UC-NRLF [CAX INSTRUCTIONS HAIR MOM, PES^ALOZZIAN INDUCTrVfi SYSTEM; TBAOHOfO MUSICALi COMPOSITION AND THE ART OF Extempommj? Interlndes and Volnntaries. A. N JOHNSON. BOSTON : OLIVER DITSON AND COMPANY, 277 Washington Street. NEW YORK: C. H. DITSON & CO, 7«« BUOADWAY. Entered according to Act of Congress In the year ISM, by O l ; y « b D i t s o If , In the ClttWt Offlcc of the District Court «f &e DUtrict of lAWM^hnMtta. ' * ' OLIVER DITSON AND COMPANY, 277 Washington Street. NEW YORK: C. H. DITSON & CO., 711 Broadway. Entered according to Act of Congress in the year 1855, byOtlVERDlTSON, In the Clerk's Offic* of the District Court of the District of Massachusetts. OLIVER DITSON AND COMPANY, 277 Washington Street. NEW YORK : C. H. DITSON & CO., 711 Broadway. Entered according to Act of Consress in the year 1855, by O I.. I V E R D I T S O N , In the Clerk's Offic« of the District Court of the District of Massachusetts. PRACTICAL INSTRUCTIONS HARMONY, VTOV THX PESTALOZZIAN INDUCTIVE SYSTEM; MUSICAI^ COMPOSITION AND THE ART OF fiitemporizing Interludes and Voluntaries. BT A. N JOHNSON. BOSTON : OLIVER DITSON AND COMPANY, 277 Washington Street. NEW YORK: C. H. DITSON & CO., 711 Broadway. Entered according to Act of Congress in the year 1855, by Olivek Ditson, In the Clerk's Offica of the District Court of the District of Massachusetts. 1 g c r PREFACE. VM r, This work is designed for the class of persons designated in tha language )f music teachers as " »e«f beginners." It professes to impart a .knowledge of Harmony, not by essays upon the varioua departments, but by exercises which the student is to write, — or so to speak, by a progressive series of problems which the student must solve. The text throughout, has for its sole object the expla- nation of the prhiciples which must be understood in order to write the next succeeding exercise. In many instances, part of a rule or primnple is explained, while the remaining parts, or the exceptions, are not given until long afterwards, for the reason that a knowledge of them is not necessary in order to write the next exercise. The utmost simplicity of language has been used in the explanations, and an attempt made to guard against misapprehension, even oa the part of an undisciplined mind. It is no part of the design of the work to advocate any particular theory, or to take sides on any disputed harmonic point. On those points on which theorists dis- agree, the explanation which at first sight has appeared most plau- sible has been adopted, but no particular investigation of the merits of the different theories has been made, nor is any opinion in refer- ence to them intended to be expressed. With regard to sources of information, the author will merely state that he studied for some time with Xavier Schnyder Von Wartensee. a celebrated theorist in Germany, and has read most works upon Harmony, published in the English and German languages. INTERLUDES AND VOLUNTARIES. Extemporising interludes and voluntaries, is in reality composing music, conse- quently precisely the same course of study is necessary that is required to learn to write musi(>, — at least, the most thorough method for learning to extemporise well, is to learn to write music well, or in otlier words, to study this book through just as it is. If, however, the student wishes to attend only to those departments of the subject of Harmony which have a direct bearing upon the subject of extempoiising interludes and voluntaries, he can observe the following directions. On page 23 two chords only are used, but each measui-e may be said to form a complete interlude. As soon as these two chords are learned, invent other interludes with them, and aj fast as new chords are learned, invent interludes which shall include them. In all places where the direction is given to " compose tunes and pieces," invent interludes and voluntaries instead. As soon as the invention of interludes is commenced, read the remarks on cadences on pages 143 and 205, and always close with a perfiect or a [jlagal cadence. After becommg familiar with major and minor common chords, study chapter XLIII, and introduce passing notes in the invention of Interludes. In all places where the direction is given to examine music, (as on page 106,) examine written iuterludes and voluntaiies instead, noticing the chords and passing notej which comp&se them. EXPLANATION. A knowledge of Hannony, consists in an acquaintance ■with all the chords int - V ' " ' ' COMMON CHORDS. Th ! first of the fore^^ninf!; chords is the common chord of C. "!t is a common chord bocause it ctmsist> of I luce lettors. the second and third of which are at the intervals of a third and fifth from the fundamental (or lowest _; note. It ia the common chord of C, because C is the fundamental note. Chords are freiiueiitly indicated by figures placed under the base. In common chords, the base note of each chord is either the fun- damental note, or the third or fifth letter from the fundamental note. In common chords, when the base imte is the fundamental note, it is not figured. In common chords, when the base note is t!ie third from the fun damental note, it is figured 6. In common chords, when the base note is the fifth from the fun- damental note, it is figured ^. Name tlie chords indicatc'l by the following base notes. P^ach note has no figure under it, and conse(|uenily each is the fundamental note of a ctnunon chord, i.e., the first indicates the common chord of C, the second the common |/d of E. &c. Name the cliords indicated by the f(dlowin2 base notes. Each' note ha.s the figure G under it, ami corisc'((Men{ly each is the third letter above tho funda- mental note, i.e , tlie first int indicates the coinuion chord of C, the second the comnibn ehord of V, cVc. 4 4 A fi 6 f, r. n n b « a r> r, r, r, g q 44 44 44 44 44 4 4 4 4 4 CHORDS OF THE SEVENTH. 7 Exercise in naming the following chords until the names are given with fluency. d 6 ('• G 6 6 6 fi G66G6G 6 4 4 i 6 6 fi 4 ?r^rf^EEE^EE-5£E:EzEI^EiEE!E?E^:E!£EE 6G 66 66 6666666 4 4 4 4 4 66 66 66 6 6 <'>5 4 4 4 4 4 4 CHAPTER III. LETTERS COMPOSI>fO THE CHOllDS OF THE SEVF.NTH. k Chord of ttje Seventh is composed of fonr letters, so arrang- ed that the second letter is at the interval of a l/a.r(/, the third letter at the interval of a//^A, and the fomth letter at the interval of a 8 CHORDS OF THE SEVENTH. aevcnth from the fundamental note. In other words, a chord of the seventh is composed of a common chord, with a letter added to it which is at the interval of a seventh from the fundamental note. There are seven chords of the seventh, viz., the chord of the seventh of A, the chord of the seventh of B, the chord of the seventh of C, the chord of the seventh of D, the chord of the seventh of E, the chord of the seventh of F, and the chord of the seventh of G. "What letters compo?e the chord of the seventh of A ? Ans. — A, C, E, G, — because, in the chord of the seventh of A, A is the fundamental note, and C, E and G, are the letters which are at the intervals of third, ffth and seventh from A. Or, in other words, because A, C and E form the common chord of A, and G is the letter which is at the interval of a eeventh from the fundamental note (A). What letters compose the chord of the seventh ofB? C? D? E? F? G? CHAPTER