BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF Henrs W. Sage 1S91 ^p.i$.X ;:1..;:......., <^\ll<\b MT SO-ofriMo"""""* "^"^ .Text book of harmony 3 1924 021 632 942 PI Cornell University y Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31 924021 632942 TEXT BOOK OF HAEMONY. TEXT BOOK HAEMONY. GEO. OAKEY, Mws.Bac. Cantab. Teacher of Harmony and Counterpoint to the City of London College, and Examiner and Teacher.to the Tonic 8ol-fa OoUege, Seventb lEditton. J. OUEWEN & SONS, 8 & 9 WARWICK LANE, E.G. Pbice Three Shillinss. PREFACE ENCOTnuGEi) by the signal euccess that has attended the issue of his " Text Book of CoTinterpoint," the author now complies with the very widely expressed wish that he would write a " Text Book of Harmony." Some of the difficulties that have been met with by the author and others in teaching the subject, which have induced the desire for a new treatise, may be briefly stated. Though there are already many works on harmony extant, and some of them are excellent as regards the information they contain, there are few that are suitable for beginners. Even in those that are avowedly written for beginners the early chapters are often crowded with much that a beginner does not require and that he cannot possibly comprehend .till some considerable progress in study has been made. The exercises to these works are also mostly unsatisfactory. Either they are in an order that has no claim to be educational, or a2 PBMFAOE. their arrangement is not truly progressive, or they are incon- sistent with the text. In one work, some of the earliest exercises embrace modulation or transition, a subject which is not mentioned till near the end of the work, only to be there dismissed as a subject of which the pupil must be content with a bare definition. In another work, the exercises carry the student through the whole range of the most extreme discords and chromatics before a simple modulation is intro- duced. Again, in one work the exercises begin with three- part writing, which every practical teacher knows is more diflScTilt to a beginner than four-part writing; and in another the exercises are all on figured basses, so that the student is never practised in the construction of a bass to the most simple air. The desideratum is a work explaining the facts of harmony in a simple, clear, and succinct manner; educational in its arrangement, thoroughly trustworthy in its information, amply illustrated by examples that are strictly pertinent to the question in hand, and supplemented by a course of exercises that win conduce to the acquirement of practical knowledge, and to the utilisation of the knowledge gained at every step. Such is the scheme of the present work. During a long experience in teaching the author has met with no treatise that in its educational plan is comparable to that of the late Mr. Curwen's " Commonplaces of Music," a large and comprehensive treatise, written specially for those PREFACE. who follow the Tonic Sol-fa eystem, which embraces not only the Bubjeot of Harmony, but musical composition in nearly all its forms. The educational plan of that work is pretty closely followed in this, though the several topics are somewhat differently arranged. But the entire subject to which this work is almost exclusively confined is here more exhaustively treated than in Mr. Curwen's work, and the teaching coincides more with the theories that are generally accepted. The terms and phraseology employed are those in common use among musicians, but so that the work may be as available for Tonic Sol-faists as for others, the examples and exercises are given in the Tonic Sol-fa notation as well as in the ordinary notation. The text, also, is occasionally supplemented by the repetition of a phrase within square brackets in Sol-fa phraseology to assist the Tonic Sol-fa student to understand that which he perhaps has had put before him in another way. Eor the kind permission to use the chord symbols of the Tonic Sol-fa notation the author ik indebted to Messrs. J. Curwen & Sons. Those who may wish for any fuller description of those symbols than is here found, are referred to " How to Observe Harmony," by John Curwen. Of the special features which are claimed for this work may be mentioned the following : — Explicit directions by which consecutive fifths and consecutive octaves may be avoided axe given at the outset and at every subsequent stage where there is any danger of encountering those obstacles, over which, for the lack of some guidance, so many have stumbled. PREFACE. and have needlessly been deterred from pursuing their course. Second inversions of chords, vhich too often receive but scant notice from writers, and over which students so often unwittingly trip, are here unreservedly disclosed, the second inversion of each chord being separately described, and the various surroundings particularised in which it may find place. The practical uses of every combination and contrivance, in addition to the rules that govern the usages, are sought to be shown, more or less, throughout, not only preceptively, but by apposite examples culled as far as possible, especially for the illustrations of the later chapters, from the works of distinguished musicians of the present age. The prevailing theories have, in the main, been adopted in explaining such discords as the Eleventh, Thirteenth, and the Augmented Sixths. It will be seen, however — ^though the author has generally avoided argument— that the theories are not in some cases accepted in their extreme application. Nevertheless, it is hoped that the attention called to the particular oases which are claimed as illustrations of certain theories, and the author's remarks thereon, will assist any who may wish hereafter to study the more abstruse works in which those theories are promulgated. So much of the elementary principles of composition are included as wiU enable the student to write exercises with some regard to structural and melodic form, attention to which insures that inteUigent understanding of harmony that renders it of real and practical value. AU the Graded Exercises take PREFACE. definite forms, and as far as possible, in the earlier stagee especially, they are constructed with some regard to melody. In the later stages, however, where it was necessary, in order to keep the work within convenient limits, to illustrate several discords or chromatic chords in an exercise, melodic form is somewhat sacrificed. The novice may be warned that seldom, if ever, will as many discords or chromatic progressions as are included in some of the exercises of the last chapterB, be found in a musical composition of the same length. In conclusion, may be mentioned the courses of study ■which should be pursued in various circumstances. First, it should be stated that a general knowledge of the rudiments of music is" presupposed. Por this reason the construction of scales, which is often given in books of harmony, is here omitted, as the author contends that that subject belongs to the rudiments, as does also the subject of intervals. As however, a theoretical knowledge of intervals does not enter into all systems of teaching the elements of music, and an exact knowledge of intervals is a prerequisite to the study of harmony, a preUminaxy chapter on them is included for those who may need it. Those who are not thoroughly familiar with intervals should, write them out in different keys. AU the early examples should also be transposed to different keys tiU the student gains the power of readily recognising the chords and their progressions in all their varied appearances and disguises. The course which is recommended for one who PREFACE. desires a thorough knowledge of harmony and has no previous knowledge of it is indicated hy the graded exercises at the end of this work, which foUow the text step by step. But some may only wish to cover certain ground for certain purposes, as, for instance, to pass some particular examination in harmony. In many of these examinations two-part and three-part writing is not included. In such cases Chapter XII may be omitted from the course of study. Again, if a student be well grounded in the elements, and is as thoroughly familiar with the Minor as with the Major scales and keys, the study of harmony in the Major and Minor may proceed pari passu, and Chapter XI may be taken concurrently with ChapterR III to YII. Upton, E. September I6th, 1884. P.S. — It should be said that the theories referred to on p. viii as adopted or explained in this work are those of the Day system as adopted and advo- cated by Professor Maofarren, to whose works the author is also indebted for the explanation and treatment of ebromatio chords and discords, and for many rules of harmony, such as those included in §J 33, 36, 78, 98, and others, whic'i find no mention in the works of other writers. CONTENTS. CHAPTER 1. ,^o„ Intervals . . .... . . I-4 CHAPTER U. Foundation Chords of the Major Scale S-6 CHAPTER in. The Progression of the Three Major Chords of the Scale — ^The Tonic Cadence — The Eleraenti-y rules of Part-writing . . 7-15 CHAPTER IV. The Discord of the Dominant Seventh and its Resolution . 16-18 CHAPTER V. The Dominant Cadence — The Plagal Cadence — The Sub-Dominant Cadence — Sections ■ . 19-23 CHAPTER VI. The Inversions of the Major Chords, and of the Dominant Discord — Bass Figuring — Uses of Inverted Chords — Rules for Second Inversions — Exceptional Progressions 24-35 CHAPTER VII. The Minor Chords of the Major Scale — The Discords of the Super- tonic Seventh and Dominant Fourth — The Interrupted Close — The Imperfect Chord. . ^ . . . • . 36-50 CHAPTER VUI. Sequences 61-54 CHAPTER IX. By-tones and Passing-tones . . 55-60 xii CONTENTS. CHAPTER X. PAGES Transitions to Dominant and Sub-dominant Keys — The Sharpened Fourth of the Scale employed Chromatically — Figuring of Accidentals ... 61-69 CHAPTER XI. The Minor Scale and its Chords — ^Modulation and Transition to Related Keys 70-g2 CHAPTER XII. Three-part Writing and Two-part Writing 83-91 CHAPTER Xm. Discords by Suspension . 92-100 CHAPTER XIV. Prepared Constituent Discords of Seventh, Ninth, and Augmented Fifth 101-106 CHAPTER XV. Unprepai'ed Constituent Discords of the Dominant Ninth, Eleventh, and Thirteenth — Accented Passing-tones — The Pedal . . 107-126 CHAPTER XVI. Chromatic Discords on Supertonic, Tonic, and Dominant Roots — Chromatic Concords — Discords of Augmented Sixths Chromatic Passing-tones ... ... 127-147 CHAPTER XVII. Transition to Unrelated Keys ... ... 148-161 ORADED EXERCISES ... . 163_200 CHAPTER I. INTERVALS. 1. The distance between any two sounds, heard simultaneously or in succession, is called an Interval. 2. The distance between adjacent tones of the scale is broadly termed a Degree or a Step, as C D or E P [d r or n f ]. Adjacent tones are not all equidistant. Those found between the third and fourth and the seventh and eighth of a major scale as E P [n f ] and B C [t d'] are smaller intervals than the others. These smaller intervals are called Semitones, from their being about half the size of the others, which are called Tones. 3. Intervals are classed according to the number of degrees that the higher sound is from the lower, the lower being counted as the first. This will be seen from the following table : — Fio. 1. Fio. 1. • ^=nr=-==|i r n f s 1 t d' ~ _ ^. o-^-^ ^===\\ d d d d d d d i 2nd. 3rd.^.^[."^.^th.8ve. 2nd. 3rd. 4th. oth. 6th. 7th. 8ve. 4 In the following table, with a descending series of notes against a note above — Fio. 2. Fig. 2. 3^^^E^E^?^31 d' di d' di d' di J 2nd. 3rd. 4th. 5th. 6th. 7th. 8ve. 2nd. 3rd. 4th. 5th. 6th. 7th. Sve B TEXT BOOK OF HARMONY. a similar set of intervals is produced, but some ot tliem have undergone a change of quality. The intervals of the 2nd, 3rd, 6th, and 7th in Fig. 2 are each a semitone smaller than those in Fig. 1. In Fig. 1 they are all major, and in Fig. 2 they are all minor. The 4th, 5th, and 8ve remain unchanged, and are called Pekfect Intervals. 5. The seven intervals are also divided into two classes — con- sonant and dissonant. The 2nds and 7ths are Dissonances and the 3rds, 4ths, Sths, 6ths, and 8ves are Consonances. These latter are further divided into Perfect and Imperfect. The 4ths, 5ths, and 8ves are termed Pekfect Consonances, and the 3rda and 6ths, Imperfect Consonances. 6. A similar series of intervals to those in Figs. I and 2 could be raised on any note of the scale, and no variety in quality would be produced except in two r—Q-: f ^® * semitone larger instances. The 4th raised on FT ffl ^ ~ , than any other 4th, the fourth of a scale thus — t7 ^ and is termed a Plu- perfect Fourth, or, from its contain fi IS a semi- tone smaller ing three tones, a Tritone. The 5th raised on the seventh of a scale, thus — ^^ '' than any other 5th, and is termed an Imperfect Fifth. Both intervals are to a certain extent dissonant, and are therefore included in the category of Dissonances. 7. Intervals within an octave are called Simple Intervals. Those that exceed the octave are called Compound Intervals. For most purposes of harmony an interval is treated as Simple even if one or more Bves are added to its simple form. Thus a 10th is still called a 3rd, unless the actual distance of one note from the other needs to be specified. To ascertain the designa- tion of any compound form of a simple interval it is only necessary to add 7 for each octave to the number of the simple interval. Thus a 4th with one octave added to it is an 11th — 4 + 7 = 11. 8. Intervals are said to be inverted when the lower of the two sounds is placed an octave higher, or the higher is placed an octave lower. By inversion a different kind of interval is pro- duced, and, except in the case of the perfect intervals, a change of quality also. The changes will be seen from the following table, which consists of Fig. 1 with the lower sounds added in the octave above, giving two sets of intervals — INTERVALS. Fro. 3. .Octave. Minor Minor 7th. eth. Perfect Perfect 6th. 4th. Minor Srd. Minor 3nd. Unison. i i^eaz izr 32= TTnison. Major Major Perfect Perfect Major Major Octave. 2ua. 8id. 4th. 5th. 6th. 7th. Fio. 3. Octave. Minor 7th. Minor 6th. Perfect 6th. Perfect 4th. Minor 3rd. .Minor 2nd. Unison d> d> d' d' d< di d> d' d r n / 1 I t d> d d d d d d d d Unison. Major 2nd. Major ara. Perfect 4th. Perfect 6th. ^r Major Octave. It will be seen that minor intervals become major by inversioiii and vice versa, bnt perfect intervals remain perfect. To ascertain the kind of interval that is produced by inversion subtract from 9 the number of the interval to be inverted. Thus 9 — 6 = 3. The unison is only classed as an interval because it is the inversion of an octave^ 9. All intervals formed by any two notes of the same scale unaltered by a Jf or 1? are termed Diatonic Intervals. There are, however, real and apparent exceptions in the case of the minor scale, the seventh of which is artificially altered for a leading note, see chap, xi, § 140. This leading note of the Minor [se] when associated with the unaltered seventh [s], or with the sixth [f ], or with the third [d] of the scale will produce a chromatic interval, as shown in §§ 10-12 ; but associated with any other note of the scale the altered seventh [se] will produce diatonic intervals, just as in the case of the Major when its leading note is associated with any other note of the scale. Thus all the following Maj. 7th. Maj. 7th. se h Maj. 6tb. se Tritone 4th. se M^j. Srd. jjjo*' jjfsr lea" jto' Min. ' Min.' junp. Min. 2nd. Srd. 6th. 6th. are diatonic intervals, being formed of the scale notes of A Minor, * See Note next page. sei Min. 2nd. sei Min. 3rd. sei Imp. Bth. sei Min. leth. TEXT BOOK UF HARMONY. *#* In the fm'egoing is contained all that it is necessary o. stvdent should know to enter upon the study of Harmony, but the following, which will he necessary at a later stage, is added here for convenience. 10. The two intervals of tbe minor second found befcvreen the third and fourth and seventh and eighth degrees of the major diatonic scale are also called Diatonic Semitones. Semi- tones can be produced in other parts tones can be produced in other parts r Q — i p of the scale by raising a note by a : (^ ^^ -^^ i^^^L ] aham or In^firinp" it hv a flat, thns — "^ ^ sharp or lowering it by a flat, thus- c e They are called Chromatic Semitones. f J^ ^ or, Xa| 1/1 SC S 11. A diatonic interval that is increased or lessened by a chromatic semitone is called a Chromatic Interval, and all such intervals are dissonant. 12. The particular intervals that are susceptible of conversion to chromatic intervals are shown in the following table, those that are more than perfect or major being termed Augmented Intervals, and those that are less than perfect or minor being termed Diminished Intervals. Fie. 4. Dim inish ed. Diminished. '^- tC 4th, 3rf. ^, 7thr^"4th! ^a. (tP^ • 1.:- .. s' fi di ra' se se se t s f d ra Unison. 2nd. 5th. 6lh. Augmented. Augmented. Like the diatonic intervals, it will be seen that the chromatic intervals undergo a change of quality on inversion. Augmented intervals become, diminished, and vice versa. Note.— The term Tritone fourth is employed in this work as preferable alike to pli:^erfeet fourth, which is an anomalous term, and to augmented fourth, which suggests a chromatic interval. It must he admitted, however, that the 4th from the fourth degree of the minor scale to the leading-note '( ^ ) is not strictly a tritone interval, not being made up of 'three whole tones, but-as it corresponds in the minor with the 4th found on the fourth of the major scale [1 j it is convenient to call it by the same name. CHAPTER 11. FOUNDATION OHOEDS OF THE MAJOR SCALE. 13. Harmony consists of a combination of sounds simulta- neously produced. The combiuation may or may not be satis- factory in itself, and is termed accordingly Concord or Discord. 14. CoNCOKD, the primary element in harmony, is produced by the combination of consonant intervals. The principal factor of a Concord is the interval of the Third, but the Fifth is necessary for completeness. 15. When two thirds are placed one above another a fifth is included, and the combination i!=i termed a Chord, as-^-^ 16. If the lower third, as in the foregoing example, be major, the combination is termed a Major Chord. If the lower third be minor, as — ' ij ^ rl the combination is termed , g gg - f l the combination' is a Minor Chord. If both /yk Q r' termed an Imperfect i *d thirdu be minor, as — ^ t Chord, for the fifth is imperfect. 17. The lowest tone of a chord is called its ^ ^ r=£z: s rg= n Root ; the next above, the Third ; and the next above that, the Fipth. These are its three constit- _ uents. The octave of the root may be added, as — ^ ^ when the combination is sometimes termed a Compiete Chord, but the octave to the root is not a new constituent. 18. Chords are named from their roots, not according to the note of pitch, but according to the degree of the scale that the root is founded upon. It is to the relation of chords to a scale or key that attention must be directed. 6 TEXT BOOK OF HARMONY. 19. There are Thkeb Major Chords in the Major key founded upon the first, fifth, and fourth degrees of the scale, and called respectively the Chord of the Tonic [D], the chord of the Dominant [S], and the chord of the Sub-dominant [F]. 20. In these three major chords are comprised all the tones of the major scale, and the chords may be called the Fotjndatiom Chords of the scale. 21 . The Dominant and Sub-dominant chords are both related to the Tonic chord. This may be seen from the following example : — Fio. 6. l^^pa sB Fio. 5. ri d'_ _d t 1 R _s n d f 3?he element of union is the note common to the two chords. Thus the fifth of the scale is common both to the Tonic and tho Dominant chords, and the first of the scale to the Tonic and Sub- dominant chords. 22. The note in common facilitates smoothness in the progres- sion of one chord to the other, and it may be remarked that those progressions of chords are the most satisfactory in which there is not only a note in common between them, but in which the root of the second chord is a fourth above (or a fifth below) the root of the first chord, as in Fig. 5. 7 CHAPTER THE PROGRESSION OP THE THREE MAJOR CHORDS OP THE SCALE. THE TONIC CADENCE, AND THE ELEMENTARY RULES OP PART- WRITING. 