 and 17. At d, c (bars 5 and 6), the 7th of the scale descends to the 6th; we have, therefore, accompanied the latter interval by the relative minor of the key+; the occurrence takes place at bars 13 and 14.¢ Let the pupil remember that, although our principal object in constructing an inverted bass is to produce a flowing and graceful melody in that part, as also an amalgamation of all the parts —yet the peculiar character of the bass, which consists in fundamental progression, must constantly be kept in view; see bars 5, 6, 7, 8, 9, 10, which are all fundamental progressions. He is recommended to read the remarks which have been made at the end of the treatise on modulation by fundamental basses, pages 57-58; and on all occa- sions to play what he may write; and in order to produce a variety of effect, he should arrange the same exercise in a variety of ways, of which a few specimens are given in the following examples. This, in fact, will constitute an elementary introduction to extemporary performance. In the following example is shown how the three inversions of the dominant chord only, with its resolution, may be employed so as to produce variety. * See Observation 5; also Ob. 2. + See Observation 7. + It will be perceived that on all these occasions a fundamental 7th has been introduced upon the dominant chord of b-flat, asif it actually proceeded to its tonic; this may here be considered as rather premature, but it greatly improves the harmony, and will be fully explained hereafter. See False Cadences. HARMONY AND COMPOSITION. 97 It will be perceived that the melodies at bars 1, 2, 3, contain only two sounds each; but the monotonous effect of the harmony at bar 1, is removed at 2 and 3, by employing other inversions. We shall now give an exercise in which will be found two distinct bass-parts to the same melody, where the above mode of selecting inverted basses is put into practice. Of course it is unnecessary to observe that these two inverted basses are two distinct exercises, and are not intended to be employed at the same time. Each of them should be taken separately, employing the same melody, and then adding the two other parts of the harmony. Ds. [ a2 + J T 4 A Ts ith ae t f y _ 7m 3 Fe eS ee + t ce oe FE Ce 1 ist Inv. Bass. § 6 4d 6 4 i e 8 6 a = SS | t a fae r == Hh Ex. 92. } 2d Inv. Bass. a 1 6 6 i. 1, 7, . J. i 1 I ok oe 1 T ses > sary fete ee ee Se oe o e e_ Tt oe 5 Td Fund. Bass. s z rE ye J E J. E J y. E 1 +H] k ~ t ; PE i = — st tH as? 7 a oe so On looking over the second bass part of the above example it will be per- ceived, in the latter part of bar 2, that had the F-sharp continued to the end of the bar, it must have ascended to G, producing consecutive octaves; instead of which, it first ascends to the 5th of its own chord, and then descends toG. Mean- while the 5th, A, in the melody, also divides itself into two notes, and, instead of descending from A to Gin the next bar, it first proceeds to the 8rd (F-sharp) which the bass has quitted, and afterwards ascends one degree toG. As the use of this interchange of intervals is of considerable importance, and as frequent reference will be made to it, we have been more than usually careful in directing the attention of the pupil to it; and to impress it still more upon the mind, we add the following: — Ex. 93. In the above example it will be perceived, Ist, that this interchange takes place during the continuance of the chord; 2nd, that the different intervals, after this interchange, wherever they may be found, proceed to their destination as pointed out by the resolution of the chord of the fundamental 7th. For instance, bar 1, the inverted bass, G-sharp, ascends to the 5th, B, and then descends to A; while at the same time the 5th, B, in the alto, descends to the 3rd, G-sharp, and then ascends to A.* Bar 2, the reverse has taken place. Bar 3, the inverted bass ascends from the 3rd to the 7th, where it resolves into the 3rd; remark the pro- gression of the soprano. -- © The iraportance of this interchanging of parts will be still more evident when we arrive at passing notes, 98 HARMONY AND COMPOSITION. This may suffice to show the principle on which these interchanges are per- formed; we shall now harmonize a simple melody, to show their practical use and effect. 1. 2. 3. 4. 5. 6. 7. 8. fe. Zz + Se Zz ao [ei Seal : -—+ a C fs te f — Le te vo» Oe. Ve x 7 iT J a e. Be ee ee z. ine L co 4 i nea Bs (Oe ee eee ea - Ex. 4 pe 2 = Ps Cc _ [7 i tt SREY - FE ae 4 L J a. T J. at tf c roa cr J i 1. t aoe ee =. Soe th a tec =~ it Bee Patek ioe = t eae oe I 1 [ T < 1th oa vey? oa a ve a ree +e % 6 § j. Ae a. ig “ at -@, ; — Pe fe Pe pe Pe ee te eee fo I Basan v te. | ie | Ae ea T “a. t i: =< Th C I a t I Tae Eee. + “ih Bar 1, the bass interchanges with the alto; at 3 and 4, with the soprano. N.B. It is not absolutely necessary that on these occasions the identical inter- vals of the chord should interchange places: — see second part of bars 3 and 6. It will now be necessary to make a few observations on the 2nd and 4th rules of harmonizing, in order to show how these rules may, under certain circumstances, be employed in a more extended form than heretofore.* We are aware that ‘‘ when the 4th of the scale descends one degree, it may be accompanied by the dominant;’’ we shall now add, that the 4th of the scale, although it may not immediately descend one degree (resolving upon the 3rd of the succeed- ing tonic chord), yet, provided it proceeds to any of the other intervals of that chord before its final resolution, it may still be accompanied by the dominant. Ex. 95. At a, the 4th of the scale, although it does not descend one degree, is still ac- companied by the dominant; because it descends to the 8rd of that chord, ana then resolves. At b, the 4th has first descended to the 5th of the dominant chord; the inverted bass takes up the 4th of the scale, and descends one degree. At c, the 4th has descended to the 8th of the dominant chord. At d, the 4th has first ascended to the 8th of the dominant chord, returned to its place, and then proceeded according to the original rule. Observation on the Fourth Rule of accompanying the Scale. The rule says, ‘‘ when the 5th of the scale is repeated, it may be accompanied by the dominant.’? Under certain circumstances, however, that interval may be go accompanied when it is not repeated; as in the following example. * See also retrospect, page 54 to 56. HARMONY AND COMPOSITION. 99 q ee e. r es 1 2. 2 es Recor Ts he 16 1 i a 1. ad ani aL 1 tye E ny iit it r asec +t Ss —1 g j w=) oe 6 es a a. Ty {| oe z iL L —Tt £ Cac + at pose Sos, it { an it Ia, i Le TG {t will be remembered that this rule, as well as the others, was given to pro- duce variety of effect; it was to remove monotony in the harmony; the very expression, ‘“‘ when the 5th is repeated,’ shows the nature of the rule. It is evi- dent also that, were the rule in the original form continually to be applied, the very evil which we desire to prevent must inevitably make its appearance. This will be readily comprehended by those who have carefully reflected upon the pre- ceding matter. : The following example will exhibit in a practical form what has been stated respecting the extension of the second and fourth rules of harmonizing. Ata, second rule. At b, fourth rule. The example which here follows may be considered as a specimen of the various ways in which an inverted bass may be constructed, and the four rules employed. p Melody. [@5t=# =e ee ey Inv. Bass. le I eS q an 4 3 j br er ekion! sih-ott s fs» 7 Inv. Bass. or 24 £ 2 SF Sasa eorir Fre oh t feet ee dA Il. T ce pe Ht 1 : 1 ha Tb = t t 6 1 -o 1% § 6 798 3 6 4 6 3 § br 6 1 Inv. Bass. [9 eee —e F— “oT —. to oH —t fore vert tte If each of the above bass parts be taken as a separate exercise, and the alto and tenor added (see example 92), the pupil will then be able to judge of the dif- ference of effect, arising not only from the rules for the choice of inverted basses, but also from the four rules of harmonizing (see page 48 to 51). Too much attention cannot be paid to what is here noticed, as it is only by comparison and a strict attention to the difference thus produced that the judg- ment can be exercised and formed, and the taste improved. 100 HARMONY AND COMPOSITION. The preceding exercise should not be regarded as merely technical, but also as intellectual; for example, here is a simple melody, it has no claim to beauty, elegance, or expression, as to its progression or rhythmetical form: this melody, however, becomes the prolific source of others;* each of which, in its turn, may also become the source of many more, and so on ad infinitum. When this fact presents itself to our mind, that all this can be effected through the instrumentality of only three chords, and these produced by nature, a wide field, indeed, is open for reflection. To give examples of all the variety which these rules so abundantly supply, would be quite impossible; we shall only remark, in conclusion, that if the pupil keeps in mind the original principle of fundamental basses,— from whence they have emanated, — the four rules of harmonizing (as arising out of the dominant chord), the variety of effect produced through their instrumentality — their modulation (that inexhaustible mine of musical wealth!), the introduction of inversions (caus- ing an amalgamation of the four parts, by which a new character is infused into the whole harmony); furthermore, if he reflects that the originating cause of all this can be traced to the simple vibration of a string, etc.,—that it is not the inven- tion of man, but the simple operation of nature; he cannot but perceive that the matter, thus considered, is of a higher order than the mere putting together of a few chords for the purpose of gratifying the ear. He will find that, abstractedly considered, it is a subject perfectly capable of creating a real and absolutely intel- lectual enjoyment.t * Mark the inverted basses, which may all become bass melodies, and then be reharmonized. + It will be seen how much more our ideas on this subject will be enlarged when we arrive at modulation by the intervals of a melody. AN ESSAY ON DISSONANCES “BY SUSPENSION: Hitherto we have employed only such harmonies as are derived from the com- mon chord, and the chord of the fundamental 7th; we shall now proceed to intro- duce some intervals which do not form any part of that harmony. In order that the pupil may have a clear view of the subject on which he is about to enter, it is necessary that he should take a retrospective view of the sey- eral processes by which the variety of effect, up to the present time, has been accomplished. Thus — He must have perceived, after the discovery of the fundamental basses,t that the harmony arising from them consisted of common chords only; +{ that this har- mony was afterwards enriched by the fundamental 7th; and that thus (another interval being added to the harmony) a new effect was produced.§ He must have observed that the four rules of harmonizing, || modulation, inversion in modu- lation, J and, last of all, inversions in melodies, ** all formed a chain of causes and effects, unbroken by a single link; and that all this resulted — not from a theory suggested by man— but from a system founded in nature, as exhibited in example 48. It shall now be shown how a new effect may be introduced into the harmony by means altogether differing from those which have been hitherto employed for that purpose. We have already stated that our harmony up to the present time has consisted of common chords, and the chord of the fundamental 7th, with their inversions, and our experience has sufficiently shown the variety.which these chords alone, by a judicious management, are capable of producing; yet, as the constant recur- rence of these (however diversified or dissimilar in their progression) must ulti- mately tire the ear, means have been found to remedy this defect by introducing intervals into the harmony, which do not constitute either a portion of the common chord, or that of the fundamental 7th. We shall endeavor to illustrate this by the following example :— Suppose we were required to harmonize the melody as at I. According to the first rule of harmonizing it would appear as at II.; and, if it were played thus, the ear would rest perfectly contented. Not soatIII. Why? Because the sound G, at bar 1, instead of immediately descending to F, is continued in bar 2, and the ear experiences a certain degree of disappoinment —a degree of pain —it desires to hear the F, and when the F at last arrives, a certain degree of pleasure is expe- rienced; which, although purchased at the expense of a little pain, we have no objection to experience again on the same terms. * Dissonances by retardation shall be explained hereafter. # See page 28. + Page 33 to 34. § Page 37 to 42. || Page 44 to 50. 1 Page 89 to 104. ** Page 97 to 102 (101 ) 102 HARMONY AND COMPOSITION. Ex. 99. The interval which produced this effect is called a dissonance,* and the chord to which it is attached, a discord. When an interval of achord is thus kept back in a gradual descending pro- gression, as at III., we shall call it a suspension, or a dissonance by suspension ; for example:— At III., as G suspends the 8th (F), we shall call it the dissonance of the 9th. as F. ———— 38rd (E), it will be the dissonance of the 4th. as E————————_i5th (D), it will be the dissonance of the 6th. These comprise all the dissonances by suspension, The following example exhibits the discord of the 4th in its different posi- tions, produced by suspending the 3rd; — At a, the dissonance is in the soprano. At 6, ——————____ alto. At c, ————_———— tenor. b. é J}. ce — Ss TC Tt ZB C HW 2 Hf [seep SESS ou earl = = ~ oe T a ee T Ex. 100. 1 —————_—$_———————— tt ea E i E aH The discord of the 9th, in its different positions, is produced by suspending the 8th, thus — a. : b c } | — = f r—) f - = 9 fi 5 = ~=—HH] th L . [ iil t L Lo ——— —— Il. : : oo Se Ty. = bo F. c— J Le i FS uy f 1 Ee Tt f ah i Aa. i Le The discord of the 6th, by the suspension of the 5th, in its three positions: — 2. 9 [ sts ft ae i paw oS é P = III. E = tf E ee Ff £ ce HH The intervals of a common chord — 3rd, 5th, and 8th — are called consonances; any other interval, there. fore, is a dissonance. N.B.— We are not here speaking of intervals arising from inversions, HARMONY AND COMPOSITION. 103 It will be perceived, that in example 96 (III.) the sounds which produce the discords present themselves naturally in the progression of the descending scale; they are first heard as consonances, after that as dissonances, and then (after having descended, or —in other words — proceeded to their respective places from which they had been detained) again form consonances. From this circumstance arises the 7 RULE FOR THE PREPARATION OF DISSONANCES. (A.) In whichsoever of the four parts a dissonance appears, in THAT PART also it must first be heard as a consonance. Or, in other words, thus:—In whatever part the interval appears which is to be suspended, in the same part also must be prepared the dissonance which suspends it. RESOLUTION OF DISSONANCES OR DIScORDS. (B.) In whichsoever part the dissonance appears, in that part it must descend by one degree into the same consonance, which was suspended.* This is called the resolution, or resolving the dissonance. For instance, in the preceding example 100, ‘ ‘ : a consonance, and AtL,a j a oy as } ath | 28 preps i soprano by the 8th, ? resolved into the 8rd in the same [part. b alto ¢ tenor = —————- IL, a————————- 9th in the soprano 5th, 8th b alto ¢ tenor —_—————_- TIl., a 6th ————— in the tenor 8rd, 5th ——————— b soprano c alto Dissonances by Suspension in the ASCENDING Scale. Were we to introduce dissonances only when the scale or melody gradually descends, the above rule for the preparation of dissonances would be quite super- fluous; but, as this is not always the case, we shall now, instead of taking the descending scale, employ the ascending, in which dissonances will not be found naturally prepared. t In the following example, at a, the harmony ascends, and consists of concords only: — : ——— 4 a. b ¢. Bes | Fi a -Fre-——-=——fq (= 1 is i | {om TT. . TH a hase itl j i i to To ; 3 43 B48 $ fT + f a ae eet ee eee ee = i oS et t “To Ex. 101. 7 Z — E A E HH j= £ b-s—t# t t u i TH =. eet 7 pes T 4 | E i E E H f — re, t. ro} Tp oz t c os ut) = t t r—] Re Ee IE UF Cc Lc i t * This rule admits of a slight exception, which shall be explained in its proper place. + Dissonances which are naturally prepared in the ascending scale, are called retardations, which will be found fully explained hereafter. 104 HARMONY AND COMPOSITION. At 6, the dissonance of the 4th is introduced in the alto. Q. Why in the alto? A. Because the 8rd, into which it resolves, is found in that part. See A, page 103. Q. Isit here prepared? No. At c, the dissonance is prepared in the same part where it afterwards resolves. In order to obtain this preparation, we have divided G (the semibreve of the pre- ceding chord) into two minims, and have allowed it to ascend to C (the 8th), as the proper preparation of the dissonance of the 4th.* All the above observations as to preparation, etc., etc., apply equally to the other dissonances. The nature of dissonances having now been explained, it shall be shown how and where they can be introduced; and let it be well kept in mind, that, in doing this, we are to be guided solely and alone by the progression of the fundamental bass. We shall commence with THE DISSONANCE OF THE 4TH. (C.) When the fundamental bass ascends a fifth, or descends a fourth (which amounts to the samet); the dissonance of the 4th may be introduced, pre- pared by the 8th, and resolved into the 3rd.t In order that the pupil may have a correct idea of the preparation and resolu- tion of this dissonance, and the manner of employing it effectively, we shall for the present deviate a little from the plan hitherto pursued; and instead of harmo- nizing an air, we will select that progression of fundamental basses which will admit of its introduction in a regular and unbroken series. The following example at I., exhibits a continued progression of basses, 5ths ascending, or 4ths descending. ae =z ae ee = E —= Sei To which, at II, common chords or concords have been added. This we shall eall a consonant harmony or harmony of concords, in contra-distinction to that which is produced by a progression of dissonances, called dissonant harmony, or a harmony of discords. tH HH ttt es I. 2. 33 4 5 6. 2 8. aa =e ee eee p- T T T Be T r : ro f oe as ES i 1 - con t | 8: ee oe ——— ~ — mr 8 4 3 8 4 3 on & 17 a Sa Sank Sok wa: T I fs racy J. _t ail T T Lm T = + + + ——| Ex. 104, 1 ete ts =o So Sr ee eS =e ~— oN | T ay yi TF js ee == se 43 oa’) et % > & t 9. Io. 11 12. 13 14. 15 16. — LoS IE La ao are Ss T bs Ih ii ee —t t acts — a. t Le a eH Q#. 1 1 oN z Z Ea = J a aaa | on t Tr T T i. tS see Toes I } = + ~| iz a + P=! a 1 zo —t } J + J. at ar Che: t aires as ats = — ~~ ——, Scie ; a § § a +t as + + t t t iL T ack, t ak T rs aie t J. ae ae zee T 4 3 + 4 a 3 oF oe _ iz At bar 1 the soprano ascends to G, to prepare the dissonance at bar 2, where it resolves into the 3rd. The soprano continues thus to prepare the dissonance until it arrives at bar 7, where the strain ends in B minor. Now let us observe that, while the soprano ascends in bar 1 to G, to prepare the dissonance at 2, the alto performs a similar operation by ascending in bar 2 to D, to prepare the dissonance at 3: and, while the soprano thus continues to pre- pare and resolve the dissonance, the alto proceeds in a similar manner, and follows the soprano a 4th lower,t until at the 6th bar, as has been stated already, the strain ends in B minor. : At the 8th bar, the alto commences and continues the same melody which the soprano commenced at bar 1, and the soprano takes up the subject of the alto at par 9. The soprano now continues to follow the alto a 5th higher as far as the 18th bar, where, by a few modulations, the harmony is carried back to the original key. We shall here exhibit the same exercise in four parts, where the tenor par- ticipates in the imitation. $+ To the Professor — We feel, however, that,in doing so, we are rather travelling out of our usual simple course. § When two or more parts mcve thus, it is called imitation. When each part is imitated as above, it is called a canonical imitation or canon. The first 7 bars contain a canon in the 4th be- low, and from the 7th to the 13th a canon in the 5th above. HARMONY AND COMPOSITION. 101 Exercise of the Dissonance of the 4th, in four parts, employed for the purpose of imitation. 2. 3 4. 5 6. a HY I QL NL i il HLL ) 4 > il 7 T 7 ak rT = Po oat . 1 t ak See ah 5 -S3 4 4 go E 4 ad — Sees ar ao a oa Ex. 105. ~-o : a Saal S o - fz: t Cg a= es Por <=. T oe. oe Ps = 7 te 1. z = t ah ot pe ] + 72 1. T oe Z tr ic —] ok 2 lk tr kn ol fay is +} | — 4 + ats 4 E 1 — { 2 + E 4 4 3 4 3 4 3 4a 3 ty i 8. 9. 10 Il. 12. 13. 14. 15. fat.J I - iz : : : es ae F + = = Po EF —————— | I ct LT t nasil: 1 te : — tH r fe I —_ aN ge js ee SS f E -—— Se 1 1: a (a — E +H ae eae = coma 4A 5 co. 2 oe. ea eo t = t E 21. i T T ro Tn ————— f =< E F i £ Hy js i a fe i Dissonance? in the Bass. * Pana o we ce a a = = c T { : aad Baty y- + aE + oT 1. = D f ——. 1 t c. Wh ok ee Tela 1 t a if mai} a J. t r - i. T LL a a ee 3 4 3 ty i This will suffice to show what may be effected by the simple rule, viz.: When the fundamental bass ascends a 5th etc., etc. We shall now proceed to the intro- duction of THE DIssONANCE OF THE 9TH. (D.) When the fundamental bass ascends a 4th (or descends a 5th), the 9th may be introduced, prepared by the 5th, and resolved into the 8th. As this is the same progression which is required in modulation (viz. from dominant to tonic), we shall make a few modulations, for the purpose of intro- ducing this dissonance. Exercise on the Dissonance of the 9th prepared by the 5th. Ex. 106. a 5 9 8 ae i 7 ke x T T iz i L +) 1 i 1 T T. t J a rE Ti o——_j—e— f- =—_ fH = & 8 Inv. Bass, bs ‘i 4, g ao 8 BB Se. 8 ae gn see = Ped a = {+—-— = 5 t 4 - i= iW = ws ~~ + Fund. Ease - + To prevent ledger lines, the tenor part is here written in the bass clef. * To be more fully explained by and by. 108 : HARMONY AND COMPOSITION. At a, the tenor proceeds from the 3rd to the 5th of the chord* to prepare the 9th, which appears at b, where it resolves into the 8th. Q. Why does that dissonance appear in the tenor? A. Because its resolu- tion is found there. At c, the soprano has descended to the 5th of the chord to prepare the 9th, which appears at d, and resolves into the 8th. At e, the alto performs the same process. As the bass at g has ascended a 5th, we introduce a 4th, prepared by the 8th. N.B. —It will have been remarked, that where the 8rd ascends to the 5th of the chord, to prepare the 9th, the first inversion, £, is employed, to preserve the harmony complete. We shall now return to our three original fundamental basses, and harmonize the ascending and descending scale, introducing both the 9th and 4th wherever the progression of the bass will permit. Ascending and descending Scale, with Dissonances of the 4th and 9th. Lit From a to b, from d to e, from i to k, from n to 0, and from o to p, the basses ascend by 5ths ; consequently the 4th prepared by the 8th may be introduced. From 6 to c, from c to d, from e tof, from g to h, from m to n, from p to y, the basses ascend by 4ths; consequently the 9th is prepared by the 5th. Q. The bass, at h, has ascended a 4th; why have we not introduced the 9th? A. As a dissonance is the representative of a consonance into which it subse- quently resolves, it is clear that the consonance and the dissonance which suspends that consonance cannot be permitted to appear at one and the same time; we must. * Let it be kept tn mind that the intervals are here always counted from the fundamental bass. HARMONY AND COMPOSITION, 109 therefore be very careful, when the 9th, for instance, is introduced in one part, that the 8th does not appear in another.part of the same chord at the same time. This remark, of course, applies to all other dissonances whatsoever; see x, where the suspension of the 8th in the alto, and the octave in the soprano appear on the same chord at the same time. Q. Why has not the 3rd of the dominant chord, at p, ascended ? A. For the same reason as stated already; in order to make room for the 9th,* the 8rd in this instance has been permitted to descend to the 5th of the tonic. We shall now introduce The Fundamental 7th, combined with the Dissonances of the 9th and 4th; Preparatory to which, it will be necessary to point out some peculiarities con- cerning these dissonances worthy of observation. ist. — The fundamental 7th is derived from Nature, and therefore requires no preparation. (See example 48.) 