IV. CHORDS OF THE SEVENTH INDICATED BY A FIGURED BASE. In chords of the seventh, the base note is either the fundamental note, or the third, fifth or seventh letter from the fundamental note. In chords of the seventh, when the base note is the fundamental note it is figured 7. In chords of the seventh, when the base note is the third from the fundamental note it is figured 0. In chords of the seventh, when the base note is the fifth from the fundamental note it is figured ^. In chords of the seventh, when the base note is the seventh from the Cmdamental note it is figured ^. Name the chords indicated by the following base notes. Each note has the figure 7 under it, and consequently each is the fundamental note of a chord of the seventh, i.e., the first is the chord of the seventh of C, the second the chord of the seventh of A, &;c. 77 77 77 77 77 77 77 77 77 77 7 CHORDS OF THE SEVENTH. Natie Je chords indicated by the following base notes. Each note has the Bo'ures I under it, and consequently each is the third letter above the funda* men al note, i.e., the first indicates the chord of the seventh of A, the second the chord of the seventh of D, &c. ;?zazf R 6 6 6 6 6 o o o 5 5 5 6 6 6 5 5 6 5 6 6 6 6 6 6 6 6 6 6 5555555555 Name the chords indicated by the following base notes. Each note has the figures t under it, and consequently each is the fifth letter above the fundamen- tal note, i.e., the first indicates the chord of the seventh of C, the second the chord of the seventh of E, &c. Name the chords indicated by the following base notes. Each note has the figures ^ under it, and copsequently each is the seventh letter above, or (which is the same thing,) the next letter below the fundamental note, i.e., the first in- dicates the chord of the seventh of D, the second the chord of the seventh of B, &e. 4444 4444 4444 4444 4444 3322 2 222 2222 2222 2222 Exercise in naming the following chords, until it can be done with perfect fluency. i 7 6 4 4 7 6 3 2 3 4 4 7 6 a 2 5 4 4 7 6 2 4 4 7 6 4 4 7 8 2 5 6 ti 764 476 447 644 532 5S2 532 'mmmmmm^m i i 10 COMMON CHORf 9. mw^mMmEm i i ' I i 764 4 7544 7fi44 7 53 2 532 53 2 CHAPTER V. FURTHER REMARKS IN RELATION TO COMMON CHORDS. When one or more of the figures 1, 3, 5, 8, are placed under a hase note, the name of the chord is the same that it would be il ihese figures were not expressed. Name the chords indicated by the following base notes. Each note has one or more of the figures 1, 3, 5, 8, under it, and, consequently, each indicatea the same chord that it would if no figure was under it, i.e., the first indicates the common chord of A, the second the common chord of C, &;c. ^5E?:PEt=EE?ip3^E^f£E*H:iE?:^£l-iEE i i i J ? I ! » ° ' I J ' i I M g U I ^, t), or t), when standing alone under a base note, or when placed under or over a figure, indicates that the letter which is at the interval of a third from the base note is i^, \}, or fcj. Name the chords indicated by the following base notes, and tell what letter in each is i^, f), or t;. The first base note indicates the common chord of D, with Ffcj. The fifth base note indicates the common chord of B, with D# ; the 5 indicates that the chord is the same it would be if no fi^re was under it ; and the i^ indicates that the letter which is at the interval ot a third from the base note is ^ gig^igigiiiiip # *? b » 4 6 ORIGINAL USE OF FIGURES. 11 #, I,, or Iq, when placed at the left hand of a figure, indicates that the letter which is at the interval from the base note denoted by the figure is #, tj, or tj. Name the chords iadicated by the following base notes, and tell what letter ia each is #, \^, or K e=^. m #5 bi ^1 be 4 H fs bs n Ans. — The first is the common chord of C, with G#. The second is the common chord of D, with A^j. The third is the chord of the seventh of C, with B^. The fourth is the eooimoa chord of A, with C\). The fifth ia the comm'fSHED Fifth. A sixth containing four steps and one half step is called a Major .•sixth. A sixth containing three steps and two half steps is called a Minor Sixth. A seventh containing five steps and one half step is called a Major Seventh. A seventh containing four steps and two half steps is called a Minor Seventh. Minor Seconds. Major Seconds. Minor Thirds. L__|__ ^:^^4^_^_ _ I J 1 — r mmmm ^j: Perfect Fourths. Superfluous Fourths. Diminished Fifths. Perfect Fifths. I 1 1 1 , J I . 1 J I 1 1 9 18 Minor Sixths. THE MAjo„ SCALJC. Major Sixths. Minor Sevenths. Major ScTenths. * IJ \Zil: CHAPTER XI. THE MAJOR SCALE. A series of seven tones, so arranged that there is the interval of a minor second between the third and fourth tones and intervals ol major seconds between the other tones, is called the Major Scale. This scale may commence on any letter, care being taken that the above-named order of intervals is preserved. When the scale commences on C, the order of inte rvals is correct. When it commences on any other letter, sharps or flats must be em- ployed to preserve the order of the intervals. The scale is said to be in the Key of the letter with which it commences. If the scale commences on A, it is said to be in the key of A, i.e., ' key of A' means that A is the first tone of the scale. Key of C. Key of A. Key of E -#-« Key of B. Key of F^. #r^ Key of C#. ^-^^=^tl'l^=^^& •-#— ~^^ THE MAJOR SCALE. 19 Key of G#. Key of M. E*!?«g: — a-#- •-* — Key of A#. KeyofE#. KeyofBff. Key of F. fJ^-iH*: KeyofBb- Key of El?. -^-#A ^ #-*- Key of A t> i«if: Key of Db- Key of Gb- )?=t6 KeyofCb- KeyofFtT. Key of Bbb- :fc^: Key o{ Ebb Key of Abb- Key of Dbb- The sharps or flats which are placed at (he commencement o.. each key are said to form the Signature, 20 THE MAJOR SCALE. The signature of the key of A is three sharps. The signature of the key B? D:?^? E? E^? F? F:^.? G? G^? ■ What letters form the scale in the key of A b? Abb? ^b? Bbb? Cb? I>b? Dbb? Eb? Ebb? Fb? (^b? There is a key formed by the use of flats precisely like each key formed by the use of sharps, and a key formed by the use of sharps precisely like each key formed by the use of flats. The key of E and the key of Fb are precisely alike, as are also the keys of G and Abb> the keys of Y^rf and Gb, &c. This can be readily proved by playing the scale in these keys on the pianoforte. To find the key formed by the use of flats which is the same as one formed by the use of sharps, or vice versa, find the difference oetween the number of sharps or flats in the signature and twelve. What key formed by the use of flats is the same as the key of A ? Ans. — The signature of the key of A is three sharps. The difference between three and twelve is nine, consequently the key which has the signature of nine flats (Bbb) is the one required. What key formed by the use of flats is the same as the key of A4f ? B? C? C^-i D> Dtt? E? E#? 1<^> What key formed by the use of sharps is the same as the key of Ab? Abb- Bb? Bbb? C.^ Cb? Db? Bbb? Eb? Ebb? I^-' I'b? Gb? VARIETIES OF COMMON CHORnS. 21 CHAPTER Xn. VARIETIES OF COMMON CHORDS. Chords are named from the letters, to denote their abstract or positive pitch. They are also named from nmnerals, to denote their relative pitch. If 071C of the scale is the fundamental note of the chord, it is called ihe Chord of One ; if two is the fundamental note, the Chord of Two, &e. The chords when named by numerals are usually designated by the Roman figures, I, II, III, IV, Y, VI, VII. Common Chords ia the Key of C. q==^=— =j===s===2==^— I II III IV V VI VII Commoa Chords in the Key of G, . — g 1*" -!