23. Progressions of chords are most easily studied in a har- mony of four parts — for four separate voices or instruments. The arrangement for Mixed Voices — i.e., for Soprano, Contralto, Tenor, and Bass — is the simplest and best for the purpose. The ordinary compass of the voices should not be exceeded in harmony exercises, and no extreme note, high or low, should be used for the commencement or close. The ordinary compass of the voices may be considered to be as follows — Bass. Tenor. '^""^ CONTBALTO. SoPBANO. -— -GL i 24. Concords navingbut turee constituents it will be necessary to double one of the constituents for four-part writing. The con- stituent which is first in order to double is the Root. Next to this is the Fifth. The Fifth also may be omitted if necessary, in which case the Root is trebled, for the Third may not he doubled except in special circumstances named hereafter. The Third also may not be omitted. 25. In a succession of chords it is not possible to get them all in the normal order in which the tones spring from their roots, as in Fig. 6. The upper parts of a chord may be distribnteo In various ways. See Fig. 6. That Distbibdiion of a chord is the best which gives the largest interval at the bottom, and the upper intervals more or less at equal distances. Except between the bass and tenor none of the parts should be more than an octave distant from one another. 26 The most convenient form of score for showing the distri- bntian of the chords and the progression of the individual parts is that known as Short [Vocal] Score. The stems of the notes in 8 TEXT BOOK OF HAKMUNY. each stave are turned upwards for, the higher part and downwards for the lower part. This is seen in the following example of chords variously distributed in accordance with the principle of the riile in § 25 :-^ Fig. 6. Fio. 6. KEY C. :53 r r n di di 1 t ri d s 1 f r t s n' fi d' s ri d d f f S| S| [In the Tonic Sol-fa notation the bass and tenor parts are writ- ten an 8ve higher than the real sounds to save the multiplication of octave signs. Thus in the first chord the contralto and bass, both expressed by d, are an Bve apart, and the s of the tenor is a 4th below the d of the contralto. The real pitch of the parts must be borne in mind in. order to comply with the rules as to dis- tribution of chords and crossing of parts named in §§ 25 and 34.] 27. The chord of the Tonic is, with few exceptions, used for the commencement of every tune, as it is without any exception used for the close. In the close it is usually preceded by the Dominant chord. This progression of Dominant to Tonic [S to D], both chords in their root positions, and the last on the accented part of the measure with the tonic note usually in the top part, forms The Peepect Cadence [Perfect D cadence]. See Pig. 7a. The forms in which the third or fifth of the Tonic is in the top part are more used for an intermediate than for a final close. These forms may be termed Semi-perfect Tonic Cadences [Semi- perfect D cadences]. See Pig. 76, c. 28. The progression of chords in the Tonic cadence serves to call attention to the normal progression of th^ chord of the Domi- nant to that of the Tonic. Thus, in the following example — Fig. 7. ^m m V -r r ■A: --g- ?z: tri ?3- Fig 7. KEV C. a b c t d' r n 8 s r n ti d r n s s s s t d< S| d S| d S| d I'liOGBESSION OF CHORDS, ^e. 9 it will be seen that the 3rd of the Dominant chord, which is the seventh or leading note of the scale, always rises to the tonic [t to d above], and this is a rule that must be obeyed, not only in a close, but elsewhere, with but few exceptions to be named in a future chapter. It should be noted that the rule in § 24 that the third may not be doubled, especially applies to the chord of the Dominant, The 5th of the Dominant chord rises to the 3rd of the Tonic chord [r to Pl] and the doubled root of the Dominant chord remains to be 5th in the Tonic chord. Elsewhere than in a close the fifth and the root of the Dominant chord in the upper parts are free in their progression, but the beginner is advised to follow the smooth progression exhibited in the cadences above, and in all progressions of chords, especially those related to each other (see § 21) to observe the following rule: — 29. In progressions of chords having a note in common between them it is advisable to keep that note in the same part in both chords, and to, move from the other notes of the first chord in the upper parts by the smallest intervals to the next chord. 30. There are three kinds of movement of parts. When any two or more move in one direction they are said to be in Similau Motion; when they moveinoppositedireotions.iuCoNTKAiiy Motion, and when one part moves while another is stationary, in Oblique Motion. The Oblique motion is generally better than the Similar motion for the outer parts (air and bass), but the Contrary motion is the best of all. The observance of this and the rules in § 24 as to constitution of chords, and § 29 as to the treatment of the "note in common," will generally prevent the infringement of the rules named in the next two sections. 31. No two parts may move in consecutive ■ fifths with each other in similar motion, thus — m Fic. 8. s i=t=zg= ai 7^ Fio. 8. KEY C. l=^B I d_jf s^ s d' r' n' n f r s s 1 t d' d f S| d 10 TEXT BQOK OF HARMONIC. nor in contrary motion, thus- Fio. 9. i Sil: ^^ A :P= jd. i ICt =p= i Fio. 9. KEY C. ni :d' t •d' 8 :d s n s :1 d :f r'_ s "d 32. No two parts may move in consecutive octaves with each other, neither in similar motion, thus — Fio. 10. r ! .. .. KEY n r -!&- 1 8 :i -r =PS= -cdz =^ :?3=t: Fio. 10. KEY C. ri :d' n' d' 8 :pi d f ri :d' 8 1 t| :d d f n I I . — ■ nor yet in contrary motion, thus — * Fio. 11. ^^^ ^ i^m Fio. 11. KEY C. r' :ni 8 :di t :di di_ s "l di 8 :d di f Neither should any two parts move in unison with one another, or from unison to octaves, or from octaves to unison, thus — Fio. 12. Fig. 12. KEY C. 8 :r t :d' d' :t s :r r :n 8 :t d> :t s :di s :r' n :8 8 :d n :8 * Ezceptionslly, consecutive octaves may be used in contrary uiotiuu when the chords are Tonic and Dominant or Tonic and Sub-dominant, but tKe student should observe the strict rule at present. PB0GBE88I0N OF QMOEBS, ^c. n 3h. But there is no objection to a* repetition of 8ves or 6th« between any two parts when t^ere is^ no melodic niOT«nient in those parts, as in the following example : — Fm. 13. i i 3 f=^ S=^°t: zsiz I =^ w, ledz =pa= - P> P> ^ Fio. 13 KEY C. s :s Is d' t n :r In n r s :s Is s s d :t| Id d S| I I I I I Here there is a consecution of 8ves between the tenor and soprano in the first three chords, and a consecution of 5ths between the bass and tenor in the third and fourth chords, but there is no violation of either of the rules named in sections 31 and 32, and it may be well to remark that there can be no -violation of the rule as to consecutive 5ths when there is no change of chord. 34. The parts may not cross ; that is, a higher part may not go below a lovirer part, as the contralto below the tenor, or - the tenor below the bass; nor a lower part go above a higher part, as the tenor above the contralto, or the contralto above the soprano. Such crossings misrepresent the actual distributions of the chords, and the movements of the several notes in progression from one chord to another. Thus, in the following example a is equivalent to &, and c to d,. Fio. 14. KEY C. a h e d 8 S 8 8 8 8 8 S tl d r n t, d t, n r' n' t d' 8 n' 8 d> 8 d s d 8| d 8| d The irregular movement of the alto; and the consecutive octaves between the bass and tenor sr en at d is what would be heard if c were played on the piano, and to some extent the defects would be heard in a rendering of the passage by voices. 12 TEXT BOOK OF SABMONY. *#* The rules of tlie next two nections are added here for con- venience, but the student need not take note of them at present,, aa tliere is little danger of vnfrmgvng these rides if the foregmmg he obeyed, 35. A lower part (as a bass) should not proceed to a higher note than the previous note of a higher part (as a tenor). See Fig. 15 a where F (f) in bass goes above the previous E (pi) of tenor. Nor should a higher part (as the air) proceed to a lower note than the previous note of a lower part (as the contralto). See Fig. 15i where Gr (s) of soprano goes below the previous A (1) of contralto. Fio. 15. Fig. 15. KEY 0. ^^sli d- s d f d di^:s n d~~ 1 f d' :t f :s 3(5. The intervals of the 8ve or perfect 5th,, when standing in the extreme parts, may not be approached by similar motion when the top part approaches the interval by leap as at Fig. 16 a. Fig. 16. a (Bad). (Good). ^n^feS ^P#^^#^s I ! J I ■ J m a ^^Et rJ ri ■A i J J I a"**^ ^ ~ ii " n fj Fio. 16. key C. ^ a. (Bad). t b (Good). 1 d' 1 :ri n' di :d' ni :ri s :f f :s f n f :r' s 1 r :n s :s n :d d :n f s di :t di di s :s d' :t s :1 1 :s fl_ d f -.s ^!_ f ^J_ _:d d_jsi d 'J, fj_:d PB0GSE8SI0N OF OHORBS, 3re. 13 1 6 — continued, (Good). (Good). :ri si;- s di;- di s :- :f n :r r f :n s n :- :ri di:t s l:s s d':- :f s :- ti d:- n d:- But the intervals may be approached by similar motion when the top part moves by degree or step and the progression of chords is that of Tonic to Dominant [D to S] or vice versa, or, ol Tonic to Sub-dominant [D to F] or vice versa, and the second chord has its root in the bass. See Fig. 16 6. The 8ve of the dominant and the 8ve of the tonic may be also approached by similar motion when the top part rises by a, 4th and. the chord is in its second inversion. (§ 63). See Mg. 16 c. The interval of the 5th may, too, be approached in similar motion in moving from the first inversion to the root of the same chord. See Pig. 16 d. 37. The Sub-dominant chord [F] being related to the Tonic [D] (see § 21), the progression to and from one chord to the other is as smooth as that from the Dominant [S] to the Tonic [D]. This may be seen by the following example — Fig. 17. i Fio. 17. KEY G. m -p^ -o- n f n S| 1, S| d d d d, fi d, Here the progression of the Tonic to the Sub-dominant is pre- cisely the same in the movement of the separate parts and in the absolute pitch of the liotes as the progression of the Dominant to the Tonic in the example of Fig. 7 a. The Inote B [n], however, in Fig. 17 being the 3rd of the Tonic chord.'and not restricted in its progression as it was in Fig. 7 as the 3rd of tlie JDominant chord, is not Obliged to be followed by the [f ], and G [d] could be substi- tuted for the middle note of the soprano. This shows the importance, which cannot be too strongly impressed upon the student, of considering chords in relation to the key. (See § 18). 14 TEXT BOOK OF HARMONY. 38. ^'he Dominant and Sub-dominant chords [S and F], thoagb both related to the Tonic chord [D], are not related to each other — there is no note in common between them. The progression from one to the other is not so smooth as are the progressions of eithe- of them to the Tonic chord. The progression is most awkward when the Dominant precedes the Sub-dominant, and this succession of chords — which may be remembered by noting that it reverses the numerical order of the degrees of the scale on which the roots stand, viz. 5, 4 — is but seldom used when the roots of both are in the bass. The progression is less awkward when the Sub-dopii- nant precedes the Dominant (numerical order 4, 5 preserved)) and this succession is most common in a Tonic cadence. The Sub-dominant chord [F] in this context enhances the cadence by completing the notes of the scale not found in the two chords of the cadence proper. FroYn the absence of the note in common there is more danger of making consecutive 5ths and consecutive 8ves in the progression of the Sub-dominant to the Dominant. But contrary motion between the bass and the upper parts will generally avert the danger, especially if the roots of both chords bo doubled in accordance with the rule in § 24. See the following example ; — Fio. 18. i — m r ^=i raz Fio. 18. llf Ml If KET C. :t d' — :r 1" . — :8 s — :s d — In this case the chord of the Sub-dominant progresses to the Domi. nant by the smallest possible movement of the parts, and the three upper parts movein contrary motion to the bass. If the 3rd of the Sub-dominant chord move to the 3rd of the Dominant chord [1 moves to t] in similar motion in thirds to the bass, as in the following example — PR0GBE88I0N OF CHORDS, ^c. IS h'la. 19. m m=^ T^ :3:2Z ZC21 Fio. 19. XBY C. 1 :t di _ f :r n — d> :s s — f :s d — there will be still more danger of consecutives. But they are to be avoided by making the other two parts proceed in contrary motion and preserving the same constitution of each chord as before. 39. In the progression just treated is exemplified a rule for the avoidance of consecutive 5ths that applies to all successions of diords whose roots like those in Figs. 18, 19 stand upon consecu- tive ascending degrees of the scale, viz., that the octave of the first chord should proceed by contrary motion to the fifth of the next chord, the roots of both chords being doubled, and not the oth. 40. The fourth and seventh of the scale [f and t] being now brought together in successive chords, it must be observed that while any of the upper parts .—q^ — p .. may move by the interval "ft k I — p — H of the imperfect fifth, as — tT ' the movement by the interval of the tritone — f :t g If :t II - [| Ut :f as constituents of entirely difEerent chords, is avoided in all ordinary part-writing. Where the notes belong to one harmony, as in the discord of the Dominant Seventh, to be next described, the inteiTal may be used in any repetition of the chord, the notes being transferred from one part to another as noticed in the close of § 68. 16 CHAPTER IV. THE DISCORD OF THE DOMINANT SEVENTH AND ITS RESOLUTION. 41. It is shown in §§ 14 and 15 t i* y'^^^ ^^ seen that a concord is built up of two I Jf ,^ r- s that a disso- nant interval,a thirds superposed. If another -^ — -^g- ,_ third be added to the concord, as-^ " 7thto the root, is included. ' Any combination containing a dissonant interval is termed a Discord. 42. A seventh could be added to each, of the chords already treated of, but on the Tonic and on the Sub-dominant the 7th is major, and the combination containing a major 7th is harsh, and requires special treatment, the con- f I is minor, and sideration of which must be post- ^ 9 §~ r' is a much poned till a later stage. But the rw o t more plea- 7th added to the Dominant concord ^ sant discord in itself than the discord of a major 7th. This discord, called the Dominant Seventh ['S] possesses such advantages in a Tonic cadence that it is used there in modern music even more often than the Dominant concord, and thus claims our next attention. 43. It should he observed that in the. Dominant Seventh the fourth and seventh tones of the soal^ are brought within one com- bination, and according to the distribution pf the notes of the discord either the dissonance of the Imperfect Fifth or of the Tritone Fourth (§ 6) will be included. These intervals occur only once in each major scale, and hence the value of the combination for defining the key. 44. The necessity for the leading note to rise to the tonic was enforced in § 28. It is more imperative still for it to do so in the Dominant Seventh with the fourth of the scale [f] (the 7th DISCORD OF THE DOMINANT SEVENTH. 17 on the dominant) sounding with it. And the fourth of the scale, dissonating both with the leading note and the root of the combination, mast descend to the third of the scale. So that if the fourth and seventh of the scale [f and t] appear (as in the normal position of the discord) as an Imperfect Fifth, the interval produced by the progression in the two parts having those notes will be a 3rd, see Fig. 20 a ; or if they appear as a Tritone, the interval produced by the progression of the parts will be a 6th, see Fig. 20 6. Fio. 20. -" — 1 ^t-^^l o H " 1 Fio. 20. KEY C. a h :f n t di :r d f m :t di ri di :s d s d This effects the resolution of the dissonance of the Imperfect Fifth, or of the Tritone, and the descent of the fourth of the scale to the third accomplishes at the same time the resolution of that note as a dissonant 7th to the root. The progression of the whole combination shown in Fig. 20 exhibits the ordinary resolution of the discord of the Dominant Seventh. It may be necessary to warn the student that the 7th, like the 3rd, cannot be doubled. 45. In the above resolution of the Dominant Seventh it should be observed that the fifth of the discord could not, as in the Dominant concord (§ 28) rise to the 3rd of the Tonic chord without producing a double 3rd. It was stated in § 24 that the Third should not be doubled except in special circumstances, but it is specially undesirable to double the Third in the final chord of a cadence. The 5th of the Dominant Seventh therefore usually falls to the key-note. Hence the Dominant Seventh is par- ticularly suitable when the melody closes with a descent of the second of the scale as in the example Fig. 21 a. It will be seen also from the same example that when the Dominant Seventh chord tB complete — has all its constituents present — that the 5th of the Tonic chord is necessarily absent. But if the 5th of the Dominant discord be omitted, as it may be, the 5th will be gained in the Tonic chord. See Fig. 216. 18 TEXT BOOK OF EABMONY. Fio. 21. a $ T?~ 221 331 FlO. 21. KEY C. a di 6 t d' ^:f n f n i:t di s s , :8 d S| d 46. Besides the advantage of the Dominant Seventh over the Dominant concord in the cadence showii in § 43, the discord gives a relation to the preceding Sub-dominant chord — a note in common. The absence of the note in common in the Sub-dominant and Dominant concords was referred to in § 38 as contributing to the danger of conseoutives. There is, therefore, less liability to this when the Dominant Seventh is used. This will be seen in the following example :— Fio. 22. a 7^ J-e± m ^ Fio. 22. KEY C. a ^^m '4 di :t di :- fi:t di — f :f n :— 1 :s s — 1 :ri di :- di:fi ni — f :s d :- f :s d — In the first case the 7th in the contralto [f ] avoids the contingency of consecutive 8ves with the bass. In the second case the seventh in the tenor avoids the contingency of consecutive fifths with the bass, which would be most likely to ensue if the Dominant concord were used, because sparce any other note for the tenor than D, the 5th [r'], could be used. 47. In the example of Fig. 22 a it will be observed that the note of the dissonant 7th in the contralto is previously sounded in the same part as a consonance. This is called the PaEPARATiou of the dissonance. But it is the special characteristic of the Dominant Seventh that the Dissonant note needs no pi-eparation — the 7tb may be approached by degree, or, as in Fig. 22 6, by a leap. 19 CHAPTER V. THE DOMINANT CADENCE— THE PLAGAL CADENCE —THE SUB-DOMINANT CADENCE— SECTIONS. 48. As the chord of the Tonic is mpst suitably used for a final close, that of the Dominant is equally suitable for an intermediate close, to give a temporary rest and to produce a feeling of expect- ancy. The ordinary form of the close on the Dominant is that of the Perfect Cadence (§ 27) reversed — i.e., the Dominant (concord) preceded by the Tonic chord [D to S]. See Pig. 23. This close is termed the Dominant Cabence, or, from the place it holds in the music, the Half Close. Fid. 23. a $ b Fia. 23. KXT C. m jdz r jSC a :d' t :— 6 r' — :n r :— s s — :s s :— di t — :d si :— d 8 — 49. It will be seen that in both forms of the cadence in Pig. 28 the top part does not, as in the Tonic cadence, close on the root tone of the cadence chord. The leading note [t] in the one, and the second of the scale [r] in the other, placed in the top part, produce more expectancy than it the root tone were in that place, A Dominant cadence can, however, be made with the root tone in the top part. But either the tone must be approached by leap, as in Pig. 24 a, which is not so graceful a movement as those in Pig. 23, or else the Dominant chord must be preceded, by some other chord ao TEXT BOOK OF EABMONT. than the Tonic, sucli as the Sub-dominant. See Fig. 24 h. In this case what is lost in the expectant effect as regards the top .part is gained by the context of the fourth and seventh of the scale in the successive chords. This form of the Dominant cadence, in which the Sub-dominant precedes the Dominant is as satisfactory as that in which the Tonic precedes, and is often moi-e convenient for the approach to the cadence. It will be seen that in Fig. 24 e the melodic form is the same as in Fig. 23 a, and that the Sub- dominant chord is equally available with the Tonic to precede the Dominant. Fig. 24. KEY C. a 6 c :n s :- 1 s :- di t - :d t,:- f r :- 1 s - :s s :- d' t :- fi r' - :d s,:- f s :- f s - The progression of chords is precisely the same as that used in the approach to the Tonic cadence in Fig, 19. 50. A cadence can be made on the Tonic chord with the Sub- dominant chord (F) preceding instead of the Dominant chord. The 5th, 3rd, or root of the Tonic chord can be in the air, as in Fig. 25 a be. Fig. 25. a b ^s^p 2t3Z ^^^^T i^um^ ^mm Fig. 25. KEY C. a b c :1 s - f n :- di d' - :f n - d d:- f n - :di d' - 1 s :- 1 B - :f d - f d:- f d - This is called the Plagal Cabencb or Chueoh Close. It is but seldom used as a substitute for the Perfect Cadence in the final close, as it is in itseH indecisive of the key, but it is used after the Perfect Cadence as an appendix. Such a use of it can be seen in CABENOES AND SECTIONS. 