2nd. — Dissonances, being artificial, must always be prepared. 3rd. — The fundamental 7th does not resolve upon the same bass. 4th. — Dissonances do resolve upon the same bass.t The fandamental 7th partakes of the nature of a consonance as well as of a dissonance. As a consonance, requiring no preparation. Asa dissonance, requiring to be resolved. Dissonance of the 4th, prepared by the fundamental 7th. The fundamental 7th, therefore, considered as a consonance, may prepare a dissonance; that is, the Tth, before resolving into the 3rd, may be suspended, pro- ducing the dissonance of the 4th; and thus when the bass proceeds from the dominant to its tonic, the dissonance of the 4th may be introduced, prepared by the 7th. In order to exhibit this dissonance in a practical form, we shall again make a few modulations. Exercise on the Dissonance of the 4th, prepared by the fundamental 7th. In” 4 3 BD 0. jee pee thee ‘ E Sapo +H # eras t rod i iL ee iL i i L [ Cc Ly I i t io c | a0 a 5. ¢ d. é f. & h. Ie 3 Se LN, eo, L ti 1 a tf i. Tole t io fon, 1 ; HP == — —— Ex. 108. | —— + f = 3 2 4 3 7 4 3 E T im ae = 2 i 1 i, iL f tO to w $ z aN cE T T i f TH [ 1 T re t Ty X E anal 1 i oe L Th rc es | C t =H t a Fund. Bass. ® When we arrive at accending dissonances, called retardations, these licenses (as they are ealled) will be dispensed with. + Exception to this rule shall be shown hereafter. 10 HARMONY AND COMPOSITION. At a, the 7th has prepared the 4th in the tenor, which at b, resolves upon the same bass into the 3rd. -At c, that dissonance is thus prepared in the soprano ; ate, in the alto; atg, in the tenor. ; The pupil is recommended (by way of exercise) to make a few modulations,* introducing the dissonance of the 4th, thus prepared by the fundamental 7th. If we examine examples 106 and 108, wé find that the progression of the bass in modulation (from dominant to tonic) is the same as ascending a 4th; and hence it follows that both these dissonances, viz., the 9th prepared by the 5th, and the 4th prepared by the 7th, may be introduced conjointly upon the same bass, thus forming a progression of Compound dissonances of the 4th and 9th. Exercise on the 4th, prepared by the 7th ; the 4th prepared by the 8th; and the 9th prepared by the 5tn. a 84 8 br bs 3. 5 8 t 4 8 a ie Diem a J. At aw ee : TH {seo ete Bi . aoe 12 sales: TT - Se ee eee ee” — a d a d. é. v g& A. Z & Z. m. 5 9 8 3 8 43 “& $ T Pk T Fe J. i T r : ft 4 = t t ( ea Te fa I Ty T L J. 1 a { — z CS }. tT Ee, Pe 1 i, Se et eh ee ee a — 9 —7 4 8 5 9 OR 1 4_bs a — I T .. Lr TT ia Ss Ex. 109 ——— tte eS A = — oe ow ~ She =aee = z_F wo S vo Oo a Nene = = § § § A Ce — —-Ss—F +f { = || wa T T- | ate T a R I Bas a a = Bhs eee eae aol Cc t Pc nv. Bass. : a es Shh § ga bf ge h 84 as = [aan eon ree eee TE T zs T 1 i { Se c FCF {est + =F t = f= t t C os. t ae T road C t I I Fund. Bass At b, the bass ascends a 5th, dissonance of the 4th, prepared by the 8th, in the soprano. - At c, bass ascends a 4th, or from dominant to tonic; the 4th prepared by the 7th. At d, both dissonances appear in the soprano and alto. Atf, in the alto and tenor. ‘ At h, in the soprano and tenur, etc. Observe the interchange of intervals between the tenor and inverted bass at e, between the alto and inverted bass at g, and between the tenor and inverted bass at i. The following is an example of accompanying, on the pianoforte, a harmony comprising discords; it contains all the harmony of the preceding example, and the pupil is recommended to play it. , N.B. — The figures point out the preparation and resolution of the dissonance. It will be observed that some of the intervals of the chords in the bass are doubled; in doing so, however, care has been taken that none of them, thus introduced, appear as suspensions elsewhere in the harmony. ? * See Part ITI, on modulation. +t See Obs. page 108, and z, at the end of example 107 HARMONY AND COMPOSITION. 111 Ex. v0. In the preceding examples, it will have been noticed that a particular progres- sion of the fundamental bass has been especially selected for the purpose of introducing the dissonances; that object having been effected, we shall now return to our original plan of harmonizing a melody; and then (guided by the progression of its fundamental basses) introduce such dissonances as those pro- gressions will admit of. A Melody Harmonized with Dissonances. o™ 84 3, SBN OB ek we oe 2s em. Ex. 101. 1 4 The consecutive 5ths, between the tenor and bass, and the consecutive 8ths, between the alto and bass, as the harmony proceeds from bar 5 to 6, are avoided by the bass moving by con- trary motion — that is, the bass DESCENDS, while the other two parts ASCEND. We shall analyze the foregoing exercise by a few interrogations. Q. (Bar 2.) By what rule are you enabled to introduce here the dissonance of the 4th ? A. Because the fundamental bass ascends a 5th.* * See page 104, C. 112 HARMONY AND COMPOSITION, Q. Why does the dissonance appear in the soprano ? A. Because the 3rd of the chord (its resolution) is found there. * Q. (Bar 3.) By what rule have you here introduced the 9th? and why does it appear in the soprano ? A. Because the fundamental bass there ascends a 4th, consequently I can introduce a 9th; t—it must appear in the soprano,’ because its resolution (the 8th) is found there. Q. On what principle have you introduced the 4th in the same bar, for the bass does not ascend a 5th ? A. Because F, the dominant, proceeds to its tonic (B-flat), we can have a 7th. This ;th prepares the 4th (in bar 2), and is resolved, in conjunction with the 9th (in bar 8). Q. But how can the 7th, which partakes of the nature of a dissonance, prepare a dissonance ? A. Because the fundamental 7th partakes of the nature of a consonance too, as it requires no preparation;} the fundamental 7th may therefore prepare a dissonance, Dissonance of the 6th, prepared by the 8rd. The pupil is aware that, when the fundamental bass ascends a 5th, the disso- nance of the 4th may be introduced. § It shall now be shown that, when the bass ascends thus, the dissonance of the 6th may likewise be introduced; consequently both these dissonances may be employed conjointly. In the following example at a and c is exhibited the simple dissonance of the 6th, prepared by the 3rd, and resolved into the 5th, as already shown at page 102; it b and e, both of these dissonances appear conjointly. —— a aa 2 a a St Ex, 112. The above exercise is' a practical illustration of the manner in which these discords may be employed with the best effect. It has been shown, and cannot be too strongly impressed upon the mind of the pupil, that the introduction of dissonances are in every case regulated by the progression of the fundamental bass; and, in order that he may see the utmost extent to which a dissonant harmony may be carried, we shall here give an example which exhibits every progression of which the fundamental bass is capable, and, consequently, every dissonance by suspension that can be introduced into harmony. Ex. 113. * Page 103, B. t See page 107, D. + See page 103, § See page 104, C. HARMONY AND COMPOSITION. 118 a, when the fundamental bass ascends a 2nd, the j ae prepared by the pe b, 3rd, 6th 8th, 9th ———_—_—_——_——- 5 th. ¢, ath, } df 6th —_——_————- 8rd. Bins j 4th —______~_-——-. 8th. c, 6th No dissonance. 9th prepared by the 8th. A7- Tth,— ; 6th ———_————_——-_ 5th. 4th ——__—_—_—_——__ 3rd. N.B. Ascending a 7th, or descending a 2nd ree oe amount to the same thing. It appears by the above example at /, that when the bass descends a 2nd, we can introduce the 9th, 6th, and 4th. But it is only the 4th that can in this instance be permitted to appear legitimately; for, as the suspension is the representative of the consonance into which it resolves, it is manifest, were we to prepare the 9th by the 8th, that the ear, anticipating the resolution, would be impressed with the approach of consecutive octaves; for instance — Ex, 114. At a, in the above example, we find consecutive octaves; at b, 9th prepared by the 8th—can this be permitted ? at c, consecutive 5ths; at d, 6th prepared by the 5th —can this be permitted? at e, consecutive 3rds; atj/, 4th prepared by the 3rd —this is perfectly correct. : ; The following exercise is a melody harmonized with dissonances; and, if the soprano be sung or played, the inner parts may be considered as an accompaniment. 4h +n nt Th At a, the chord of the § appears by inversion, and at b and d, by suspension;* at e, the 9th is prepared by the 5th; at/ g, prepared by, the 3rd.t * See Example 120, a, b, and explanation. + See example 113, a. 114 IIARMONY AND COMPOSITION. It will be necessary, before we pursue our subject of dissonances further, to make the pupil acquainted with what is called the Accented and unaccented Part of a Bar. To enter fully on this matter at present would be out of place; all that it is necessary for our purpose now to state is, that in a bar of common time, whether it contains two minims, two crotchets, etc., or their equivalent, the first part only is called accented, and the second half unaccented (as in the example I.). When a bar contains three minims, three crotchets, etc., or their equivalent, then the last portion is called unaccented (at II.). . L II. Ee 1 a ACS: oT T mat = oz r ae He a = = oe +H Ex. 116. 16 F f -— {5 == = tt 4 —|= peeks ee ee ed a, “uu a Hu, a wz a “uu It is a general rule, that dissonances should be prepared on an unaccented part of a bar (example 117, a), appear on the accented part (b), and be resolved on the unaccented (c), and that the note which prepares the dissonance be at least of the same duration of time as the dissonance itself. * It is necessary to observe, that these rules have reference chiefly and primarily to compositions of the old school, the strict style, as it is calledt (in contra- distinction to what is called the free style) { the latter of which does not command a very close observance of them. The following example is an illustration. “wu a “wu a ua a u, a uu Ex. 118. Here, although the dissonances are prepared on the unaccented part of the bar, and by notes of equal duration with the dissonances themselves, yet they do not (except at the 5th bar), resolve (strictly speaking) on the unaccented part of the bar. The following example exhibits a still stronger illustration of what has been stated, for, at bars 1 and 8, the 6th is prepared upon the accented (instead of the un-accented), and is struck on the unaccented, (instead of the accented) part of the bar. “Never were there rules which admit of more exceptions, or are less regarded, especially in the composition of modern mu8ic, than the above. _ t Church music, fugues, ete. + Modern music in general, sonatas, concertos, songs, ete. HARMONY AND COMPOSITION. 116 Ex, 119. Ex, 120. This deviation from the strict rule of preparation and resolution of disso- nances, may be considered as the medium between the strict and free * styles of writing, From what has been shown above, it is clear that there are two chords of the #, one arising out of the second inversion of the common chord,{ and another out of suspensions.{ They may, however, be easily distinguished, as the former requires neither preparation nor resolution, and-the latter requires both. This distinction is clearly demonstrated in example 120, where at a, the chord of the § by inversion (being derived from a concord) prepares the discord of the $ at b; and thus the nature of each chord, and its origin, is immediately discovered. As frequent opportunities will hereafter present themselves for illustrating this subject, we shall at once proceed to the inversions of discords ; and let it be observed, if the pupil has well understood and practised what he has learned of inversions (as explained throughout Part IV), he will not experience the slightest difficulty in comprehending the subject upon which he is now going to enter. With respect to the figuring of the inverted basses with dissonances, the pupil is advised to read with attention what is stated at page 116 and 117 on that subject. We shall select the ascending and descending diatonic scales for our next exercise, presuming that the pupil himself has harmonized it with inverted basses, that he has carefully examined the progression of the fundamental basses, has ascertained where dissonances may be introduced, and figured the basses, as shown in all the preceding examples; then let us ask the following questions. I, 2 3 4 5. 6. — 8. pe i T c — [ete ae Se ee ee | Bs {—1 | | Ie ale vr i Ho Inv. Bass. —_ 4 § hr te 3 Gi uf cS 2. a ee | Fund. Bass. ivr fr tf4 oy ae 1 4 3 C I Es x I~ rT ; ere Se = i Q. What dissonance can we introduce in the second bar? A. The fourth, Q. Why? A. Because the fundamental bass ascends a fifth. Q. In which of the four parts must the dissonance appear? A. In the inverted bass. Q. Why? A. Because the third of the chord is there. Q. How has the 4th been prepared? A. By the octave in the preceding chord. * The free style even admits dissonances ef every description unprepared, although they are generally resolved. + See Example 83. + See 113, d. 116 HARMONY AND COMPOSITION. Q. Has the 4th resolved properly? A. Yes; it has descended into the 3rd* of the chord. Q. How has the 4th been prepared in bar4? A. By the fundamental 7th in the preceding chord. t Q. From where have you that 7th? A. G, the bass, is the dominant to C, and thus a 7th may be introduced at 5; the dissonance appears again in the inverted bass at 8 in the tenor, prepared by the 7th. Q. Why has the 4th not been introduced at bars 3 and 6, as the progression of the fundamental bass would permit? A. Because the 8rd of the chord is in the soprano; and were we to suspend it in the tenor where, in fact, that disso- nance would be prepared by the 7th), then the 8rd, as well as its suspension, would be heard together. } ‘ Let the pupil now introduce the dissonances into the descending scale. Inv. Bass. 2 3 9 8 ey bg bf § 4 3S § 4 3 Ex. 122. @g—= = : ee ————— | i t 1 a Loa 1. - t Paty ue rake cal < Sa Rf ak mal Fund. Bass. mos : b 3 - + T 7. - a a4 an |= { at =r 4 1. t oi Th 5 is alk | 2 I + a4 t | mh = =k E A. BE i L ani] os = = zs In the above exercise, bar 3, the dissonance of the 9th is prepared by the 3rd; and at 4 and 7 the dissonance of the 6th is combined with the fundamental 7th. This mixture of dissonances is very effective. That the dissonance and the consonance which it suspends must never be heard together, has been stated more than once; nevertheless, as an error in this par- ticular is easily committed when dissonances are introduced into inverted basses (especially when a licensed 7th is employed), the pupilis advised to pay great attention to the faulty progressions which are exhibited at c, e, g, and h, in the following exercise. At a, a licensed 7th appears in the tenor; which, at b, has descended into the 8rd, and thus far all is correct; but, at c, that 3rd is suspended, while, at the same time, the 3rd is heard in the scprano. At d, the 5this in the tenor, and descends into the 8th, as it ought; § but at e, the 5th, instead of descending to the 8th, suspends that interval, whilst the soprano has ascended to it, and thus the 9th and 8th are heard together. At/, allis right; but, at g, the 3rd appears in the tenor, while the inverted bass suspends it at the same time. At h, licensed 7th in the inverted bass, 8rd in the soprano— wrong. * See page 103, B. t See Example 108. “¢ See page after Example 107, a § See Example 120, bars 4 and 6 HARMONY AND COMPOSITION. 117 The following melody is harmonized with various dissonances. I. 2. 3 4. 5. 6. 7. 8. 9. 10. Ex. 124. £4 In bar 4, the alto, after having resolved the 9th, ascends immediately to the 5th, to prepare the 9thin bar 5. This ascending to the 5th was a necessary step, as the melody ascended.§ At bars 7 and 9, the 4th is prepared by the 5th. Why? Because the funda- mental bass ascends a second. || At bars 7 and 9, the fourth is prepared, but the 6th is un-prepared; this pro- gression is called a cadence, which will be found explained at example 125, c. _ N.B.—It would tend very much towards the improvement of the pupil (not merely as it regards dissonances, but in other respects also), were he to re-har- monize the above exercise, without dissonances or inverted basses, proceeding after that to add the inverted basses and dissonances, and then to compare his own production with the original exercise. We shall now (at least for the present) discontinue to harmonize melodies with dissonances, and proceed through a short course of modulation, into which they shall all be introduced; preparatory, however, to this it will be necessary that the pupil be made acquainted with a certain progression of chords called a cadence, which, when heard towards the end of a composition, or judiciously interwoven with modulation, is calculated to conduct the ear gently to a state of repose. There are several species of cadences; the most simple of these is— The Perfect Cadence, When the chord of the fundamental 7th, or dominant chord, proceeds direct to the tonic. All the others may be considered as auxiliaries, preparing the way, and lead- ing to this, by which a final close is ultimately effected. Ex, 125. AtI., is exhibited a perfect cadence, with which the pupil is fully acquainted (excepting, perhaps, only the name). § Sce.Example 101, and observations. | See Example 113, a. * Example 128, bars 1, 2, 3. t Ditto, bar 42. + Ditto bars 12, 13. 18 HARMONY AND COMPOSITION. It must have been observed, that by a continued course of modulation the ear is kept in a constant state of excitement, approaching absolutely to a painful sen- sation, so that it becomes desirous of rest. To stop suddenly, however, upon any tonic, or key, at which we may have arrived, would be anything but satisfactory; therefore, when we may have modulated to any key, and desire to come to a decided and satisfactory close, there the ear must be gradully prepared and soothed into a quiescent state by the introduction of a few chords, so constructed that they shall not only have a tendency to conduct to astate of rest, but shall also be calculated to produce a strong impression of the key in which it is intended the close shall take place. The only chords suited for this purpose are those of the subdominant and dominant, for it will be found that these chords, together with that of the tonic, embrace all the intervals of the diatonic scale, so that, in fact, by hearing these three chords at the close of the modulation, we receive an impression of every interval of the key in which we thus desire to conclude. The above cadence at a, is a specimen. However, as a frequent recurrence of these chords would produce monotony, the dissonance of the 4th is introduced (as at b), which, in some measure, removes this objection. On account of the frequency of the final cadence, composers have not only been induced to seek for every possible variety, but sometimes have even endeav- ored to avoid it. * In seeking for this variety, some liberties have been taken; for instance, the dissonance of the 6th has been introduced unprepared, producing thus a discord of the § (c). Another liberty was subsequently taken with the chord of the sub- dominant, by adding to it the 6th, and calling it ‘“‘the chord of the added 6th,” t omitting the chord of the ¢ altogether, as in the following example 139 (d). Ex. 126. N.B. — The 5th in the chord of the added 6th is generally prepared, as if it were a dissonance. Sometimes the 5th of the subdominant chord is omitted, and the added 6th doubled (e); and sometimes the octave is employed instead of the 5th (f). N.B.— When the key is minor, then the chord of the subdominant must be minor too (f, g). Figuring Inverted Dissonances. Having explained the nature of such cadences as are immediately necessary for our purpose, we shall now show their practical use in a course of modula- tion, in which shall be introduced every dissonance, as exhibited in example 126. A few hints respecting the proper figuring of inverted basses when disso- nances are introduced, as also the principle upon which this figuring is established, shall first be given; and to this it is requested the pupil will pay strict attention. * From this circumstance have arisen those cadences called false, imperfect, ete., all of which shall be explained in their proper places. + The pupil must not consider this chord as the first inversion § of the fundamental 7th. See other side. ‘HARMONY AND COMPOSITION. 119 First of all, let him remember that, besides the bass, there are only three inter- vals which form the common chord, 8, 5, 3; and as each of these intervals, in its progression, may be suspended, it is clear that there can be only three suspen- sions, viz., 9th, 6th, and 4th : that all dissonances by suspension (in whatever form they may appear) are comprised in the above. The 8th, suspended by the 9th, which may be prepared by any consonance except the 8th. 5th, —________6th, prepared by any consonance but the 5th. 3rd, ————_——_———_4th, may be prepared by any consonance, as also the fundamental 7th. From this view of the subject, it is evident that, were no other than fundamental harmonies employed, the figures exhibited above, together with the fundamental 7th, would suffice to express every chord required in harmony.