=■ i II III IV V VI VII What letters compose the common chord of I, in the key of D ? Ans.— D, F^, A. What letters compose the common chord of II, in the key of D ? The chord of III? IV? V? VI? VII? Remark. — It will be well for the student to pass through all the keys in thia way, telling what letters compose the common chords of I, II, III, IV, V, VI and VII, in each key. A common chord, composed of a fundamental note, a major third and a perfect fifth, is called a Major Common Chord. The common chords of I, IV, and V, are major common chorda. A common chord composed of a fundamental note, a minor third, and a perfect fifth, is called a Minor Common Chord. 22 VARIETIES OF COMMON CHORDS, The common clioids of II, III, and VI, are minor common chords, A common chord composed of a fundamental note, a minoi thifd and a diminished fifth, is called a Diminished Common Chord. The common chord of VII is a diminished common chord. "Write the major common chords in the keys of C, G, D, A, E, B, F^. Gp, Db Ab Eb B'b and F. Major Common Chords Major Common Chords in the Key of C. in the Key of G. Write the minor common chords in the keys of C, G, D, A, E, B, Fff, G\) Db, Ab, Eb, Bb, and F. Minor Common Chords Minor Common Chords in the Key of C, in the Key of G. -A- ,'- 1 jf rr II III VI Write the diminished common chords in the keys of C, G, D, A, E, B, F^, Gb, Db. Ab, Eb, Bb, and F. Diminished Common Chord Diminished Common Chord in the Key of C. in the Key of G, • m Ex feEEF^EEff SEES-Elf^^- vii VII Remark. — It will be well for the student to practice all the chords in all th( keys upon the pianoforte, first playinp: the major common chords in every key, then the minor common chords, and finally the diminished common choixls, cc^o- tinuing t lo practice until fluency is attained. BEST POSITIONS Ot' COMMON CHORDS. CHAPTER Xni. BEST POSITIONS OF COMMON CHORDS. A very common progression in all varieties of musi« is for the chords of I and V to follow each other. The following are the best positions for this progression. Key of C. fixERCISE No. 1. I=^= 1 1 3= =5- =R=I= — — Ef=;i _£=-p- — i — 9 V I — 'r 1 i i-T ^^— r , -*- ._•_ — ii_ —\ — _S Exercise No. 2. The same example in the Key of Gr. 1 1— — l- I V I -f- Write the above example in the keys of C, G, D, A, E, B, F#, Gb, Db' Ab, Eb, Bb. and F. Practice the above example upon the pianoforte, playing it in the keys of C, G, D, A, E, B, F#, Gb, Db, Ab, Eb, Bb, and F, continuing the exercise until fluency is attained. Remark — ' Progression' means the manner in which chords move, or follow each other. Another common progression is for the ch^ius of I and IV to follow eacb other. The following are the best positions for this progression BEST POSITIONS OV COMMON CHORDS. Exercise No. 3. I IV I --« — F — *^T=* F m Write the above example in the keys of C, G, D, A, E, B, F#, Gj?, D[>, Ab, Eb, Bb, and F. Practice the above example in all the above-named keys, upon the pianoforte, continuing the exercise until fluency is attained. The following are the best positions for the progression in which the chord ol II is most commonly introduced. Exercise No. 4. #- '0- m — \0 mUSi ?-^^^ 11 Write and practice the above example in the same keys as in the previous examples. The following are the best positions for the progression in which the chord of in is most commonly introduced. Exercise No. 5. ' ' --!H— ' I III IV 11 V I H— Write and practice the above example in the same keys as in the previooi •xamplcs. yORMS. 25 The ibllowing aie the best positions for the progression in which the chord oi V I is most eomuionly in reduced. Exercise No. 6. !^in-n'r:ni:^:-n:z+TZ|-^_— 5 I V VI II V I ' Write and practice the above example in the same keys as in the previous examples. Remark. — It is very important that the student should be so familiar with the above examples as to be able to play them from memory in every key at any time ; in short, so familiar with them that they will never be forgotten. CHAPTER XIV. When the base note of a chord is the fundamental notCj the chord is said to be in the First Form. When the base note of a chord is the third, the chord is said to be in the Second Form. Wlien the base note of a chord is the fifth, the chord is said to be a the Third Form. Common Chord of C, first form. Common Chord of C, second form. mmm Comninn Chord of C third form. [31 id When the cliords are designated by the Roman numerals, the fona is usually indicated by a figure placed over the numeral ; thus, I o danotes the cl ord of one, first form ; I the chord of one, second form, &.C. "Write the following chords in the key of C — ] '2 3 2 ] 3 I 111 VI II IV VII I V 13 3 1 Vll IV V VI ^ l\ 2 1 2 3 VI III Vil I 2 3 3 IV 11 III Example. ESEEPEEI: |EE|^e. ii^l^i: S l?==FF&c. I III. 3 VI. [V.' Remark. — It is imraaterial in what positions the parts upon the treble staf are written. The design of the exercise is to impart a knowledge of the forms. The chords in the exercise are not designed to have any harmonic connection with each other. I Write the above exercise also in the keys of G, D, A, E, B, F#, G[j, I>\), Ab, Eb. I^b. and F. Best positions for a progression consisting of the common chords i i! f ^' i Exercise No. ._l_. I. N±?.=EEizEEE!iE?EcEEEEE?:I:!EcEEiEi?;[l: i 11 f ^ 1 Write the above exercise in all the keys, and then practice it thoroujrhly io ftU th) k»ys upon the piano, until the ability to play it from memory is attained. 27 Remark. — The keys which have the signatures 7, 8, 9, 10, and 11 sharps, being precisely like those which have 5, 4, 3, 2, and 1 flats, and the keys which have the signatures 7, 8, 9, 10, and 11 flats being precisely like those which have the signatures 5, 4, 3, 2, and 1 sharps, it is not customary to use more than six sharps or flats for signatures. When directions are given to write or play an exercise in all the kevs, it will be understood that in all cases th* keys of C, G, D, A, E, B, M Gb, J)\), K\), Eb, Bb, and F, are meant. Best positions for a progression consisting of the common chords 3 1 1 I V I 1 III 1 IV Exercise No. 2. Il.llll 1« » m m * ft i^ ^-<'-'d-^-*-#-^-'=[--;rff-;r-r-h-'=F-pp-F-F-F=P-tt ^^iszczppzrzfziizpt-rippir^rzfzp: Jill I III IV II 3 1 1 I V 1 Write and practice the above exercises in all the keys. Best positions for a progression consisting of the common chords Exercise No. 3. 2:— i-izJ- =s:=q:=2: -m — *- — w — 1^ — »- ::E!:EEEEEE5^EEEE?EE r II VI II i "^ :f:_#_#- L_f:_^ . — » — w — « — r — 1^ — m iii^^^^i^g^l Write ind practice the above exercise in all the keys. 28 FORMS. Write and practice the following exercise in all the keys. KxBBOIfiB No. 4. 2 IV -4- -' i ^ i iV n — n — i- — I — I — I — I — I — I — n — i — ir 2 — «— « — « — 2 — «— « — #1— 2-— • — « — *• 'x=.z-i,z:!Lzs=z.--. m w — w — w — ^ — I ^ "■ ^^ rzz^: :|Lgzzgzzezz H-g_rz: _g_r i- -V-#— » a-T-S— £— S— .»— 5 -1 — !•— i — I iiil^giE^iglNiiEs i » • » 2 ",•— I — f ._ — I — I — I — l- T — ' — ' — ' — r rF Kemark.