21 the choruses, "And the Glory of theLord " andthe "Hallelujah " of Handel's Messiah, or in the " Amen " that often follows the last verse of a hymn-tune. The cadence can also be used, like the Dominant cadence, for an intermediate cldse, but it should always be preceded by some progression which includes in its chord the leading tone, in order to decide the key. The use of the cadence for an intermediate close may be seen in the first line of the tune "Melcombe," which is in all the tune books. It may be noticed from Figs. 24 i and 25 a that when the sixth of the scale descends to the fifth .in the air [1 s] the Dominant cadence or Flagal cadence is equally available. 51. As the Tonic cadence reversed produced tbe Dominant cadence (§ 48), so the Plagal cadence reversed produces a Sub dominaat cadence [F cadence]. See the following example : — Fig. 26. |1J I y. h:^ J- mz IB I Fio. 26. KEY C. ?2= =g= I :s 1 :- n f — :n f :- d d — :di d' :- s 1 — :d f :- d f — This cadence is not so much used as the Plagal cadence, and finds little or no mention in other treatises, but it serves the purpose of contrast and variety for an intermediate close when there are a number of cadences to provide for. A good illustration of its use may be seen in Sir Arthur Sullivan's tune " St. Gertrude," for the close of the third section (see § 52). As the Sub-dominant cadence is in itself just as ambiguous as the Plagal cadence, it needs to be preceded by progressions that will define the key. 52. The divisions of a tune or musical sentence which are made by the cadences are termed Sections. Thus each of the Exercises 3, 4, 6, 6 consists of two sections. A section is the smallest symmetrical division of a musical composition. The section may be sub-divided into Phbasbs, which may or may not be of a regular length. But a section usually consists of an even number of measures, as two or four. The sections m a simple tune or short sentence are usually of a uniform length. In compositions of a more complex kind the sections are sometimes contracted or 22 TEX'l BOOK OF HARMONY. extended, but generally, as says Dr. Hullah, " some law of proportion will be found to prevail in all well-constructed movements." The structure of extended compositions can only be understood by a study of the subject of " Musical Form." But it is well that the student of harmony should understand the principles of the construction of the smaller forms and the relation of sections to one another. ~ 53. Variety and contrast is specially desirable in the closes of the sections. The various cadences already described furnish the means for contrast and variety as far as the chords of the cadence proper are concerned. And, says Mr. Banister, "one of the first elements of musical construction is the proper management of the cadences, especially the avoidance of tautology : —i.e., the too frequent and too proximate recurrence of the same form of cadence." But the relation of section to section in the closes often includes several notes in approach to the close. Even where the cadence is of the same kind in any two sections a variety and con- trast may be obtained. This may be seen in Ex. 4, where the last three notes of the first section are imitated a 6th higher in the closing section. A less regular imitation may be seen in Ex. 3, where the third last note is the same in each section, but the last two notes of the second imitate the corresponding notes of the first section a 3rd lower. When a different kind of cadence is used in any two sections more contrast and variety is obtainable. Thus of a Dominant cadence could be replied to in Tonic cadence either by ice p^ 1 w 221 :t Idi;— In' :ri Id' :— || in similar mo- tion. could be replied to in a Tonic cadence by contrary motion, or by ^S in similar mo- tion, or, less regularly, by ^@i \r^r-\ CADENGES AND SECTIONS. 23 Variety is also obtainable between cadences of the same kind by the nse of a different form as regards the bass. It will be seen in the next Chapter, §§ 61, 65, and 68, that in the cadences already described either or both the chords can be used in other than the root position. Such cadences are less conclusive than those in which both chords of the cadence are in their root position. The forms which avert the finality of the Perfect D cadence may be termed inconclusive cadences. It will also be seen in the next Chapter, §§ 64 and 66, that the cadences can be ornamented by the use of second inversions [c positions] of chords. This ornamentation of a cadence throws its conclusion, so far as two of the upper parts are concerned, on the unaccented pulse. See Fig. 29, meas. 3 and 7, and Fig. 30, meas. 7. One or more dissonances are, too, sometimes introduced into the cadence chord similarly delaying the conclusion in the upper part. See a case in Fig. 38, meas. 3. There are also cases in which the ordinary accent of a Tonic cadence is modified so that its whole conclusion falls on an unaccented division of the measure, as in the foUowiug close of Dr. Dykes' tune " Lux Benigna " — KEY A 8l d -.ti ti d . n. S| -.fi f, n, . d n - .r r d . S| — S| S| :d, . 54. A relation of the sections to one another in their opening phrases is also desirable for unity, and greater contrast and variety are produced if there is some relation within the section — i.e., a relation of the closing to the opening phrase. Thus in Ex. 3* the opening notes of each section are the same, while variety is gained in the third and fourth notes, which in the second section are a 3rd lower than in the first section. Again, in Ex. 4 the first four notes are imitated in the opening of the second section a 3rd higher. The relation within the sections may be seen in the upward movement by degree after the repeated notes B E [n n] and the return to the B, repeated with a different accent followed by a downward movement by degree and return to the original note. A similar relation is observable in the second section. The student may test the application of these principles in the construction of the Old Hundredth tnne. " See Graded JixeroiseB at the end of this work. 24 CHAPTER VI. THE INVERSIONS OF THE MAJOE CHOEDS, AND OP THE DOMINANT DISCORD — BASS FIGURING - USES OF INVERTED CHORDS — RULES FOR SECOND INVERSIONS — EXCEPTIONAL PRO- GRESSIONS. 55. Thus far only the root positions of chords have been used. When any other constituent of the chord than the root tone is in the bass the chord is said to be inverted. The chords of the Tonic, Dominant, and Sub-Dominant have each besides the root position [called the a position], two inversions, and the Dominant Seventh has three inversions. The first inversion of a chord [called the h position] is when the 3rd of the chord is in the bass. The second inversion- [called c position] is when the 5th of the chord is in the! bass. The third inversion [called d position] is when the 7th is in the, bass. See the following example, in which all positions are given of all the chords : — Fig. 27. Tonic. DoHmANT. SUB-DOHINAIIT. DOMINANT SEVENTH. S n d Da s d< n s D* Do t t r s s t| r Sa Sb Se d' fl II 1 d' fl f 1 di Fa Tb Fc t S 'Sa ' .9 t s f r 'Sc f 'Srf ' The explanation of the figures is given in the following eectiona. THE INVERSIONS OF OEOBBS. 25 56. The difEerenfc positions of chords are indicated by figures placed under the bass part. The figures represent the intervals of the chord in their normal order (as shown in Fig. 27) reckoned from the lowest or bass note. Thus, in the root position of a chord the order of intervals is 3rd, 5th, or if the octave be added, 3rd, 6th, 8th. The full figuring of all chords in their root positions is I The figures are, however, but seldom used for the root position, it being understood that a bass note unfigured bears a chord in its root position. [The a is understood, thus D means Da]. When it is necessary to figure this position, any or all of the figures may be used as occasion requires, as will be shown further on. 57. The figuring of all chords in their first inversions £6 positions] is §. In this case the 3 is understood, and the 6 alone is generally sufficient. See Fig 27. 58. The figuring of all chords in their second inversioi«s [e positions] is |, and this cannot be abbreviated. See Fig. 27. 59. Proceeding with the Dominant Seventh in the same way as with the other chords we should find that the full figuring of the root position would be |. But the 7 which represents the characteristic interval is generally sufficient. The figure that rep- resents this characteristic interval is retained in all the inversions. Thus in the first inversion [6 position] it is a 5fch to the bass, and the figuring is g ; in the second inversion [c position] it is a 3rd, and the figuring is |. In the third inversion [d position] the root is a 2nd, and the figuring is I (see Fig. 27). In both the second and third inversions the 6 can be dispensed with ; in the second inversion it is the leading note [t], which it is understood must not be omitted, and in the third inversion the 6 is the 5th of the chord, which it was shown in § 45 is an optional note. The contracted forms are therefore f for the second inversion, and | for the third inversion. 60. The root position of a chord is in itself the strongest position, ihe first inversion is weaker, and the second inversion weaker still. 61. A well-ordered succession of chords in their root positions gives a broad and massive harmony, that, performed in slow time, is of imposing grandeur. But the exclusive use of root positioni 26 TEXT BOOK OF HARMONY. considerably restricts the flow of the bass, which, next to the air, should be as melodious as possible. Hence the use of mTersions. 62 The first inversions of chords [6 positions] can be freely used to enhance the melody of the bass and for their own efiect in variety to the root positions. The alternation of root position and first inversion of the same chord is often of advantage to set off by contrary motioa the reverse movement of 3rd and root in the air, see Fig. 28, meas. 4, first two chords, and meas. 5, last two chords, or in similar motion as in meas. 3, first and second chords. A first inversion, too, is used in alternation with the root position of another chord to set ofl by stepwise oblique motion repeated tones in the air, as in measures 3, 4, and measure 8, second and third chords ; or even for similar motion with the air stepwise, as in measure 2, first and second chords ; or by move- ment of a 3rd in both parts, as in measure 2, second and third chords. A succession of first inversions is also of advantage for movement of the bass by degree, see Fig. 28, second to third chords, and a succession of first inversions can often be used with good effect in a movement by the fourth ascending in imitation of their root progressions, as in measure 7, third and fourth chords. The first inversion of the Dominant could be succeeded by the first inversion of the Tonic in the same way.* But it' should be observed that the contrary movement of the descent of a fifth, as from the first inversion of the Tonic chord down to the first inversion of the Sub-dominant [n 1|], or from the first inversion of the Dominant down to the first inversion of the Tonic [t n] is loss used. The particular adrantage of the first inversion of the Dominant in approach to the Dominant close in meas. 4 of Fig. 28 is that it saves the anticipation of the cadence form that would ensue if the root position were used there. Fig. 28. * This movement of the leading-note to a note above the tonic is sometimes used in an upper part, especially in the air, as in Fig. 28, meas. S, but the next succeeding melodic movement must not be in tbe same direction. THE INVERSIONS OF CHORDS. 27 P i ?= ^=r Fio. 2 f |ni :di 8. 2 r' KEY C. :n' Id' :1 IS :f r :s If :f )|d> :di s :s Id' :d' i Id :1, t, :d 11, :f [ In' :d' 6 r' !n' |d' :s )|s :s s :s If :n 1 Id' -.d' s :b Id' :di ( Id :n ti :d 11, :d Id' :d' 4 d> :ni |r' :di 5 t Is :1 s :s Is :s 8 Id' :di d' :di |r' :ni r' In :f n :d It, :d s Is :di 8 t :di Id' :t d' Is :f r :s if :r n Id' :d' r' :d< 11 :s s In :1 s :ri If :s d The first inversion of the Dominant is also of use instead of the root position to precede the Tonic chord for an intermediate close, to avoid the finality of the Perfect close. See Ex. 20, second section. 63. The second inversions [c positions of chords], like the first inversions, are used to promote a melodious bass, as -well as for their own special effect, but, unlike the first inversions, the second inversions are restricted in their use to certain rules' as to the chords that may precede or follow them. Though some of the conditions apply equaUy to the use of the second inversions of the Tonic, *Dominant, and Sub-dominant chords, each chord has conditions attaching to its use in the second inversion that do not apply equally to the others. Hence each chord is treated in the following sections separately, that the attention of the student may the better be directed to the different usages. • The Dominant Seventh is throughout this chapter to be taken as indnded except the contrary is specified. 28 TEXT BOOK OF HARMONY, 64. The second inversion of the Tonic chord [Dc] finds its most common use preceding the Dominant chord of a Tome cadence, and is especially suitable when, as in Fig. 29, the air closes with the stepwise descent from the third of the scale to the key-tone — n . I ,. II -^ smoother approach to the - ^ i ~r~T^~il ) r" ■' Dominant is gained by the 'ti'^ ■ ■ ' I 'I 1 Qge of the second inversion of the Tonic chord than could be had by the root position or first inversion ; the first inversion could not be used without infringing the rule as to doubling the third. Fio. 29. I * 2 1^ m ^ ^l ^ ^ r -^rr-' m ^ M ^ ^ 1 — r i ^ i 7* *8 a^ i f=f= T-r A ^JJ . ^J^^ , ^' 'ijM-OJ. p ^jg -j'-f-fr - ^ f f ir- r rr I r ^-B r-n Fig. 2 I * Is :1 9. 2 S KE-S :di c. * It di !* di :t 1^1 :di 4 * s :1 Is :f In :f n :s Is :s s :- Is :s n :d Id :t| |di :di di :di |r' :ni ni :r' jn' :ni di :di is :s Id :d d :n |r :d s :- Id :d d :f In :r |di :r' 6 n' * :ri Id' 1 1 :s |1 * :t 8. * di :di in' :ri Id :s s :s Is f f :n If :f s :1 Is :f Is :s di :t Id' d> di :- 11 :s di :d' Id' :t In :t, d :r In f d :- If :r n :f Is :s n d s d d' n d> d TKE INVERSIONS OF OHOBDS. 29 It must be obserred, first, that the second inversion itself is placed at a more strongly accented part of the measure than the Dominant chord that follows ; second, that the fifth of the chord is -doubled and not the root ; and third, that the root tone which stands at a 4th to the bass [the d] is prepared (§ 47) and resolved as a dissonance. The 4th to the bass is usually prepared when- ever that tone is furnished by the previous chord. This second inversion may be approached by step from the root position or first inversion of another chord, or by leap from the root position or first inversion of its own chord, or from the root position only of another chord. In the third measure of Pig. 29 the second inversion of the Tonic chord finds its next most common use. Here it furnishes an ornamentation of the Dominant cadence. The in air [d'] and the E in Tenor [n'] are somewhat in the nature of grace-notes or appoggiaiwras to the notes which they precede, and those notes took that form before second inversions were in vogue. In old music the passage would be written as follows with the intention of being performed as in Fig. 29, meas. 2-3. i 4- ^ g= KEY C. -Jr-hL ^^ :di "t — :s s :d s — In each of the cases referred to there are two chords upon the same bass note, and hence it is necessary to figure the second chord as well as the first. Thus the figuring under the G [s] in measure 3 would be | i, and the figuring is useful in this case to draw attention to the necessity of the 6 to go to the 5 and the 4 to the 3. In the close the figuring in full under the Q would be 1 1, but the progression of the notes being under- stood, the figuring is more often abbreviated to | 7. It may be noted that in the close the Dominant chord could follow the Becond inversion - - •- - ' ' ~ ■ - ■ ^ 3 I il d :— of theToMointhe , ,_ .. ,1 6 7 Dc '8 octave below as — i ,i. -r. • or were the second inversion at a lower octave the Dominant 30 TEXT BOOK OF HARMONY. < i^ i n.j II II" ' r '- oonld follow- in the octave above, thus... f ' Dc 'S When the second inversion of the Tonic chord is used in orna- mentation of the Dominant cadence and the Tonic precedes in its root position, as in Mg. 29, the quasi dissonant 4th in the second inversion [the d in Dc] need not be directly prepared, but may be approached from the third of the scale [pi] if another part move from the key-note to the third in contrary motion. Thus in Fig. 29, meas. 3, the C B of soprano [d' t] could change places with the E D [ni r'] of tenor. 65. The second inversion of the Dominant chord [Se] stands next in order of frequency of use, though it stands last in chrono^ logical order of introduction in modern music. Dr. Crotch, in the second edition of his " Elements of Musical Composition," publishec only half a century since, says that " the chord of the | on the second note of the scale [Sc] is avoided by all good composers." Later still. Dr. Goss in his " Introduction to Harmony and Thorough Bass," issued in 1852, declared that the chief use of the § was confined to the chords of the Tonic and Sub-dominant [Do and Fo]. Thi^ second inversion of the Dominant finds, perhaps, its most frequent use in the approach to the Dominant cadence, in the same place that the first inversion is used, as referred to in § 62 and Fig. 28. especially when, as in Fig. 29, measure 2, the first inversion is not available through the leading note being in the air. It also is in frequent use instead of the root position in a Tonic Cadence for an intermediate close, where it is desirable to avoid the finality of the " Perfect" close as in Fig. 29, meas. 4, and elsewhere whenever a stepwise bass is desirable. See Fig. 29, meas. 6. In all three of the oases referred to the second inversion of the Dominant is both approached and quitted by a step or degree of the scale, and this is the sole condition attaching to its common use. It may be introduced at the accented or the unaccented part of the measure, the 5th of the chord (the bass note) may or may not be doubled according to convenience ; and there is no restriction as to how the 4th to the bass (the root) may be approached or quitted as there is in the case of the second inversion of the Tonic. It may be noted that in any of the following basses, according to the rule laid down, the middle note THE INVERSIONS OF GSOBDS. 31 would be available for this second inversion of the Dominant equally with the basses referred to in Fig. 29. There is an exception to the stepwise approach in the case of the second inversion of the Dominant Seventh ['Sc], which may be approached by leap from the Sub-dominant chord [F]. See Fig. 29, meas. 7. 66. The second inversion of the Sub-dominant chord [Fc] finds common use in the same sort of ornamentation of a Plagal cadence that is accomplished by the use of the second inversion of the Tonic in a Dominant cadence. See Fig. 29, meas. 7, and compare the treatment of the second inversion there with that of the second inversion of the Tonic in measure 3. An equally common use of the second inversion of the Sub-dominant chord is found in the case in which it is both preceded and followed by the chord of the Tonic in its root position. See Fig. 29, meas. 1. In this case it is immaterial whether the second inversion occur at the accented or unaccented portion of the measure. 67. Before proceeding further it may be stated, negatively, that no second inversion may be approached by hap from an inverted position of another chord, nor may a second inversion itself leap- to another chord. The less common uses of the second inversions and the similarities and differences existing between the three chords may now be noticed. (1) The second inversion of the Tonic [Dc] may be used in the same way as the last-mentioned use of the Sub-dominant second inversion named in § 66 — i.e., between two root positions of chords on the same bass note [between two S chords]. See Fig. 30, meas. 2. Fio. 30. ^ 112* * 3 * 4 P ^ ^ S =t P r r ' f ' I. I ^■^■^ J ^-j-.-^ J J.J J J - ^ ^=nr=^ -\ — r I 32 TEXT BOOK OF HARMONY. JJ-J: J-^-iJ'J. J. J I I a d -f^~m- ^ S^Ete f^^ ?= Fio. 1 |ni :t 30. KEY C. 2* * d' :s If :s Is :s n :r |d :n |di :ri di :t |di :di Id :s s :s 11 :s lis lid' In * :s .