* But, as these chords may be inverted,t it follows, when an inversion takes place, that.the name, as well as the figures of the original intervals,t must be changed also; and were we to employ no dissonances, then the figures which are required for the purpose of expressing the three inversions of the fundamental 7th, and the two inversions of the common chord, would suffice to express every chord in music;§ but, as the intervals which arise from inversions may be suspended, it follows that the sus- pensions must necessarily require to be figured also. Under these circumstances, it is evident that an entirely new kind of figuring would become necessary; and chords, the figuring of which in their simple inver- sions were easily understood and as easily remembered, would now become so complicated and involved, that unless some means were found to remedy this evil, great embarrassment would be the consequence. .To this end it was found advis- able to figure the dissonance only, and then to extend lines back over the bass from those figures the intervals of which remained unsuspended, and thus the inversion of the chord, in its simple state, would instantly be recognized. We shall illustrate this. pe > I. 2 3 4. 5: eft ay fe 2 — = a ; ti ss eS oe SS _Ex. 127. a — \ =i) gee =} det ee ‘a = ee al a ~~ le ne --_ * In bar 1, is exhibited a modulation from C to A minor by the first inversion. Here we have introduced the dissonance of the 6th,|| but (in consequence of the inversion) it requires to be figured with a 4, and thus the chord would require to be figured 33 quite a new chord to all appearance; however, this ambiguity is pre- vented by the mode alluded to. At 2, we have the second inversion of the dominant chord, in which we have introduced the dissonance of the 4th, which (in consequence of the inversion) is figured 7, thus 4, another apparently new chord would be presented, but avoided, as in the example. * See page 87, below. +t See inversions, Part IV. + Intervals of the fundamental bass § The chord of the fundamental 9th excepted, which shall be explained in its proper place. | Q. Why? A. Because the fundamental bass ascends a 3rd. 120 HARMONY AND COMPOSITION. At 3, 4, the dissonance is in the bass, and therefore its resolution only requires to be figured. Some composers do not express this chord by lines, but figure the dissonances from the bass 3, 2: Both methods are here exhibited. At 5, we have the same modulation and dissonance as at 1; here, however, the dissonance is found in the bass. This chord would require to be figured thus, 3. another new figuring which is avoided as in the example. What has been said as regards the method of figuring the above dissonances, when inverted, may be applied to all the other dissonances when inverted. With these few observations, we now present the pupil with the following exercise, in which he will find much useful matter and practical information. Let him make it a matter of study, and then play it: above all, lethim examine most minutely each progression of the fundamental bass, for by it the whole mass of harmony is guided and directed. Let him remember that it is by this means, and this alone, that he can clearly understand the matter contained in this and all preceding exercises, and thus be enabled hereafter to put into practice that knowledge which he has already acquired, and which, perhaps, will at a future time be to him an inexhaustible source of enjoyment, gratification, and delight. Very few of the inverted basses are figured; this the pupil (we believe) will be able to accomplish himself, from the previous information afforded upon the sub- ject, especially as the fundamental basses are figured throughout. Exercise on Modulation, Dissonances, and Cadences. I. 2. 3: 4. Ex. 128. Cadence. Fund. Bass.7=- 5. 6. 7 8. — The letters refer to cadences. A. See Ex. 125, a. G. See Ex. 125, g. $+ See Ex. 120, bars 2, 5. * See Ex. 127, 5, 7 See Ex. 127, 2. HARMONY AND COMPOSITION. 121 te 13. 14. 15. 16. 17. c oe. f b 9 ay b Ie + T | res SE 1. —F ay iE — k tee — 9 zd he 4 a a r D. See Ex. 125, e. E. See Ex, 125, f. C. Ex. 125, d. F. Ex. 125, f. + See Ex. 127, 2, * See Ex, 127, 1. 122 HARMONY AND’ COMPOSITION Es le : o cl EE = c * 2 EF. t i ED | { iE =| re. Paar isa LC a aol seh ws ZI Tho. oe C | cE =f =I iE a= cl | a oe dim. smorz, pp B. Ex. 138, 6. * Ex, 140, 3, EXTENDED HARMONY. It will have been observed that hitherto our harmonies have been written so that between the soprano, alto, and tenor, no Space was left for the introduction of any other part. A harmony thus constructed we shall call Compressed Harmony. : I. II. a a. b “‘ a, é t. a =} — + x Hf ae a + ———H] 3. does” I u I | +H Sa. Ex. 129. Compressed Harmony. Extended Harmony. \ “oR a J se 7. mY Can T 1 |e 1. ok 1 ed. ee J PaLT ce + P <0t 5 & —— —_tt Lot a amd 1 oe mat) z I i. 1 a —Th If we examine the three positions of the common chord (at I), we find that in the second position of the chord (a), the 8rd is placed immediately under the 5th; in the third position (b), the 5th is immediately under the octave; in the first posi- tion (c), the octave is immediately under the 3rd. If, however, we remove the 3rd from the chord at (a), and place it an octave lower (as at d, II), we shall find that the alto (at a) has changed place with the tenor (at d);— that is, the note which was the tenor (at a) occupies a place next the soprano (at d). If we remove the 5th of the chord (at b), and write it an octave lower (as at e), a similar change takes place; and so with the octave (at ¢ and f). This new arrangement of the ‘intervals of the chord we shall call Extended Harmony. By which a new and striking effect is produced. Compare the following har- mony at I and II. Compressed Ex. 130. br g br g In the preceding example (at I) is exhibited compressed harmony, as usual, which at II) appears extended; the original alto (at I, a) is transferred an octave lower to the tenor (at II, b); and the original tenor (c) simply becomes the alto (at d). (123> 124 HARMONY AND COMPOSITION. The effect produced by the new distribution of the two parts will be better understood by playing the alto and tenor together without the other parts, first as at I, and then as at II; but that the pupil maystill more clearly comprehend the nature of extended harmony, let him harmonize the following exercise (148, III) in compressed harmony, and play it, —then play it in extended harmony as it now stands, and compare the different effects: this is the only legitimate way of form- ing a correct judgment, and it cannot be too carefully studied.* TI1.—Melody harmonized with Extended Harmony. Ex. 131. N.B. As the alto, when transposed thus an octave lower, is rather too low to be written in the treble clef, it will be more convenient (in order to avoid ledger lines) to write that part, at least for the present, in the bass clef, as in the example.t We shall now suppose the pupil engaged in harmonizing a melody in com- pressed harmony, which he intends shall subsequently be changed into extended harmony; in this case, the two following rules must be carefully attended to. First, ‘‘ The bass part must not approach the Alto nearer than an Octave,” otherwise, the alto, when transposed into the tenor (an octave lower), will be found below the bass ; and thus the tenor will in fact become the bass. This is clearly shown in the following example, where the bass (in the compressed har- mony at a) is nearer than an octave to the alto; in consequence of which, the tenor (at a) is found below the bass (at 6), and the harmony, as far as regards its inversion, changed. eo 55 pa a Ht tH te=h LSS se =H Ex. 131. a 7 es Serer Se ae] Sey SS Ett =e io j 2-8 eo Ceo2 j 6 3 6 i * A melody harmonized with extended harmony may be played by two performers on one pianoforte, producing the effect of a quartet. + It may be here noticed that almost all our modern arrangements for soprano, alto, tenon and bass, are confined to the two clefs, soprano and bass. HARMONY AND COMPOSITION. 125 By this interchanging of parts, it is evident that a 4th must become a 5th; therefore in the compressed harmony observe this Second Rule, ‘‘ Consecutive 4ths must be avoided; ” for, when the harmony is afterwards extended, these consecutive 4ths will become consecutive 5ths, which are not allowed. For example: —at ¢ (compressed harmony), are consecutive 4ths, which, at d (extended harmony), become 5ths. The improper progression (in the present instance) arises from having selected the third inversion of the fundamental 7th as the bass. By employing the second inversion (as at e), this faulty progression is avoided (as at f). If the pupil carefully attends to these two rules, he may, without the least apprehension of making mistakes, re-harmonize his former exercises with extended harmonies, and thus produce new and unexpected effects. Several other advantages result to us from this extension. Forexample : when a melody ascends or descends by great intervals (as in the following example at a), the skipping of the chords, which naturally arises from compressed harmony, is not only avoided by a partial extension (as at b), in the following example, but a smooth and flowing progression of the inner parts is obtained; the superior effect of which, when contrasted with that at (a), needs scarcely to be noticed. b. Ex. 132. a id i When the melody falls by a great interval (as at a, in the following example), the alto, in order to obtain a smooth progression, is permitted, but sparingly, to cross over the soprano (as at 0). 5. Qa e Oo e ee. ee. q iE T — Be [ rs =} . L. Hf = oo or . anay Ty. t tt. i i 1 a 7 oy ok it = J. Ti T rr v a 0 us o o T 7 a t & + foot iui — aid 1 ney ft _@- @- 1 r i £ ft tT anuy iz = pat re o { t La I if iit Ex. 133. — y et T 1 T T 1 T a i 1 1: T- 7. Sa mek rf af Ty . J. int L —! i ~@. I a0 Te u al it 2 = t To Ce: oe 6 j 6 6 — 6 = : = S rT Hq 7 1 - - 1 tt cal | les oH ch t iad 1 t i bec! — } 1 This will suffice to show the nature of extended harmony, and its application; and whether we employ it to prevent skipping, or for the purpose of interchang- ing the parts (as exhibited in example 130), it will be found a most important auz- iliary. The best advice that can be given the student, in order to make himself fully and practically acquainted with the extraordinary diversity of effect thus produced, is to re-harmonize his former productions with extended harmonies, and 126 HARMONY AND COMPOSITION. then to play them. A few modulations written by him thus (as in the following example at I), and played, will be found exceedingly useful; particularly so, if they are first written and played in compressed harmony. This extended har- mony may be diversified, as at I1.* I.—Modulation with Extended Harmony. foes a bene ye ee gis APEC Ry Ag oo } y= | Peery iret reer cere rrrs ttre Ex. 134. MAJOR AND MINOR. It has already been stated that a major key stands closely allied to another called its “relative minor” ;t and that it is by the 8rd of a chord we discover whether it is major or minor.{ If we carefully examine example 63, we shall find that the harmonics there exhibited, as they arise from the vibration of a string, do not produce a minor but a major chord.§ We shall now proceed to explain THE MINOR SCALE. Its Origin, Construction, and Harmonies. This will be found a most interesting subject, inasmuch as it opens to our view a new and unbounded field of harmony. Itis true the student is not alto- gether unacquainted with the nature of minor chords as regards modulation; but it is only when major and minor chords are employed conjointly in harmonizing melodies that their effect can be fully appreciated. The major scale is derived from nature, as already shown: but the minor scale is partly artificial; itis evident that a union of these two scales must produce an effect altogether different from that which has hitherto preceded; and of which the pupil is not at present capable of forming an adequate conception. The minor scale, then, as already said, is artificial; but, in explaining its con- struction, we shall as much as possible keep in view, and take for our model, the major (or original) scale as produced by nature. If we examine the scale of three sounds in example 65, we find that the 3rd or last sound is the same as the 8rd of the chord of its generator (as appears also in the follcwing example at a). * See also Ex. 23 and 47. + Page 58, Ex. 46. + Ex. 44. § See page 61, 62. HARMONY AND COMPOSITION. 127 As the tonic chord* has a major 3rd, and as the third sound of that scale is a repetition of the 3rd of the tonié chord, the scale is major. o. 2 3 -. 40 ff. ii Ex. 135. TH Should we give the tonic chord a minor 3rd (as at b), then the scale, according to the above principle, will be a minor scale; for the third sound in that scale is a repetition of the 3rd of the tonic chord. ; **Minor Scale of Six Sounds.” In constructing this scale, we shall pursue the same principle as that by which we were enabled to construct the major scale.t The following example (at I) exhibits the major scale as we first discovered it, and in which all the chords are major; -but at II, the chords are all minor, the effect of which (when compared with the original scale at I) is very far from being satisfactory. = IL, rn R fr ——s | ae’ 1. Ty ae eet i=e—e—2 4 i] “3 Major. Minor. A tt oat —_- Ti oe 1. aor: 1. uit UO. o. ee Co a ee. Let us try whether we can modify this scale so that, while we retain the impression of the minor key, we shall still in some measure keep in view the prin- ciples by which the minor scale was established. In order to effect this object, it will be necessary that we change onE of the minor chords, at II, into major; but, as the first and third chords must be minor, it is clear that the second chord only can be made major, see (a) in the following example; that the second chord is the one which ought to be major is evident also from its being the dominant proceed ing to its tonic, and necessary to establish the key. Having arranged the harmony of the first scale of three sounds according to this principle (as at a), the second scale must be arranged exactly in the same manner (as at b). Thus, by a union of two scales (at a and b) a scale of six sounds with its proper harmonies is produced, * The first chord of a scale we shall call the tonic chord. + See page 62, 128 HARMONY AND COMPOSITION. Here, however, we find that a modulation to D minor has taken place; and, as we modulated to that key by its dominant A, so'we must modulate back to the original key of A-minor by its dominant E, and we are furnished with the two last intervals of the scale of A-minor, viz.: G-sharp to A,* at the same time, clearly showing the reason why from the 6th to the 7th of a minor scale must be a tone anda half. Thus, then, we have a complete scale, artificial in its construction —inasmuch as it is composed of major and minor chords. Ex. 138, Ny coor If we examine the preceding minor scale, we find that the second, fifth, and seventh, are accompanied with major chords — characteristic of the major scale; and, as the basses of these chords are dominants, the fundamental 7ths are added.t If it should be asked, Why is the fundamental 7th noé added to the third chord (k), that bass being dominant to D? We answer, it is true Ais dominant to D, but because the 8rd is minor itis not a dominant chord (for every dominant chord requires a major 3rd), and consequently the fundamental 7th cannot be added. Not so at (a), for there the chord is major, and the 7th may be added. If we further examine this minor scale, we find that the distance between the 2nd and 8rd, 5th and 6th, 7th aad 8th, are semitones, and between the 6th and 7th a tone and a half. These are all distinguishing characteristics of the minor scale; but especially the progression between the 6th and th; the wailing and melancholy effect thus produced is peculiarly suited to express deep sorrow and grief. The 6th of this scale is sometimes raised a semitone, to avoid this progression of three half-tones; but is it not thus deprived of one of its most essentially characteristic beauties ? and is not also the preponderance of minor chords weakened, by one more than necessary being made major ? Having now explained the minor scale on fundamental principles, we shall take that scale and its harmony (as it appears in the last example) for our guide, and harmonize a melody according to its principles; preparatory to which, it is only necessary to state that the rules are (with very few exceptions) the same as already taught in the preceding part of the work; that is to say, the four rules of harmo- nizing,{ the adding of dissonances, etc., etc., are all applicable here; the only additional rules refer to those parts of the scale which require major chords — as follow: “The second and seventh of the scale must always be accompanied with major chords.” ‘“* The fifth of the scale may be accompanied with either major or minor.”’ * The pupil is strongly advised to read very carefully what has been stated upon that subject at page 63. t See page 42. 3 See page 31, 44,47, 50. We are desirous to draw the attention of the student %o these four rules of harmonizing, in order that he may see their applicability to the harmonizing of minor melodies. HARMONY AND COMPOSITION. 129 : With respect to the accompaniment of the 5th, some judgment and caution are necessary; because, as the fifth of the scale and the jifth of the tonic (or key chord) are the same intervals, a mistake in the-selection of the harmony of that interval, with reference to major or minor, might easily be committed; however, by a little reflection and practice, this may hereafter be effectually avoided. For further explanation the pupil is referred to example 151. » Jt must not be expected that minute directions will be given how the pupil should ‘proceed on all occasions; that would indeed be impossible; he must put into practice the knowledge he has acquired, and exercise his own ingenuity; if he does so, and carefully examines the exercises with which he will be furnished as he proceeds, it will be a wonder if he misses his way. The following is an illustration of what has been stated, and we will analyze it. A Minor Melody harmonized with Extended and Compressed Harmony. 8 = 5 It. ie 13. 14. 15. 16. fe oe \ . | a ! kes teal at agers oz E Ee owt Soa Posies re Z=e 2 \ Ss Se ide 2) ow Jest See ee ee —— yg eg — « “4 TF * The exercise commences with the 5th of the scale, which must have a minor chord; why it must be thus accompanied requires no explanation. N.B. As the 5th is here repeated, we have employed the fourth rule of harmonizing.*— At 2, the second rule has been introduced.t because the fourth of the scale descends one degree. Bars 3, 7,15, cadences.¢ At4, dissonance of the o At 5, the octave being repeated, the third rule is employed §. At 6, the fifth accompanied by a minor chord. Why? Because the second part of the minim is accompanied by the fourth rule, which requires a major chord; had the 5th been accompanied by a major chord, then ¢wo major chords would have followed each other in immediate succession, which for the present should be avoided. At 9,a 7th by license is introduced in compressed harmony; at 10, the harmony is extended, to prevent skipping.|| Bythe introduction of this licensed 7th, the harmony of the succeeding chord is of course deprived of its 5th; which, however, is amply compensated by the effect produced by the 7th. Compare the effect produced at bar 5 in extended harmony with 13 in compressed. The attention of the student is particulary directed (at 10) to the progression from F to G-sharp; the peculiar effect this progression produces has already been alluded to in page 128, Ex. 138. * See page 50. + Page 44. + See. cadences, page 117-118. § Page 47. || Ex. 132. 130 HARMONY AND COMPOSITION. It has been generally remarked, and with great truth, that one example often effects more towards elucidating a subject than pages of explanation; we shall, therefore, give a few specimens, showing how certain portions of the preceding melody may be variously harmonized; more especially with regard to the accom- paniment of the fifth of the scale, as exhibited in the following example. Bar 17. The fifth of the scale accompanied by a major chord. Compare this harmony with bar 6 Bar 18. The fifth, accompanied first by a minor, and then bya major chord. Compare as above. Bar 20. In order to preserve a flowing melody in the bass, the 7th in the tenor is permitted to ascend. This liberty, however, must be used sparingly. Compare the progression of the bass at 19 and 20 with that of the alto, 21, 22. These specimens also exhibit several modes of extending the harmony. It will be observed that, in bars 22, 23, 25, itis extended beyond the limits pointed out in Ex. 130; nevertheless, it may be employed thus with very great effect. Compare these specimens from bars 19 to 20 with bars 9, 10, 11. To enter into a full explanation of these various specimens would only tend to frustrate our design, which is, that the student should examine and judge for himself, and become practically acquainted with that, which no specific rules can ever convey: — viz., general effect. Let it be observed, that no new rules have here been introduced; all has been effected by the simple application of the “‘ four rules of harmonizing,” with which the student was before familiar. We shall now proceed to introduce a most important chord in harmony : viz. THE CHORD OF THE MINOR NINTH. It will be in the recollection of the student, that, when we explained the reso- lution of the chord of the fundamental 7th,* we were particularly anxious to draw his attention to two intervals of that chord : viz., the 3rd and 7th; the former of which ascended a semitone direct to the octave of the tonic, while the latter descended a semitone to the 38rd of the succeeding chord. Itis a fact worthy of notice, that when these two intervals are heard together, in the situation repre- * See page 39, also 52. HARMONY AND COMPOSITION, 13] sented at (a) in the following example, an immediate and powerful tendency ta attract each other is manifested between them.t a. 4 C a. a sa a 7 = 7 Bee 00 HB gas eg ee to OT BSG Ex. 41. Major. Major. Minor. Minor. $ $ $ ¢ 5 L $ a t fT. i jt} £ A L. 4y a ——— = oe Hy i oo x ra] 1. i i C 2. aug When these two intervals, however, are placed in a reversed position (as at b), then how opposite the effect! no sympathy is manifested between them; no desire to approach each other; indeed a contrary feeling is exhibited: —a desire to separate; to fly off in opposite directions. It is by these two intervals, ascending and descending by semitones, that the whole mass of harmony is guided and directed.t Now let the student mark well— when the 7th descends a semitone, the chord into which it descends will be a major chord (a, b); but when the 7th descends a whole tone, the chord into which it descends will be a minor chord (c, d). In this latter case it is evident, that, in consequence of the 7th descending a whole tone, the equilibrium which subsisted, as it were, between these two parts before, is now destroyed; and, in order to restore it, some other interval must be found, by which this object shall be accomplished; in other words, an interval must be added to the chord of the fundamental 7th, which (while the 3rd ascends a semi- tone) shall descend a semitone; and as the 7th in the first instance indicated the approach of a major chord, so the interval sought for shall be calculated to indi- cate the approach of a minor chord. Here the question arises, — where, and how, shall we find this interval? — We answer, —by applying once more to that inexhaustible fountain from which we have obtained all our previous knowledge. In examining example 48, we find that the harmonics of the generator produce not only a common chord,j{ the chord of the fundamental 7th, and a scale with its fundamental basses;— but the chord of the fundamental 9th also; and this 9th, let it be well observed, is a major 9th. See the following example 140 (a). The student is requested to pay particular attention to what follows. That nature furnishes a major chord, and that a major chord may be changed into a minor by lowering its 3rd a half tone, has already been shown: * now the (referring to the following example) let us proceed upon the same principle with 9th; and, as we have lowered the rHrrD of the common chord a semitone, and made it a minor, let us lower the NINTH a semitone and make it likewise minor (6); it will then descend a semitone upon the 5th of the tonic (c), while the 3rd ascends a semitone to the octave, and thus the equilibrium of these two intervals in their progression is preserved. ; The whole of the chord of the minor 9th is exhibited at (d.) It will be observed, that at (a) the major 9th descends into the Sth, a whole tone, while the 7th descends but a half tone, producing a major chord; but that at (d), while the minor 9th descends a half tone into the 5th, the 7th descends a whole tone into the 3rd, pro- ducing thus a minor chord. * The truth of this observation w/ll be attested by every intelligent vocalist and performer on wind and string instruments (not the pianoforte). + A major chord (let it be remembered), not a minor. + Page 56-57. 