— The exercises in this and the previous chapters are progressions (or Buccessions) of common chords which occur very frequently in all kinds o^ music, ChorJs can succeed each other in an infinite variety of pi i>gressiong, and composers are continually inventing new arrangements. In a treatise on harmony it is only possible to notice the most common successions. If the stu- dent has followed the directions, he is now practically familiar with progressiona of common chords, some of which will be found in every strain of nearly every species of music. It will be noticed that in each of the exercises of this and the previous chapter, that each succession of chords is written in three different po« sitions. These positions are explained in Chapter XVI. CHAPTER XV. When two parts move the same way, they are said to progress m Similar Motion. When one part moves and the other remains stationary, they are said to progress in Oblique Motion. When two parts move in different directions, they are said to progress in Contrary Motion. Similar Motion. Oblique Motion. Contrary Motioa, I mm T Rule I. — Two parts which form perfect fifths i?i a chord, must not form perfect fifths in the next chord^ miless they progress in oblique or contrary motion. Remark. — This is commonly called the rule of consecutive fifths. The mean- ing of the rule is, that if two parts (the treble and alto for instance,) form per- fect fifths in a chord, those two parts (i.e., the treble and alto.) must not form perfect fifths in the next chord, if they progress in similar motion. Observe that the rule does not forbid such fifths if made by different parts, (i.e., if the treble and alto form perfect fifths in a chord, it does not forbid the treble and tenor, or the alto and base, (&c.) from forming perfect fifths in thfe next chord,) but only forbids consecutive perfect fifths between the same parts, (i.e., if tha treble and base form perfect fifths in a chord, the treble and base must not form perfect fifths in the next chord ; or if the tenor and alto form perfect fifths in a chord, the tenor and alto must not form perfect fifths in the nest chord, &c., &c.) Observe, also, that the rule forbids such fifths only when the two parts progress in similar motion ; that the prohibition is against perfect fifths only, (not against diminished fifths); and that it does not forbid consecutive fifths between two parts in consecutive chords when the two parts are stationary [3*] 30 Consecutive perfect fifths between two parts progressing in similar motion. Wrong. 'm Consecutive perfect fifths between two parts progrestiiiig in oblique motion. Rigiit. Consecutive perfect fifths between two parts progressing in contrary motion. Right. Consecutive perfect fifths between the upper and lower parts in the first chord, and the upper and middle parts in the second chord. Right. #1- «- I Conse^ itive perfect fifths betweer two pirts which remain stationary on the same degrees of the scale. Right. :~n: --F--F- Consecutive diminished fifths pro. gressing in similar motion. Right Remark. — The term " Consecutive Fifths," is always understood to wean consGcuUve perfect fifths, although the word " perfect" is not usually rxpressed. Point out the consecutive fifths in the following example. Exercise No. 1. 3 4 5 7 8 9 10 11 12 13 1.4 15 16 17 18 19 20 21 -i-n-i^ lii^^iifE^i-^siifi Remark. — In all exercises in this work, the highest part will be consi- iered as the treble, the second part as the alto, and the third part at il»« CLOSE HARMONY. * 31 In the foregoing example the alto and base form consecutive fifths in tho 3d and 4th chords, the tenor and base in the 5th and 6th chords, the treble and tenor in the 7th and 8th chords, the tenor and base ni the 10th and 11th chords, the treble and base in the 13th and 14th chords, the treble and alto in the 15th and 16th chords, and the alto and tenor in the I8th and I9th chords. CHAPTER XVI. CLOSE HARMOVr. When chords are so arranged that all the letters composing the 3hord, except the base note, are placed as near the treble as possi- ble, the chord is said to be in Close Harmony. mmm In the above example, the common chord of C is arranged in close har- mony in three positions; i.e., the letters composing the common chord of G are placed as near the treble as possible. When the letter which is the fimdam,ental note is the treble note, the chord is said to be in the First Position. When the letter \vhi(*h is the third is the treble note, the chord is said to be in the Second Position, W'.en the letter which is Xhe fifth is the treble note, the chord is said to be in the Third Position. In the above example, the first chord is the common chord of C, first po. sition — because the treble note is the letter which is the fundamental note The second chord is the common chord of C, second position — because the .reble note is the letter which is the third. The third chord is the common chord of C, third position — because the treble note is the letter which is the 5fth m CLOSE HARMONY. When chords are arranged in close harmony, each chord must be m the first, second, or third position, unless such an arrangement ei)lates the rules, in which case an irregular position maybe taker.- In Exercise No. 6, Chap. XIII, (page 25,) the tliird chord is placed in an irregular position, because a consecutive fifth would have been made, (i.2.. Rule No. I would have been violated,) if it had been in the regular position. In Exercise No. 1, Chap. XIV, (page 2G,) the second chord in the third measure is placed in an irregular position, because if it had been in the regular (third) position, Rule No. 1 would have been violated. Point out the chords on the 27th and 28th pages, which are placed in irregular positions to avoid violating Rule No. 1. Some of the chords in those pages are placed in irregular positions to avoid violating other rules. Notice that it is required to point out only those which are so placed to avoid violating Rule No. 1. Remark — It w" be well to notice that the P^xercises in Chapters XIII and XIV, are all ^ ranged in three positions, i.e., the first and last chords in the first nieasuz-e of each example, are in the first position ; the first and last chords in the second measure in each example are in the second posi- tion ; and the first and last chords in the last measure in each example are in the third position ; the other chords in each measure being arranged in the best relations to the first and last chords. Write the following exercises in close harmony, using regular positions, except where such positions will violate Rule No. 1. Remark. — The chords required in the exercises are indicated by the figured base. The student must use the treble part here given, i.e., he has to write only the two parts next below the treble, placing them so as to form a first, second, and third position to each chord, unless such a" position will violate the rule. In all subsequent exercises, if the treble is printed, the Etudent is only required to add the alto and tenor, using always the printed treble for his highest note. Exercise No. ligg-ipgE^pi^iii ^ig=lil 6 6 CLOSE HARMONY. ^ .«_ 3o ::f=:^:-=-+- s ExERcrsE No. 9. Remark. — In the above exercises the student must carefully avoid conse- «iutive fifths. Care must be taken to notice the progression of each part. In tlie Pii-st of the following examples tbe tenor in the first chord is D, nnd it moves to E in the second chord. By so doing it forms consocutive fifths with the base. This consecutive fifth is avoided in the second exam- ple, by causing the tenor (D) in the first chord to move to C in the second cbi fd.