•n :di :s Is Idi :s :r :t n :r 3 1 f d> f 7* 1 f di d - It :t - |r :r - {s :s - |s ;r * 4 :n * :di :f :1 :d :s idi :n |s :s |s :d In 5 :ni ri : :s s : :di t : :d si : :s :s :d * |r' Is It :t :f (2) The second inversion of the Tonic is also employed in the same way as that of the Dominant second inversion — i.e., approached and quitted stepwise. See Kg. 30, meas. 2.* (3) The second inversion of the Sub-dominant chord can be used in the same way. (4) Both the Tonic and the Sub-dominant second inversions [Do and Fc] may be also used approached from their own root positions or their own first inversions and then quitted by step, as in Fig. 30, meas. 5 and 7 ; or these second inversions may be preceded by other chords on the same scale note and quitted by step. Thus the second inversion [Dc] in meas. 5 could be preceded by the Dominant chord [S], and the second inversion in the last pulse of meas. 7 could be preceded by the Tonic chord [D]. (5) The Sub- dominant second inversion [Fc] may also be approached from the second inversion of the Dominant [Sc]. See Fig. 30, meas. 7. " This," says Sir George Macfarren, " is the single case in which one second inversion may follow another." The progression is chiefly, if not solely, used when, as here, the second inversion of the Sub-dominant is in the nature of ornamentation to the Tonic chord that is expected after the Dominant second inversion, and which is only temporarily delayed by the intervention of the * See Appendix for additional cases. TEE INVERSIONS OF CHORDS. 33 Sab-dominant second inversion. (6) The second inversions of all three chords may also be preceded and followed by another note of its own chord in a direct succession through the tones of the chord (arpeggio J, but if the succession does not pro- ceed till the note of the root position is reached again the bass must return to the note next above or below the second inversion. See Fig. 80, meas. 3; C [d] is the note that the second inversion D [r] would have proceeded to had not the first inversion B [t|] intervened. (7) The second inversion of the Dominant may also leap to its root position (especially if the 7th be included) provided the return be made to the Tonic note. See the close of Pig. 30. (8) It may be noted that while the Tonic and Sub-dominant second inversions both imitate the common usage of the Dominant second inversion, that of the Dominant never imitates the common usages of the others explained in § 64, 66, in being followed by a chord on the same bass. The student is enjoined to confine himself to the common usages first, and at present to regard those named in § 67 as some- what exceptional. The second inversions in Fig 30 occur very much in the order of frequency, or rather of jnfrequency of use. The next chapter will show how unusual it is to have a second inversion of the Dominant in such a bass as that of the close of Fig. 30. 68. The third inversion of the Dominant Seventh [^Sd] is used for the effect of the dissonance in the bass, and liie the first and second inversions is used for stepwise melody in that part. Such uses of it can be seen in Fig. 31. meas. 2, 3, 6. In the last-mentioned case it is of use for producing another form of intermediate close on the first inversion of the Tonic chord instead of on the root position. The dissonance, when in an upper part, is more effective if approached by a leap than by a step. It is still more effective when in the bass it is approached by leap. See Fig. 31, meas. 5, where it is approached by leap from the tonic, and measure 8, where it is approached from the second inversion of the Dominant. In this latter case is another illustration of the indirect progression of the second inversion mentioned in § 67 (6). The 7th of the Domi- nant [f] must of course proceed to the 3rd of the Tonic [n], and here (in Fig. 31, meas. 8) that note stands as the goal of both second inversion and third inversion. The F [f ] of measure 8 could change places with the D [r] of measure 7, when the dissonant 7th would still be satisfactorily resolved and ths second inversion properly quitted, the third of the Tonic, as before, standing in a D S4 TEX-r HOOK OF HARMONY. dual capacity. The only restriction to the use of the third inversion of the Dominant Seventh is that the 7th may not bo approached by a leap from any note above it. In a repetition of the chord in the same or any other position the 7th may be alwajB transferred from one part to another so long as the 7th is resolved when the Tonic chord follows. Thus F [f I] could take the place of D [r'] as third last note of soprano of Fig. 30. The leading, note can also be transferred from one part to another. See Fig. 31, meas. 2 not rise, but may fall as. in meae. 6. In a cadence on the Dominant the leading-note need FiQ. 31. i I I ^ ^^ r J_J_J^J_:J:_:^ -^ --- J -L I I J f-r\—t ^^ P LL 84e t^ ^3 2±: ^ m ^ p Fia. 31. KiiY C. Is :d< In :f |di :di |di :1 t :ri Idi :ri r :s |s :s ri :t Idi :t s :f In :r 3 * - |s :s s - Id :r di - Is :t d - In :f 4 5 S :s Ini :di ri : n :f In :s s : di :t Id' :di t : n :r Id :n s : * |ni :t |s :8 I js :s Id :f di :fi In' :ri s :f |s :s di :di |d> :t n :1 Is :f |s :s ir :r It :t Is :r 8* S di |ni ;ri d' :- r s |s :f n :- t di |di :t d' :- f n Is :s, d :-|l THE INVERSIONS OF GE0BD8. 38 69. In all cases thus far noticed the 7th of the Dominant has been resolved on the 3rd of the Tonic. The sole exception to this is, that when the discord is in its second inversion ('Sc) and the bass rises to the 3rd of the Tonic, the disBonaut 7th may rise to the 6th of the Tonic. See Fig. 29, meas. 7-8. This upward progression of the 7fch is a necessity whenever in the second inversion the bass moves upwards, unless there is the opportunity to double the 3rd of the Tonic chord under the condition named in § 73. The root of the Dominant Seventh in an upper part (not in the bass) may proceed to the 3rd of the Tonic in contrary motion to the regular resolution of the dissonant 7th as in Fig 31, meas. 4, but not in similar motion, for no two contiguous notes of the scale may proceed in similar motion to a unison or an octave. 70. When the Dominant Seventh follows the Tonie [when 'S follows D] the imperfect 5th may follow theperfect 5th descending without objection so long as the fifths are not in the two outer parts. See Fig. 29, meas. 4 and 8. In the close this progression is inevitable with the stipulations as to the use of the second inversion of the Tonic mentioned in § 64, when, as in Fig. 29, the key requires the tonic and leading note to be in a lower part than the fifth and fourth of the scale. 71. The imperfect 5th may also precede the perfect 5th ascend- ing in the case mentioned in § 69 with the second inversion of the Dominant Seventh rising to the third of the Tonic chord. This consecution of 5ths is inevitable if the 7th of the Dominant in the case mentioned be in the air, or if it stand in any part above that containing the leading note. 72. No part may move in consecutive (perfect) 4ths with the bass. But there is no danger of such a progression except in the case of succession of two second inversions named in § 67 (5), and illustrated in Fig. 30, meas. 6-7. The tritone 4th may, however, follow the Perfect 4th between the bass and an upper part without objection. See Fig. 31, meas. 6. 73. It was prohibited in § 24 to double the 3rd of a 'chord, but in the root position of the Tonic and Sub-dominant chords the third may be exceptionally doubled, especially if one of the thirds be in the air. See Fig. 31, meas. 4, and Fig. 29, meas. 7. In the first inversion of these chords the 3rd may only be doubled if in both parts it is approached and quitted by step and the parts move in contrary motion to one another. See Fig 31, meas. 4. 36 CHAPTER VII. THE MINOR OHOEDS OF THE MAJOR SCALE— THE DISCORDS OF THE SUPBETONIC SEVENTH AND DOMINANT FOURTH— THE INTEREUPTED CLOSE —THE IMPERFECT CHORD. 74. There are three minor chords in the major key. They are founded upon the Second, Third, and Sixth of the scale, and are called respectively the chord of the Supertonic [E], the chord of the Mediant [M], and the chord of the Sub-mediant [L]. 75. The chord of the Stjpektonio ,[R] is perhaps the most common of the three minor chords. It may be regarded more or less as a substitutionary chord for the Sub-dominant, with which it has two notes in common. See the example. Fig. 32, meas. 2. The Supertonic chord most easily succeeds the Sub-dominant, but the reverse progression, in which the Supertonic, a minor chord, precedes the Sub-dominant, a major chord, is somewhat ungainly. Fig. * t— ^ — r ^S 1— " "' r l - r^r^^^"^ I I :f2- T^ MINOR CHORDS OF THE MAJOR SOALE, ^ 37 FlO. 32. KEY C. 14' :8 1 :r' |t :d' 1 - Is :t di :ri |di :t d' :- \n :s f :1 Is :s f - In :r 8 :f In :r n :- Is :d> d' :f' |r' :pi' di - |di :s s :1 Is :s s :- Id :n f :r Is :d f - Id :f n :r Is :S| d :- It will be noticed also from the example Fig. 32, meas. 2, that the Supertonio chord has a note in common with the Dominant chord. When as there it precedes the Dominant chord the chord- progression is that noticed in § 22 as the strongest. In this respect of chord progression the minor chord of the Supertonic has the advantage of the Sub-dominant, which it was shown in § 38 was not related to the Dominant. The Supertonic can there- fore he freely used in approach to the Tonic cadence before the Dominant concord or Dominant discord when the context renders it more convenient, or when the third last note of the air is the super- tonic note itself. The chord of the Supertonic would be much more in place for the third last chord of Fig. 30 than the second inversion of the Dominant, which, as intimated in the close of § 67, was very unusually employed. The chord of the Supertonic can also be used not only to precede the Dominant, but also before the second inversion of the Tonic, which it has been seen so often precedes the Dominant in a Tonic cadence. See Fig. 32, meas. 4. In this case the treatment of the second inversion of the Tonic chord differs a little from that named in § 64. The 4th to the bass cannot now be prepared. But it is approached in the next best way, by degree or step from the note above, and the interval of the 4th is in the two parts approached in contrary motion. This second inversion of the Tonic, too, has hitherto only been approached by leap from its own root position or first inversion. The approach by leap from the root position of the Supertonic chord is equally satis- factory, especially when the supertonic note [r], as in Fig. 32, is in the air. 76. The first inversion of the Supertonic chord [JR.6], which gives the sub-dominant note in the bass, is even more in use in approach to the Tonic cadence than the root position, perhaps ou account of the first inversion giving the same steady and dignified approach to the close as that secured by the Sub-dominant chord [F]. See Fig. 33, meas. 4— 3S TEXT BOOK OF HABMONT. Via. 33. 12 « 3 4 dtf rrrr I I I J 'I j _ijj ^ =t ^ t=t: ^PP i * 7 • * I fs — I #: f-rr^-n 1 — r^ M (> r ^ ^ r r r V j^4j.j,-^-j-.;-^ ^£ ^ =t=t F Fig. , 1 Is :s i3. 2 n KEY C. :f|s * :f 3 r :- It :s 4 f :n \x :r In :r d :d Id :r ti :- It, :d t, :d |r :t, Is :s di :1 Is :1 s :- Is :s s :s |1 :s Id :t, d :f In :r s :- If :n r :n If :s Is .-s 6 1 :t Id' * 7 t :- Id' :f' 8 n' :r' Id' :t Id :n d :f In :r s :- Is :s s :1 Is :s Is :s f :s Id' :1 ri :- In' :t d' :f' In' :ri In :d f :r In :f s :- Id :r n :f Is :si where the Supertonic immediately precedes the Dominaut, and meas. 8, where it precedes the second inversion of the Tonic chord; The first inversion of the Supertonic chord is also used instead of the Sub-dominant in a Dominant cadence. See Kg. 33, measure 6. The use of the root position of the Supertonic in a Dominant cadence is not so welcome, because of the bass being like the perfect close in the key of the Dominant. , But the root position can be used if the third be in the air, as in the first cadence of Fig. 33. The chief MINOR CH0BD8 OF TSE MAJOR SOALE, Sfc. 39 other use of the first inversion of the Supertonic chord is in a step-* wise succession of chords in their first inversions [5 positions]. This will be illustrated when the other minor chords are treated of. Except in such a succession of first inversions, or in the places named in the cadence or the approach thereto, the fourth of the scale [f ] in the bass is always better harmonised with either the Sab-dominant chord [F] or the third inversion of the Dominant Seventh ['Sd], according to the context. See Fig. 33, fourth note, and meas. 3, second note. 77. It was forbidden in § 24 to double the 3rd of a chord, but in all minor chords the third may be freely doubled without even the restriction as to contrary motion named for the doubling of 3rds in major chords in § 73 *#* Though the foregoing is all that should he necessary to prevent a wrong use of the Supertonic chord, it may he well to add thenegative rules named in the next two sections. 78. The chord of the Supertonic [R] may not be followed by ihe Tonic [D] (numerical order reversed, see § 38) except both chords are in their first inversion,*or except the Tonic chord is in its second inversion, as mentioned in the close of § 75, and illustrated by Fig. 32. 79. The second inversion [c position] of the Supertonic is disallowed, the use of second inversions being confined wholly, as is implied in § 63, to the Tonic, Dominant, and Snb-dominaut chords. 80. The commonest discord next to that of the Dominant Seventh is that of the Supbbtojjic Seventh ["R]. In this, as in the other discord, the 7th to the root is minor. The 7th must resolve by descent to the next note below, which will be the leading-note [t], so that the chord that follows the Supertonic Seventh must be the Dominant. The 7th on the Supertonic, unlike that on the Dominant, -must he prepared (see § 47) in whatever position the discord is employed. The 3rd, unlike the 3rd of the Dominant Seventh, is as free in its progression as in the Supertonic concord. The following example shows the discord in its root position. • This is a safe rule for the student at this stage. The exception where the Supertonic in its root position is followed by the Tonic in its first inver- rion with good effect should be reserved for later study. 40 TEXT BOOK OF JIABMONY. Fig. 34. Fig. 321 3±: :?= 34. KEY C. 321 w ^ ^^ dl :t dl f :r n 1 :s s r R :s d It will be noticed that the discord occurs at the accented portion of the measure, which is by far the more usual place for it, whereas the Dominant discord was more often found at the unaccented part of the measure. The preparation of the dissonance and the non-restriction of the 3rd are features that are common to all discords of the Seventh other than the Dominant Seventh, and the chord that succeeds a discord of the seventh must iq all cases be one whose root is a 4th above (or 5th below) the root of the discord. There are, however, some apparent and real exceptions, one of which may be noticed in the next paragraph, and another in § 88. The figurings of the discord in its various positions are the same as the figurings for the Dominant Seventh. See § 59. 81. The most frequent use of the Supertonio discord in its root position ['B] or in its first inversion ['E6] is in approach to the Tonic cadence in the places where the Supertonio concord was found and noted in §§ 75 and 76. Thus in Fig. 33, in approach to the second cadence the discord could be introduced by changing the D [r] in contralto of fourth measure into [d], which would give the first inversion of the discord. If again the F [f] of bass were transferred to the air and the D [r] put in the bass we should have an example of the root position of the discord. Another example of this could be seen in Fig. 32, by changing the D [r'] of fourth last note of air into C [d']. In this case the discord is exceptionally at the unaccented portion of the measure. Moreover the 7th does not get im- mediate resolution, for the Tonic chord does not furnish the note required, bui the resolution is only " delayed " — the dissonant note is carried through the second inversion of the Tonic, and the leading-note naturally follows the note that has now become 4th to the bass, as has been seen in § 64. The first inversion of the discord is used in the same place even more often than the root position. Fig. 32 could close thus — MINOR CHORDS OF THE MAJOR 8GALE, ^c. 41 Fio. 35. KEY C. d' :d< |di :t d :r |n :f s :1 Is :s n :f Is 'R4 :s In these circumstances the discord is more like the chord for which it is substituted — i.e., the Sub-dominant [F]. The note D in contralto [r] somewhat appears to be the intruding note. Hence some theorists call this the chord of the " added sixth " — a 6th added to the Sub-dominant chord. But the 6th to a root is a dubious interval as the constituent of a chord, as will be seen in a later chapter, and in this case the supposed 6th is under no restriction.* In the example of Fig. 35 it could be approached by leap from G [s] above it, whereas the C [d'] in the soprano must be prepared and ultimately resolved. The discord, either in its root position or first inversion, thus commonly used on the unaccented part of the measure in approach to the Tonic cadence, is seldom used in the Dominant cadence instead of the concord [B] seen in Fig. 33. 82. The third inversion of the discord with the dissonance in the bass ['Ei] is the only other inversion available. It can be used anywhere in the music when preparation and resolution can be obtained for the dissonance. The smooth melodic passage which the preparation and resolution involves effectively sets off in the bass a leaping passage in the air. See the following excerpts from tune " Farrant," 3rd line, in Fig. 36, and tune " Salisbury " (BavengcrofC B Psalter), first line, in Fig. 37. Fig. 36. Fic . 36. KB d V G. f :f |h d 1, :si Is, n r :r Id d d 'Brf :t, Id t % * That is, as a dissonance. The root of the Supertonio Seventh [r] may not, however, proceed to the root of the Tonic chord [d] ; but shoulil pro- ceed to the 3rd or 6rd [m or s]. 42 TEXT BOOK OF HARMONY. Fia. 37. KEY G. r ll f d 'Ed :f :r :s :t, In Id Is Id Ib both these cases it may be noticed that the resolution of the Supertonio Seventh is upon the Dominant Seventh. For the purpose of the resolution the discord is equally available with the concord. 83. The dissonance of the first and second tone«i of the scale [d and r] just exhibited in the discord of the Supertonio Seventh is also employed the chord of the Dominant, thus — Id d* s The discord is called the Dominant Pottrth [*S]. ' It is not, as in the discord of the seventh, a combination that adds a dissonance to the .concord, but one that substitutes a dissonance for one of the consonances. The 4th is a substitute for the 3rd, upon -which it resolves. The 3rd can never therefore be sounded with the 4th. The 4th which dissonates with the 5th must be prepared as in the Supertonio Seventh. The 5th should not be omitted, as its absence renders the combination dubious. The chord of the resolution is the same as that in which the dissonance appears. The discord belongs to the class termed discords by suspension. These will be fully explained in a later chapter, but the one just introduced demands attention in advance for the reasons that here follow. 84. When in a Tonic cadence the final note of the melody has been preceded by repeated notes of the second degree of the scale as in the second cadence of Fig. 33 [|r :r |n]> or the last cadence of Ex. 29 [|r :r |d], the first of the two repeated notes has been appropriately set off by the use of the Supertonio chord ; as the Dominant chord necessarily comes on the succeeding note to form the cadence a change of chord is secured for the motionless air. When the discord of the 7th was introduced into the Supertonio the air was still futher set off by the movement in an inner part of the 7th, at the distance of a 2nd (or 9th) belaw, to its resolution In the second section of Fig. 38 — MINOR CHORDS OF THB MAJOR SCALE, ^o. 43 i Fig. 38. 1 2* 3 * i^ m ^ ^ i ' f r r • f r ffrr '- 1 I 3^ i mt ^ 1 — r 2 — 6* i ^ 2i: ? f^?