132 HARMONY AND COMPOSITION. aan 1 ae Ex. 142. t Major 9th. Minor 9th. bo Be a F b r yt} F- 4. 1 we TT. wt ft In ee == | Ra a | a fe —tH a i i a Rae: i Having fully explained the nature of the minor 9th, and from whence it is . derived, and having shown the necessity of its introduction, we shall now proceed to point out “* How practically to incorporate the MtNoR 9th with the Chord of the Fun- damental Tth.” As the minor 9th will be found a major semitone {t above the octave, it is only necessary to remove the octave, and insert in its place a note a major half tone higher, and that note will be the minor 9th. As this minor 9th (like the fun- damental 7th) requires no preparation,§ we shall call it The Fundamental Minor 9th. || which may be introduced into any dominant chord. At (e) in the following example, II, is the chord of the fundamental qth; the octave is marked to be expunged. Atjf. The minor 9th is inserted in its place. Atg. The minor 9th is resolved, descending a semitone, into the 5th of the following chord. Ath. The chord in different positions. Ati. The 9th is resolved on the same bass into the octave, like a dissonance by suspension. As the minor 9th resolves into the 5th, another dissonance of the 6th presents itself, prepared by the 9th; the rule for which is: ‘* When the fundamental bass ascends a 4th, the dissonance of the 6th, pre- pared by the 9th, may be introduced.” See the following example at a; and, as the same progression of the fundamental bass admits of the 4th prepared by the 7th, these two dissonances may be com- bined, as at b. t See Ex. 48. + A note, raised or lowered a semitone without changing the name of that ot is called a minor semitone. A note, which changes its name when thus raised or lowered, is called a major semitone. § Thus it may eas'ly be distinguished from the dissonance of the 9th by suspension, which requires preparation. {| Or chord of the minor 9th; the fundamental 9th; or simply the minor 9th; by which the whole chord is to be understood. q See Ex. 108. HARMONY AND COMPOSITION. 138 Before we proceed to the inversion of the fundamental chord of the minor 9th, the student is recommended to exercise himself on that chord, by modulating through all the relative minor keys; a specimen of which is given in the following example. Previous to entering upon that exercise, however, a few preparatory questions like the following will be found useful. Q. How do you discover the minor 9th? A. The minor 9th is found a major semitone above the octave. Q. What is the minor 9th to G? A. A-flat, Q. Why is it not G-sharp?—For G-sharp and A-flat are represented by the same key on the pianoforte? A. Because G-sharp is not a major semitone above G, but only a minor semitone: it would be a sharp octave to G. Q. What is the minor 9th to B-flat? A. C-flat. Q. What———_—__—_—_—_———_ G--sharp? A. A-natural. Q. What——___________ D-sharp? A. E-natural. Q. What-———_———_—____—_- E--flat’? A. F-flat. Modulation through the Relative Minor Keys, with the Minor Ninth. 0. Ex. 144. i 3 : b i b ————— = N.B. A modulation (such as the above) consisting entirely of fundamental chords of the minor 9th, is not very grateful or soothing to the ear; quite the con- trary, indeed; but, when judiciously introduced, these chords produce effects quite electrifying. Hl Inversion of the Chord of the Minor 9th. As the chord of the fundamental 7th contains three intervals besides the bass, and may therefore be inverted three times,* so the chord of the fundamental 9th, because it contains four intervals besides the bass, may be inverted four times. It is necessary to observe that any inversion of the fundamental 7th may at once be converted into an inversion of the minor 9th by merely removing the interval which represents the octave, and writing in its place a note a major half tone higher; as in the following example. * See Part IV, on inversions. . 184 HARMONY AND COMPOSITION. Chordof Chord of First Second Third Fourth the 7th. the mincr 9th. Inversion. Inversion. Inversion. Inversion. Ditto. Ex. 145. At 1, the chord appears as the chord of the fundamental 7th, with the octave marked to be expunged. At 2, the octave is expunged, and the 9th, E-flat, written in its place; which 9th resolves on the 5th of the following tonic chord at 3. At 4, this chord appears in the jirst inversion. D, the octave (which would here appear as aéth), is expunged, and the minor 9th put in its place, which, in consequence of the inversion, requires to be figured with a7. The chord is called the diminished 7th.* N.B. Had the minor 9th not been introduced, it would have been the chord of the 6 At 5, is exhibited the second inversion, rf x N.B. Had the 9th not been introduced, it would have been the chord of the :. & At 6, third inversion, : or . N.B. Without the 9th, it would have been $4 At 7, fourth inversion. As the 9th itself is in the inverted bass, we need only figure the original 3rd, thus: #2 (sharp 2nd), as at 8. Having now shown the four inversions of the chord, it will be necessary to make a few observations upon each of them. Observation I. As the essential intervals of the fundamental 7th are the 3rd and 7th,t so those of the minor 9th are the 3rd and 9th;} by these two latter intervals we are always enabled clearly to distinguish the chord of the fundamental 7th from that of the minor 9th and its inversions; nevertheless, the fundamental 7th must not be omitted when we write that chord; for, the omission of that interval would deprive the following tonic chord of its 3rd. Observation II. The 8rd and 9th must therefore be continually kept in view; and, under what- ever figures these two intervals may be represented in the various inversions, they are at once recognized; for, the 3rd will always require a mark of elevation (such as a sharp or natural), and the minor 9th one of depression. In one word, these two intervals are always marked by accidentals of an opposite nature (which can never occur in an inversion of the fundamental 7th), and therefore musi always be figured; the other intervals of the chord need not be figured, unless they require accidentals; for instance, in the preceding example, at 4 (first inversion) the original 3rd, F-sharp, is in the inverted bass; all, therefore, that is required is to figure the 9th, which is here represented by a flat 7. At 5, second inversion, the sharp 6 represents the original 3rd, F-sharp; and the flat 5 represents the original 9th, E-flat. At 6, third inversion, the sharp 4 represents the origina] 3rd (F-sharp) and the flat, the original 9th (E-flat). * Because this 7th is one semitone less than the fundamental 7th. N.B. This chord has beer most unaceountably mistaken for a fundamental chord. See page 130, minor 9th, and Ex. 141. t See Ex. 141, u, b. t See Ex. 142, c. HARMONY AND COMPOSITION. 135 At 8, fourth inversion, the sharp 2 represenvs the original 3rd, F-sharp; and the inverted bass that of the 9th, E-flat. We shall now illustrate what has been said on the preceding examples, by giving separate exercises on each of the inversions. Exercise on the Chord of the Diminished ‘th. I. 2. 3 4. Ex. 146. It will be observed that, at bar 4, 5, the 9th, instead of descending into the 5th of the succeeding tonic, descends into the octave of the same bass; and thus the chord of the minor 9th is changed into the fundamental 7th.* See example 155, IT, i. N.B. This exercise, as well as the following, the student is advised to play. At II, the same exercise with extended harmony. The tenths between the tenor and bass produce a good effect. N.B. The tenor from 2 to 3 has ascended, by which the 8rd of the chord is doubled, which produces a good effect; especially in a minor key. At III, the same exercise diversified, which the pupil is required to finish him- self, and then play. N.B. It is necessary to observe, that an imperfect 5th is always allowed to precede or succeed a perfect 5th in consecutive progression; the law is only against a consecutive progression of perfect 5ths. Let this be well kept in mind. The consecutive 5ths between the tenor and bass, therefore, in the above example (z} are permitted; this may, however, be easily prevented, as at y and z. * Partaking of the character of the 9th by suspension. 136 HARMONY AND COMPOSITION. Exercise on the Second Inversion of the Minor 9th. < ¢—— original 3rd. Figured ,5 original ath. I. 2. 3 4. Ex. 147. #8 ba i _*s = In the above example the 5th (B) in the inverted bass, bars 1, 2, instead of descending as usual, ascends, to prevent the appearance of consecutive 5ths between the tenor and inverted bass. 4 Exercise on the Third Inversion of the Minor 9th. 7 4— original 3rd. i Figured é s——original 9th. Enharmonic Changes. a I. 2. 1 Ex. 148. i se ght eo ° the pupil. The only observation which we shall make upon the preceding exercise is that, at bar 1, the note B, the original 5th (but here the 6th from the inverted bass), instead of descending upon A, the octave, ascends in bar 2, to E the 8rd of the bass.* By thus proceeding, the 3rd of the inverted bass is doubled, which pro- duces a very good effect. Let'the student write this exercise in extended harmony and play it. The commencement of it is as follows at II; to which the student may add such dissonances as he finds most effective. Extended Harmony. Exercise on the 4th Inversion of the fundamental 9th, or Sharp Second. 2% original 3rd. Bass original om a . * This process may always be adopted when the dominant chord is in the 2nd position, and the third inversion employed. \ HARMONY AND COMPOSITION. 137 At a, the 9th being in the inverted bass, resolves of course upon the 5th of its tonic (b), and produces the second inversion of that chord, ({t). Atc, we have the sharp 2 again; here, however, the 9th resolves into the octave. When the chord of the sharp 2 resolves into the 8th, it produces the effect of the ¢ by suspension, which is not very satisfactory. The following example shows several modes of avoiding this. I. 2: 3: 4. fa. at. ‘fm. 1 Pusat: faut Ty fora ~—. oe ‘foe fo Th E =f F=—=fF-F- t +-——ft + = f H=+ t “44 a a, is atk 10 Ii § 1 7 § 1 zy tt t t aos E =I —t I TH Sal 1 i th i th In the preceding exercise at b, the resolution of the § is treated as an unpre- paredt discord by suspension. At c nearly so; because the § is not resolved upon the same bass, but is immediately followed by an inversion. At d, another method. We shall now introduce the student to the FIFTH AND LAST RULE OF HARMONIZING, “* When the 6th of the Scale descends one degree, it may be accompanied by Dominant, to which it will be a Minor 9th.§” When the above rule is employed, the 5th of the scale, whether preceding or or succeeding that interval, must be accompanied with a minor chord. See a, b. Z S é. By ly T r 2 J = q o bh coo Ex. 151. i ? Hh I bets a In like manner, should the fourth of the scale, in descending, be accompanied by the dominant, then the fifth of the scale immediately preceding that interval must also have a minor chord, c. When several intervals of the chord of the tonic immediately succeed each other in a melody, they must all be accompanied by minor chords (d); and it would, therefore, be incorrect to accompany the 5th as at e. || + See Ex. 145, bars 7 and 8. * See N.B., page 135. + See Ex. 119. § This rule could not be introduced sooner, as it is founded upon the chord of the minor 9th. 1 See page 129—Observation on the accompaniment of the 5th in minor scale, and Ex. 139. 138 HARMONY AND COMPOSITION. N.B. When the fourth rule of harmonizing is employed (which we know refers to the 5th of the scale), that interval may be changed into the 6th, and then accompanied by the fifth rule. For example, the key is A-minor, the 5th of the scale is E; and, as that 5th is repeated, we have accom- panied it according to the fourth rule,t viz., by the dominant (see Ex. 150, II,). At 2, however, we have changed the 5th (E), previously accompanied by the dominant, into the 6th (F), and then accompanied it according to the fifth rule. At 3 and 4 is exhibited a similar process, which is preferable to the jirst. Let us now harmonize a few melodies in the minor keys. In order to show the variety which may be produced in harmonizing even by the chords of the tonic and dominant only, when aided by the minor 9th, the fol- lowing melody is constructed so that no other harmony is requieed but what arises out of the progression of these two chords (as will be seen by the funda- mental bass), assisted by a few dissonances which naturally present themselves in the course of that progression. Air harmonized with the Minor 9th. 1. i he, 7 t I t ry { = ~~ w a : a Bars 2, 11, the fifth rule of harmonizing is introduced. The melody at 7 and 8 in the soprano is imitated in the bass, at bars 8 and 9. Bars 9 and 10 in the alto are imitated in the bass, 15, 16. Bars 9 and 10 in the tenor are imitated in the soprano, 15, 16. The dissonances of the 4th, bar 2 (tenor), combined with the minor 9th in the soprano (arising out of the fifth rule), will be found very effective. The gradual descending progression of the alto from the 9th to the 10th bar, while the tenor thus ascends to the 9th, is very effective, and produces two melodies, which are subsequently imitated by the soprano and bass (bars 15, 16). At15is the fourth inversion of the minor 9th. + See page 50. *In bars 3-7 we have employed first the 8th and then the 9th, by which a more melodious harmony is produced in the tenor. In Ex. 147, and others, we permitted the minor 9th to descend an octave; here this progression is reversed. At bar 9, the minor 9th in the alto descends to the 9th, while the 8th in the tenor ascends to the 9th. These interchanges amongst the parts never fail of producing a good effect. HARMONY AND COMPOSITION. 139 19, 20. 21. 225) 33, 24. 25. 26. Ex. 153. k tf This example exhibits the second part of the preceding melody, and is so constructed as to admit the harmony of the subdominant; which will be found a great addition to the general effect. In the latter part of bar 19, the 5th of the scale is accompanied by a major chord; and, as it thus becomes a dominant, we are enabled to introduce the fun- damental 7th and minor 9th. Let this be particularly remembered, as much depends upon it; for, had the fifth of the scale at 19 been accompanied by a minor chord, then all the advan- tages which we have derived from the 7th and 9th would have been lost: we would reiterate, let this be well kept in mind. The remarkably smooth and flowing progression observable throughout all the parts, is, in a great measure, to be attributed to the introduction of the minor 9th. If the pupil examines and compares the harmony of bar 19 with that at 23, he will perhaps better comprehend and more fully appreciate the importance of the rule: ‘‘ The 5th of the Minor Scale may be accompanied by either a Major or Minor Chord.” And no less important is the fourth rule of harmonizing, viz.: “The 5th, when repeated, may be accompanied by the Dominant.” : Again we would reiterate —Compare THE SIMPLE MELODY OF BARS 19 AND 23; then the harmcny, and then the rules by which it has been effected. CHANGING MAJOR MELODIES INTO MINOR, FOR THE PURPOSE OF HARMONIZING. The themes which are furnished in the former part of this work * may be changed into minor in the following manner: first, by merely altering the signa- ture; in this case, the name of the key remains unchanged. By way of illustration, let us take a theme written in C-major; we will change it into C-minor.t How? By placing three flats as a signature, + and then, by raising the 7th of the scale (wheresoever it may appear) a minor semitone, the theme will be in a minor key. In the key of C minor, the 7th is B-flat; we therefore place a natural before it, to raise it a half tone. Secondly, the major key may be changed into its relative minor by merely transposing it a minor 8rd lower; in that case, the name of the key is changed, but the signature remains unaltered. Q. Suppose we were to change theme No. 2, page 32, into minor, according to the first ease, what signature would be required? : A. Two flats; and /, being the 7th of the scale, should be raised a semitone. * See page 32, 38, 49, 51. ¢ Called irrelative minor. ¢ See page 57. 140 HARMONY AND COMPOSITION. Q. Suppose we change it into minor according to the second case, what signature will it require ? A. The signature will remain as it now is; but the theme must be transposed a minor third lower, and D be raised a semitone, as being the 7th of E minor. When. a theme has thus been changed into minor, the five rules of harmonizing may be employed. In pianoforte music, especially, the minor scale is frequently employed as a mere passage of effect; in this case, composers have agreed sometimes to raise the 6th of the scale a half tone in ascending (a); but, in descending, to lower the 6th and 7th a half tone (as at b in the following example), some authors write the descending scale as at c, preserving thus the true and genuine character of the minor. Minor Scale, arising out of Passing Notes. This apparent anomaly arises from the scale on these occasions being chiefly composed of passing notes,* of which, in the present instance, the common chord of A minor is the foundation. We shall here harmonize the minor scale descending; employ the minor 9th, and add such dissonances as may produce the best effect. ddd. Seiad: _ add sd J) d tddd edd Ex. 155 pel lifnsendidtehiade te tee i a hc ae T i t L Ld. 7m ; ca oe ry} t oe I aah a > a as Se —e HTT Litt TT. rr = i E fF See t In the above example we have taken advantage of the 5th rule of harmonizing, by accompanying the 6th of the scale with the dominant, instead of the subdomi- nant; and thus the progression from the dominant to the subdominant (which would have involved consecutive 5ths and 8ths) is avoided. The following example illustrates, in a practical form, and in a regular and uninterrupted progression, all that has been said on the subject of the four inver- sions of the chord of the minor 9th; to which are added such of the dissonances as are calculated to produce the best effect, interspersed with cadences; so that the whole receives thus a rhythmical form. As the fundamental and inverted basses are all figured,t a minute and par- ticular analysis of the exercise is not requisite; but the few observations at the end may assist the pupil. *To be explained hereafter. + A separate staff has been added, to prevent the figured bass appearing crowded. HARMONY AND COMPOSITION. 144 I. 2. 3 sauaue Sostenuto. p rinf. 4 t FE { T ia b — bes: Hy at eS Ex. 156. Te : eS = = 2 a ba bi —-— 6 et —_ a { E — 4 Inv. Bass figured. b: if b i leg = E j r A bs 1 a. $e oath ete = ie ao r a Fund, Bass. 4. 5. 6. 7s = SS ~~ 4 be a ce as bo * Produced by the suspension of the 6th by the:6th, prepared by the minor 9th. See fundamental bass, also Ex. 143, 142 HARMONY AND COMPOSITION. am SHORT ANALYSIS. Bar2. The Sra of the chord, C-sharp, is selected as the inverted bass, consequently first inversion of the chord of the 9th — diminished 7th. See Ex. 158, bar 4, and Ex. 159. Bar 12, The 5th has been selected—second inversion,b§. See Ex. 145, bar 5, and Ex. 156. Bar7. The 7th——————_——- third inversion, $4. See Ex. 145, bar 6, and Ex. 148. Bar 20. Th 9th-—--———-——_— fourth inversion, p2. See Ex, 145, bar 7, and Ex. 150, d. This will suffice to show how the inversions of the fundamental 9th may be employed most effectively. We shall now point out a few of the dissonances which are introduced in the example. See fundamental bass. From bar 4 to 5 bass ascends a fourth, dissonance of 4th in soprano, prepared by 7th. 5 to 6 nd, 5th. 10 to 11 ——-———— fourth, --—_———- 4th in bass, —---—————8tth. 11 to 12 ——_——— fifth, —————--——- 4th in alto, -————_——8th.. 7 fourth, 6th in alto. —————————9th.. Bars 9, 14, 19, 23, various cadences. ARRANGEMENT FOR PIANO-FORTE. Ex. 157. + In order to produce the proper effect, when playing this and the following exercise, it should be kept in mind, that they both form one exercise, and must be performed without interruption. HARMONY AND COMPOSITION. 148 33- 34. 144 HARMONY AND COMPOSITION, 56. 58. 59. 60. 61. 7+ smorzando, — =e The above Ex. may be viewed as a continuation of the preceding, written for the pianoforte ; the subject in the bass at 24 and 25 is (with an occasional slight change) carried through the whole exercise. From bar 32 to 35 the subject appears for the right hand. From bars 36 to 41 the subject is reversed in the bass. As this interesting matter will be resumed hereafter, we shall for the present only impress upon the mind of the pupil the necessity of studying what has been already said, with care and attention. MODULATION IN MELODIES BY THE INTRODUCTION OF ACCIDENTALS.