- mmm ^ 1 mm^^ J4 CONSECUTIVE OCTAVES. CHAPTER XVII. CONSECUTIVE OCTAVES. The scale may be repeated at a higher or lower pitcli. -*. # I II III IV V VI VII. I II III IV V VI VII. The interval from VII of a scale to I of the scale next above, is a half step (minor second). The interval from a letter to a letter of the same name in the next higher scale is called an Octave. For example, the interval from C in the lower scale to C in tlie upt>er scale, in the above example, is an octave, as .ire also the intervals from 1) in the lower to D in the* upper scale, from E in the lower to E in the upper Bcale, &.C. Rule II. — Tiro jxirls which form octaves in a chord. Tn?is( 7ioi form octaves in the next chord, unless they progress in oblique or con- trary motion. Remark. — This is comnionly called the rule of consecutive octaves. All the remarks which have been madi; in reference to consecutive fifths, also apply to consecutive octaves. In Exercise No. 1, Chap. XV. (pnge 30,) consecutive octavos occur in the following chords, viz. in tliL- 3d and 1th chords, between the treble and base; in the 5tli and 0th, and t'.c lOth and 11th chords, between the alto and ba.se; and in the 15th and It th, and the 18th and 19th chords, between the treble and tenor. In Exercise No G, Chap. XIIT, (page 2.5,) consecutive octave.s are avoided in the second and third chords, by the irregular position of the third chord, i.e., if the third chord had been written in the regular second position, the alto would have moved from G in the second chord to A in the third chord, which would have been in consecutive octaves with the base. Point out the chords in the exercises in Chapters XIII and XIV in which consecutive octaves are avoided by irregular positions. Write the chords indicated by the figured base in the following exercise^ lakiiig care that Rules I and II are observed. Rkmakk.— In he exercises, which the student is required to write, when CONSECUTIVE OCTAVES. 35 ft-ogressions occur like those of which examples were given in Chaptern XIII and XIV, it will be well for him to imitate those examples. Exercise No. 1. ^=?=^=FFr=fEH 1 — ' ^^ r ' ' ^=«=Ei!E£EE:EEEEBf=tE 6 6 4 mmmmm^^. :p:p: mm mm mi^mm 6 € 6 6 Exercise No, 9. « S :^-*^-t:t Si^^^ iE»EEfe£rE^:ERFE!EEEEiEEEiE-1^: 6 e 6 6 6 6 ^« i-l-r ?-: f^^PS^ its: 1 m'^^^^m^^s 6 G 4 36 MODULATION. CHAPTER XVIII. MODULATION. A tune or piece of music is usually said to be in the key denoted by i J signature; thus, if the signature is one s-harp, the tune is s;iid to be in tlie key of G, &,c. It is veiy seldom the case, however, that all the chords ol a tune are in the same key. Tlie following example, according to the sig- nature, is in tie key of C. A ch)se examination, however, ^hows that only the first and last three measures are in that key. The third chord, if in the key of C, would be the chord of II. The chord of II, however, nuist be a minor common chord. Tliis (^kl) chord is a major common chord, an«l consequently is either the chord of I, IV, or V. A comparison with the chord next to it proves it to be t!ie chord cf V, in the key of G. In the above example the 1st chord is the common chord of I, in the key of C. The 2d chord is the common chord of IV, in the key of C. The 3d chord is the common chord of V, in the key of G. The 4th chord is the common chord of I, in the key of G. The oth chord is the common chord of V, in the key of A. 'i'he 6th chord is the con)mon chord of I. in the key of A. The 7th chord is the common chord of VII, in the key of D. The 8th chord is the common cliord of I, in the key of D. The Oth chord is the common chord of.VII, in the key of G. The 10th chord is the common chord of I, in the key ofG. The 11th, r2th, 13th, 11th, and loth chords are the chords of Vll, 1, IV, V, and I, in the key of C. When chords wliich do not belong in the key indicated by the signature are introduced, the chords are said to modulate, and t!ie progression is called a Modul.ation. Rr.MARK. — Tt i.s not ea.«;y to give definite direction.^ by which the student can infallibly determine in what key the modulation !.-». The first requisite is always to determine whether it is a major, minor, or diminished common chord. If it is a major common chord, it is either the cliord of I, IV, or V ; »r if it is a minor common chord, it is cither the chord of II, III, or VI. MODULATION. 37 A con parison with the chords before or after it, will generally determine in what key the chord is. For example, the third chord in the above example is a major common chord, and is consequently either the chord of I in the key of b, the chord of IV in the key of A, or the chord of V in the key ol G. A comparison with the chord after it, renders it easy to determine that It is the chord of V in the key of G. If the chord is a diminished common chord, the key is of course infallibly determined, for if it is a diminished common chord, it is the chord of VII, which will enable the student at once to decide what the key is. For example, the 7th chord in the above example is a diminished common chord, and consequently is the chord of VII. It is the chord of C|r, and C# is VII in the key of D, consequently the 7th and 8th chords in the example are in the key of D. The sharps and flats form a tolerably good guide to the key. If F4f is the letter which produces the modulation, it is tolerably certain that it is the key of G, because Fsf is the distinguishing sign of the key of G. If G^ is the letter which produces the modulation, it is tolerably certain that it is the key of A, because Gff (in con- nection with F^ and Cfr) is the distinguishing sign of the key of A. A chord is not allowed to stand alone in a key. At least one r*.hord, before or after it, must be in the same key. When a chord has modulated to another key, the subsequent chords are always in the same key with the modulating chord, until another modulation takes place. 17 18 19 The above example is in the key of F. The 6th chord modulates to the key of C. No other modulation takes place until the 15th chord, conse- quently the 6th, 7th, 8th, 9th, 10th, llth, 12th, 13th and 14th chords are in the key of C Write the following exercises, and place over each chord the Roman figure which indicates the chord, i.e., over the first place I, to indicate that it is the chord of one; over the second place IV, to indicate that it is the chord o four ; over the third place V, to indicate that it is the chord of five, (in th< key of G,) &c. [4] B8 Exercise No. MODULATION. ?^EE!E!zEPEEFPZ:EEEE^i:PE'l »-r-l r+-i-ri-: ?^i@ggi@iliiii|i;| Exercise No. 2 /ia*in=n;t^-;ri=pir3f--a_-r,:=^-r-=_=Trrfr;-;| \f~?5!=E?£EFzEFEEEzEEE=Eit=pTp:l:pl:I ^EEE^LEE?EE^E!iFE5SpEFEEE5:iEr-E:-EE # 6 # 4^ Rkmaiik. — In all exercises which arc given for the student t'l write, ifthe tieiie and base are both printed, (as they have been in all the exercises thui» DISPERSED HARMONY. 