~r^^^TT ::gr z±: I I I r J I ud^ I ! rrrrrrTJ^m m ?z: ?3= T • 4 - 5 7 i 3 Fig. I |s :n In :d |s :8 Id :d |s :n Id :d Is :8 In :d 38. KET C. 2* r :s |n r :r |n R :s |s d :t| |d 6* r :r' |d' :r' d :t| Id :f s :s |s :1 r :r |n :f 3* s r di S| r t r s s In :f Id :d |d> :di Id :1 :- |n :s :- |s :t :- Id :f i * 8 :1 |r :r d :d Id :t, d> :d> Is :s n :f |s :s s< :d> jdi :t s :f jr :f di :di |ri :r' n :1 Is :s it will be seen that the air is similar to that referred to in Fig. 33, bat here the context does not favour the use of the Supertonio chord, and both notes preceding the Tonic must be harmonised with the Dominant. The air and bass are therefore both motionless. The interest which was gained by the use of the dissonance in the Supertonio Seventh is most desirable, here, and this is effected by the use of the dissonant 4th in the Dominant. di:- - Id':- 44 TEXT BOOK OF HARMONY. In a final close the repeated note on the second degree is followed by the key-note thus — or the repeated notes are written as one of the same value as the two, thus- This is a form of close that prevailed when the stepwise descent to the tonic from the third of the scale (see § 64) was not available because the second inversion of the Tonic was not in use. At that same period when the air closed as in Fig. 38 the fourth on the Dominant was used for the harmony of the third last note as here shown, instead of the second inversion of the Tonic that is now in more common use in that place. It is often even convenient to use the Fourth on the Dominant for the nfielody of the inner parts, as in Fig. 38, or when it is wished to imitate the efEect of the older form of close. The discord can also be used to ornament the Dominant cadence instead of the second inversion of the Tonic. In Fig. 29, first section, the E D crotchets in tenor of meas. 3 could b^ replaced by a minim D [ | n' : r' could be replaced by I r' ; -]. See also another example in Fig. 38, meas. 3. 85. The dissonance of the 4th can also be introduced into the second inversion of the Dominant to set off a motionless bass. See Fig. 38, meas. 6. And as in the case of the ' Supertonio Seventh the dissonance, under the same conditions named for that in § 82, can be taken in the bass. See Fig. 38, meas. 2. 86. The Dominant Fourth may be either succeeded by the Dominant concord or by the Dominant Seventh, as may be convenient. The 7th of the Dominant may also be introduced with the 4th. In the close of Fig. 38, D in contralto could be F [r could be f ]. 87. The figuring of the discord of the 4th in its various positions is as marked in Fig. 38. In its root position it is fully figured I but the figure 4 is generally sufficient. The concord or discord that follows is also figured to show the resolution of the 4th. In the second inversion of the discord in meas. 6 the dissonant 4th is a 7th to the bass that takes the place for the nonce of the 6th. The figuring is therefore J. The second inversion of the concord that follows instead of being marked % as usual, has the 4 shown by a line drawn opposite that figure in the MINOR OHOBDS OF THE MAJOR SCALE, ^o. 45 previons chord. This is called a continuation line. If in tho root position of the discord in meas. 4 it had been necessary to include the 5 the figuring of the two G's would have been | 3, che continuation line showing that the 5th is retained in the chord when the 4th has moved to the 3rd. The inversion with the dissonant 4th in the bass (see meas. 2) needs the continuation lines after the figures to show that what was 5 and 2 to the dissonance are retained during the resolution. 88. The chord of the Sub-mediant [L] comes next in order of the minor chords. It is almost exclusively used in its root position. One of its most familiar uses is in an intermediate close after the Dominant or Dominant Seventh where the Tonic chord has here- tofore followed. It is particularly useful when, as in Fig. 39, close of first section, the air has the key-note for the final of the cadence, as it avoids the form of the perfect close. This cadence is called the " interrupted close " [surprise cadence]. It should be noticed that in this progression of the Dominant Seventh to the Sub-mediant ['S to L] all the notes of the discord proceed as they do when it moves to the Tonic with the exception only of the bass. So that a double 3rd in the Sub-mediant chord is the inevitable result, but to this there is no objection. The progres- sion may be used anywhere in the music as well as in a cadence. 89. The chord of the Sub-mediant is also used both in and out of a cadence in succession to the first inversion of the Dominant [S6 L]. See Fig. 39, meas. 8. This illustrates one of the two instances in which the leading tone in the bass as a chord constituent is allowed to descend. It may be well to caution the student here that the 7th cannot be introduced mto the first inversion of the Dominant in this case, as the resolution of the 7th on the 5th of the Sub-mediant would induce an objectionable consecution of 5ths with the bass. J Fig. 39. j 46 TEXT BOOK OF HABMONT. Fig. 39. key C. |di :t In :f |s :s Id :r di In' :r' 1 Is if di |di :t f Is :si Id' n' Is s Id' d' In d 6 fi :ri Is :s 7* 1 : f :f If :h PI : 1 :1 Is :di d' : r :r It, :d Ir : |di :ri In :f |di :1 II :r - |d' :di - |s :s - |di :ni - In :d 4 t :di s :s s :s s :n 8 * a :di s :n ri :di t, :1, id' If 11 If |ni Is Id' |S| * 5 di t n di 1 :ri :f :t :si 90. The Sub-mediant is followed (as well as preceded) by the Dominant. See Pig. 39, meas. 5. This is the most common and pleasant progression downwards of chords whose roots are upon consecutive degrees of the scale. But as there is no note in common between the two chords care is necessary to avoid consecutive fifths- The 5th of the first chord should, as in the example, proceed by contrary motion to the 8ve of the next. This is the converse of the rule given in § 39 for the avoidance of consecutives in the ascending progression of chords on consecutive degrees of the scale. 91. The chord is frequently found in approach to the Tonic cadence where the first inversion of the Sub-dominant chord [Ffe] has been used, as in Fig. 39, meas. 8, and it freely succeeds the Sub-dominant chord, with which it has two notes in common, see Pig. 39, meas. 4. Again it as freely succeeds the Tonic with which it also has two notes in common, and this progression is used for a cadence on the Sub-mediant, see Fig. 39, meas. 7. This is not an " interrupted close," because the Sub-mediant is not preceded by the Dominant. The chord should not be followed by the Tonic MINOR CROBBS OF THE MAJOR SCALE, 4-0. 47 chord (the minor chord preceding the major, see § 75) except the Tonic is in its first inversion, as in Fig. 39, meas. 7, or, as in meas. 8, in its second inversion. It quite easily moves into the Supertonic chord, as in Fig. 39, meas. 3, giving the progression of roots named in § 22. The reverse progression of the Sub-mediant succeeding the Supertonic (R L) is equally good. 92. The first inversion of the Sub-mediant chord is only occasionally foixnd in a stepwise succession of first inversions! like those illustrated in Fig. 40, or in a stepwise bass with con- trary motion of the upper parts. 93. The chord of the Mediant [M], though as perfect in itself as either of the other minor chords, is not so well related to the key. Each of the notes, too, of which the Mediant is composed can be harmonised with chords that better establish the key. The Mediant in its root position is therefore not allowed except in a sequence, to be described in the next chapter.* 94. In the first inversion [M6] the Mediant is less object- tionable. It is conveniently used in a stepwise succession of chords in their first inversions [6 positions] either ia a descending or ascending passage, especially with the air in 6th, to the bass See Fig. 40, measures 2 and 7. * I 3 I * i , ^ j ^ I -^J.JL^ iJ. fTfrffrfarg I I A =t=t ?=- * The chord is used in the Ecclei'iastical style of writing and iDstancea of its use occur in the modem style apart from a sequence, but it is better that the student should not use the chord till some ezpenence has been gained of the vaiious effects of the progressions of chords. 48 TEXT BOOK OF EARMONY. Fig. 4 1 Is :di 0. KEY 2 * ri :ni c. If :r' 3 n' •- Id' :rf 4 r' :s Id' :n' 6 r' in :s 1 :s If :s s - Is :n f :r |s ;8 s - ( ||d> :d' 1 :t Id' :r' d' - Id' :t 1 :t Id' :d' t - ( |di :n f :s 11 :t d< - In :s f :f In :d s - 6 Is :di * t :di 11 :s 7 f * - |fi :ni 8 r' :d' Id' :t d' t_ )|s :f s :s If :n f - If :s 1 :s If :f n - l|d< :d' ni. :di Id' :di d' - Id' :t 1 :d' 11 :s s - In :1 s :n If :s 1 . - 11 :s f :n |r :s d - These passages also illustrate the use of the first inversion of the Supertonio in the stepwise succession referred to in § 76. The first inversion of the Mediant is less commonly approached by leap and quitted by step, as in Fig. 40, meas. 3, or approached by step and quitted by leap, as in meas. 6. To both approach and quit it by leap gives a weak progression. 95. The leading note as 5th of the Mediant in the downward succession of chords in their first inversions naturally succeeds in an upper part by descent to the 5th of the next chord (See Fig. 40, measures 3 and 7), and as 3rd of the Dominant in a similar succession it succeeds in the bass by descent to the 3rd of the next chord. These with the case named in § 89, form the only exceptions to the rule that the leading note should rise. 96. In the first inversion of the Mediant the root or 3rd must be doubled in four parts, for the leading note may not be doubled in this chord any morfe than in the Dominant chord. 97. The chord on the Lbading-kote [T], as noticed in § 16, has an imperfect 6th, and is called the " Impbepbct Chord." In its root position it is dissonant, and may not be used except in a sequence, as mentioned in next chapter. 98. In the first in- , q ., t much of the dissonance version of the chord ^ g H f is removed by the con- on the Leading-note [T6] ^y c> r sonant 6th which the bass supplies to the root, and by the transfer of the interval of the imperfect fifth (or tritone fourth) to the upper parts. The first inversion is therefore available, subject to the resolution of the imperfect (or tritone) interval formed between the seventh and MINOR GH0BB8 OF THE MAJOR SOALE, ^c. 49 fourth of the scale that was required in the Dominant Seventh, see § 44. The first inversion of the chord on the Leading-note is often considered as the second inversion of the Dominant Seventh with the root omitted, and it is convenient to regard it as such when the Tonic chord follows. The progression of the several notes of the chord are mainly the same— the bass either rises to the 3rd or falls to the root of the Tonic chord, the leading note rises to the key-note and the 5th of the chord falls to the 3rd of Tonic, or the 6th may rise to the 5th of Tonic providing the 3rd in one part rises to the 3rd of the Tonic. See Fig. 41, meas. 2, P Fig. 41. 1 4* 3^E ^ IT.i I I I ^^ J. J.J. I -e a ^ ^ 1=^ m * 6 I m A J. J J. y^ I I ^ ■ij. j-j- J I ! I ^ ^ ?=: Fig. 4 I Is :d> 1. 2 1 KBT C. :t Id' * :r In :d f :f In :f Id' :s d' :ri Is :t Id :n f :r jn :r |di :ri 6 n' :s 11 * :t IS :f n :d If :f Id' :t d< :di Id' :r' !p) :r d :n If :r Id' :1 Is :f |d> :di In :f |1 :s If :d Id' :di If :n. 4* t :di Ir' :di f :n |s :s f :s |s :n' r :d |t| :d 8* f :d' Id' :t f :n |r :r t :di |1 :s r :d If :s 5 t :- s :- E 60 TEXT BOOK OF HABMONT. 99. As the leading note may not be doubled one of the other two constituents must be doubled to make four parts. The bass note [r] may be freely doubled. The 5th of the combination (though dissonant with the leading note as in the, dominant seventh, see § 44), may also be doubled, in which case one goes to the 3rd of Tonic and the other rises to the 5th, or if it be in air it may leap upward to the root of the Tonic chord. See Fig. 41, meas. 4 and 8. 100. The first inversion of the chord of the Leading-note may be used in all places ia cadences or in approach thereto, or other- where in which the second inversion of the Dominant has been heretofore used (see Fig. 29), especially when the dominaht tone does not come freely into the parts, or a better melody in an upper part is secured by the use of the first inversion of the Leading-note. It is the chord that was used before the second inversion of the Dominant found place. 101. The first inversion of the chord on the Leading-note can also be followed by the chord of the Sub-mediant [T6 L], in which case it is not considered as a portion of the Dominant Seventh. The bass leaps, but the progression of the other notes is naturally the same as when the Tonic chord follows. See Fig. 41, meas. 6. 102. A second inversion of the chord on the Leading-note would correspond to the last inversion of the Dominant Seventh with the root omitted. This is but rarely used except in three- part writing. 51 CHAPTER VIU. SEQUENCES. 103. When a snccession of intervals is repeated upon other notes of the scale a Sequence is produced. Thus in the following example — Fio. 42. i IpC ^ 3=C Fio. 42. :ni KEY C. :r' I ni :d' |d> the succession of the first two notes is repeated a step lower in regular order to the close. The pattern of the sequence is that of an alternately ascending second and descending third. The quality of the intervals is necessarily different according as they present themselves 'in the scale. Thus at the first repetition the melody rises a major "ind instead of a minor 2nd, and then falls a major 3rd instead of a minor 3rd. 104. Such a sequence as that just descrihed, in which the intervals belong to one scale, is termed by some writers a Tonal Sequence in contradistinction from a repetition of a phrase in exactly similar intervals which involves a change of key, and which will be noticed in Chapter X. 105. A sequence of melody, as Pig. 42, may occur in any upper part without the bass or other parts progressing in any regular order. But mostly a sequence of melody is accompanied by a sequential bass, and when the bass moves in sequence every other part should move in sequence also. See Fig. 43. 58 TEXT BOOK OF EABMONT. Fio. 43. i iii i J^J I ^ ^ 8 ; r ^m Fi :s 8. 43. KEY C. f :1 Is :t 1 :di It :r' di :n' |ri :1 :n d :f |r :s n :1 If :t s :di |1 :f :s 1 :1 It :t d' :d' |r' :ri n' :n< |f" :r :d f :r Is :n I :f It :s 6} :1 |r' :f t :ri Id' r :f In ri :t |di s :s Id 106. In the preceding example the bass alternately rises a 4th and descends a 3rd to the fifth last note, the limit of the sequence. The soprano alternately falls a 2nd and rises a 3rd, the contralto alternately falls a 3rd and rises a 4th, and the tenor alter- nately rises a 2nd and remains stationary. Though in each part the succession of intervals is different the notes in the repetition are uniformly a degree higher in each part than in the original phrase, and so on throughout the sequence. 107. As the two chords of the pattern phrase are both in their root positions it follows that the others must also be in their root positions if the sequence is to be kept up in all parts. Hence the chord of the Mediant in its root position [M] comes in on the fifth note, and the chord of the Leading-note in its root position on the eighth note. These chords in their root positions, not allowable in ordinary writing, as mentioned in §§ 93 and 97, are without reproach when used to preserve the symmetry of the sequence. But it must be observed that they may not occur in the first phrase of a sequence. The progressions in the first .phrase must be as regular as if there were to be no movement in sequence. Care must be taken, too, that the last chord of the pattern phrase will progress regularly to the first chord of the repeated phrase, when all will go well throughout. 108. The symmetry of the sequence that justifies the use of the chords just named also justifies the double leading note, either in the Dominant chord or in the Mediant, or when the leading- SEQUENCE a. 53 note is itself treated as a root. See Fig. 43, chords 6 and 8. So also the melodic interval of the tritone-fourth heretofore disallowed, is without objection in imitation of the perfect 4th, as in the bass and contralto parts of Fig. 43, meas. 3. 109. The sequential repetitions may be upon successively higher degrees of the scale, as in Fig. 43, or upon successively lower degrees, as in the second section of Fig. 44 — Pig. '44. ^ ^ ^ ^m a m ^ I 1 4 J I r I I ^ Id' "■iG. 4 :t 4. 1 KEY C. :s If :n |8 :8 n :n Id :d In' :r' d' :t 11 :s Id' :g 1 :n If :d In' :r' r' :d' Id' :t U :f s :n If :f Id' :1 t :s 11 :s 11. :r s, :d If, :si or either ascending or descending at intervals greater than the distance of a second from the original phrase. See the first section of Fig. 44, which repeats the pattern phrase a 3rd lower. 110. The first phrase may consist of two chords only, as in the foregoing examples, or of three or more, as in Figs. 45 and 46. Fig. 45. -! U P 3= ^ :4i r — ^ J. r ^ ^ A L :?2- :n' :s i:n' :d' Fig. 46. kbt C. r' — :d' t — 1 8 — f n — 8 — :n n — d d — ti d — S> t :d' n' S 1 d' n f g — t s :1 8 PI f n d r d — 64 TEXT BOOK OF HARMONY. Via. 46. ! I . I S S^= zi; •1*- — -*--*---*-^ J -*- s i^^T :£ 1 1 L-l 1 I I Z2Z ?Z= FlO. 46. KEY 0. ' In' :f s' :- Id' :r' \|di :di t :d' |1 :1 ilsi :f< r' :d' In' :ri ( Id' :1 s :n 11 :f n' :- 11 t s :1 If f t :1 Id' t n :d If r d' :- 1- :t d' - n :f |r :r n - s :f |1 :s s - d :1| |r :s, d - The progressions may consist wholly of chords in their root positions, as in Figs. 43 and 44, or of root positions and first inversions intermixed, as in Figs. 45 and 46. But chords in their second inversions cannot be used. The Dominant Seventh in its usual form of an unprepared discord is also unavailable, as it would lead to other unprepared discords. But a sequence can be made of prepared discords throughout, and this will be illustrated in a future chapter. Any of the sequences can be omarapnted with the Tjy-tones and passing-tones next to be noticed. 56 CHAPTER IX. BT-TONES AND PASSING-TONES. 111. So far, in progressing from chord to chord, all the parts have had notes of equal value, and there have been no divisions less than the aliquot of the measure. This simultaneous move- ment of the parts has accomplished that direct and regular harmonic connection of chord to chord which is the foundation of pure part-writing. It is now in order to notice the use of notes incidental to and mostly independent of the chords and their pro- gression, of shorter duration than a beat (or pulse), that promote life in melody and variety in rhythm. 112. In the following example from the opening of the tune to the Austrian Emperor's Hymn — Fig. 47. i ~m * J m- I ! ^^ J. I J. ^ ^■^ J=^ ^ 1 — r FlO. 47. KEY G. -.r in .T f :pi Ir.t, :d -.ti|d :si d :d |sr :si -.8 Is -.s.ld :8 f 1. :s :si Iti.r :d If. :n. 56 TEXT BOOK OF HARMONY. there are in the melody two notes in the third beat of the second measure. The second of these is in the nature of ornament, and as it belongs to the same chord as the first it is named, after Eichter, an Habmonio Bt-tone. The by-tone affects the harmonic progression, and the occurrence of it in one part often involves, as in the present example, the use of a companion in another part. If the tenor part had not taken a second note at the same time the soprano moved there would have been a double leading note and consecutive 8ves. If any other note had been used for the first in the tenor the 3rd would have been absent at the first stroke of the chord. Care is therefore necessary in the use of by-tones to see that essential constituents are not driven out, and that con- secutives do not occur. The by-tones are particularly of use in conjunction with the more decidedly incidental tones that are now to be mentioned. " 113. In the following example ^Fio. 48-2* 3 — \ — ^^ — I i F — h i *4 4c 1 — i — r J.J. 4-5ia , a- ^^JU J. ^ &iz f^= I t=±s T 5 61^ FlO. 48. KEY C. I 2;ic il.t:di ld< :di * *, 6-5 87 4 3 - Is :di.s \n :s |di :di , Id :n f :s II :s fi:pii.ri|n' id' r :d II :n.f :di.t :s |di :ni In :d #4 * l.t:di |di :t f :s |s.l:s.f fi :ni |ri.di:ri * r :n.f|g :S| all the notes with an asterisk are, unHke the by-tone, approached and quitted by a degree of the scale, and they are ail foreign to the chord in which they occur. These are called Passing-TONES. In the example they move in four diEEerent ways : — ^that in the soprano of measure 2 (as well as others) moves upward in the Bams direction as it is approached; that in the soprano of BY.TONES AND PASSING-TONES. 67 measure 3 moves downward in the same direction as it is ap- proached; that in the contralto of measure 4, third beat is ap- proached by ascent, but returns to the note from which it came ; and that in the tenor part of same measure is approached by descent, and returns to the note from which it came. The two first mentioned are the more common forms of movement, and these promote scalewise melody to which the by-tone in the first measure of the ezaniple also contributes, while the less common forms of passing-tone in the tenor part of measure 2, and in the contralto and tenor parts of measure 4, break the monotony of repeated notes. 