* It will be observed that all the melodies hitherto harmonized, commenced, continued, and ended in the same key; and that all diversity of harmony (shown in so great a variety of examples) was produced through the instrumentality of the three fundamental basses (tonic, dominant, and subdominant); by the employ- ment of the four rules of harmonizing; by inverted basses, etc., etc. It shall now be shown how a melody, commencing in one key, may, through the means of an accidental, be made to modulate into another. This is a subject of considerable importance, and calculated to open a very wide field for our future opperationsin harmony. In order that the student may be enabled fully to enter into its nature and spirit, and to understand the prin- ciples on which it is established, he is strongly recommended carefully to re- peruse what has been stated respecting the origin of melody and harmony,t and scales of three sounds.t From what has been said, it is clear that a scale consists in reality of only three sounds, accompanied by two fundamental basses (tonic and dominant §). The intervals of these two chords, including the fundamental seventh, will be found to comprise, in all, six sounds; thus: Now let it be carefully observed, that, while we employ no other intervals in constructing a melody but such only as are contained in the above example; and use no other fundamental basses but the tonic and dominant; then the melody and harmony will remain in the same key; nor can any departure out of that key take place. The following melody is constructed on this Principle, and continues therefore in the Original Key. oH Te | | rr LL Tye (=) < i= i t —p |= : Ex. 159. 2 Ee ¢- 2: c= T - f- - \ eet £ t + fe t f 4 t fa f o—H That no accidental can be introduced in the preceding melody without imme- diately disturbing the natural order of the progression, is self-evident; therefore, whenever we perceive a sharp or any other accidental placed before an interval in ot LI Li Eo * Sharps, flats, or naturals. + Page 60 to 66. + Ex. 50, etc. § The subdominant can be considered at present in no other light than as the tonic of another scale of three sounds. (See Ex. 52, etc., etc.) (145) 146 HARMONY AND COMPOSITION. a melody, which does not belong to that melody or scale, we must conclude that a sound has been introduced which is foreign to the original key, and with which, consequently, the two fundamental basses of that key can have no connection. Under these circumstances, it is clear that another bass must be found to accom- pany that foreign sound. For example; let us suppose that we are required to harmonize the following melody, written in the key of C:— . £ a Fs ee SSS ee = st [a i I (ee Bes We know that the key of C has neither sharp nor flat; but here we meet with an F-sharp. Now, as this F-sharp forms no part of the key of ©, it cannot be accompanied by either of the fundamental basses belonging to the key of C; and the question is, how shall we find that other bass with which this F-sharp may be accompanied? We reason thus: This F-sharp belongs to the key of G (to the octave of which it ascends by a half-tone); we conclude, therefore, that a modulation to the key of G is contemplated.* Now, as no modulation can be effected but through the instrumentality of the dominant of the key to which we modulate;t and as D is the dominant to G, it follows, that D is the only proper bass, which, on this occasion, can accompany the note F-sharp; and thus a modulation to the key of G is established. . N.B. The foreign interval, introduced thus, we shall call “ A note (or the note) of modulation.” In illustration of the above, we give the following example: Ex. 161. Melody. Inv. Bass, § __,Cadence. s. ia: iT dooce od Lor J. eed + = Fund Bass, (Og 9 ee el Generator.> = [ ne Generator.> N.B. The notes placed under fundamental basses point out the generators of the scales of three sounds.or key in which we are for the time being; and the dominant, marked thus cr may be considered as the door which leads to the new key. See modulation, Ex. 51 and 52. The preceding melody continues in the original key of C until it arrives at F-sharp (bar 3). Here a modulation takes place to the key of G, by “‘the note of modulation,” F-sharp. This F-sharp is accompanied by D. Why? Because it is the dominant to G. * The key of G is the first which presents itself in the circle of keys requiring a sharp. (See page 73.) + See page 64, Part III, on Modulation, Ex. 54. HARMONY AND COMPOSITION. 147 N.B. After a modulation has been thus effected, every succeeding interval of the melody must be accompanied by the fundamental basses of the new key (thus —G is now the tonic, and D the dominant), until another ‘‘note of modulation” presents itself, by which we are directed to another key.* Q. In what key is the above melody written? — A. In the key of C. Q. Does F-sharp belong to that key? — A. It does not. Q. How does F-sharp proceed? — A. It ascends a half-tone to G. Q. With what bass have you accompanied F sharp?—A. With D; because D is domi- nant to G. : Q. As the note F-sharp has ascended by a half-tone to G, you conclude that a modulation to G has been effected. Now suppose the key to be G,and you should meet with a C-sharp, to what key would you modulate? — A. To the key of D. Q. With what bass would you accompany the note C-sharp?—A. With A; because A is dominant to D. Q. But suppose G-sharp had been a note of modulation? —A. Then I should modulate to A, by the dominant E. Q. Why is the note A, bar 4, accompanied by the bass D?—A. Because A is the second of the scale of G, and requires to be accompanied by the dominant. Q. Is F-sharp, bar 5, a note of modulation? — A. No; it is the 7th of the scale of G. This will suffice to show the nature and property of a ‘‘note of modulation,” and how it is to be treated when it ascends a half-tone.t We shall now proceed to point out another ‘‘note of modulation,” the pro- gression of which is diametrically opposite to the former; for it descends a half- tone, and modulates to a key, tothe tonic of which the note upon which it has thus descended will be a major 3rd. By this descending ‘‘ note of modulation” we are enabled to modulate back to the original key. . The following Melody modulates out of the Original Key, and afterwards returns to it. I. 8. Se oe cstdalfd de oes ls Alto. eTrcr... Aas ded ay Tenor. ae id 2 2 Sina lest Bass. eet er Ct Se ett eee Figured sd Bagel f 6 if ae 6 f = Inverted & cana bee tty Sua | sf [=e er ANALYSIS. The first 5 bars of the above example are the same as those in the preceding, except the last note, F-natural; and, as that note does not belong to the key of G, it indicates a modulation out of it. This F-natural becomes now a “note of modulation;” it descends a half-tone, on the major 3rd ‘of the following tonic, C, to the key of which it modulates. As we have now returned to the original key, it follows, as a matter of course, that the remainder of the melody must be harmo- nized according to that key,—C being now again the tonic, and G the dominant. * See Part ITI. + Let it be keptin mind that the half-tones here spoken of (whether ascending or descend ing) are major half-tones. 148 HARMONY AND COMPOSITION. There are three things which the pupil ought well to keep in mind:—1, that there are two ‘“‘notes of modulation;”’ one of which ascends a half-tone, and the other descends a half-tone: — 2, that the former modulates to a key which lies a half-tone immediately above it; and that the latter modulates to a key to which, when it has thus descended, it will be a major 3rd: —3, that, in the first case, ‘‘ the note of modulation ’’ is a major third to the dominant; in the second case, ‘‘ the note of modulation” is the fundamental Tth to the dominant.* Having fully explained, and illustrated by examples, how modulations in a melody may thus be effected by the introduction of accidentals, it shall now be shown how that cbject may be attained even without the aid of these accidentals. No doubt these agents are in most cases not only the plainest, but also the most certain indications of modulations in melodies; yet it is certain that a simple melody contains within itself not only the GERM of many modulations,t but of melodies also. The discovery of those intervals in a melody by which we are thus enabled to modulate, and their practical application in harmony, form perhaps the most interesting subjects for intellectual pursuit that can well be imagined. The materials which it supplies for the purposes of harmony are so abundant, so rich, and so extensively applicable, that a melody, the most uninteresting, the most monotonous and unmeaning, may be made the means of prodvcing almost endless variety; not only as it may effect the harmony as a whole, but also as it respects the melodious progression of the inner parts separately. We shall now turn our attention to the discovery of modulating intervals not indicated by accidentals. It has already been shown that a note which is raised by an accidental and ascends a half-tone, modulates to a key which lies a half-tone above it; we may therefore conclude that any note which proceeds thus, whether indicated or not by an accidental, will modulate in thesame manner. From this consideration arises THE FIRST RULE For discovering and employing, for the purpose of modulation, those intervals of a melody which have not accidentals. A. — “ The note which ascends 4 HALF-TONE modulates to a key, the octave of which lies a half-tone above that note.” A. B. — “ Or, it may modulate to the relative minor of that key”. B. Ex. 163. Modulation to F Major. Modulation to D Minor. * It may have been observed that, except at the close of an exercise where the cadence has been introduced. the subdominant has not been noticed. A careful perusal, however, of what has been said (page 61. and examples following) will suffice to show the reason why that bass, as one of the three fundamentals, must for the present be left out of view. ¢ See Part III, Modulation, from Ex. 55 to 64. HARMONY AND COMPOSITION. 149 é In the first case, the “note of modulation” is a major 3rd to the dominant of the new key. A. In the second case, the note of modulation is a 5th to the dominant of the new key. B.* It will be observed that although the “notes of modulation ” in both cases, ascend by half- tones, yet how very different are the results. In the former cases (A), we modulate to a major key; in the latter (B), we modulate to a minor key. To show the variety which may be produced by the application of the first rule only, we here present the student with a melody which, for monotony, can scarcely be equalled; written thus designedly, to show the efficacy of the rule. A Melody harmonized according to the first Rule of ‘‘ Modulating by the Intervals of a Melody” which have not Accidentals. Ex. 164. Soprano. Alto. ANALYSIS. This exercise commences in the key of C, in which it continues until the 2nd bar, where the note of modulation,” E, (marked thus x), ascends a half-tone, and modulates to F major. Bar 3. E, the same “ note of modulation,” ascends a hailf-tone; but, instead of modulating to F major, it modulates to the relative minor + of that key—D minor. Bar 4. Same ‘“ note of modulation’? modulates to F major.+ Bar 5. B-natural C major.t Bar 8. Ditto —————-——_——_________—__ A minor.§ Bar 9. Ditto ————-——_—_—_—______—_ —C major.t Q. At bar 2, youhave modulated to the key of F; could you have modulated to ary other? A. I could have modulated to D minor. Q. Suppose that you had modulated so in bar 3; how ought you to have treated the note of modulation in bar 4? A. LI would have modulated to F major, and then, in bar 5, to D minor. Q. At bar 5, you have modulated to the key of C, by the note of modulation, B-natural; could you have modulated to any other key? A. Yes; to the relative minor. Q. Suppose that you had modulated, at bar 6, to A minor, instead of C major; how would you have proceeded afterwards? A. I would have continued in A minor until I had arrived at the note of modulation, B-natural, in bar 7, and there I would have modulated to C major. The following example exhibits the same melody reharmonized, showing how this rule may be differently employed. Let the student carefully examine and then compare the effects of both, bar by bar; not only as regards the modulations, but also as regards the inverted basses and inner parts; and let it be remembered, that as a change in the inverted bass necessarily brings about a correspondent change * As the rule naturally divides itself into two parts,—to prevent confusion in the practical application of it, we have distinguished the one from the other by the letters A and B. Let this arrangement be kept in mind. + First rule, A. t See chord of the minor 9th, Ex. 124, on which this ruleisfounded. § First Rule, B. 150 HARMONY AND COMPOSITION. in the other parts likewise, su new melodies will naturally arise, which (as shall be explained hereafter) may be themselves converted into principal melodies, and harmonized as such. The same Melody harmonized differently by the same Rule,* 1 2. 3 4. 5. 6. 7. 8 9 To. Ex. 165. % Soprano. Alto. Tenor, « Bass. Fig. Bass. ~o eo me wr Let it be borne in mind that the foundation upon which all this variety rests is modulation as produced by the intervals of a melody. The student may put this rule into practice more extensively, if required: for example —let him select one of the themes given inthe early part of this work,t and harmonize it simply according to the four rules of harmonizing,{ with inverted basses.§ Then let him search out all those intervals which ascend by half-tones: these he may employ (if he chooses) as notes of modulation; but (let it be remembered) he is not obliged to do so; that is, he is not obliged to modulate. This must be left entirely to his own taste and judgment. SECOND RULE Of modulating by the intervals of a melody. “ The note which DESCENDS a half-tone modulates to a key, to the tonic of which the note to which it descends is a major 8rd.” C. “Or, to its relative minor” D. Ex. 166. Modulation to F major. Modulation to D minor. In the first case, the “note of modulation” will be the fundamental 7th of the dominant .of the new key. In the latter case, the note of modulation will be the minor 9th || of the dominant of the new key. * Let the pupil carefully examine and compare the progression of the alto, tenor, and bass of the present example with the one immediately preceding, and mark weil the difference. t See pages 44 to 51. + Themes, pages 46, 49, 51. + § See inverted basses, Part IV. | This rule is also founded upon the chord of the minor 9th. (See page 148.) See also the {th rule of modulation by intervals of a melody, page 156. HARMONY AND COMPOSITION. 151 A Melody harmonized according to the Second Rule of modulating by the Intervals of a Melody. . 5 . . 6. 3 Ex. 167. i © 3 4 5 . 5 7 Soprano. p P ; i . Alto. Phe oor ce aie eee Deke SSL _ eo Tenor. + Seer s reais a gt = $205 Bass. 8 rat yt pee ee I f ot Gt ee Taw Pe a § 66% $ : br 8 ac & - _ Fig. Bass. SEGRE af tet 5 Gr: _ pid, witigve hed H PSE: Fp Sis y pb 3 = 2s ANALYSIS. The key is C to bar 2, where the “note of modulation,” C, descends a half-tone to B, and thus modulates to a key, to the tonic of which that Bis a major 3rd. Q. What key is that? A. G major. Bar 4. The ‘note of modulation,” B-flat, descends a half-tone, and modulates to the key of F major.t Bar5. Here the “note of modulation,” B-flat, occurs again, and descends a half-tone; but instead of modulating to F major, we modulate to the relative minor (D minor). Bar 5. The last note,C (note of modulation),descends { ae ee \ Ssiwion. ‘Besoutbnules Bar 6. Same note, C, E minor. Ditto. Bar 6. Note F, Cmajor. Ditto. Bar 8. —— C-sharp, a d. Dminor. First rule. Bar 9. —— C-natural, d d. G major. Second ruie. Bar 10. —— D-sharp, ds E minor. First rule. Bar 11. —— D-natural, di ds Aminor. Second rule. After proceeding through several other modulations, this exercise concludes with a cadence in the original key. The student, by way of exercise on this rule, may here again follow the directions given, immediately after Ex. 165, page 150. Q. Suppose that you were in the key of E-flat, and that the note E-flat DESCENDED a half tone; to what keys are you enabled to modulate? A. To B-flat major, or its relative minor, G minor. Q. By what rule? A. By the second rule. (See page 150.) Q. But suppose that the note D occurs, and ASCENDS a half-tone; to what keys can you modulate? A. To E-flat, or its relative nvinor, C. Q. By what rule? A. By the first rule. (See page 148.) * Ex. 166. + Ex. 163. 152 HARMONY AND COMPOSITION. Q. Suppose you had met with B-sharp, and that it had ascended a half-tone; to where could you have modulated? A. To C-sharp major, or A-sharp minor. Q. By what rule? A. By the first rule. Q. Suppose that you modulate by the second rule; what interval will the ‘note of modula lation”? be to the dominant? A. In the jirst case, it will be a fundamental 7th; in the latter case, it will be a minor 9th.* Q. Suppose that you modulate by the firs rule, what interval will the ‘‘ note of modulation ” be to the dominant? A. In the jirst case, it will be a major 3rd; in the latter, a fifth.t Exercises such as the preceding (by question and answer), when pursued by the student to any extent, m1y be made the source of real mental enjoyment; they will be found exceedingly useful, indeed especially so, when they are written in notes and carried out into actual practice. Heretofore our attention has been directed solely to those intervals which proceeded by half-tones only (ascendiny or descending); and upon those progressions were established our first and second rules. Now, however, the attention of the student shall be directed to those intervals which descend by WHOLE tones; this naturally leads us to the THIRD RULE Of modulating by the intervals of a melody. “The ‘ note of modulation’ which descends a@ WHOLE TONE, modulates to a key which lies @ WHOLE TONE below the ‘ note of modulation.’”’ E. “ Or, to the RELATIVE MINOR of that key.” F. Ex. 168. Modulation to”B flat major. Modulation to G minor. At E, the “note of modulation,” C, descends a whole tone, and modulates from G minor to B-flat major. At F, the same “note of modulation,” C, descends also a whole tone, but modulates from B-flat major to G minor. In the first case, the “note of modulation” is 5th to the dominant of the new key. aa the latter case, the “note of modulation’’ is a fundamental 7th to the dominant of the new key. A Melody harmonized according to the Third Rule. I 2. 5 ; 6. i 8. Ex. 169. = i ; 3 Soprano. Alto, r * Tenor. Bass. $6 33 Fig. Bass and Fund. oe ee = = eo | os eo *See inversion of dissonances, page 119, Ex. 127, 2. TEx. 163. HARMONY AND COMPOSITION. 153 ANALYSIS. The exercise in G minor continues in that key until the commencement of bar 3; here the note of modulation,” C, descends a whole tone to B-flat, and modulates to that key. The second part continues in the same key to the end of the 6th bar, where the “note of modulation” again descends a whole tone, and modulates to the original key, in which it concludes. The following example exhibits a still more extended application of this rule. It will be observed that, in the preceding example, we modulated simply from a minor key to its relative major, and vice versa. Here, however, we have enlarged our operations, and, by the same rule, have modulated to others which are more distantly related to the original key. A Melody harmonized by the same Rule. Ex. 170. Soprano. Alto. Tenor. Bass*, ANALYSIS. Bar 2. The “note of modulation,” D, descends a whole tone, and modulates to C minort (relative minor to the subdominant of the original key.) Bar 3. The ‘‘note of modulation,” A, descends a whole tone, and modulates back to the original key, G minor. The second part, at bar 5, commences with the relative major without modulation (that is by progression +); a modulation, however, to that key takes place on the second part of bar 5. N.B. The consecutive 5ths between bars 4 and 5 are admissable, as a new strain commences at bar 5. Bar 7. G, the ‘note of modulation,” descends a whole tone to F, and modulates to D minor (relative minor to the dominant of the original key), to the tonic of which this F will be the minor 3rd.§ This may suffice to show, in a slight degree what may be effected by the third rule. It is, however, only by practice, and a careful study of effects, that a thorough knowledge can be acquired of the variety which these rules afford in harmonizing. FOURTH RULE Of modulating by the intervals of a melody. “ The ‘note of modulation’ which ASCENDS 4 WHOLE TONE modulates to a key, to the tonic of which the note, when it has thus ascended, will be a major 3rd.” IL Il. ql. fe i— = | x a J peo ay ae te Ex. 171. § 23 Moduiietion to the key wee C. Modulation to the ene of D. Modulation tol B flat. * Let the student figure the inverted bass himself. + See page 148. + See lower part page 62, also 63. § See page 152, Ex. 168. 154 HARMONY AND COMPOSITION. e At I, the kevis G major. The “note of modulation,” D, ascends a whole tone to E, and modulates to the key of C major, to the tonic of which E is 3rd.* At II, the ** nute ot modulation,” E, ascends a whole tone to F-sharp, and modulates to the key of D major.+ At III, the key is G minor. The “note of modulation,” C, ascends a whole tone to D, and modulates to B-flat.+ N.B. There are other keys to which this rule would enable us to modulate; but, as they are rather too far removed from the original § key, they should be avoided. The above three modulations, therefore, are not only the most effective in general practice, but contain sufficient variety for all our purposes. N.B. The fourth rule admits of only one modulation, in which the note of modulation is 5th to the dominant. A Melody harmonized according to the Fourth Rule of modulating by the Intervals of a Melody. 2. . A F 6. i 8. » IO Ik 12, Ex, 172. 3 aes a : ? Soprano. Alto. I. Andante, st Tenor, Bass, Inv. Bass. ANALYSIS. Bar 2. The “note of modulation,”, D, ascends a whole tone to E, and modulates to the key of C major.|| Bar 3. The “note of modulation,” F-sharp, ascends a half-tone to G, and modulates (by the jirst rule ) to the original key. : Bar 6. The “note of modulation,” E, ascends a whole tone to F-sharp, and modulates to the key of D major. Bar 9. The “note of modulation,” A, ascends a whole tone to B, and modulates to the original key. * This is amodulation to the subdominant of the original key. + A modulation to the dominant of the original key. + The relative majorof G minor. § Extraneous keys. || This is a modulation to the subdominant of the original key. HARMONY AND COMPOSITION. 155 Bar 13. The ‘note of modulation,” D-sharp, ascends a half-tone to E, and modulates to E minor (by the first rule). Bar 23. The ‘“ note of modulation,” A, ascends a whole tone, and modulates to the original key.* Having disposed of those notes of modulation which ascend and descend by half tones and whole tones, the student shall now be introduced to the FIFTH RULE Of harmonizing by the intervals of a melody. ‘When any interval is REPEATED in IMMEDIATE SUCCESSION, the interval thus REPEATED modulates to a key, to the tonic of which it will be a 5th.’ + I. Hy III. 6 TV 8 I. 2. . a - fe ki . 