39 far,) he lia3 only to add the two parts next below the treble Where (as in he followincT exercise,) the base alone is given, the student is to write the 'uU chord, (i.e., three parts on the treble stuff,) indicated by the base note. Write the chords indicated by the following base notes, carefully avoiding .he vrotation of Rules 1 and 2. Exercise No. CHAPTER XIX. DISPERSED HARMONY. When chords are so arranged that the treble, alto, tenor and base ports, are each at their appropriate pitch, they are said to be in Dis- persed Harmony. Remark — Chapters XTIT and XIV gave examples of some of ti.e mosi common progressions of common chords in close harmony. The following are principally the same progressions arranged in dispersed harmony. Practice the following exercises upon the pianoforte, in the keys of C, G, D, A, K, B, F^, G[), D\), A\), E[-), B\), and F, continuing the practice until the ability to play them fluently from memory in every key is attained Remark — If the student cannot reach the two notes which form the in- terval of a tenth in the first and last chords of each third position, he can play the base note of those chords an octave higher. -F- mmmm^mmi^ 40 DISPERSED HARMONY. EXEKCISE No. 3. (fc=iJ=^3^E?E*EfeE^fFEEEpE?E^i ( I IV I V I .0. .0 ^ .M. IV I V -i — » [- — p~t* \ — i — i -r- Ei Efe *^ iiiiiS Exercise No. 4. 4-l-4~i'-T-,— ,•■ 1 I I IV --EEEEE='"' Exercise No. 5. r— •-- L-p- 1 ^ I r" I — Jzr r" ~^E^E^E^EteSEPE|EP:fe^ 12 3 11 ?EEPE^EE^EfEPpEE^E?Ep';B DISPERSED HARMONY. 41 Exercise No. 6 i I I I ! I J I ' —0- 1 III 1 IV -£ — ^ — I f — E — I" _ P — ?? — # — «- f— •—! ^ 1 1 i r ^ I^EEEEEE^EIE^EEEEEEEErEEEEEEEZf! 4 4 If i E / 1 ( XERCISE No. 7. F5-i5=2=;f; 1 2 3 J 1 2 ] 1 I II I V VI 11 V I 6 4 t-Sz::E=:?=;«: iiiili 4 -i — -1—1 — -p- :SEt v-:c~.r: f- ^ /- ^- f - -5-_E f : "i — r" ;r; [4«] 12 CONSECUTiVE UNISONS. Revark. — The successions of common chords given in tin preceding ex- ercise, are such as occur most frequently in all kinds of music. They are consid;red the best positions for the four parts, in the three pf)sitions. It is not possible always to retain these positions in musical compositions, but composers generally prefer these when they can he taken without violating the rules. The design of requiring the student to become perfectly familiar with these exircises in all the keys, is, that he may never be at a loss with regard to the most desirable positions in which to arrange thi se chords For example, if he wishes to arrange in dispersed harmony ilie ci.nrds III,. IV, the best possible poitions are those in Exercise No. G. II he wishes to arrange the chords V, VI, the be*t possible positions are those 1 Exerci-e No. 7. If he has practiced the exercises according to the direc- tions, he is already perfectly familiar with all the best positions of these chords. CHAPTER XX. CONSECUTIVE UNISONS. -LEADING NOTE. When two parts sing the same tone they are said to be in Unison. Rule III. — Tv:o paj'ts which are innnison u,.th each other in a chord, must not be in tmisoji with each other in tlie next chordo. Remark. — This is commonly Ca..'ed the rule o'' consecutive uni'^ons, (oi consecutive primes). All the remarks in relation to consecutive fifths and octaves, also apply to consecutive unisons. 1 2 3 4 5 G 10 11 12 13 14 15 ;ir-px=-=p-|=r :iE&il^EiE»E-j:|E35-a=^J§_E^ Treble. I 1 1 1 — H •— « — » n — n i"T — ci~i 1 — »■ Baae i'^': mw ^^igiiigii^i^ii LEADING NOTE. 43 In the Qd chord of the (receding example the tenor and base are in uni- Bon, and these two jj irts ^re also in unison in the 3d chord, consequently the tenor and base form consecutive unisons in the 2d and 3d chords. The treble and alto form consecutive unisons in the Gth and 7lh chords, and the alto and tenor form consecutive unisons in the 9th and 10th chords. Remark. — When a part does not ascend or descend, but remains upon (he same degree of the scale, it is not considered as possessing motion, con- sequently in such progressions Rules 1, 2 and 3 cannot be violated. In the 11th and 12th ciiords of the foregoing e:;ample the tenor an ii base are in uni.son, but as thb/ remain stationary upon the same degree of the scale, the rule is not violated. VII of the scale is called the Leading Note. Leading Note Leading Note Leading Note in the key of C. in the key of G. in the key of D. liifl liiiP piii- VII. VII. VII. Rule IV. — The part which sings the leading note, in the next chord must si,ng the next tone above the leading note. In Exercise No. 3, Chap. XIV, (page 27,) the part which has B in the fourth chord, has C in the fifth chord, to avoid violating this rule. Remark. — Some rules are considered of more importance than others. The rule of the leading note is one of the least importance, or, in other words, it is one which may be broken when there is a good reason for violating it. Most composers hold that the rule of consecutive fifths (Ride No. 1,) must never be violated. In Exercise No 2, Chap. XIV, (page 27,) in the progression III, IV, either Rule No. 1 or Rule No. 4 must be violated, for if the part which has the leading note (B) in the chord of III, should have the next note above the leading note (C) in the chord of IV, the treble and base would form consecutive fifths. Rule No. 1 being considered of much more importancf; than Rule No. 4, it is observed, and Rule No. 4 is vio* Jated. 44 DIMINISHED COMMON CHORDS. CHAPTER XXI. DIMINISHED COMMON CHORDS. Chords which produce a pleasant sensation to the ear are callca IJONCORDS. Chords which produce an unpleasant sensation to the ear are called Discords. Major and minor common chords are concords. Diminished common chords are discords. Remark. — The term " Discord, ' as it is used in harmony, has two signi- fications, sometimes applying to the whole chord, (signifying that the effec produced by the chord is unpleasant,) and sometimes applying to the single part of the chord which produces the unpleat-ant effect. For example, the diminished common chord is called a discord, because the sound produced when that chord is played or sung, is unpleasant. It is the tone which forms the interval of a diminished fifth from the fundamental note, however, which jiroduces the unpleasant effect, consequently this tone is called /Ac discord. That this is the tone which produces tho unpleasantness, may be readily seen, by substituting for the tone which forms a diminished fifth with the fundamental note, one which forms a perfect fifth. The unpleasant sensation will disappear, and the chord will become a concord, (a minor common chord). Rules relating to the progression of discords, apply to the single part of the chord which produces the discordant eftect, and not to the entije chord. The tone which produces the discordant effect is allowed to move only one degree. There are three varieties of discords. Discords of the first class produce only a slightly unpleasant effect. In discords of this class the tone which produces the discor- dant effect is allowed to ascend or descend. Discords of the second class produce a harsher effect than those of the first class. In discords of this class, the tone Avliich })roduccs the discordant effect is allowed only to descend. Discords of the third class jjroduce a very harsh eflcct. In dis- cords of this class, the tone which produces the discordant effect requires a preparation, and is allowed only to descend. DIMINISHED COMMON CHORDS. 