114. The by-tone often saves a faulty progression of the parts. Thus in the example (Kg. 48), without the by-tone the air and bass would have proceeded in the first chord in second measure to a perfect oth by similar motion in contravention of the rule in § 36. But a passing-tone does not save a faulty progression of parts. Thus in the following example — i m =S: d> :d> n :d s .f :n d :1, the effect of consecutive 5ths between the tenor and bass is not saved by the interposition of the passing- tone. Care must also be taken that the introduction of a passing-tone does not itself cause a faulty progression. In Fig. 48 had the tenor moved to D [r'] for the first note of measure 3 consecutive 5ths would have ensued with the bass, though without the passing-tone the parts would have moved correctly. It should also be noticed that a passing- tone at the distance of a second from another part should not move to the unison, as — m n m 8 :s n.r:d di :d' d :n ^^ d :d l,.t,:d f :s f :n 58 TEXT BOOK OF HARMONY. 116. Though all the passing-tones in Pig. 48 "are foreign to the chords in which they occur," they are not aU dissonant with the rest of the chord. The B [t] in the first chords of measures 2 and 4 is in both cases consonant with the remainder of the chord. It may be called a ChordaIj Passing-TONE, since it pro- duces a quasi second chord in the beat. In the cases referred to it serves to bridge over the faulty progression of Supertonic chord moving to the Tonic chord, mentioned in § 78, interposing what is practically a first inversion of the chord on the Leading-note. Hence the chordal passing- tone is always figured, as in the example, wbUe the ordinary (dissonant) passing-tone is not taken notice of in the figuiing except the 7th occurring in the Dominant chord, as in the close of 3?ig. 48, and except when the passing-tone occurs ji the bass as in Fig. 48, measures 2 and 4, where the " continua- tion line " is necessary to show that the second note does not itself bear a chord. 116. (1) Passing-tones may be taken in two or more parts at a time, provided they are consonant with one another (see Fig. 48, measure 4, contralto and tenor, and Fig. 49, measure 3), or that if dissonant with each other they move in contrary motion (see Fig. 49, measure 2, soprano and bass). (2) A by-tone in one part may also be taken simultaneously with a passing-tone in another part, provided they are consonant with each other (see Fig. 49, first and third pulses). In both combinations a second chord is often incidentally produced, as in Fig. 49, second and third pulses, and measure 3, fourth pulse, and in such cases it is often optional to consider that there are two chords in the pulse, or one chord with incidentals. In the fourth pulse of measure 4, however, there is no option, as the chord that is produced m the second half of the pulse is essential to form the close. In this case both chords are to be figured, according to the rule named in § 64, p. 29. Fio. 49. 1 L i m id. ^^ ^(^^ ST-T0NE8 AND PASSING-TONES. 59 Fio. /Is :d' 49. KEY C. 2 di :s |s.l:s.d> 3 t :-|s :d' 4 di :8 |l.r':di.t d':- )|n.s:f.n f.n:r.f|n :s s :— |n.f:s.l s :n If :n.r n :— |di.t:l.s l.di:ri.tldi :n' ri :— Id' :d' d' ;-.t|l :s s :— Id :d d :t,.rid.t|:d S| :- |d.r:n.f n :d |f.r:s d :- 117. All the passing-tones jiist noticed that occur in the unaccented portion of a beat can be used for a full beat at the unaccented portion of the measure, and this concludes the explanation of the commonest forms. But to complete the series, a few other forms of incidentals of less common use that are ordinarily classed among passing-tones, will now be shown. 118. In Fig. 50, meas. 4, the semiquaver [d'] is approached as a passing-tone, but instead of moving by degree it anticipates the final note. This may be called an Aitticipation-tone. It is of frequent occurrence in the cadences of solos of the Eandelian type, and no doubt has its origin in the soloist's introcluction of the ornament for effect. Fig. 50. 1 2 ^ ^ J-JS-fe 4 I i3ti ^ ■ S ] ri ^ I I J J. J- J. -^ JLJ. -iJ-J. J m f- r-r-f= ^ p p EE^ =P2= Fia. 60. KXT C 1 (Is :n.l )ln :d /Is :8 ild :d 2 S :d' |ni.t:di.,ri 3 t : r :s.f|n :n s : t :di Id' :d> r': f :n.r|d :1 s : — Is :d'.r' — I s :n .f -id' :d' -In :1 n' .-s' |f'.n':r'.,d' s :s II :f d' :di |d' :t s :n |f : s 119. In Fig. 50, meas. 2, again, the semiquaver is approached as a passing-tone, but it leaps by a third to the note that would naturally have followed the previous note. The intruding note is often, as in this case, an Lstdibect Awticipation'-tone— anticipat- ing a tone of the following chord, though not in the same part. As in the previous case, it probably owes its origin to the soloist. 60 TEXT BOOK OF HARMONY. 120. In Fig. 50, second beat, and meas. 2, third beat, the second quaver [1 and t] moves to the next chord-note as a passing- tone by degree, but it is approached by leap. The interval of the leap is immaterial. The device is of use when it is not con- venient to harmonise both notes ■with two separate chords, or when the notes do not belong to any one chord that would make a good progression with the context. 121. Two passing-tones may be taken in consecution, but the second must proceed in the same direction that it was approached till the note of the same or following chord is reached. See in the following example the semiquavers [quarter-pulse notes] in the contralto part. Fio. 61. From " Hail, Judea," Judat Maccabims, Handel. 3 ^E^ '0~p~ =t^ ,N iN J- ..i- m Fig. 81. key D. 1 .t,d':x^ .el' It .dW-n* •»•' d ,r,n:f .n |r .mj':s ,f 1 .« :1 It .1 :t f .ra :r .n/|s ./ :n ./,« 1 .« :1 .t |d' d' ,r',vi> n di .t fi .si 1 .s di .ri The accompanying notes in the soprano part may also be con- sidered as paBsing-ton.es, though the second of the two is really a note of the chord. This example exhibits the ornamentation of a sequence by passing- tones referred to ia the close of § 110. The passiiig-noteB are printed in small notes [in the Sol-fa notation ia italics] that they may the more easily be recognised, and that the structure of the sequence may be seen. 122. All the passing-tones now introduced have occurred, after the chord has been struck, but it may be well here to say that there are others that occur simultaneously with the stroke of the chord. The consideration of these must, however, be deferred till the discords are fully treated. 61 CHAPTER X. TEANSITION TO DOMINANT AND SUB-DOMINANT KEYS — THE SHARPENED FOURTH OF THE SCALE EMPLOYED CHROMATIC ALLY — EIGUR- ING OF ACCIDENTALS. 123. All the foregoing examples and the exercises that accom- pany the previous chapters remain in the same key in which thoy begin. But, as Banister says, "few compositions except very short ones continue throughout in one key." A change, hrief or extended, to one or more other keys than the prevailing one, according to the length of the composition, furnishes a pleasant variety to the music. This change of key is here termed, after many writers. Transition.* The term "Modulation" is, however, frequently employed for a change of key, but this term js reserved for a change of mode, which will be described in' the next chapter. 124. The most common changes of key are those in which the music passes into the key of the Dominant or the key of the Sub-dominant. These are sometimes called the Attendant, Relative, or Auxiliary keys. The change to the Dominant k:ey is by far the more common of the two, and this will be described first. 125. On comparing together the scales of any given key and its Dominant (as of C and G) it will be found that the only note in the one that is not contained in the other is the seventh of the scale of the Dominant key, which stands as a sharpened fourth in the original key [fe]. This at once shows the strong relation of the scales, in having so many notes in common, and the • It may te well to say that some writers use the term for changes of a particular kind, and some for very brief changes of key. The qualified uses of the word appear to the author to be alike unmeaning and arbitrary. 6S2 TEXT BOOK OF SABMONY. :f|n:fels distinguishing character of the seventh" of the Dominant key. In the following phrase, then — we have present the primary element of a transition to the key of the Dominant. Yet, as will presently be shown, a change of key is aot necessarily involved by the mere introduction of the altered note. The accompanying harmony is necessary in such a case to determine whether a change of key takes place, and the consider- ation of what effects a change of key is also necessary to the determination. 126. It has been seen that the natural harmony for the leading note is the chord of the Dominant or Dominant Seventh, and that the natural progression of the Dominant or Dominant Seventh is to the Tonic. If, therefore, the chord with the sharpened fourth is followed by the chord of the Tonic to which the altered note belongs a transition to the Dominant key takes place, as in the following harmony of the phrase above. Fio. 62. w ^^ Fio. 52. KEY C. :f I :r :s :t n :fe s d :d t, s :r r d :r S| 8 CS D) 127. The Dominant chord of the new key stands on the Supertonic of the original key, the old chord being converted from a minor to a major chord. In the foregoing example the change is immediate, but it is commonly made in a more gradual manner by the introduction of chords common to the two keys. It will be seen by the following diagram that the two keys have tour chords in common — Fig. 63. i i =^ ^ TRANSITION TO RELATIVE KEYS, ^e. M Fio. 53. 8 :»d ri :'is ni :nii t :tn n :''li t :tn d< :dif s :»d d ^■'fi s :'d . :ir n :"1, These chords can be used before the new Dominant in such a way as to effect a foreshadowing of the change bj progressions which are familiar in approach to a close. In the following example — Fig. 54. L-UL ^^1 -0~P' 1 — r^ ! I I I I J -•- J . I'' I ! I III m i ?c=p: f^M^ -| — r -r^ I I Fig. 54 Is ni In s Id' d> Id d I. KEY C. r' :di It 1 s :- |di :ni s :1 Is fe s :- Is :s ri :n' |ri -di t :- Id' :di ti :d |r r s :- In :d si fi Itni r' di - s 1 Is -.f n - di di |di t di - n f Is S| d - (R4 Dc S'S D — ) the fifth chord by association with the context unquestionably belongs, to the new key as the second inversion of the Tonic chord, and the preceding (fourth) chord is scarcely less definitely the first inversion of the Supertonio of the new key [E6], rather than the first inversion of the Sub-mediant of the original key [L6]. The change is impending at the third chord, which is at once the chord of the Dominant of the original key and the chord of the Tonic in the new key. 128. Another element of the change of key is the form or shape of the air, which, without the harmony, or even the characteristic note of the new key, is from the fourth note of Fig. 54 to the end of the section as clearly in the Dominant key as is the corresponding phrase in the close in the original key. A similar Dominant melody is seen in the bass of the first section of the following example — TEXT BOOK OF EABMONY. Fio. 55. i J-^J-^U ■3±: --^ ?-r ^^^ I I ! I -J- -J. i I I ii—^ jMziMz :^ju. J=^3U m =^ =Pi: !> F^ I Fio. 55. In Is Id KEY C. :s js ;r |n ^s |d> :t, II, (Dd'H •i ;fe :d :di ;l. S r t S| D -) :di :s :di :n :d> Id' |r H If Here the defining chord of the transition is the first inversion of the chord on the Leading-note (considered as the second inversion of the Dominant Seventh with the root omitted, § 98). The chord that precedes it identifies itself most strongly with the new key as the prepared Supertonic Seventh* ['R] (§ 80), and the approach to this favours the association of the fourth chord with the new key. 129. The chord of the Mediant of the original key becoming the Sub-mediant of the Dominant key is the least used as a chord of approach because of its indifferent relation to the key. The Mediant that is in process of becoming a Sub-mediant should be used in close proximity to the new Dominant chord or in a strongly- defined progression of chords in the new key, following sonie chord that is common to both keys, as in the following example — Fig. 56. Fio 56 KEY n :r C. n :s |1 :1 d :r d :t| Id :d s :s s :s |n :fe d :t| d :n 11, (L ■'K :r 'S D -) * Though the discord just admits of this description, which is a convenient one to use here, it will be seen in Ch. XIII that it is more correctly a suspended discord. TBANSITION TO RELATIVE KEYS. ^e. 65 130. Transition to the Dominant key is used for variety in the close of the first main division of a sentence or tune in the place where the Dominant "half close" has been used. It sometimes embraces just the few chords associated with the cadence, as in the preceding Figs. 54, 55, sometimes the whole section, and some- times extends beyond a cadence into another section. A complete phrase or section is often immediately repeated in the Dominant key, making what is termed a real sequence, § 104. And again, a complete section in the Dominant key in the first half of a tune is imitated in the original key in the closing half of the tune, an example of which may be seen in the tune Tallis's " Ordinal " in nearly all the tune books. 131. Though the transition is more commonly made in the gradual way that has been described, it is sometimes made suddenly without any intervening chord, as in the following example — FiQ. 57. Fig. 57. KEY C. :d' r' di t :s f 1 s :di 1 r' ri :n f :fe s CS6 D) 132. In making such a sudden transition as this it is necessary to observe the rule that an altered note as the FJf [fe] in Pig. 57 must appear in the same part that contains the unaltered note in the previous chord. The violation of this rule produces False Rblatios of the parts. Thus if in Fig. 57 the second bass note were D [r] there would be "false relation" between the contralto F and the bass FJ. There are some exceptions to this rule, but the notice of them is delayed till a more opportune occasion for their use. The strict rule should be observed at present. 133. The "altered note" calls for remark as to its treat- ment in figuring. When in a chord or discord in its root .position the 3rd is the altered note, the 3rd is included in the figuring with the accidental before it as ^{3 or ij3, or more commonly the acidental is used alone to represent the altered third. See Fig. 52. When any other constituent is the altered note in a chord or discord, or when the altered note occurs in a chord or discord in an inverted position the figure that represents the 66 TEXT BOOK OF HARMONY. altered interval is preceded by the corresponding accidental. Sea Pigs. 55, 61, 62, 63. When the interval is raised a Semi-tone, as in Fig. 55, whether, as there, by a #, or by a 1} it is often expressed by an oblique line drawn through the figure. 134. In confirmation of what was said in § 1 25 that a change of key is not necessarily involved by the mere introduction of the altered note, the commonest chromatic uses of the sharpened fourth will now be shown. In the following example — Pio. 58. Fio . 88. •KEY :s C. fe :f n :d r :t, d :s 1 :s s :n r :8| d the altered note is harmonised with the same chord that is used to effect a transition to the Dominant key, but instead of the chord moving to the Tonic chord of that key it goes at once to the Dominant Seventh of the original key. The chromatic use is in this case most obvious. 135. In the following altered version of Mg. 52 the chord that follows that with the sharpened fourth is the Tonic of the original key instead of (as in Fig. 52) the Tonic of the Dominant key, and hence the threatened transition is not consummated. Fio. 59. ^^^S J- I mr. Eio. 59. KB-S :f C. n fe :r d d :s di 1- :ti d r 7toR A more common progression of this major chord of the Super- tonio [f"B.] either with or without the seventh in the first inver- sion, or with the seventh in the second inversion, is into the second iiiversion of the Tonic chord, as in the following examples : — TRANSITION TO RELATIVE EEY8, #•«. 67 n^ KET C. a di:r' di:t di:d< d':t s :r n:r n:fe s :- di:l s :- s:ri n>:t> n:fe B :- d:l, s,:- fRb "•Be The second inversion of the Tonic is hardly less characteristic of the original key than the Dominant Seventh for the chromatic progressions of the altered chord. This progression is frequent in the approach to the Tonic Cadence, and wherever the Supertonic chord or discord has heretofore been used behind the second inver- sion of the Tonic chord there the sharpened fourth can be introduced. In Kg, 35, for instance, F in bass may be 'made FJt [f may be fe]. It should be noted that the third in this altereil chord of the m^ijor Supertonic ri&es to the fifth of the scale as in a transition, and that the seventh of the discord continued as a consonance in the next chord, as in Fig. 59, is accepted as a resolution of the dissonance. 136. On comparing together the scales of any given key and its Sub-dominant it will be found that the note in the one that is not in the other is the fourth of the scale of the Sub-dominant key which stands as a flattened seventh of the. original key. The distinguishing note is not in this case the leading note nor a constituent of the Dominant concord, but it is a constituent of the Dominant Seventh of the S,ub-dominant key. This discord stands op the Tonic of the original key. If this is followed by, the Tonic chord of the key to which the flattened seventh belongs a transition to the Snb-dominant key takes place. See the following example. Fio. 61. 1 f d> f 68 TEXT BOOK OF EABMONY. 137. In the foregoing example the transition is, as in Mg. 62, immediate. It cannot be made in so gradual a manner as the transition to the Dominant key, as there are fewer available chords common to a given key and its relative Sub-dominant. Only by distinctive forms of melody can the transition be made a shade more gradual than in Fig. 61. In the following example Fig. 62. J J. J. J-J-i J. ^^^^ J Fio. 62. KEY 0. d' Is :d> 1 :s If :ta 1 n Ir :s d :n If :n f s It :di di :di |di :di di d |r :n f :d |1 :s (S DS'Pc f there are four intervening chords between those that are characteristic of the original and Sub-dominant keys. But these four chords are made up of only two difierent chords in alternation, viz., the chords of the Tonic and Sub-dominant of the original key, which may be regarded as Dominant and Tonic chords respectively of the Sub-dominant key. These are the only chords common to the two keys that can be used in approach to the defining chord of the transition. The change in Fig. 62 is impending at the beginning of the second measure. 138. As in transition to the Dominant key, that to the Sub- dominant key can be taken suddenly without any intervening chord. See the following example — Fio. 63. Fig. 63. KEY C. :di t :ta 1 :s s :s f :ni r' :di d> :d r :n f CSJ D) TBAN8ITI0N TO RELATIVE KEYS. ^o. 69 The same care is necessary to avoid " false relation " that was mentioned in § 132. In this case the leading note of the original key, instead of rising as usual, descends by a semitone to the distinguishing note of the Sub-dominant key. 139. Transition to the Sub-dominant key is most often of but brief duration, except in some instrumental forms and in composi- tions of an extended character. Sometimes it consists of but the two chords that determine the transition, and it is commonly thus employed for a mere passing efFect in the harmony. A complete phrase or section is occasionally repeated in the Sub-dominant key (as in the Dominant key noticed in § 130). See the following excerpt from Sir Geo. Blvey's tune " St. George." ^ ^ ^^^ hi:^ d • r mn' -e±i .L=U -^ J-. A &^ KEY G. t, :-.t,|r :t, d :r In — S| :-.s,|S| :si si :fi |si — r :-.r|t, :r d :-.t,|d — S| :-.sH8| :f, Hi :r, |d| — f.C. "t .-.t Iri :t d< :ri |n> •,r :-.r|s :8 s :f In is :-.s It :ri di :-.t|di *|8. :-.s,|8 :f n :r |d A transition is often made to the Sub-dominant key just previous to a change into the Dominant key to enhance the effect of this latter change by contrast. A phrase or section in the' Sub- dominant key can also be completely imitated in the Dominant key without any intervening chord. See the following excerpt from Dr. Dykes' tune " Bairington." b m b KEY C. f:s :d ):8.1 :n.f s :f.n|f :1 1 :s.fe|s d :d |d :r r :r |r ta:l.s|l :l.t di:t.l It 8 :d |f :fe.8 1 :r Is The reverse change from Dominant to Sub-dominant key is also available, though instances of its use for imitation are rare. 70 CHAPTER XI. THE MINOE SCALE AND ITS OHOED&— MODULATION AND TEANSITION TO BELATED KEYS. 140. The MlNOB ScAlE— the scale of the one MnfOB MoDB which among various other minor modes of the Greek system has survived — is founded upon ^e sixth degree of the major scale [1]. FiQ. 64. -^^ Fig. 64. r-a- ,i-.o r» ■^ -„ Fig. 64. ^ o_gjr^ ^ H 1 t di ri ni f si 1' It will he seen that in this scale the order of tones and semitones is different from the major scale, but the most striking difference is that the seventh rises to the eighth by a whole tone. This to modem ears is quaint even in melody, but is quite inadmissible in liaimony. The seventh is therefore chromatically raised a semitone to provide a leading note to the eighth, and the modem minor scale for harmonic purposes is as follows : — ^ Fig. 65. , ^ rj '-^ J 1 4- ;i -.1 ^. o r^~g"^^ I 1 t d' ri ni fi sei 1' 141. The original scale in Fig. 64 had all its tones common to the major, and, even with the alteration of the seventh, the form in Fig. 65 has six tones in common with the major. It is there- fore called the Relative Minob of the key with the same signature. The Minor is broadly distinguished from the Major by the accidental necessary for .the leading note. THE MINOR MODE AND MODULATION. 