8 x5 2 3 8 x 4 5 e 2 * s 4 x f ‘in t aa | ae Hi i os SSS = Se == ql Mod. és C. Mod. to A minor. Mod. to C. Mod. t to E minor. At I, the example is inG major. At bar 2, the note G is repeated, and we modulate to C major, to which that Gis a 5th. N.B. Had the key been minor (for example, G minor ), we should have modulated to a minor key (C minor). At II, bar 4, the note E is repeated, and, as the key is minor, we modulate to A minor. It is necessary to notice, that the above remarks refer only to such “ notes of modulation ”’ as are derived from, or originate in, the octave of the preceding chord. At III, as the “note of modulation,” G, bar 6, is derived from the minor 3rd of the preced- ing chord, we modulate to a major key.t Here, however, at IV, bar 8, the ‘‘ note of modulation,” B, is derived from a major 3rd in the preceding chord; we therefore modulate to a minor key. Let this distinction be well kept in mind. N.B. The “note of modulation ” will then be an octave to the dominant of the new key. It may be observed, that the harmony, as we proceed with these rules, increases in richness, and becomes more and still more interesting. The fifth rule, especially when combined with some of the others, will be’found a most powerful auxiliary in this respect. A Melody harmonized according to the Fifth Rule of modulating by the Intervals of a Melody. Ex. 174. 2 3 4 5 ie 7 8 Soprano. pot} +--+ sh qe — Alto. = ee o- 2 aa ETE e ‘Ba, eqepie eee ek 3 Inv. Bass. * When the fourth rule is employed, a licensed 7th becomes indispensable. (See licensed ith, page 43.) + Observe the analogy between this rule and the third rule of harmonizing by fundamental basses, Ex. 38. + See Ex. 56, page 67, m, n. 156 HARMONY AND COMPOSITION. The same Melodg as the preceding in Extended Harmony. 9. Io. Il. 12. 130) 14 15. 16. ANALYSIS. Bar 1. The last note, B (“note of modulation”), is repeated. "As this ‘“‘note of modula- tion” is, in the preceding bar, derived from a major 3rd, we modulate to a minor key —E minor. (See Ex. 173, IV.) Bar 2. B, the ‘‘ note of modulation,” ascends a half-tone, and modulates to C major.* Bar 3. C, the “note of modulation,” descends a half-tone,t to B, and modulates to G major. Bar 4. A, the ‘“‘note of modulation,” descends a whole tone,t and modulates to E minor. Bar 5. G, the “note of modulation,” Jescends a half-tone,t and modulates to D major. Bar 6. F-sharp, the “note of modulation,” repeated, derived from a major 3rd, modulates to Bminor. See IV. : From bars 9 to 16 is in extended harmony, by means of which a new effect is produced, not only with reference to the harmony collectively, but also in the melodious progression of the alto and tenor; and, as these inner parts may hereafter be converted into principal melodies and then harmonized, it is a matter of some importance that the pupil pay particular attention to what has here been said upon this interesting subject, and reflect upon it. Besides this, there will also be perceived a difference in the application of some of the tules: for instance — at bar 10, B, the ‘‘note of modulation,” ascends a half-tone; but, instead of modulating to C major, as at bar 2, we have modulated to the relative minor (A minor); in which _ key the harmony remains until it arrives at the “note of modulation,” A, bar12. These altera- tions and changes in the modulation should be very carefully attended to; they produce new melodies. Bar 17 commences in D minor. Bar 18. D. the “note of modulation,” descends a whole tone, and modulates to A minor.t Bar 19. The last note, A, is repeated, and modulates to D minor. Bar 20. The last note, A-sharp, ascends a half-tone, and mcdulates to B minor. Bar 21. B, the last note is repeated, and modulates to E minor. See Ex. 173, II, and obs. Bar 23. D, the second note ascends a whole tone, and modulates to C major.§ The following example in E minor will be found a most interesting and use- ful study. Let it be observed, that, in harmonizing this melody, we have employed principally the fifth rule. For the jirst five bars, the melody is exceed- * First rule. + Second rule. + Third rule. § Fourth rule. HARMONY AND COMPOSITION. 157 ingly monotonous (being designedly confined nearly within the compass of two intervals*), and consequently affords a fair opportunity of testing the efficacy of that rule. By employing it on the present occasion, all the monotonous effect of the melody is not only removed, but such a melodious progression is imparted to the inner parts (especially to the tenor), that we have been enabled to convert that part into a principal melody, as exhibited in Ex. 175, II. A Minor Melody harmonized according to the Fifth Rule. Ex. 175. I. 7 dias - > . > e Soprano. Alto. es a | a Tenor. Bass. aid If the above and the following exercise be carefully examined, the difference between them will be found to be very great indeed; for the former is in a minor, from which the present one, which is in a major key, has been extracted or derived. The following Melody was the Tenor in the preceding Exercise. I. Ze 3 4 5 6. 7 8 Ex. 175. II. Andante. a QO este Ky tery Soprano. J tet Alto. — Above all things, let it be kept in mind that the above melody originated in the preceding exercise, in which it was the tenor; that exercise was in the key of E * Three of these five bars contain, indeed, only one note. 158 HARMONY AND COMPOSITION. minor; and that the present one is in the key of G major. Between them, there is little or no resemblance. The rhythm alone, being the same in both, may perhaps be said to produce some resemblance, but that is all. The following example exhibits a portion of the foregoing melody, with the rhythm changed from common time to {. This rhythm also is an important study, which shall appear in a subsequent part of this work. Part of the preceding Melody, the Rhythm being changed. I. Moderato. Ex. 175. Il. The following example, which is written for the pianoforte, exhibits the fifth rule in quite a different character. The effect produced by that rule in the preced- ing examples was soft, and, as it were, conciliating. Here, however, the effect is quite contrary. Another Exercise on the same Rule,t written for the Pianoforte. Con spirito. 8: (5) 1) (4 Ex, 176. (3) (2) (5) rinf. rinf. * + The figures between the parentheses show what rule has been employed. HARMONY AND COMPOSITION. 159 (3) dim. After the minute analyses of preceding examples, it may suffice to say that the observations made already may be applied here with equal force. SIXTH AND LAST RULE Of modulating by the intervals of a melody. “ When the ‘note of modulation’ ASCENDS a, PERFECT FOURTH, or (which is the same thing) DESCENDS @ PERFECT FIFTH, we may modulate to a key, to the tonic of which that note, when it has thus proceeded, will be an octave.” G. Or, toa key to which that note will be a 5th.”* HH. 1.—G. Ex. 177. At I, G, the “note of modulation,” B, bar 2, ascends a fourth, and modulates to the key of E; to the tonic of which, that E is the octave. ( See fundamental bass. ) The “note of modulation,” A, bar 3, ascends a 4th to D, to the key of which it modulates.t At II, H, the “note of modulation,” B, bar 5, ascends a fourth to E, as at bar 2; but how VERY different is the modulation! For example: At I, G, bar 2, we modulated to the key of E. At II, H, bar 5, by the same “note of modulation”’ we modulate to the key of A. The great importance of this rule in harmonizing, and the vast influence which it exercises in modulation, will be better understood when practically illustrated. N.B. When this rule is employed, it is good to let the inverted basses and melody proceed by contrary motion; as the ‘“‘note of modulation,’”’ therefore, ascends in example 178, G, we prefer the third inversion; and, for the same reason, when the ‘‘note of modulation”’ descends, we prefer the jirst inversion, as in the following example: — Ex. 178. * These keys may be efther major or minor. ; As this rule is also divided in two parts, we have, in order to distinguish them, employed the letters G and H for this purpose. 160 HARMONY AND COMPOSITION. The employment of the other inversion (the second) is not, however, to be rejected; nor should we confine ourselves to contrary motion only, as that would produce a monotonous effect, which should be carefully avoided. As the harmony of the following melody will hereafter become the root or parent of many other melodies, the pupil is strongly recommended to examine it most carefully — most minutely; especially where the difference of effect produced by the employment of the rule with reference to G or H, is introduced. A aloey harmonized according to the Sixth Rule of modulating by the Intervals of a Melody. Ex. 179. Soprano. Alto. Tenor. Bass. “tt e-: jon 3 § pS ee ee eg Inv. Bass. \ (Saree Se 10. Ir. 12. = 14. 15. 16 oe oy sfae sh Seid ie) | SS SS Se et a #, 8 ore ¥ ; |} = Jes me Cc 2. = = ae SS SS T t t T r | 7 P od tt i ty §,—- i zs ii a i 4 4 F f i ag +h eee foe SS aS ee ee 17 18, 19 20. 21. 22 23 24. p#_t. | 1 x| powcr SEE x} 1 | jf pS = Zee Seas fing 2 e i Ea fre Beets AES lestee ge fie pte ess = # . 8 Ha g $ ia be. sg # «#8 g $ cf T CZ oO C-. r or. Cc * Notes of modulation, according to G. + Here, in order to obtain a flowing melody for the tenor, we have permitted the funda mental 7th to descend to the bth, prior to its resolution. HARMONY AND COMPOSITION. 161 ANALYSIS. As the “note of modulation,” B, bar 2, ascends a 4th, we might have modulated to the key of E; instead of which, we have continued in the original key. Why? It is not good to modu- late so soon out of the original key. Compare this bar with bar 6, where we have modulated to the key of E. Bar 3. The ‘note of modulation,” A, ascends a 4th, and modulates to the key of D,* by the first part of that rule (G). Bar 4. We have modulated back to the original key, by the second rule. (Page 150.) Bar 5. Compare this bar with bars 2 and 6. N.B. There, in order to procure a flowing melody in the bass, we have employed the jirst inversion, although it does produce similar motion. Bar 6. We have, for the same reason, employed the second inversion. This will suffice to show the most efficacious manner of choosing inverted basses on those occasions. Bar 6. The “note of modulation,” B, ascends a 4th, and modulates to the key of E, in which key the first part closes. Bar 9. The ‘note of modulation,” B, ascends a 4th to E, and modulates to the key of A (the original key).t Here the second part of the sixth rule (H) is employed. (See Ex. 177, II.) Bar 13. C-sharp, the ‘‘note of modulation,” modulates to F-sharp minor,} by the fifth rule. (Page 153.) Bar 17. F-sharp descends a fifth to B, and modulates to B minor.§ Bar 18. Modulation to the key of A. Bar 21. Modulation to E minor. Bar 22. Modulation to D major. Compare these two modulations with those at 17 and 18, and observe that, although the “notes of modulation” and the progression of them are the same in both cases, yet how very dif- ferentis the result. There, we modulated to B major andthen to A major. Here, we modulate ta E major and then to D major. Observe also the difference of the progression of the inner parts with close attention, as well as that produced by the same “notes of modulation,” bars 25, 26, 29, and 30. N.B. From bar 25 to 32 the rule is exhibited in a minor key.|| It is unnecessary to enter more fully into the analysis of the present exercise, as the subject which we are now going to present to the intelligent pupil, will afford ample matter for this purpose —a subject one of the most interesting and intellectual, and at the same time, to the practical harmonist, one of the most important that can well be conceived; viz., extracting or selecting from a harmo- nized melody one or other of its inner parts, or inverted basses, converting it into a principal melody, and, having harmonized it, extracting again out of that har- mony one of the inner parts, and converting it also into a principal melody.{ During this process, we shall not always select the entire of an inner part, but extract such portions of each as shall, when formed into a principal melody, produce a pleasing and melodious progression. We have already exhibited a specimen of this sort**; but we shall now enter more fully upon the subject. Our first care should be to examine the progression of the alto, tenor, and bass of those examples out of which we intend to make our extracts. The following exercise contains 4 melody which has been extracted from different parts of example 179. To discover from which of the parts the present * Subdominant. — Let it be remembered that we are not obliged to modulate. + The note D, in the inverted bass, is the dissonance of the 4th. (See dissonance, Ex. 127, bar 3.) + Relative minor to the orginal key. § Relative minor to the subdominant of the original key. || Irrelative minor to the original key. { Hinted at in pages 148, 150. + Ex,175, IL 162 HARMONY AND COMPOSITION. new melody has been constructed, let the student compare bar with bar as they are numbered; for the numbers of both examples correspond. A Melody extracted from the Harmony of Ex. 179, and harmonized here in a variety of ways. Tenor of Ex. 192.¢ Alto of Ex. 192. I. z 3: 4. 5 . 7: 8 Ex. 18. Bass of Ex. 192. Tenor of Ex. 192. . Io. Il. 12. 13. 14. 15. 16. | = ft arse) al Tenor of Ex. 192. Alto of Ex. 192. 18. 19. 20. 21. 22. 23. 24. 17. Minor. 25. 26. 27. 28. 29. 30. 31. 32. Let the student attend to the following directions: — 1. To examine and compare the harmony of both examples, bar by bar; not superficially, but very carefully. t The notes of embellishment which appear in this example, called “ passing notes,” shall be explained in the next number. They do not form an essential part of the harmony. § The 3rd, in the alto, descends to make room for the dissonance of the 9th in the soprano (See Ex. 107, page 108, and explanation.) || The 3rd of the dominant, in the soprano, afterwards in the alto, descends here by license; the tenor, however, in the first instance where that 3rd is doubled, makes amends for this seeming impropriety by ascending. HARMONY AND COMPOSITION. 163 2. To note particularly the progression of each of the three parts, with a view to their being hereafter converted into principal melodies. 8. Occasionally to change close harmony into extended, and vice versa; because by this process a@ NEW progression of the inner parts will naturally follow. This isa matter of great consequence, the value of which may perhaps be properly estimated by and by. 4. To alter, sometimes, the inverted basses; for, by that means also, a new progression is introduced into the inner parts. As the several parts of Ex. 179, from which the new melody of Ex. 180 has been extracted, are sufficiently marked, we shall refer only to such matters as may assist the student in his reflection, while engaged in this pursuit. ' When we examine Ex. 180, the melody, the first object that arrests our atten- tion is the new combination of harmony and modulation which presents itself at every step; for instance, the note of modulation, D, in the soprano, bar 5 (original tenor), enables us to modulate to F-sharp minor. Now, let it be observed that this is a modulation which the original harmony did not admit of. Thus not only isa new effect produced in the harmony generally, but alsoa new progression occurs in the inner parts, which, by a little management, may be turned to good account. In bar 6, by selecting the alto, we are enabled to introduce C-natural, the minor 9th; thus producing the chord of the diminished 7th (a most effective chord), from which we were excluded in the original. In bar 11, the note B, in the soprano (bass in the original), enables us to modu- late to F-sharp minor. From bar 12 to 16, we have selected the tenor, and modulated to the key of A, bar 14; while in the original, we modulate to F-sharp minor. To enter into a particular analysis of each bar of these two examples would be endless, and calculated rather to ,etard than advance the pupil in his studies. Examples are before him, the corresponding bars of which are ail numbered, and to them a constant and careful reference is recommended. It will amply repay him. The following is a melody extracted from the tenor and bass of Ex. 179, com- mencing at the 9th bar. Compare this harmony with the original. . The Tenor of Ex. 192. The Bass of Ex. 192. 9. Io. Il. 12. 13. 14. * Here again the third of the dominant chord descends on the 5th of the tonic, in order te enrich the harmony. These, however, are licenses, which must be used very sparingly. 164 HARMONY AND COMPOSITION, The following melody is extracted from the alto in Ex. 179, commencing at bar 9. 9. 10 II 12, 13 14 A pt cs ; oe. — Tere Fas?) ee. a + | BI 2 ah oe - 182. ! | ppg ttt ane i dt dt td 16. 17. 18. 19. 20. ——}{ = ¢« ve 1 il +e ae He ff = : a i C i 19 | asf r t ( ae C It ft Ad I rie \e_ i Holt T T ps i i Compare the progression of the inner parts of the harmony from 13 to 16 with 17 to 20. Heretofore we have selected our new melodies from Ex. 179. That example’ we will call ‘‘ the Original,” and Ex. 180 ‘‘the Branch.”” We shall now make our selections from ‘‘ the Branch,”’ and construct from it new melodies for harmo- nizing. The following melody (ending in C-sharp minor) exhibits the tenor of Ex. 180 (which ended in G major.) A few passing notes are introduced, to render the progression more smooth and melodious. Se se t zz = 4 Here we have the bass and alto of ‘‘the Branch’? as a new melody, from bar 1 to 8. The Bass of Ex. 193. The oe of Ex. 193. is 4 ; : 7. Although far from being exhausted, this portion of the subject must be con- eluded with the next example. The pupil is advised to stamp these rules indelibly * The fundamental 7th in the tenor is omitted, in order to enrich the succeeding tonic chord with the 5th. HARMONY AND COMPOSITION. 165 upon his memory by patient practice and careful study. The thinking faculties should be brought into active operation; the variety of effects should be heard, examined, and accurately compared: thus will the judgment become gradually matured, and produce the accomplished harmonist. Be not too anxious to proceed; reperuse and reflect; follow the advice of the sage Lord Bacon: “‘ Make haste slowly.” N.B. This present Part is eminently worthy of pecuilar attention; it brings to light a vast mine of musical wealth, opening up inexhaustible stores of melody and harmony, otherwise perhaps forever lost; and it may be pardoned were we to go so far as to say that it is sufficient of itself to furnish a fund of elegant ideas, even to the student who has none. A part of Ex. 179, harmonized in the relative minor. a) page 160.) 1. 2. 3. ie 8. pie HOT aUE. Ex. 385. ai fe : ZS Ca e G. -* is 4 Ga 4. x f fo: = 3 ” 3 I a ee oe we = ~~ > - see 10 II 12. 13. 14. 15 16. 4 7 Co —4 4. = aI Sj — = = —! + Poe te | rrr esa 2 2 1 = = : o_. ned =] | a) 1 a a T = SS eS : ce ; - | eng ee sf, f ee Raa pe te ee {|—< : = 17. 18. 19. 20, 21. 22. 23. * pat |— | 4 =z a to yl 2. a t — SS eee ee == BE Pe _* pote ea i | Gi =—— 7 aid J 9 2 ~t% , | 2a ee ee ss zi s I rt t } A Eg == et Hl 2 * Compare these with bars 12, 13, 14 N.B. The next number will comprise the subject of Passing Notes, Auxiliary Notes, and Secondary Harmony. HARMONY AND COMPOSITION, NOTES OF EMBELLISHMENT, PASSING AND AUXILIARY NOTES. Preparatory to entering upon this important branch of harmcny, it is neces sary to explain what is understood by the Three Motions in Harmony. When two or more parts proceed together, ascending or descending, they are said to proceed by similar motion, as at (a) in the following example. When one part ascends or descends while another remains in its place, an oblique motion is produced, as at (b). When one part ascends while another descends, they proceed by contrary inotion, as at (c). a. b. ze = i o. a << ue. —o— TT ar »— = T oc QW | ae Et 1 ack t t i o T ft ai -—t+ «+ f fl 1 Ex. 186. Similar. ~ Oblique. f. es ES o- @ #- + -o ferent Fee ~ = a — Soe some ie f t t ——H es é d J ee f fag we Oe t { S=}=" Es, a +H] on a 4 fe — ee as aia a 2 ae | } Se Se Se { t t The student will examine carefully and perform the two examples, compar- ing one with the other, and particularly noticing the variety of the imitations. In the latter example it will be perceived that the scale commences with the 1st violin, but is continued in that part for only three bars; after which itis taken up by the second violin for the following three bars, by which an imitation between these two parts is effected. * Re-peruse what has been said on passing notes by half-tones, Ex. 192. 190 -HARMONY AND COMPOSITION. It has been fully shown that all dissonances, whether by suspension or retard- ation, have been produced by one simple circumstance, viz., by arresting the natural progress of the intervals of a melody while ascending or descending. These dissonances therefore are in fact artificial; they do not exist in nature; but why are they introduced? They are introduced to heighten the effect of the returning consonances, and thus produce in a greater or less degree that light and shade in a composition which is so striking in the works of great masters. A careful study of this branch of harmony is strongly recommended; indeed, the importance of it must, ere this, have been evident to every intellectual student. When we treated on the chord of the minor 9th,* it became necessary to draw particular attention to two intervals of the chord of the fundamental 7th, viz., the 8rd and 7th; the former ascendiny a half-tone, the latter descending a half-tone;t by these two intervals ascending and descending by half-tones, the whole machin- ery of harmony is guided. In order to impress this strongly on the mind, we shall repeat here a portion of Ex. 141, the whole of which, however, the pupil is strongly urged again to peruse. - “ae a. b. oe d. i 3 a SN 8g 7 4 3 3-——~7, Rg] rT f: A oe ini ey ih: a T Log: 1 T IF f az J— fF. t oe Z Zz rE 1. | oe Ty coe 4. t ah eae re i Ll { 3 1. tee ae (a. 3 1 Tv L “———"" I~—|4 [3 Ex. 222. T R 4 3 1 5 = far] | f: a i oe . re T ok eg . U YW tT (a = wt I iJ 1. { ae. i [ 7. i E 7. 1 = RTM) iat i ; Og iis a os <— e f. & h. 7 = ae “1 == —}— gd. =4—d- — SS tr ——————— = ee ee a. Exhibits the essential notes of the chord of the fundamental 7th. b. The ascending dissonance of the 7th. (Retardation.) c. The descending dissonance of the 4th. (Suspension.) Now observe. If these two opposite dissonances are united (as at d), they will produce a new chord, called The Chord of the Eleventh. Let it be well remarked, that it is through the instrumentality of these two principal intervals of the fundamental 7th that this chord is produced. We may introduce the dissonance of the 9th also (as at e)t; but the chord is not thereby changed, it still remains the same in name and character; or we may introduce a retardation, the 2nd ascending into the 8rd (as atjf). Here the note which at (e) is a dissonance by suspension (the 9th into the 8th), is at (f) a retardation, the 2nd into the 38rd. Again, we may have both the suspension and retardation at the same time (as at g), where the 2nd in the soprano ascends into the 8rd, and the 9th in the tenor descends into the 8th; and if we add the octave to the dominant, the choré * See preceding. + See example 141. t Zxample 2:7, IX. HARMONY AND COMPOSITION. 191 of the 11th will appear (as ath). If the question be asked, what the chord of the 11th really is, the reply is simply, The chord of the dominant or fundamental 7th placed over its tonic : for instance, take the bass-note B-flat as the tonic, (the domi- nant of B-flat is F), write the chord of F, with its fundamantal 7th, over the B-flat, and the chord of the 11th is produced: its resolution follows as a matter of course. Why is this called the chord of the 11th? The chord takes its name from the dissonance of the 4th, prepared by the 7th,* because this 4th is the 11th interval, counting upwards, from any given bass. In thus counting upwards, we must necessarily pass beyond the 7th and 9th, before we can arrive at the note which constitutes the 11th; so that, in this case, the interval in question is not a 4th, but really and truly an 11th. Chord of the Eleventh, prepared. Hitherto, the chord of the 11th has appeared on the accented part of the bar, having been prepared on the unaccented; but this is not necessarily the case; as it originates in the chord of the fundamental 7th, which requires no reparation, so the chord of the 11th is entitled to the same privilege: this is exhibited in the fol- lowing example, where all the chords of the 11th are unprepared. Chord of the Eleventh unprepared. 1, 2. 5: 3. R 4, # 2} 3] at a ¢ Zl .9| a gg Pee = —— > Ex. 223. at i = "} See bl Bees i i +0 ee a | In bars 1 and 2 the melody ascends; consequently, the retardation of the 2nd is introduced, figured with a (2 thus, 4); but as, at bars 3 and 4, the melody descends, the supension of the 9th is employed, and the figures required are = Bs the chord of the 11th may therefore be introduced, prepared, as in Ex. 222; or unprepared, as in Ex. 223. The following is a practical illustration of this chord with both these charac- teristics: — The Chord of the Eleventh practically illustrated. Andante ioe ee a ase = tla ae Pet eo iret oc pil Te ve t f= re —e— == - i oe i z “te f EE ir t Es = a = re a I ef ir 0 Bar 2. “Bar 5” Bar 6: Bar 8. In the preceding Ex. all notes of embellishment have been carefully avoided, and other dissonances excluded, that this chord may appear in the simplest pos- sible form.t ; * See i, Ex. 222. + In Examples 224 and 225, bars 2, 5, 6, 13, the chord of the 11th is unprepared. Bars 8, 10, 12, 16 —-—-———-~--- prepared. 192 HARMONY AND COMPOSITION. N.B. When the chord of the 11th is employed UNPREPARED, and the melody ascends, the note which represents the fundamental 7th may ascend. At bar 5, the fundamental 7th ascends in the alto, and at bar 6 it ascends in the tenor. The following Example is in substance the same as the preceding; but here it is embellished with passing and auxiliary notes; and the student will be amply repaid for the trouble of a careful comparison: — The same Air as the preceding embellished. Andante. Bar Io. = ~ Bar 12, ts i eg =_) 5 = { 4 } ig ——F oe = = ma r is ar Sostenuto. # | eae ate | | a : | o. é # eee be oe Bx. 295. { er = Ee a = ‘| ie te SSS Figured Bass. bs = 3 g 3 q 5 § ge ee 3 ee T im T ae) apne 3 f 1 = ee tte Ef ¢ = —e Bar 16 ==@. e a @. }: 1. pt i 4 © a | —— | @ > £ oh Eel