45 Remakk — The expression, " the tone is allowed to move, &.C.," strictly Bpeaking, is incorrect, inasmuch as a tone cannot move. It is an expression, however, commonly used in harmony, for brevity's sake. The meaning is, that "that part (base, treble, &c.,) which sings the tone which produces the discordant effect, must move, &c." In other words, " the part which has the tone which produces the discordant effect, in the next chord must have the tone next above or below it," (as the case may be). It is also common to say, " tlie fifth mu.-t move so and so," "the seventh must mcive so and so, &c." These expressions are literally incorrect, but they will nevertheless be used in this work for the sake of brevity. It will therefore be understood that the expression " the fifth must move," &.c., &c., means " that the part which sings the tone which forms the interval of a fifth from the fundamental note of a chord, must move," &c., &,c. In other words, tlie part which has the tone which forms the interval of a fifth (&c.) from the fundamental note of a chord, must in the next chord have the tone next above or below that tone. Rule V. — The diminished fifth must move but one degree^ ascend- in ce}iding. The diminished fifth is a discord of the first class. It produces but a sligiuly harsh or unpleasant effect, and is therefore allowed to ascend or descend. Discords of the second and third classes are allowed only to descend. The meaning of Rule V is, that that part which sings the tone which forms the interval of a diminished fifth from the fundamental note, in the next chord must sing the tone next above or next below it. The exercises in the previous chapters have contained only major and minor common chords, i.e., only the chords of I, II, III, IV, V, and AT, have been employed. It will now be necessary to become familiar with the most common progressions of the chord of VII. This is a diminished con. mon chord, and contains a diminished fifth. As its fundamental note is the leading note, the progression of this chord is much circumscribed, for its fundamental note can only ascend according to the Rule of the leadincr note, ( Rule 4.) and its fifth can only ascend or descend according to the Rule o( the diminished fifth, (Rule 5.) Practice the following exercises (except those printed in small rotes,) in all the keys. Exercise No. 1. 1 1 VII. I J:^=i 46 DIMINISHED COM-MON CHORDS. FiXXBCiss No. 2. 111 VII. I. M^=Ef s VII. I. ii=i Exercise No. 3. pil VII. t==,SEElEJ=S=E^EE[f ExExlCISE No. 4 :t=b VII. . I. i i^=iliL^Ei^EE=fPiHil |^]XEIICISE No. 5. (* -H- — « — VII. I. iiiiiii, Miiliiiiilli [iEjEEE3 VII ^iprs DIMINISHED COMMON CHORDS. 47 JKEMAUK. — It will be readily seen that in all discords the motioi Df one or more of the parts is circumscribed. The number oppositions, (regular knd ir;egular,) in which chords may be arranged is very great, but each common chord h-is but three forms. In the foregoing exercises, examples are given of each form of tlie chord of VII, going to each form of the chord of I, miking in all nine progressions, viz., (1) the chord of VII, going to the ch ird of I , (2) the chord of Vll, going to the chord of I ; (3) the chord 3 1 1 of VII, going to the chord of I ; (4) the chord of VII, going to the chord 2 2 2 ^ of I , (5; the chord of VII, going to the chord of I ; (6) the chord of VII, 2 1 3 going to the chord of I ; (7) the chord of VII, going to the chord of I ; (8) 2 3 3 . the chord of A'll, going to the chord of I ; (9) the chord of VII, going to 3 the chord of I. The following is a tabular view of these nine progressions : — 1 VII VII 2 i 1 1 VII 3 I o VII 1 ^ 1 VII 2 I 2 vli 3 I 3 VII A i 1 3 VII 3 I Two positions of each of the foregoing progressions are given in the exer- cises on pages 45 and 46. Although many more positions are possible, if the student practices these two thoroughly in every key, he will make him- pelf familiar with the best positions for the progression VII, I. The pro- gression VII I, in these exercises is printed in small notes, because it can- not be made without violating Rule 5, as in this progression the diminished fifth (which is the base note) would be compelled to descend four degrees, .12 whi.e the rule requires it should descend only one. The progression Vil I is printed in small notes, because it cannot be made without violating Rule 4, as in this proo;ression the leading note would be compelled to ascend four decrrees, while the rule requires it should ascend but one. The progression 1 3 VII i is printed in small notes, because it cannot be made without violating Rule \. 3 VII Remark. — The progression Vll 1, in the exercises', is printed in small notes, because although not strictly in violation of rule, it is consi- dered best that the diminished fifth should descend when it is in the base, 48 THIRD FORMS. DIMINISHED FIFTHS. The natural progression of all discords is downwards, and although the diminished fifth is allowed also to ascend, in consideration of the fact that it produces hut a slightly discord.^nt effect, it is not deemed advisahle that it should avail itself of this lihc.cy when it is the base note. Remark — Discords are allowed to move but one degree. When it is aid that a discord may ascend or descend, the meaning is always that it may ascend or descend one degree only. The term " discords are allowed to move, «Sic.,'' is a term common in harmony, although, strictly, incorrect. It means, " the Dart which produces the discordant effect may move, &c." CHAPTER XXn. THIRD FORMS. DIMINISHED FIFTHS. Common chords are composed of three letters. In four part com- positions one of the letters must be repeated, or doubled, (either in octaves or in unison). In most cases it is not material which letter is doitl'cd, but in some, the one which must be doubled is prescribed by rule. RuleYI. — When the common chord of I is in the third form, the fifth of the chord must be doubled, and the parts which have the fiin- damcntal note and tltird must descend one degree. liilpliiiiil 8 1 3 1 I V I V 3 . In the first measure of the above example, the chord of I is written in close harmony. G is the fifth, and there are two Gs in the chord, one in the base and one in the alto. The treble part is the fiindamental note, and in moving to the next chord it descends one degree; the tenor i» the third, and it descends one degree. In the second measure the chord of I is writ- teji in dispersed harmony. The tenor is the fundamental note, and it descends one degree; the treble is the third, and it descends one degree; the base and \lto are both the fifth, which is. therefore, doubled THIRD FORMS. DIMINISHED FIFTHS. 49 Remauk. — A common chord in the first form produces a pleasanter (or more concordant) effect than the same chord in either the second or third •orms. A common cliord in the second form produces a le.