71 142. The minor scale is also somewhat related to the major Boale founded on the same pitch note, haying five notes' in common -with that major scale. It is therefore by some theorists considered as the minor of the same tonic as the major which has three sharps more (or three flats less] in the signature. Hence Fig. 65 is described as in A minor. 143. It is advantageous to study the Minor in both the fore- going relations, and it will therefore be viewed in each relation as occasion serves. 144. In the Major it was seen (in §§ 19 and 20) that the " foundation chords " comprising the scale were characteristically all major. In the Minor, to be equally characteristic, the founda- tion chords should aUbe minor. But only the chords of the Tonio [Z] and the Sub-dominant [^] are minor. That of the Dominant [iejif ] becomes major by the " altered seventh" of the scale. The chords and their relation to each other are seen in the following example — Fis. 66. Lah is A. t 1 1 Fio. 66. se m which is a transposition into the " relative minor " of Fig. 5. 145. The progressions of the Tonic chord to the Dominant or vice versa, ■ or the Tonio to the Sub-dominant or vice versa, are precisely the same in the Minor as in the Major. This may be seen and tested in Fig. 13 by adding three flats to the signature and restoring each B by a natural for the " leading note," and in Fig. 17 by substituting the signature of two flats for that of one sharp. In each case the examples would be converted into the " minor of the same tonic." 146. The progression of the Sub-dominant to' the Dominant it was seen in § 38 needed some care in the Major ; but in the Minor the progression needs stiU more care. While the example of Fig. 18 could be converted into the minor of the same tonic in the same easy fashion as that iust mentioned for Fig. .13, the 72 TEXT BOOK OF HARMONY. example of Fig. 19 could not be so converted. The soprano part would move from the first note to the secoiid by the interval of an lugmented second (§ 12), and it is forbidden for any part to move by an augmented interval, except in some few instances to be mentioned hereafter. 147. The restriction in melodic movement just noticed is only one of several instances that the use of the altered seventh in- volves. If to the example of Pig. 65 another note B [t'] be added it will be seen that there are two tritones to guard against— an interval that is to be avoided. See § 40. Besides the two imperfect fifths that are produced by the inversion of the tritones a diminished 4th will ensue in moving downwards from the third of the scale to the seventh, and a diminished 7th in moving down- wards from the sixth of the scale to the seventh. In all cases of movement by an imperfect or diminished interval a return must be made to some note within the interval. Fio. 67. a * e $ ff^P ISX. ^m U^ '^¥iJ-S^ -e — r±- FlG. 67. KEY C. r> se 1 II d> se 1 || f< se 1 || r' se t 1 1| d< se t 1 1| f i se r' di || When the diminished intervals just named occur in a descending melody the " return " wiU mostly be by semitone — to the tonic as the natural home of the leading note. See Fig. 67, ah c. But it was seen in § 68 that the leading note may be transferred from one part to another. In such case the return might be as at Fig. 67, d e f. In the last example the return from the diminished 7th is by another diminished interval, from which a return is made to C [d']. All three of the diminished intervals also occur, thongh more rarely, in ascending melody. The return may be to any note within the interval. 148. While there is less freedom in melodic movement when the " altered seventh " is concerned, there is a slight compensation gained in other circumstances in the freedom to double the third TSW MINOR MODE AND MODULATION. 73 of both the Tonic and the Sub-dominant chords, even when the chords are in the first inversion, ■without the conditions for the doubling named for those chords in the Major in § 73. 149. The uses of the chords of the Tonic, Dominant, and Sub- dominant in their root positions and first or second inversions are precisely the same in the Minor as in the Major. 150. The Dominant Seventh, it was stated in §§ 42 and 43, has certain advantages over the Dominant concord, and is mostly preferred to it in m.odem music in a cadence. The preference for the Dominant Seventh is still stronger in the Minor. The dissonant seventh has the advantage of modifying the somewhat too bright effect of the major chord of the Dominant placed between the two minor chords of the Sub-dominant and the Tonic. All the rules and exceptions with regard to the tise of the Dominant Seventh in the Major apply equally in the Miaor. The only (incidental) difference in progression is that the 7th of the Dominant in the Minor falls a major 2nd to its resolution instead of as in the Major a minor 2nd. Thus — Fio. 68. ! I -^ ■ ^- -e>- Fib .63. Lai lis 1 :se 1 f :n n r' :ri di r :n li It r^M L 151. The final chord is occasionally made major by "ac- cidental" alteration of the 3rd. This is called Tiebce de PlCAKDlE. The cadence proper is then precisely the same as in the Major, though the effect in the context of the minor Sub- dominant chord is quite difEerent from the close of a composition in the Major key. 152. The chord of the Stipeetonic in the Minor is imperfect, corresponding to the diord of the Leading-note in the relative Major.' It cannot, therefore, be used in its root position. But in its first inversion [2'Zi] it is available in aU the places and under the same conditions noticed for the first inversion of the Supertonio in the Major. The 5th, too, though dissonant to the root, is, in the first inversion, as free in its progression as is the perfect 5th of the Supertonic in the Major, so long as it does '3ot, when the Dominant chord follows, move by a tritone. See § 40. 74 TEXT BOOK OF SABMONY. 153. As a 7th could be added to the Supertonio in the Major, a 7th can be added to the Supertonio in the Minor, subject to the same conditions and rides as those mentioned for the Major ia §§ 80-82. With the 7th added the root position is also available, but the 5th, being imperfect as a semi-dissonance to the bass, mostly receives preparation and resolution as well as the decidedly dissonant 7th, thus — Fig. 69. I Kg. 69. 1 :1 Tiflh is A. 1 :se 1 ^ ) n :f f :n n — di :1 ri It di — { li :r i s t| :n It "M li — The Sth, however, is not, when the 7th is included, a necessary constituent, and if the preceding chord does not furnish a note for the preparation of the 5th it can be omitted. 154. The chord of the SrB-MEDlAHT [^], which is a minor chord in the Major key, is a major chord in the Minor. It has the same uses in its root position in an "interrupted close" and elsewhere as noticed for the Major in § 88. It is also more freely used in its first inversion than is the first inversion of the Sub- mediant in the Major. There is, too, no objection to the doubUng of the 3rd even without contrary motion. 155. The progression in which the Sub-mediant succeeds the first inversipn of the Dominant, referred to in § 89, and illustrated in the last section of Kg. 39, would, if UteraUy imitated in the Minor, produce a movement of an augmented second. To avoid this it is permitted in this case and in others in which the bass descends by degree to use the first inversion of a minor chord of the Dominant. This is the only case in which the unaltered seventh of the minor scale [s] can be used as a constituent of a diatonic chord, and even here it may not be used in an upper part. Fig. 70. * 4c i ^ .^_j_ #: fe i : r pfeg i THE MINOB MODE AND MOBTLATION. 7o Fio. 70. n n d> 1 L :se "Mb 156. Lah ia A. 1 d 1 f Mb F :t :n f :n :n d :n :t d' :t :se 1 :s "¥6 Fl Mb 1 r 1 f Eh For the reason just mentioned there can be no real chord on the Mediant of the Minor. Such a chord would be altogethei foreign to Minor harmony — the very Tonic of the Major. Bat the thu-d and fifth of the Minor scale [d and pi] can be used as a quasi chord especially with the fifth [n] in the bass. Either of the notes may be doubled to make up the number of the parts thus, — Fio. 706. 3^ ^ Fio. 70* Lah 19 A. ■I vTT^ Bfe^H •.A* t :d' 1 :se 1 :n f :n r :r d -.6} r' :d r' :t 1 :1 r Di f :ri 1 No 5th can be added to the apparent root as the altered seventh \ [se] would produce a discord. See § 219. 157. The chord on the Leading-note in the Minor, as in the Major, is imperfect.and can only be used in its first inversion [HEh], All that is said as to the use of the chord in the Major in §§ 98— 100, and as to its derivation, applies equally in the Minor. It may be noticed that the progression corresponding to that mentioned in § 101 can seldom be used, as the bass could not descend by a tri- tone, and were it to ascend by the imperfect fifth w(Jnld scill be restricted in its progression by the rule named in § 147. 158. To the chord on the Leading-note can be added another third, which will produce a 7th to the root — f rl This 7th is dim- inished. Hence gg the combination '££ is termed the 7th is in this chord no chord of the Diminishiii) Sevemth. The more dissonant to the root than are any of its constituents to one another. Whichever constituent be placed lowest, if the others succeed in regular order the intervals will he practically a succession of minor thirds, as in the original position. The chord is therefore in itself more of a concord than a discord, but the 76 TEXT BOOK OF EABMONY. fl :n' pi :d' t :di se :1 1 two imperfeot oths (or two tritones),that it comprises involve, as shown in § 44, dissonant treatment. The 7th must, as in the case of other 7ths, descend to the note below, the progression of the other notes being the same as without the 7th — The chord is available in its root position and i" all its inversions, and the progression of the several notes is the same in each, with the exception that when the chord is in its first inversion the 3th may ascend in 3rds with the bass, which must rise to avoid objectionable consecution of fifths, as in meas. 2 of the following example. In the last inversion it is especially necessary that the 3rd rise to the 3rd of the Tonic in order that the tritone fourth to the bass be not followed by the perfect fourth. Fig. 71. iN iii f 4i ^ -g---*--*-- - - --*-^-*- w ^ ^^ =p=l= f^ f^ 7 ffl 6 t* 6 S .4 S 6 4 i2 4 5 s 7 t- 10. 71. Lah i8 A. di :fi Ini :ri ni :t Id' :1 se:l 11 :se 1 1 :t Id' :se 1 :se|l ;n r :d If :n.r d ni :r' id' :fi ni :fi In' id' t :di It :t 1 li :sei|l, :ti 'SE iSEb d .:r Id :n f :n |r :n SEd 1) The chord is strongly characteristic of the key, as the two dis- tinguishing notes of the modern Minor scale, the minor 6th and major 7th [f se], are brought into contact. Hence the chord is almost as freely used out of a cadence as the Dominant or Doninant Seventh. 133. The "unaltered seventh" of the Minor scale [s], though only available as a chord constituent in the single instance men- tioned in § 155, is available as a " passing-tone " in either of the forms named in § 113, in moving to or from the sixth of the scale [f ] thus— THE MINOR MODE AND MODULATION. 77 FiQ. 72. Fio. 72. Lah 19 A. J- J J* J- J- J^ p^s: 1^ :1 se:t^ n :f.s l.sif.s 1 :se f :n 1 n :di t :t di :di t :ri d' :li n :r d :f r :n li The xinaltered seventh in these cases avoids the movement by an augmented 2nd, that wotild have ensued had the altered seventh been used. In the following case the sixth of the scale [f ]' is not on either side of the passiug-tone, which is a leading seventh, in accordance with the scale of Pig. 65. Fio. 73. Fig . 73. LaJ 1 lis A. 1 :1 n di 1 .se :r :1 1, d :f se n t n 160. The Shaepened Sixth of the Minor scale [ba] is also available, to avoid the movement by an augmented 2nd, as a pass- ing-tone in either of the forms named in § 113 when the altered seventh [se] precedes or follows. Fio. 74. ^^^^ 4- ^ J* ^. * J _ -"J- -mL J _ J lltz! z r @j= r=^^=r=^=B^ :di :1 :lt Fig. 7 * .ba 4. Lah is A. d' . :1 * se .ba :se se .ba :n 1 :n .f n :- ri :t n' .r' :di t :t ti :se, 1, .t, :d .r n :n •r 78 TEXT BOOK OF SABMOm: 161. When tlie seventh of the scale succeeds the sixth, both being passing-tones, as in a passage from the fifth of the scale to the first,' HbAy may either be both major (altered) as at o, or minor (unaltered), as at b. . Fig. 75. I I ^rfi i r- j. r^ f i n ba.se 1 f n :f .s 1 — d — ■ n r d :— n -- 1 — d' se 1 : — di — d — 1. ti d :— li — a Fia. 75. Lab is A. b ]'■' i :se (:t, 162., It has been shown in the preyious chapter that Transition often occurs to another key, and that in the Major the commonest transition is to the key of the Dominant. In a composition in the Minor the change is in most instances into the relative Major rather than a Transition to the Dominant. The passing from the Minor to the Major, or vice versa, is properly termed MoDTJLATIOlf. ' 163. To establish Transition it was seen that it was necessary to have a progression of the Dominant to the Tonic in the new key. To establish a modulation the like progression will be necessary. Fio. 76. Minor to Major. Major to Minor. , FlG. 76. * ' 1 Labia A. Minor to Major. Major to Minor. a b :se l:t di r' di:t 1 :n n :s s r n :r 4 :t diiri n' s s :se 1 :n l:s d' ti d :n li 164. The Modulation at a is ;" immediate " (§ 127), and at 6 it is "sudden" (§ 131). But, as in transition, the change is often-' ■efieoted in a more gradual manner by the introduction of chords :1 Is :n - I- 63 CHAPTER XII. THREE-PART WRITING AND TWO-PART WRITING, 171. It was noticed in § 23 that progressions of chords are most easily studied in a harmony of four parts. By the four-part score the completeness of the chords has been mostly obtained^ and thereby the individual progression of each constituent has been shown. But three part-writing has advantages that are not necessarily obtained in four-part writing. The three-part writing, as Richter says, " is especially calculated to make the leading of the voices more skilful and many sided." As the progression of the parts is more easily noticed by the ear it is necessary to give greater attention to the individual melodies, and completeness of chord has more often to be sacrificed to melodic demands than in four-part writing. The consideration of what constituents may be omitted, and in what circumstances they may be omitted, form the chief matters for attention. 172. In § 24 it was stated that the 5th might be omitted wheiji necessary. It is the constituent that is the most often omitted in three-pai-t writing both in concords and in the discords of the Dominant Seventh or Snpertonic Seventh. In the chord of the Diminished Seventh on the Leading-note of the Minor the 5th is retained in preference to the 3rd for reasons that will hereafter be given. In all other cases the 3rd must be retained as in four-part writing. 173. Though the root and 3rd. are the essentials which cannot ordinarily be omitted, there are cases in which the flow of the parts necessitates the omission of the very constituent upon which the combination is founded. The most common case is in the second inversion of the Tonic chord when used behind the Dominant in a cadence with such an air as the following — 84 TEXT BOOK OF HARMONY. Via. i 85. * ^ T m^ = f^ Fig. 85. KEY C. s :1 Is di:f Is :ri d':- :f n :- :s d :- I- In this case the 3rd is also absent in the Dominant chord, and some theorists object to the omission of the leading note in a final close even in three-part writing. To have the leading note in this case would necessitate C for last note of contralto, which is rather high for ordinary voices. So that with snoh an air in this or a higher key the arrangement in Fig. 85 may be allowed, especially if the key has been well defined just before the close. If the same air were in a key that brought the tonic note well within the range of the voice then it would be preferable to have the leading note in the Dominant chord rather than the 7th. To approach the leading note by leap after the previous stepwise movement would be somewhat inelegant, and to substitute the tonic note for the dominant [d' for s] in the previous chord would bring about an ungainly approach to the 4th in the second inversion of the Tonic chord. A compromise can be effected as follows — Fig. 86. KEY A. n :f In :r d :- 1- : S| :lr |s|.d:t| d :- 1- : d :fi |si :s, d :- 1- : Here the root is omitted at the first stroke of the third chord as in Fig. 85, but it comes in at the second half of the beat, and smooth motion is secured in moving from chord to chord, the leap being within the chord, by a by-tone. It may be noted that what is gained in the Dominant chord — a 3rd, is lost in the close, which merges into (practical) unison. When the leading note, however, is in the air there is no difficulty in obtaining the 3rd for the last chord, which should be secured when possible. 174. Other cases of the omission of the root occur in first inversions of the Tonic and the Dominant, in the second inversion THEEE-PABT AND TWO-PART WBITINO. 85 of the Dominant, and in the second inversion of the Tonic used as mentioned in § 67 (2), whenthe smoothness of the parts require the 5th of the chord to be doubled at the sacrifice of the root. See the examples in the following — Fig. 87. i ^ xt: 1^ ~» — »- - — r t=t i I I T-r ^^ J. ^ 4 Q ^^^ ^_l__^ P _| L ?3= TTTZ'n i I I I :t=^ ■j-j-^nnj: ^ zt =t- Fio. 87. KEY C. S.S.C. Id' :s l.t:d> |f> :fi n' |n :s f :n |f :s s Id :n r :d |1| :t| d |di :ri.n' fi : Is :s t : in :f r : n' |r' :di di Is :n d It, :d t :- r :- 8| :- di :n' ri :d' |r' -.vi fi : - It :di ri :di |di :t di s :s t :di |1 :s 1 : - If :n r :n.f|s :f n n :d r :n |f :s f • - !r :1, t| :d In :r d It may be noted that the chords with an asterisk could not be regarded as chords of the Mediant and Leading-note respectively, as there is no 5th present, and the 5th is a necessary constituent to both those chords. 175. In three-part writing the lowest part must at all times conform to the rules of* a bass, but if the lowest part be for a contralto or tenor voice it will move from chord to chord much as in a four-part score, with smaller leaps than are common to a bass part. The inconclusive forms of cadence (§ 53) will be more used 86 TEXT BOOK OF HARMONY. for intermediate closes than in four-part writing. But for the final close either the Perfect cadence must be used or the close found in the example of Fig. 87. 176. According to the oast of the score it will be necessary at times to employ notes that are at the extreme of the range of the part. Thus if the lowest part be for a tenor or a contralto it will occasionally be necessary to take lower notes than is customary for the part in a four-part score; or if the lowest part be for bass it may be necessary to go higher than usual, especially if the next upper part be for contralto, as it would be desirable in this case not to have the bass too far distant from the contralto. But in all cases extreme notes of the range, high or low, must be carefully placed and sparingly used. Note that even in the close score of Fig. 87 only one low note is used for contralto, that it is on a prominent degree of the scale, and it is so approached as to be easily produced by a contralto of ordinary compass. 177. Two-PAKT Wbiting is often employed in a composition for a number of parts for variety and change, and the elements of it may now be studied. By two-part writing is not meant those duet passages that are often met with, and which have their use, where a melody is wholly accompanied either in the interval of the 3rd or the interval of the 6th below. There is no individuality in the parts in such passages — one melody is but a reflection of the other, — and there is no skill required for this kind of writing. 178. It is necessary in real two-part writing that " the two notes in combination should have reference to a complete and definite chord." * And the skeleton chords should succeed one another according to the principles which have already been explained for four-part and three-part writing. To fix the attention to this it is desirable to figure the lower part according to the chord [name , q - _ for instance, would ordinarily be the chords] in- :^— ^[] taken to be the chord of which tended. This, i^ -g- * the lowest tone is the root, but it might be necessary to consider it as the upper 3rd of which A [1|] is the root, in which case it should be figured 6 [marked 6]. 