2) original 5 N.B. When the chord of the 13th is immediately preceded by the chord of the fundamental 9th (as in the above Example), the chord is prepared. When it is not immediately preceded by the fundamental9th (as in the following Example), then it is unprepared, and may be treated precisely as the chord of the 11th. = e blee. oes =3 8 Ey Ex. 231. ns § The preceding Ex. 231 is the Diatonic Minor Scale of C; but, in order to mark the interval of the chord of the 13th as much as possible, no signature is employed to denote the key; the accidentals are all expressed where required; the fundamental basses are also added, which may be found useful in more respects than one. Before we proceed to give a lengthened example on the employment of this very important chord (the 13th), it will be found necessary to make the student acquainted with the chords of the sharp sixth and compound sharp sizth. Q. What is the chord of the sharp sixth (#6)? A. Itis neither more nor less than the second inversion of the dominant chord, the inverted bass being lowered a minor semitone. In the following Example (at a) is exhibited simply the 2nd inversion of the chord of the dominant: — a a (Reese Se Sa Ex, 232. re a tt ia) ad bel | J abe o a. 12], — = 1 re ee 5 Os b, _——————— b b, bs bs b i. T To lat ae SF —— Se — | 1 Cadence to A flat. IIL. Cadence in the relative Minor. * Before the student proceeds, he is strongly recommended to peruse once again the com mencement of the subject of cadences (pages 117,118); of which the following may be com sidered a continuation. HARMONY AND COMPOSITION. 201 D Minor. IV. Cad. in A Minor. iis 2 D ig ie V. Cad. to By Major. + 4. — —_ = a eS = Spa hee a SS SI a 6 2 f bo Hy ‘ 6 bg bz | s. Ct escent: a Si ahaa lili =. © = = SS ay In the preceding Ex. (238) the pupil commences in the key of D major at I. If, instead of closing in that key, he were to make a cadence in the key of its dominant, it would be an irregular cadence; — irregular —because it does not close in the key to which modulation has been made. At II, he modulates to F minor, and makes a cadence in the relative major. At ITI, he modulates to A-flat, and makes a cadence in the relative minor. At IV, D minor is the key, and a cadence is made in A minor. At V, a modulation to D minor — cadence in B-flat. N.B. Let it be observed that the irregular cadence must always bear some relation to the key to which we modulate. It occurs frequently, that instead of proceeding direct from the tonic to the subdominant, a minor chord is first introduced, whose bass, when we are in a major key, is a minor 8rd below the tonic, as in the following Example (I). On the contrary, when we are in a minor key, this bass must be a major 8rd below the tonic (II). I. II. ae —— : go es G2 Bebe ae 2 2 se eee Ex. | ‘a - - § E be ie TT b i me a i Pf ba hess b —t Bee a eee When the cadence is made in a minor key the added sixth may be written minor instead of major. See III, following Ex. 240. k be b q = as H: = E z fs ml i E ta fet TI a At IV, the added minor sixth is doubled and the 5th omitted. N.B. This chord is emineatly calculated to express a feeling of the most poignant grief and sorrow, and should be sparingly used. 202 HARMONY AND COMPOSITION. Sometimes a cadence is written as at (V) in the following Ex. being the first inversion of the minor 9th (diminished "th. ) Or as at VI, 2nd inversion of the same chord. Or as at VII, compound sharp #6. Or as VIII, sharp 6. Ex, 241. In the following Modulations, the preceding cadences are introduced: — fae oh Og o Se wo = oe al =. — ee ee a ae 6 z 1 os be te @. = He: t 4 Er t i + + oF 1 >t =e Fe aa ¢-—_—___ b: g 7 br br be bs p bs___ sg ‘ a Ex. 250. HARMONY AND COMPOSITION. 207 Great Cadence. In the perfect final cadence, the tonic is always preceded by the dominant. In the great cadence, on the contrary, the tonic is preceded by the subdominant. oa rt =. aT = = = 22S Ae Ex, 251. \ el = This cadence is usually employed in sacred music to the word Amen!. It pro- tluces an effect calculated to create in the mind a feeling of reverence and awe. Equivocal Modulation. In order to form a clear and distinct idea of the principles on which these modulations are established, a few preliminary remarks will perhaps be necessary. It has frequently been observed that the two principal intervals of the dominant 7th, in their progression, insensibly lead the ear towards the chord of its tonic; the 7th having a tendency to descend and the third to ascend. This incessant inclination of these two intervals to proceed thus will be found on investigation to be occasioned principally (if not entirely) by the 3rd in the chord being major, for, were we to make the 3rd minor, this inclination would immediately cease, as will be evident on performing the following Example :— La GOON PGT RET OS I. IL. Iii. Iv. V. Vi. VIL. Vil. Ix. X. { —f — —t =o b = t | | ao bsSs3 % 75 3 ; —" —_ Ex, 252. Tl .* by bg a == he | — See SESE re IE = ee The chords at I, II, III, having minor 3rds, no expectation is excited in the mind that these 3rds ought to ascend, although each chord contains a fundamental ith: the ear (as it were) remains passive, and without the smallest reluctance per- mits these 3rds to be changed in the course of their progression into Tths. AtIV, however, the case is very different, for the 3rd (G) being major, the ear immedi- ately expects this 3rd to ascend, and the chord of the tonic (A-flat) to follow: thus the chord of the minor 9th at (V), having a major 3rd, must necessarily proceed to its tonic (A); at VI, to D minor; and at VII, toG minor. Now let us recollect, that this important interval forms a major 8rd with the fundamental bass only, and with no other interval. If, therefore, the fundamental bass be taken away, no major 8rd will be found in the chord to guide or direct our ear. See VIII, IX, X. We are left, as it were, in complete uncertainty as to where the chord will proceed; for the remaining intervals of the chord (after the fundamental bass has been removed) are all minor 3rds, no one of which possesses any peculiar power or qual- ity to guide the ear. But if we lower any one of these four intervals of the chords at VIII, IX, X, a half tone, it will produce a major 3rd, giving thereby a decided direction to the course of the modulation (which was before equivocal). Now as the interval thus lowered will be the dominant of the key to which we modulate. 208 HARMONY AND COMPOSITION. and as each of these four intervals may alternately be lowered a half tone, it follows that an equivocal chord may be converted into four different dominants, and may consequently modulate to four different keys. The three remaining intervals of the chord undergo no alteration, except what may be occasioned by an enhar- monic change, which may perhaps be found necessary when once the dominant is established. 2 3824 8 6 %. 8 9. 1. TL iz. 33 Ex. 253. Ati: is the chord of the diminished 7th. It has no decided character but what it receives from the fundamental bass, which has been placed under it, by which the modulation goes to D minor. The C-sharp, in the inverted bass at 2, isat 3 lowered a semitone to C-natural, and thus E (which at 2 was a minor 8rd) is changed to a major 3rd; and as the C- natural is the dominant to the key of F, we modulate to that key at 4. N.B. All the rest of the intervals remain as before. Here we see that by only lowering one interval of the chord of the diminished 7th, we are enabled to modulate to F instead of D minor. At5: The chord appears again as originally written at 1, but at 6, the E is lowered a half tone to E-flat (forming thus a major 3rd with G), and as E-flat is the dominant to A-flat, we modulate (at 7) to that key, instead of D minor. N.B. All the intervals remain as before, except C-sharp, which must be changed enharmonically to D-flat; because the fundamental 7th to E is D-flat, and not C-sharp. At 8: The chord appears again written as at1. The Gis lowered at9 a half tone to G-flat; and as G-flat is dominant to C-flat, we modulate (at 10) to that key instead of D minor. N.B. Two intervals must here be changed enharmonically, viz., E to F-flat, and C-sharp to D-flat. The reason is obvious. At 11: No change of modulation has taken place, for, by lowering (at 12) the B-flat to A, we produce the same fundamental bass as at 1:.the only difference is, that, as the minor 9th is removed, we have moduiated to a major, instead of a minor key. N.B, Any inversion of the minor 9th may be thus employed, as well as the diminished 7th, instances of which are given in the following example: — (A | wa ? f 22 I | | Ex, acy. a :F_¢, —E =o t SS 5 ts * Ml HARMONY AND COMPOSITION. 209 4, 5. 6. fen) ten. hed. Pl Lit Lit 210 HARMONY AND COMPOSITION. 14, 15. j & = se ma TT z wees *. indi ee o-4- 4 bs “te te 8 * fe 4 Bs- 16. 1%. 18, HARMONY AND COMPOSITION. 211 - 0 r * + : == | LE. ae 3 oe os 28. rs pp» 4 Fett Foe 2 Ee ot o te (= = === ee 49. z be 4 4 2 ¢ ¢ 2. = : j bs 7a : —_ | F = In the preceding example — At2: A demonstration is made to modulate to D minor, by the third inversion * of the minor 9th; but by lowering G (the inverted bass) at 3, the half tone to F-sharp, a modulation is effected to B-natural minor (at 4). At 5: A demonstration is made to modulate to A minor, by the first inversion of the minor 9th; but B-natural being lowered (at 6) a half to B-flat, the modula- tion goes (at 7) to E-flat. At 8: We make a demonstration to modulate to F minor, by the second inversion of the minor 9th; but, the B-flat (at 9) being lowered to A, the modulation pro- ceeds (at 10) to D minor. At 11: The demonstration is made to C minor’ but (at 12) B-natural is lowered to B-flat, and we modulate (at 13) to E-flat. Although the ear cannot recognize any change having taken place between the chords at 14 and 15, when played on the pianoforte, yet, if we examine the fun- damental basses of these two bars, it will be evident, that in order to modulate to 212 HARMONY AND COMPOSITION. G minor (at 16) this alteration of the chord became necessary; for as the dominant to G is D, and not F, we could not have modulated directly from the chord at 13 to G minor at 16, it would have been ungrammatical, as modulating without a dominant. At 20: We make a demonstration to modulate to B-natural; changing this determination, however, by lowering the A-sharp to A-naitural (at 21), we makea demonstration to modulate to D; here, however, the course is again changed, by resuming the dominant F-sharp (at 20), and we seem to modulate once more to B-natural; instead of which, however, we lower the C-sharp (at 21) to C-natural, and modulate (at 13) to F. ea 2 The preceding exercise, which is written for the pianoforte, not only abound in secondary harmonies,extended, passing and auxiliary notes, but is likewise calcu- lated to point out some of those contrivances in composition, by which a series of modulations or progressions may be made pleasing and interesting; for example: from the commencement to the end of bar 12, the right hand plays variations, founded on secondary harmony, interspersed with extended, passing, and auziliary notes, while the left hand accompanies this variation by the simple chords. In order to produce still more variety, the right hand, from bar 13 to 25, plays a simple melody without the least embellishment, while the left plays a variation, founded on the intervals of the chord. At bar 26, the right hand again commences a varia- tion, the left hand accompanying as before. The example concludes with a cadence, commencing at bar 28, in which the minor 6th has been introduced. Equivocal Modulation by the Compounded Sharp Sizth ys This chord is another powerful agent, which may be employed with great effect in producing an equivocal modulation. If we lower the bass of any inversion of the chord of the minor 9th a minor semitone, the chord of the - already explained in examples 235 and 236. N.B. We must be careful not to mistake this chord for one of those just des- cribed in example 253; because the note which was there lowered became a dom- inant; whereas, in the present case, it becomes a false 5th, and (being the bass) is the second inversion of the dominant chord. In the following example (at bar 2), is the first inversion of the minor 9th. will be produced, after which we can modulate as The bass being thus lowered (at 3) a semitone the e is produced, and thus, in- stead of modulating to A-minor, we modulate (at 4) to F-sharp major. Ex. 255. The following example will show the application of this method of treating the chord, which will be found particularly effective when introduced immedi- ately after the imperfect false cadence: — HARMONY AND COMPOSITION. 213 1. 2. 3. 4. 5. 6. Ex, 256. Imperfect Ped. False Cadence. oe eo os Ti+ be a eee eo 7 : Ped. * Ped: x Ped. * le . 3 ! = = At2: An irregular false cadence having taken place upon the first inversion of the minor 9th, this inverted bass F-sharp is lowered a half tone in bar 3, to F- natural, producing thus the #§. Here we ought to modulate to E, instead of which, however, we make that E a dominant, apparently with the intention of proceeding to A (for at 4a regular cadence commences in that key); but instead 214 HARMONY AND COMPOSITION. of proceeding to the tonic, the dominant chord at 5 falls again at 6 a major half tone, as it did at 2, and thus produces once more an irregular false cadence on the chord of the diminished 7th. The same process is observed through each succeed- ing four bars of the Example, until we arrive again at the key from which we set out. Deceptive Modulation —in which the Fundamental Seventh} resolves into the Octave. It cannot be too frequently impressed upon the mind of the learner, that the chord of the Fundamental 7th hasa natural tendency to guide the ear to the chord of its tonic only. When, therefore, either of the principal intervals of the dominant chord, (viz., the fundamental 7th or 3rd), do not proceed thus, though they may resolve into consonances, a kind of deception is practised. In the following Example, at 1, the 7th of (G) the fundamental bass descends as usual, but instead of proceeding to the third of its tonic (C), it falls, at 2, in the octave of the following dominant chord. The 8rd, instead of ascending into the octave, remains in its place, and becomes a 5th. The 5th likewise remains in its place and becomes the 7th; and the bass, instead of proceeding to its tonic (C), ascends a minor semitone, and forms the major 8rd:* thus we modulate to A minor instead of C. { (2322 53= = jtecqeackeyq Ex. 257. o - N.B. All the inversions of the fundamental Tth may be here employed; the most effective, however, are the first and third. The effect which these deceptive modulations produce will be better under- stood by the following short example of Recitative: — ——— ae ee a RECITATIVE. Modulation. Tremolando. Ex, 258. ox % *This must, however, be understood as referring only to the inverted bass, because the fundamental bass falls on this occasion on a minor 3rd. HARMONY AND COMPOSITION. 215 DErepuNE Modulation, ~ ee Modulation. = SS | SSP GS ig PE a ge- oe { ft . [ ec F f= E S = 2 = <= f oOo &c. = FS f === — Ez B. Le t=: Ee t C -s— j é #4 it g Deceptive Modulations —in which the Fundamental Seventh resolves into the Fifth. In the following Example, the dominant (G), instead of proceeding to its tonic (C), ascends a whole tone, and becomes (asin the foregoing Examples) the domi- nant of another key, which latter we prefer to be minor, as being the relative minor to the subdominant of the expected key, c. a. | | 2. a ; pies See ESE 7 an o 2 2 tL ao 7, $ j Ex. 259. ) : ee (22 t [ x BIT | : 4 . 4 a (e) HL In this deceptive modulation the 7th descends on the 5th of the new dominant; the 3rd ascends into the 3rd in the inverted bass, and the octave remaining in its place, prepares the 7th in the chord of the new dominant. The different inver- sions of the above chords are exhibited at b and c. The following Example is an exercise on the preceding: — a 22 3 4 | @. Ex. 260 216 HARMONY AND COMPOSITION. Observe, that the subject of the two first bars in the tenor, is imitated in bars 3 and 4 by the bass; in bars 5 and 6 by the alto; in bars 6 and 7 again by the tenor; and in bars 8 and 9 by the soprano. Protracted Modulation. If the 3rd of the dominant chord, instead of ascending to the Sth, continue to fall a minor half tone on the 7th of the following dominant, it will produce alter- nately the : and 3, and form thus a continued chain of unresolved dominant chords, by which the expected tonic is omitted, and the final close of the modu- lation deferred, or protracted, as in the following example: — O s ie oo. g 2. ae f aro i t E 5 Ss SSS ev Ex. 261./ | . ij 2 be &c. i 3 $ § bs D5 2a = ; i = a Ze 1 — c be a a > eS ee ee q | b = & ho tg ts bi » bie t iS Ee i — t { 1 IE = = eae ee —— = oe ba Tv Bo At b: Dissonances are introduced, by which the imitation which naturally arises out of these modulations is more apparent. The following is a protracted modulation with the addition of the chord of the minor 9th: — = > ! tee = ie | ‘tf 6 ae HARMONY AND COMPOSITION. 217 ) R ts Ata: A modulation, such as has been exhibited in Ex. 255 (b), is here intro- duced. At b: Appears the imperfect false cadence, as shown in example 256. The following example shows another kind of protracted modulation, by which the inverted bass is enabled to descend by semitones through the whole octave: — <-——- —beo : bs Ex. 263./ e: Ee t H T E b z a i 7 a, a os 5. 6. 4. 8. pat = = + 5 om as me —-e£ < o—e Sas eer cea ae ce per ae =| eF § (a= = | be 7 os g (a) \e 4 <3 =] ee 9. 10. if, 12. 28) , Eee oe fee = =e c=TSEs a Se ————— i — po Fe ES \ = 5 = = el E- FE eres ac To $ t pss = = = = == os At 3: Is the first inversion of the minor 9th, changed at 4 to the chord of the compounded sharp sixth by the inverted bass being lowered a semitone.* * See example 255. 218 HARMONY AND COMPOSITION. At 5: The resolution of the chord of the § has been omitted, but we proceed as if it had taken place, thus: ja é At 6: The chord of the diminished "th. At 7: The chord of the compounded sharp sixth. At 8: The resolution of the § again omitted. At 9: The first inversion of the minor 9th. At 10: The 9th of the preceding cherd changed to a 7th. See example 265, MODULATION THROUGH THE ASCENDING AND DESCENDING CHROMATIC SCALE, _In the following example the fundamental th is changed to a minor 9th, by which the inverted bass continues to ascend by half tones: — IL IL. III. — ———— He ge eg ao 2 f coe en ae ee =| — — Li and eS age a i z Best (Ga eee < voy “i 7 [ar a, Cc. CHE E on i fy ees —| { te Ea a aime t a 4 + + The above modulation bears a strong resemblance to example 257. Here, however, the 7th is not resolved into the octave, but changed into a 9th, which occurs again at II, and III; and in this manner we are enabled to modulate through the whole ascending chromatic scale. In the preceding Example the fundamental 7th was changed into a minor 9th; in the following Example, on the contrary, the 9th is changed into a 7th, by which the inverted basses continue to descend by half tones: — HARMONY AND COMPOSITION. 219 The following example will show how the several inversions of the minor 9th may be employed with effect. Ex. 266, The first five bars contain only the chord of the minor 9th. The bass com- mences with the interval of the 9th, and passes from thence to the 7th, 5th, and 8rd successively; the rest of the parts interchange places, during which the alto proceeds from the 7th to the 9th; the tenor from the 5th to the 7th; and the 220 HARMONY AND COMPOSITION. soprano from the 8rd to the 5th. The same occurs frequently in the course of the example. From the commencement to the end of the 5th bar we are led to expect the arrival of the key of C minor; however, the 8rd (B-natural) in that bar having been lowered a half tone to B-flat, in the sixth bar, we modulate in the seventh bar to E-flat.