^s concordant k ffect than the same chord would produce in the first form, and some liber- ties are allowed to the second forms of common chords which are not allowed to the same chords in i\ie first and third forms. A. common chord in the third form produces a much less concordant effect than is produced by the same chord in iha Jirst fonri, and is also less concordant than the same chord in the second form, so much so, that by some authors a common cliord in the third form is considered a discord. These remarks apply to the effect produced by a chord when played alone, by itself, and not to effects pro- duced by the progression of chords. Although Rule 6 applies to the third form of the chord oi one, careful composers apply it to the third forms of all the common chords ; and it is recommended to the i^tudent, in writing the exercises in this work, to observe the rule in reference to the third form ol all the clifirds, unless the construction of the exercise renders its observance impossible. Wkeii a part ascends or descends one degree in obedience to a rule, it is said to Resolve. When a chord is repeated, or when the tone requiring a resohition is repeated in a different chord, the resolution is not required to take place until a chord is taken which does not contain the tone requir- ma: a resolution. In the first measure in the above example, the first chord contains a lead iug note and a diminished fifth, both of which, according to Rules 4 and 5, require a resolution. Neither resolves, however, because the second chord ss a repetition of the first, in a different postion, and both leading note and diminished fifth appear in it again. The third chord. does not contain either the leading note or diminished fifth, so in passing from the second to the third cliords, they both resolve according to the rules. In the second mea- sure the leading note appears in the first chord, in the chord of V, and again in the second chord, in the chord of III. It is not, therefore, required to resolve in passing from the first to the second chords. It does not appear in the third chord, so in passing from the second to the third chord it r( solves according to the rule. [5] 50 THIRD FORMS. DIMINISHED FIFTHS. Exercise H^o. ! ! ^ 1 I ! ^ I J f ^ 1 2 1 VI II V ?=Rr: 6 6 1 ! ! ^ I 5 ^ ^ J ! ^ >^l fl ^r •E-^E^'E-E=E§^E-Eg?E"E=^F 3 # 6 « # # ^ 1 ! I 1 1 1 V I li fi n ! ^ 1 :jE*EiEEEE!E'EEEEEEEEEcEE fi 6 b b •; 4 4 4- Write the chords indicated by the foregoing base notes, in close harmony. It will be noticed that the 5th, Gth, 7th and 8th measures are in the key ot G, all the others being in the key of C. In this and all other exercises which tlie student is required to write, he should endeavour to place the chords in such positions that when played the exercise will sound well. For example — -E^EjE3EfflEM=rg=fE:FpB=E &C In writing the above exercise, carefully observe all the rules, particularljr Rule 6. After writing the exercise in close harmony, write it also in din- persed harmony. Rule VII. — A jjcrfect fifth must not follo7v a d'wiinished fifth, in iiinilar mntioHy unless the chord containing the perfect fifth is in ttu second form. THE MINOB SCALE. 51 In the foregoing rule, one of the expressions commonly used in harmony for the sake of brevity, is employed. It means that if in a chord two parts form diminished fifths with each other, the same two parts must not form |)erfect fifths with each other in the next chord, if they progress in similar motion, unless the chord which contains the perfect fifth is in the second form. It will be seen that this is a kind of consecutive fifths, somewhat dif- ferent from those prohibited by Rule No. 1. Observe that this rule does not forbid a diminished fifth from following a perfect fifth, nor a diminished fifth from following a diminished fifth. Wrong, Right Right. Right, In each chord in the above example, the treble and tenor form fifths with each other. In the first measure a perfect fifth follows a diminished fifth, but it is wrong, because the chord which contains the perfect fifth is not in the second form. In the second measure, a perfect fifth follows a diminished fifth, and it is right, because the chord which contains the perfect fifth ia in the second form. In the third measure a diminished fifth follows a perfect fifth, and, in the fourth measure, a diminished fifth follows a diminished fifth, neither of which progressions are forbidden. CHAPTER XXIII. THE MINOR SCALE. A second a half step greater than a major second is called a Superfluous Second. A third a half step smaller than a minor third is called a Dimin- ished Third. A fourth a half step smaller than a perfect fourth is called a Di- minished Fourth. A fifth a half step larger than a perfect fifth is called a Super- fluous Fifth. A sixth a half step larger than a msyor sixth is called a Supeb" rLUOus Sixth. 52 THE MINOR SCALE. A seventh. a half Step smaller than a minor serenth is called a Diminished Seventh. A series of seven tones, so arranged that the interval from the first to the second tone is a major second, from the second to the third a minor second, from the third to the fourth a major second, from the fourth to the fifth a major second, from the fifth to the sixth a minor second, and from the sixth to the seventh a super- fluous second, is called the Minor Scale. Remark. — It is customary to express the word " minor," when speaking of a minrir key, (thus, key of C minor, key of G minor, &,c. ;) but it is not usual to express the word " major" when speaking of a major key. The term "key of C," &c , is understood to mean the " key of C major," &.C., although the word '* major" is not ex{ Kay of A minor. Key of E minor. Key of B minor. Key of F?r minor. Key of C4r minor. Key of A^ minor. Key of E^ minor. Key of B# minor. Key of Fx minor. / THE MINOR SCALE. 53 Key cf CX minor. Key of Gx minor. Key of D minor. -•-^*-^5 Key of G minor. Key of C minor. Key of F minor. Key of Bb minor. Key of Ef? minor. Fb:5Tzz= -^*- Key of At) minor. Key of Df? minor. '^'^^=^^^^E??: Key of G[? minor. Key of Ct> minor. -^-»^!5#- Key of Ft) minor. Key of B^b minor. [5] 64 THE MINOR SCALE. What is the sifriiafure of the key of A minor? A flat minor? A shar| minor? B minor ? Bflatniinor? B double flat minor ? B sharp minor C minor ' C flat minor Y C sliarp minor? C double sharp minor? B minor? D flat minor? D sharp minor? E minor? E flat minor? E sharp minor? F minor ? F flat minor ? F sharp minor? F double sharp minor? G minor? G flat minor V G sharp minor? G double sharp minor ? What key formed by the ust; of flats is the same as the key of A niinor? Csee page iiO ) B minor? Brf minor? C^ minor? CX mmor;' D# minor? E minor? Efr minor? F:fr minor? Fx niinor? G:fr niinor' Gx niinor? W^liat key formed by the use of sharps is the same aa the key of A minor? A [j minor? Bj) minor? Bl;|? minor? C minor? C() minor? D minor? })\) niinor? E,\) mim r? F minor? F\) minor? G minor? G[) miiu^r? Double flats are always represented by two single flats placed together (bb). Double sharps are sometimes represented by two single sharps placed together {^^), and sometimes by a cross (x), it is immaterial which. VII of the minor scale must always be a half step higher than the signature makes it. Sharps, flats and naturals, when placed before the notes, arc called Accidentals, to distinguish them from sharps and fiats in the signature. In the foregoing examples of the niinor scales it will be noticed that Vil is always raised, by an accidental, a half step higher than the signature would make it. This is done in the keys of D minor, G minor, A minor, E niinor, B minor, F^ minor, and Cfr minor, by placing an accidental sharp (t=) before it; in the keys of Gr!^ niinor, D:fr minor, A^ niinor. Eff minor, an