* From thence to the twelfth bar is continued the chord of the minor 9th of F, and thus a demonstration is made to modulate to B-flat minor; but, by the introduction of the in the 13th bar,t we modulate to G, and from thence to C minor. Modified, or Secondary Basses. The only fundamental basses which have hitherto been employed in harmo- nizing melodies are the tonic, dominant, and subdominant. We have seen that from these three basses, with their harmonies, inversions, occasional introduction of modulation, dissonances, passing and auxiliary notes, we have been enabled to proceed thus far with sufficient variety. Let us now, however, make an attempt to discover other basses than these hitherto employed, and thus procure a still greater diversity of effect. It has already been stated, that the natural scale consists of three sounds only; that our modern diatonic scale is compounded of two of these scales; that, were we to continue the succession of these scales of three sounds, we should continue to modulate ad infinitum; that, in order to avoid this, we are necessitated to break off at the sixth sound, and modulate back to the original key, by which consecu- tive fifths and octaves are produced. Let us now, instead of breaking off at the sixth sound, continue the scale, with- out paying any regard whatever to the semitones which should occur between each of the subsequent scales of three sounds. If we continue to repeat the figures 8, 5, 8, in succession, over the intervals of this scale, and write the funda- - mental basses as indicated by these figures, we shall find that (after the first two scales) the intervals which follow, instead of being accompanied by the tonic, dominant, and subdominant, will be accompanied by other basses; the chords of which (except those arising from the three original) are either minor or imperfect. t If we divide the above continued scale into scales of three sounds, and place under each its generator, or tonic, it will produce a progression of harmony, whose basses continually ascend by fourths, or descend by fifths. 8 5 3 2 BOS . 0. 8 2. o. 2 aig tig Ss. eS é « oe aa x C= = Ce Fiat - ny 8 —5—~—Te—# t : oe tT & i:—te—# E t t —E t —| a Lc i. @ a | | os 12a 4th SS ee Ex. 267. ; s ; : . — +s t = Z oz. cS =| be tr Tes: L ac AE 3 Wil tanniaiiaaaaiet E E Ee E E fe E— E = E Spe * See example 253. + See example 255. ¢ An imperfect common chord has its 3rd and 5th minor, thus: The imperfect common chord of B is B,D, F. D — D,Ff, A-flat. HARMONY AND COMPOSITION. 221 In accompanying the scale as above, it is evident that we have deviated (com- mencing with the third bar) from the path pointed out by nature, and conse- quently the harmony produced is often obscure and crude. Yet this very obscurity we shall endeavor to turn to advantage, and by introducing it judi- ciously amongst the harmonies of the three original basses, produce still more light and shade than heretofore. Having premised thus much, let us enter into an examination of each interval of the diatonic scale, and see how the chords, as exhibited in the above Example, may be employed in our future Exercises. The first sound of the scale we know may be accompanied by two basses, viz., the tonic, which is an 8th below, and the subdominant, which is a 5th below.* Now, if we take the note which is a minor 3rd below (as at a in the following Example), we shall procure a new bass (which is neither one cf the original three belonging to the scale, nor a dominant by which we can modulate), and which, for distinction, we shall call a modified or secondary bass. Ex. 268. In order to show the application of these basses, and enable the pupil to form a just idea of their effect, let him compare the accompaniments to the melody at b, c, d, in the example with those at e, f, g. At b: The first of the scale has been accompanied according to the third rule of employing fundamental basses. t At c: According to the second rule of modulating in a melody.{ At d: Both are united. At e: Modified bass, with third rule of accompanying the scale. Atf: se with second rule of modulation in a melody. Atg: +s followed by the chord of the sharp 6th. At h: When the key is minor, the modified bass to the first of the scale has a major chord. The second of the scale, as we know, has only one original fundamental bass, which is a 5th below, and thus admits of two modified, viz., one an octave, and the other a third below {see a in the following example): — * Third rule of accompanying the scale, page 44 + See page 44, ¢ See page 150. 222 HARMONY AND COMPOSITION. Ex. 269. ao 3 . . eo 2 6 a ee eee ee =F =f Ss — 4 — por =H ° i —— mm mM Mm ; It is necessary to remark, that the modified bass, which is an octave below, produces a better effect than the other, and should therefore have the preference; the reason is this, —the chord produced by the modified bass, a 3rd below, is an imperfect common chord having a minor 3rd and false 5th. The false 5th and octave of this chord, when heard together, ‘produce the same effect upon the ear as the two principal intervals of the fundamental 7th (to the first inversion of which the imperfect common chord in its effect bears a strong resemblance). But as the false fifth in ascending (d), and the octave in descending (e), have the same effect as if the fundamental 7th had ascended and the 3rd had descended, the ear feels a certain degree of dissatisfaction, particularly when this chord is employed fundamentally (c); when inverted (d), the defect is not so very perceptible, owing to the octave not being doubled. The third of the scale, having but one original fundamental bass, may be accompanied by two modified basses, viz., a 5th and 8th below: the first of these, being the chord of the relative minor to the original key, produces the best effect, as in the following example, at a: — a. 4. a 2. oo Ex. 270. eee e ities —a— EH The fourth of the scale may have two modified basses, viz., a 3rd and 5th below (b). The former is preferable, the latter being the imperfect common chord. The fifth of the scale has but one modified bass, viz., a 8rd below (c )s An application of the preceding modified basses will be found at d. The sixth of the scale has two modified basses, viz., a 5th and 8th below (as in the following example at a), both of which are — _ (ete Ex. 271. t re. Pe: + ——- t i % fot nt [ 1. if Th me L. t n ee iE TO The seventh of the scale has two modified basses, viz.,a 5th and 8th below. The first is preferable, as the latter produces the imperfect common chord. It is necessary to remark, that the introduction of modified basses demands great care and circumspection, as in employing them more mistakes are likely to occur than on any other occasion; these, however, will be prevented by a little attention to the following observations: — HARMONY AND COMPOSITION. 223 1st: Employ the modified basses very sparingly; for, as melody is derived from the harmony of the original fundamental basses, they should be more frequently employed than any other: they originate with nature, and, therefore, are the most satisfactory and pleasing. On the contrary, by introducing too many modified basses, the beauty of natural harmony accompanying a simple melody is fre- quently obscured, and crudities arise which we should endeavor to avoid, 2nd: Very seldom employ the imperfect common chord fundamentally; to the first inversion of that chord, however, no objection can be made. 3rd: Those modified basses which produce the relative minors of the tonic and subdominant should be employed in preference to any other, particularly when introduced as fundamental basses; they are on these occasions exceedingly effective. 4th: No modified basses should, on any account, be introduced until the melody has first been harmonized with the three original basses, employing the five rules, and rules of modulation, as occasion may require; after having done so, we should carefully examine where the modified basses may, with most propriety, be introduced. In order to show the application of these basses, and give some idea of their effect, the simple melody at I, in the following example (written within the com- pass of a 6th) is variously harmonized. Ex. 272. 0. EA een eee OR Ree & ox Ei LE fest eta fee ee ee aes ed mr Harmonized with the original ie interspersed with a few modulations: — 9 fe pa | Ps ge SS sy ! —— a w— — sas eae 3 SSS = Z| II ¢ 4 § 2: 2 @ o be . ‘eo be ce: = o . a} z {==p]= (ca EF T if | r = t f t cs E t t = Ht fe = 3 EE With other modulations: — pes a ee ee ee — ee toes a SHE a = Tia an to sagt ee pysitid, a = 224 HARMONY AND COMPOSITION. eS H ) , ae 1 | } | | ! 4 ! SS 3 aa o_-y— cw 2 7 eee ee ee ee te er eg J e eo es: l \ pata rt dg nog m3 : 8 i a ie fe —e—e—e — 0 —}-0 2 = oH} CT oo. a de CO pp r Iv. | * @ a 2 5 a @ he o ne 7 <. 2 4 s + 2 £ = =H = Stee FS ee f t re tg t 7 o r br 4 Peres ose Mek et seeped Bence Sh 7 7 |e ae ee a ae ee a. ; — tf 7% = een eS i he ae —vorw eos FoR ot eee Pe teem Pn bo 6 & 6 UL I oe 2 eo 2 o 2 Tae Ls «& 1: eat - t & i ae ae Cm +1 r f= Fs rs t C 2 + a Hy t +t + f = E pease oof iL p ft = : ae at} v or = a a t i 7 f 7 t 7 JF FH 7 If, instead of permitting the 38rds of the basses, in the preceding Example, at a, b, to ascend, we let them remain in their places (as at c), they will produce a succession of 7ths prepared by the 8rds. Atc, the 7th appears only alternately; but if we add another part, as at d, we shall have an uninterrupted chain of Tths, as at e, where it will be perceived that, in consequence of the uniform progression of the bass, we are enabled to treat the 3rds of the new part which was added at d, exactly in the same manner as those at ¢. These sequences of Tihs seem to partake ina great measure of the character of unresolved retardations, —see f, where the retardation of the 7th, has been regularly resolved upwards. If we write the preceding exercise in four parts, asin the following example at a, each chord will be accompanied alternately by a 5th or 8th: that is, —the 8th remains in its place, and, by the progression of the bass, is changed into a 5th, similar to a progression of fundamental 7ths. io 28 fens spies Gaines sie = a ee ae. 3 oe £ pede Se Spy Oe gt 7 * In this peoprestion of. sequences a most admirable symmetry is observable. It was the great source from which the ancient sompoters drew their subjects for fugue, and the ground upon which they chiefly constructed their church compositions. Ex. 274. 228 HARMONY AND COMPOSITION. At b, this exercise appears in five parts; and the interchange of the 5th and 3th takes place between the second soprano and tenor alternately. Observe that the preparation of the 7th may be effected by any interval of the common chord. At (c) the 7th is prepared by the 8rd; at (d) by the 5th; and at (er by the 8th. Characteristic difference between the chord of the fundamental 7th, and that of the 7+h in Sequence. The choril of the fundamental 7th is produced The chord of the 7th in sequence is produced by nature.* by art. It stands between consonances and dissonances,as_ Itisadissonant chcrd, and must be prepared. it requires no preparation, but must be resolved. By its means all modulations are effected. It prevents modulation. In every other respect both chords are exactly alike. The 7th by sequences has its inversions like the Fundamental 7th: — Ata; First inversions. At b: Second inversions. Atc: Third inversions. In the above example, sequences of the 7ths and common chords succeed each other alternately, which produces a much better effect than an uninter- rupted succession of 7ths. Intermizture of the Fundamental Tths with Tths in Sequence. When the 7th in sequence is a half tone higher than the fundamental 7th, the chord will be a major chord (a): — Ex. 276. tt uy T tt +n ut i L i 0 When the 7th in sequence is a whole tone below the octave (like the ‘anda mental 7th), the chord will be either minor as at b, or imperfect as at c. If, therefore, in the first case (at a) the 7th be lowered a half tone, as at a; or the chord changed from minor to major, as at e; or from imperfect to perfect, as at f; the chord of the fundamental 7th will be produced. If, during the progression of sequences of 7ths, we change any one of the chords to a dominant chord, a modulation will immediately be effected to the succeeding tonic, upon which a close, though not a final one, may take place; or, if we choose, we may, upon this last tonic, commence a progression of sequences, and continue as before. * See example 48. HARMONY AND COMPOSITION. 227 Observe that, in a progression of sequences, no sharp or flat can be introduced which dves not belong to the key in which the progression takes place; for a mod- ulation to another key would be the immediate consequence, as will be seen by the following ae — 3. 4, 5. el Lai | geez a eS SS t T { if eo -s- Ex. 7 2 Es a i f J a) os apa : out} te SS Sa ell - “o- The sequences continue to the 3rd chord (inclusive); the fourth chord, having been made major, modulates to the key of A minor at the 5th chord, after which we close with a cadence. The progressions of sequences may be intermixed effectively with a progres- sion of tome thus:— In the preceding example, the same progression of the fundamental bass is continued throughout; but, after the first three, instead of sequences, we have employed dominant chords, by which a protracted modulation is effected at 4, 5, 6. The following example will show how admirably these sequences, when inter- mixed with dominant chords, are adapted for imitation and variety of effect: — 1. 2. 3. 4, 5. Oak % 8 9. [~~ Ae (| pe cle eee = oie hee alte ay —TtT r i ea ee) i J ioos Jam 7 "ets rhe jer eo J Ex. 279. a . > i wy in | 7 1 7 7 1 1 bz bz - = i. Lies be 2 =| a Se — + or 10 11 12 13 14, 15 16. 17 be 1 bw fo | be va be “0 ao —he 7 “7 : ae Leni = | br By 7 7 Ob br 5 5 bs b o bz ie t Cc 1. T ay! fe 1 d f ae A of Ble on Lh. | t SS (nz } 4. ze Tire 1: Te A a a 228 HARMONY AND COMPOSITION. 18, 19, 20. 21, vitard. ir In the preceding example, at 1, 2, the soprano commences a short subject, selected from the two first chords of these sequences; and, in ordex to give this subject more character, two notes of secondary harmony have been introduced. At 2, the alto commences the imitation, which is continued to 6; here the tenor takes up the subject, with a slight variation, and pursues it as far as 10. where it is resumed by the alto, and subsequently imitated by all the parts alternately. The bass, at 1, 2, also commences a short subject, founded on the two first fun- damental basses, with their first inversions. This subject is answered at 11 by the tenor, and at 14 again, slightly, by the bass; which part, at 15, takes up and con- tinues the subject of the soprano to 19. The sequences continue as far as 7, consequently we remain in the original key. At 8, commences a protracted modulation,* which ends in the key of E-flat; for, at 11, the modulation is arrested in its progress by the introduction of sequences, which continue to 14. From 15, a mixture of protracted and deceptive modulationst leads us back to the original key. In order to ascertain whether a bass melody, about to be harmonized, will admit of sequences, it is only necessary to examine whether it contains any of the following progressions: — 7 a 7 3g 2 7 2 Ie es SO gk oe NG ae St & { rd ae ‘= ——f}=—F c= 2+ E a +—f] Ex. 280, rs f io + ——H e ! : ct he —H a. ‘ 4. ar a oe a ee oe Be 2 ge fied T t ea eS T a ¢—7h a ae gy — qr Et f t ree t tH i= Tea ir t —+-= @ ea Hf ff fat t HH — ‘ zs (= a, - At a: Is the progression of the fundamental bass itself. At bd: The progression of its 3rd. Atc: The progression of the 7th; and as that interval must be always pre- pared, itis easily distinguished from any other, by two notes of the same denomi- nation being tied together. The first of these notes is the preparation of the 7th, the second is the 7th itself, and the note which follows is its resolution. Although the progression of the 5th is similar to that of the 7th (see d), yet the effect is not so good, and therefore it ought to be sparingly employed, ® See page 216. t See page 214. HARMONY AND COMPOSITION. 229 BASS MELODY WITH SEQUENCES. Let us suppose that we were required to harmonize the following bass melody: — ee eee ee ee ee er ee =| Ex. 281, ePa soe ara a ae ee } Ao See Pew Soto Pe nH LL | tL 1 (eamst t T fey jest T 7H pl {= to {eh ne It is evident, from the progression of the intervals of the above theme, that the greater part of them may be considered in three points of view: — First, They may be treated as a progression of sequences, as follows: — 7 7 1 .—~3 6 7 7 6 7 a Ges Se ae oa SS ee ee eh Secondly, As a progression of dominant 7ths, and thus modulate: — eee ae ee a 7 i C | ae Lo a t ne I te: Thirdly, As partaking of both: — f bz 1 yh 6 é br Z i 2 SESS Be t L oh In the following example, at a, the bass melody of example 281 will be found harmonized throughout with sequences, except where the progression of its intervals rendered it impracticable: — pp} i> J] o—y = ~—t FS i = ——— = Ee . r roy ~T Pot 1.8 ' I mM aes ee ee ae ee, et = fo = t = i [ x: : es Tt a ae +: = 7 tA 7 6 a vr : ‘ “e 7 rT : 6 7 " 3 1 “bog oe I~! | ' 1 | 1 : o. a oe ow ; p# wo a ——— = 7 =r f=. fe Fe se & onl 4 = r | | tot Joc HP Va mele ofa 809 eatin ea) oft —— : | — i Le t et ee} —— 4 7 7 | o@ey to ls gy ~ DO af al -t ) \ 4 I S app ; Yr om yet — o_o wy —s y= z = ~ = jee p-hb—9--+s bw ne | =e oo op oe 5) J ~ S Ty f eo rome Ce—5, he aI = re t r a a eo So ae 2) é J 3-4. a Sarg SS eee fe @:-@he-o-@. SS 7 v 7 ‘a — i i a 7 ° 56 g Dy 4 | J =e + (eset fa? fF = ww oe tye * =| ee a a ——— - ° = { uJ (e) { — — l | 6 a ae é a oe OS es omental anaes ie = Fo ae SS - mm zy =] F . x eo neo t + Fr = te —— qi eS [ 4 Ea SN tr pp RS ——— ee] yy i a = — = =< er t — } ae ry < HH vy —1 SS PB Ta v pp |{™“——" ; rs 3 | — 27 ew ee = bw ew ne | hy i. 2 t Hl . hee - — c 7 br fe 7 ic bs 4 N.B. The 5ths, atc, between the soprano and tenor by contrary motion, are aliowable.* * See example 289 (/). HARMONY AND COMPOSITION. 231 Those basses, which in the preceding example were treated as sequences, are in the following example treated sometimes as duminants: the rules of ‘‘ modula- tion by the intervals of a melodyt”’ have likewise been employed; and thus an effect is produced, so very different from that in the preceding example, that one would scarcely imagine both to have emanated from the same bass melody. The student will find much improvement in a careful examination and com- parison of these two examples. [Ps eS ee = Sp ee gate And (rae ip a aero ae oe Ex, 283. Naan kee re Legato F| | | 1 ! \bex qe a t [ tr "hp 7 - fe Lek r 1 ¢ assault z ac i $ 7 ng calando. N.B. In the second bar a deceptive modulation takes place.* Lastly. The melody, in example 282, which has deen extracted from the bass melody of example 281, is, in the following example, re-harmonized with other basses, according to the five rules of employing fundamental basses, and ‘‘ modula- tion by the intervals of a melody.” [—_ =| TC a = =< z ry-2 Kee ee to ee ee Ex. 284. 27 ay tee a a oid ptr f eS 7 p= 3s te § 8% * Page 148. to 161. t See example 260. (a) See Licensed Resolution of Dissonances, Ex. 345, (b) See Ex, 242. (e) See Ex. 210, f. (d) Ex. 255, s 232 HARMONY AND COMPOSITION. eo 6 wo us 7 By comparing the bass and harmonies in this example with those of the two preceding, we shall perceive what a variety may thus be created; and those who are inclined to study composition, will, even in these few examples, find ample matter. The preceding specimens will sufficiently show how 7ths in sequence may be employed with etfect; their introduction not only prevents frequent mod- ulation (thus impressing the present key more strongly on the mind), but also adds strength and vigor to the texture of the harmony. They contribute, more- over, materially to cement and interweave the several sections of which periods are constructed*, thus forming a still more connected chain throughout the whole composition. Sequences of 6ths, 6 5, and 7 6. From the progression of fundamental sequences of common chords, at a, arise those at b and c. Ex, 285, & aot 5 ez t = TT =, i t t A eae a J. J. + + H i T T at ae i w. 1 HA 1 7: a J. gz, ae ! et = au = | ——e3——] Z| =5 {——s— je Se 5 6 —. & 6 6 6 a *See Periods, example 307. HARMONY AND COMPOSITION. 233 et 7 p# 4 a | ot: § ——1 ey + Fo J t i r ( eC — t | P es 16 oe 4a ——— Bs. 2 e T. a 1: sh TT. f 1h { 1 i. say eat ee ae =. me Seal: ity L L 1. [ Wy + 1 os 1. it) = a ce oO NX f ae J. OF. c s i o iO ae | a ae | re fT: £ oe Ec mil c= H = bre aE -H Pee fos oO [ i E c = oO cee | P v T C 76 = e =. see ea fe aS {7 L - t f or i} o Cs Ht E ; pot i t u E c H | z &. =. fT. | iT ES TW] _ —! th = ——— || ; a oe oC : ro} oo. ae: U r eo = { Pe \ fr 1 sop 6 6 6 6 oh Es TT [ fi + t ae [ ray is (i Hi L 5 a L iif c C oo I oO = z Z, { 2 ———-f\-— a — | Ss —— fF SH 1 Toe oar Ay eS mail a c or ~_ f a. a To o i 1 eo SF 6 6 6 ‘5, 6 = f{——ez — Hf FE: | tL Ty. i ime th 1 iri i il C In employing the progressions of the preceding Ex., it may perhaps be better to let the 6th appear on the accented part of the bar (as at b), because the 5th in that situation produces in some measure the effect of consecutive 5ths: this obser- vation, however, has only reference to what is called the strict style of writing.* By omitting the common chord in the progression at c, a sequence of the chord of the 6th will be produced (as at d), the effect of which, when judiciously employed, is very good. From the descending progression of the 6th at e, is derived that at f, which indeed is nothing else than the dissonance of the 9th resolving into the Sth; in this case, however, the interval of the 9th (which is the 7th to the present bass) must appear in the soprano: were we to give it to the alto, as at g, consecutive 5ths would be produced; for the intervening dissonance does not obviate the improper progression. This is shown at gg, where the dissonance is omitted; should we, however, consider the proper fundamental bass to this progression to be, as written at h, then the 7 6 arises from a sequence of 7ths, and these two intervals may appear in the alto. Tt may be observed, that a sequence of 6ths is better calculated for a harmony of three parts than four; because, in avoiding the consecutive 5th atl, the tenor is obliged (as at i, k) to proceed by great intervals, which disturbs that smooth and graceful progression for which sequences of 6ths are distinguished. * See Strict and Free Style. 234 HARMONY AND COMPOSITION. How admirably Haydn has treated a progression of sequences of this de- scription will be seen from the following specimen, extracted from one of his quartets: — 2 a & a a i é 3 7 = fee eee eo " ee a 7 3 7 BAN T 3 7 3 Ex. 286. —s— = eS eee » rs et t 4 £ J 1: | eras z E Te T. Zz te s ees 7s = The following example, which is written for the pianoforte, exhibits all the preceding sequences in their various forms, ascending and descending. They are written chiefly in three parts; and still more clearly to show their effect when written thus, a contrast is produced by writing the harmony on every other occa- sion as full as possible. QD. 174 3 = t ia a zh fa é repre Sid te, eae espe eee: @ ot = = ——— tea fi Me a a co —™~ p = TE -#: be Pz o— 2 = f £ = = =. ! 2 Jy SS E =e > C 6 6 é 6g 6 5 6 5 3 6 4 | yee 6 ae = Oty d | es | 1 al 9 — He t = ; aS —- 5 2 = = pet pe ope Ply oy e fe - ee i Tose ie r fe ee ee —T_. ye — Wao 5 pot}.