179. The intervals of the 3rd and 6th are those chiefly used, but that the parts may be distinct there should'not be more than three or four of either interval in succession — the 6ths and 3rds should * See the Author's Text Book of Coimterpoint. TSBEE-PABT AND TWO-PABT WRITING. 87 be interspersed. By this ia meant the succession of actual 3rds, for if an 8ve be added and a 3rd beoomes a 10th the objection to the repeated succession is avoided. In this passage i Fio. 88. f ^ r rr PiQ. 88. KEY C. |s :n In :d di :s |fi :ni li :n |r :d all the intervals but the last are in their simple form 3rds, but distinct melodies are produced by the conversion of some of the 3rds into lOths. 180. Two major 3rds may not succeed each other (except in continuation of a passage wholly in 3rds, as named in § 177), when both parts move by a whole tone, thus — i: --^ is I but such a succession is un- objectionable when the parts move by semitone, thus — se n 181. The interval of the 5th is naturally more sparingly used than 3rds or 6ths. But it may be used even at the accented portion of the measure for a Dominant cadence, as in Fig. 88, or in approach to a perfect cadence either at the accented or unaccented portion of the measure should the lower part be a baas, thus — Pig. 89. • b i m E6^e -rrs- ^ J r F— ;- ^m Fia. 89. KEY n'^idi |r' :- c. di :- 1- :- n' :d' Ir' :r' di d :n |s :si d :- 1- :- d :n If :8 d 88 TEXT BOOK OF HARMONY. in the example a the 5th is even similarly approached, but it is in accordance with the exception named for the extreme parts in § 36 Its use with similar motion of the parts is founded on the horn passage — i I di n :s :di The contrary or oblique motion in approach to the 5th is, however, in most cases to be preferred. A 5th can also be used on the unaccented portion of the measure when one part moves stepwise while the other part is stationary, as at Fig. 90 a; or there ia oblique motion between the parts in approach to the 5th, and contrary motion in quitting it, as at 6 and c. FiQ. 90. i zt ^^ =^= I I FlO. 90. KEY C. di :d' di :— - f :f Is t| :d r r d' It :- s :s If :- Also a 5th may be taken by leap aiter the 3rd of the chord to which the 5th belongs. Fio. 91 I I f fr flF^ l Fio. 91. KEY C. ni :si If :- di:d' II :- d':di |g :- 1 :f In :- 182. The interval of the perfect 5th may not be approached even in contrary motion when both parts move from a 3rd by degrees thus — IIS if i: ;J THBEE-PABT AND TWO-PABT WRITING. 89 183. The imperfect 6tli can be approached freely by contrary motion, and even by similar motion witli one partmoving by degree, as at a, or ■with both parts moving from the 3rd on the Dominant as at b. Fig. 92. FlO. 92. KEY C. a b d' :f' In' ; 1 :t |di :- t :fi |ni :- s :t Idi :- 184. The interval of the 4th is in itself the least satisfactory of all intervals for use in two-part writing. As a rule, it should only be used as a prepared dissonance. It may, however, be used on the accented portion of a measure in places where a second inversion has been acceptable in four-part writing, as in the approach to a close, provided the 4th is approached by degree in contrary motion. i Fio. 93. zz: Fio. 93. KEY C. ^ ~i~W' ^ zz di :ri |di :t n :f Is :s d :- The 4th can be freely used on the unaccented portion of a measure as a passing-tone with the other part stationary or in part oblique part contrary motion. Fio. 94. III I I r ' Fio. 94. KEY C. n :f PI d :d n ;f |s :- d :d |t| :- It can also be taken by leap, like the 5th, after the 3rd of the same chord if both parts are proceeding through the tones of the chord to which the 4th belongs. Fio. 95. i Fio. 95. KEY C. S :d< n 90 TEXT BOOK OF HARMONY. As consecutive 4ths with the bass and any other part wero pro- hibited in four-part writing (§ 72), it were scarcely necessary to say that consecutive 4ths are disallowed in two-part writing, save to mention that the prohibition applies without exception. 185. The interval of the octave may be occasionally used both at the accented and unaccented parts of the measure, in contrary motion, with both parts moving by degree or by leap as at Fig. 96 a, h, or with the lower part moving by leap as at c, or more seldom in similar motion, with the upper part moving only by degree when the progression of chords is that named in § 36, as at d, e. Fio. 96. i r^TTi-i '^^i ^ ^ l^g^ ffrrTTT^'^T^ Fig. 96. key a b ri :di :t s :di :t t| :d :r n :d :r si :fi :ni d :f :s d ni :fi d :f r t :di 186. The interval of the 8ve may not be taken even by contrary motion when the upper part leaps and the lower moves by step to the octave, thus — ^* s< :di ti. :d d' :s' 1 :s 187. The unison is more rarely used than the octave except for the commencement, or for a close. Elsewhere it may only be used at the unaccented part of the measure. 188. The 7th on the Dominant may be taken without prepara- tion both in its original position and with the interval inverted as a 2nd so long as the dissonance is regularly resolved. THBED-PABT AND TWO-PART WBITINO. 91 Fio. 97. i mm Ifeg^B ^i* FlO. 97. KBY C. di :f' :ni :- 1 :8 Id' :- t :f' In' :r' s :s II :f I I d' n s :s Id' :- t, :f In :- But all other dissonanceB may only be taken at the unaccented parts of the measure as passing-tones (§ 113), or at the accented part of the measure prepared like the dissonance of the 7th on the Supertonio already shown in § 80, or like those that are to be described in the following chapters.* 189. The commencement of a complete exercise or composition in two-parts may be unison, an octave, a 3rd, or a 5th. The close should be with the unison or 8ve of the key-note, or if the leading note be in the upper part as the penultimate, the lower part may close on the third of the scale in 6th to the key-note. • Examples of these dissonances in two parts may be seen in the Graded Enrcises (en intervals) 1 and 56. 92 CHAPTER XIII. DISCORDS BY SUSPENSION. 190. It was stated in § 83 that the discord of the 4th on the Dominant belonged to the class of Discords by Suspension, the full explanation of which was deferred. Before proceeding to this it may be well to call attention to the points already noticed, viz., that the dissonance required preparation— i.«., to be sounded as a consonance in the previous chord in the same part ; that it was resolved upon the note for which the dissonance was sub- stituted ; and that the resolution was effected within the chord in which the dissonance appeared.* This last feature is one of the chief characteristics of a Discord by Suspension. Another feature is that the discord'occurs at the accented part of the measure or of the pulse. A third feature is that the dissonances are limited to certain intervals. The dissonant note, too, is more commonly sustained from the preceding consonant f-^— c- Fw— note (by a tie) produc- ing syncopation, thus The sustaining of the dissonant note from the preceding note is, however, not essential ; the dissonant note in the above illustra- tion might be restruck, but it would still come under the class of a dissonance by suspension. 191. The chief dissonances used for suspension are the 4th and 9th to the root. They may be introduced in the several chords heretofore described either in their root position or in the inversions of the chords that are available. 192. The following examples illustrate all the available ppsitions of the suspension of the 4th on the tonic. The figuring by which each position is indicated in exercises ia placed underneath the bass of the illustration in every case. * See Appendix for exception. f - :n' di di :- 1 s :- f d :- mSGOBDS BY SUSPENSION. da Via. 98. a 8 :f - n d :d d - f d' :1 8 - 1 n :f d D f d' :- - :pi 8 :- :t :r s :- :si 193. To elucidate what was said in di :- c di di - :t di - n :- f 8 - :f n - s :- 1 8 - :s s - d :- f *De Di d - § 191 about available chords or inversions for the suspensions, it may be noted that the suspension as it appears at 6 could be taken in no other chords but that of the Dominant and Sub-dominant ; that the suspension as it appears at a could not be taken on the chords of the Leading- note of either Major or Minor, nor on the Supertonio of the Minor. But as these chords are available in their first inversions, BO is the last position of the suspension as at c, which in the resolution produces the first inversion. 194. In § 83 it was stated that the 3rd can never be sounded mth the 4th. In other chords than the Dominant the 3rd may by rare exception be sounded with the 4th, provided the 3rd be at least at the distance of a 9th below the 4th, and that the 3rd be approached by degree in contrary motion to the path of the dissonance. Fio. 99. 6 I I J I I J Fio. 99. , KEY C. » -»- -*- -C2. I.S - i( ni:si - f di:r' di 8:di 1 - n :f n - di:d' ri s:t d' - di:n f > R d :si 5 li - This exception more often has application when the chord ia minor, and when the 3rd is in the bass. 94 TEXT BOOK OF HARMONY. 195. The suspension of the 9th displaces and resolves upon the octave to the root. The root therefore may not occur in any upper part, but only in the bass. In all the inversions of the suspended discord the root is not sounded with the 9th, but appears when the dissonance is resolved. The following examples illustrate all the available positions of the suspension of the 9th on the chord of the tonic of the Major. These as well as the suspended 4th8 just described and illustrated have their exact counterparts in the Minor. Figs. 98, 99, and 100 could be converted into the "Minor of the same tonic " by the process named in § 145. Fig. 100. FiQ. 100. a di :r> - :di b _ di c - :di :t di:- d * di:t n':- n :s s :- n :f s - f n :- :r n :- s :s s :- s :ri n':- d' :1 s - 1 s :- :s s :- di:ri s :- d :t, d :- »D D d :f n Di f s :- :si 'DcDc d :- n :r r :d »DeD The inversions of the 9th have somewhat the appearance of a discord of the 7th, and the figuring of the dissonance is the same as in the discord of the 7th. But the inversions of the suspended 9th may always be distinguished from a discord of the 7th by the resolution being effected within the chord in which the dissonance appears. The figuring of the dissonance of a sus- pended 9th is always followed by other figuring or continuation lines on the same bass, which expresses the position of the (con- sonant) chord that is produced when the dissonance is resolved. The last inversion, as at d, is sometimes indicated by an oblique stroke (/) placed under or over the dissonant note, showing that the chord is according to the following note. 196. In the inversions of the suspended ninth the root may by rare exception be sounded with the 9th, provided the distance between the two be not less than the interval of a 7th, and that * To comply with the rule in § 195 that the root be not sounded with the Jth the leading-note in an upper part either rises to the 3rd of the Tonic as liere, or to the 5ch, ur falls to thu 5th. as in Fi^. 107, meas. 1, BISGOEBS BY SUSPENSION. 95 the root be approached by degree in confcraiy motion to the path of the dissonance. FiQ. 101. KEY C. [ ni-ri -:di l:t di;- \ s :s 8 :- f :- s :- i di:t d':- di:ri n':- d:r n :- DbBb f :r r:d 9DeD The exception more often has application in the last inversion, as at b. It should not be resorted to in the other inversions in a less number of parts than five. 197. Besides the 4th and the 9th the intervals of the major 7th from the Tonic and the minor 7th from the Dominant are included among those that may be suspended. These suspensions have peculiarities of their own. They may only occur when the chords are in their first inversions, except in one instance presently to be named. The dissonant note resolves by moving npwards to the root of the chord. On account of this peculiarity of resolution the dissonances are termed by some theorists Betakdations. a Fig. 102. i^=^m I i"=r' W . r m f5 a Fio. 10 1 :se J. La his A. 1 b d> KEY C :t — t di 1 r' — n' n :r n — f :b s — f — s 8 di :r' d' — 1 :f 8 — di ri — d' • d 'Lb Lb f :r n 'Di D* i t, s d The dissonances standing at the interval of a 5th to the bass give to the combinations the appearance of chords on the Mediant and 96 TEXT BOOK OF HARMONY. Leading-note respectively. But the resolution on the 6th " with- in the chord " removes all doubt. It may be noticed that the suspended 7th in the first inversion of the Tonic of the Major as at & is a perfect 5th to the bass, and therefore the dissonance is dissonant in theory only and not in realitv. 198. In none of the cases just illustrated may the root occur with the 7th, except in the Tonic chord where the major 7th is occasionally suspended with the root in the bass — Fio. 103. Lah is A. l:se|-:l KEY di:t 3. di n:r n :- s:f n - di:ri di;- s :s s - d:t, li:- n :s d 'D D This suspension of the 7th with the root in the bass more often occurs in combination with other suspensions than singly. See § 205. 199. A suspended dissonance stands in the stead of the following consonance upon which it is resolved. If the consonant note placed on the accented part of the measure would cause consecutive 5ths or 8ves with any other part the interposition of the dissonant note will not save the error; thus, a b are equal to c d ; — Fio. 104. E3^= a ■^.Jnl^ ^i r miz ?z: Fio. 104. KEY C. a b c d di :1 8 - s :1 1 :s di :1 8 :- 8 :1 8 :- 8 :f S - n :d r :- s :f 8 :- n :d r :- n' :ri - di di :di t :- n' :ri di :- d' :di t :- d :f n - d' :1 8 :- d :f n :- di :1 8 :- DISCORDS BY SUSPENSION. 97 200. When the dissonant note is mstamed [continued] from the preceding note the preparation note should not be shorter than the dissonance, but when the dissonant note is re-struck the preparation may be by a shorter note than the dissonant one. 201. An exception to the dissonance of a suspension being prepared by a previous consonance is allowed in the 4th on the Tonic, which may be prepared by the 7th on the Dominant— the resolution of the 7th being thus delayedby the suspension of it as a 4th in the chord of resolution * FiQ. 105. Fig. 105. xsy C. di :t :s :8| 202. Any suspended dissonance may move by degree or by a leap to another consonant note of the chord before proceeding to the note of resolution as in Fig. 106, meas. 2 and 4, and the interval between the consonant note and the note of resolution may be filled up by a passing-tone as in meas. 3. This is known as " interrupted resolution." No notice is taken of it in figuring. Fi8. 106. _^ i ^^ s * ^m ^ r- V^ mz SE :?=c FlO. 106. KEY U :r' It — -rl r s :— — :- s ;— ♦s int.m. -:n'.r'|di 8 :- I- 8 :- I- n : — im am int. re» :s 1 — 1 — — 8 — | — :— di f d If — d' r In :— ='v — d =t- mi. ra. * In any of the Prepared Discords of the Seventh named in next chapter the dissonance may be delayed as a suspension before being resolved. us TEXT BOOK OF HARMONY. 203. The suspended dissonance may also leap downwards by a 3rd to the note that is one degree below the note on which it is to resolve. See last meas. of Fig. 106. COMBIMBD ST78FENSI0NS. 204. Two or more dissonances may be suspended at the same time, especially when the dissonances are in 6ths or Srds to each other. The most common combination is that of the 9th and 4th. This is exhibited in the following example in all the positions in which the combination is available. Fio. 107. P J J | ^'--rJ -d ^^ se±: ra=r ?2= ^ P I q m. >V^^j.;-aj i^-^^4i j. ^Ttn^f^ rr 4 3 1 4 - 3 3 Fig. 107. KEY C. :d< 1 - :t di :r' :n' fl - :- - :n' :r' - :di :t di - :s - f :- n :1 :s f - :- s w :1 s :- :f n - :ni - r':- di :1 :di - t :- 's :si :fi - .-n' :r' d< - :d 9 r i=^' li:f :n 9 *Te r :- T4 9 - :d ;f 'De D 9 s :- :si d - In the first case the combined suspension is in the root position, in the second case the 4th is in the bass, in the third case the 9th is in the bass, and in the last case the suspensions are over a second inversion. 205. The suspended 9th may also be combined with the major 7th on the Tonic either in its root position or first inversion, or, more rarely, the 9th with the 7th on the first inversion of the Dominant- DISCORD BT SUSPENSION. 99 Fi a 108. J i:^=;^ 1 a ^tj-^^N^^^ ilzJ I m: i ?=: ^ ^ r I? FlO. 108. KEY C. a :ri — di 6 1 :se — 1 di 1 — s n :f n — d :r n — n f — s B :t — d> d> :t — 1 s r' r' — d d 'D D li =*'. d 'Zb Zb d •'S4 Si 206. The suBperidied 4th may also be combined with the 7th on the Tonic as at Fig. 109 a, or 9th, 7th, and 4th may be com- bined, as at h. Fig. 109. KEY a di:t c. di n':ri -:d' n:f - n s:f -:n s :s 8 - di:t -!di d:8,. d D ^•■\ d:- *D D 207. The cases just illustrated are also examples of the suspen- sion of one chord over another. When, as in these examples, the Dominant Seventh is the chord of suspension, the preparation of the dissonances maybe dispensed with, see Fig. 110, and any note belonging to the Dominant Seventh may be introduced that was not in the chord previously, see Fig. 110 6. lOO TEXT BOOK OF HARMONT. Fio. 110. ^ Fio. 110. KEY C. / a d':t i ri:d' n':f' r':di ) s:f f :n s :s f :n \ dirri t:di s:t t :di f n:s d:-| 974D D d:si d :-l| s"D D 208. Any chord may be suspended over another when the pro- gression of roots is, as in that of Dominant to Tonic, by rise of a 4th. In this case the notes suspended move in the same way as they would were they consonances and not dissonances, provided that they do not move more than one degree. Fio. 111. , >sj J J J^l J ^ j^J J- ?2Z rr^rT'r^ Fio. 111. KEY C. d' :- 1 — — :t di — 1 — ri 1 — t — di n :— — f — :s n — — r 1 f — s s — s :di — ri r' :- d< — — ri fi — ri — — ni d :1| r — si :— li — f — r — s — d — The " continuation lines " represent suspensions of notes of the previous chord, and the figures following the lines represent the chord in which the suspensions take place. 209. One or more dissonances by suspension may be intro- duced into the Dominant Seventh, or into any of the discords ot ohromatio chords mentioned in the following chapters. CHAPTER XIV. PBBPAEBD CONSTITUENT DISCOKDS OF SEVENTH, NINTH, AND AUGMENTED FIFTH. 210. The discord of the Seventh on the Supeitonic (§ 80) belongs to the class that is often termed Prepared Discords. The discords of suspension described in the previous chapter are also prepared discords, so that the term is somewhat indefinite to apply to another class. The chief difEerence between the two classes is that in the ordinary discords of suspension the dissonant note is one that is substituted for a constituent note (§ 190) of the chord, while in the discord of the Seventh the dissonant note is one added to the chord, not displacing any of its original constituents, but becoming with them an element of the whole combination. Pkepabbd Constituent Discords seems, therefore, a more definite term to apply to the class of which the Supertonio Seventh may be taken as a representative. Like that, all the discords of this class resolve as a whole upon a chord whose root is a 4th above the root of the discord. These discords, unlike the suspended discords, may occur at the unaccented part of the measure, though, as was stated in § 80, their occurrence at the accented part of the measure is the more usual. 311. The 7th can be added to any other concord than the Supertonic, and the discord that will be created will be available either in the root position or in the first inversion, according as those positions have been available for the concords, provided that the chord required for resolution is also available. It may be necessary to remind the student, for instance, that the 102 TEXT BOOK OF HARMONY. 7th. could not be added to the Mediant nor to the chord on the Leading-note in their root positions unless in sequence, and the 7th could not be added to the Sub-dominant in its root position because the resolution chord on the Leading-note is not available. The second inyersion of discords of the Seventh is unavailable except in the case of the Dominant Seventh, whose dissonance, it has been seen, needs no preparation. But the last inversion, that in which the dissonance is in the bass is available in all discords of the Seventh, both of the Major and the Minor. Fia. 112. i =J=J i ^JLJ- 4 j-j- lii.^ ^^ P FlO. 112. KEY C. |di :t \n :r |s :s |d :s t 1 Is :8 d f In :s s di |d> :di n f Id :n 1 :t f :- di :ri n :r ■'Fd |di :r' In :f |di :t 11 :- 4 2 5 t :di idi :t s :n |f :- n' :1 jri :ri s :- If :s 'Lrf'EJ'S 212. In the Minor the 7th on the Tonic, for the reason stated in § 155, will necessarily be a Minor 7th, and the discord necessarily will be only employed in its last inversion. See meas. 4 of the following example. Fio. 113. I iJ=^ ^^Cg-^j^I^^gg T J-0- ^^^^ I I I ^~il^ r 6 4 6 S 2 S 6 4 S 6 7 2 5 it * When the leading-note becomes a dissonance it yields its regular pro- cession to that which the dissonance requires. PBEPABUD CONSTITUENT DI800BD8. , 103 FlO. 113. KEY C ( Id' :1 1 :se|l :f f :n In irf ni :r'.di|t :t 1 - )|n :- f :r In :n r :- |d :n 1 :- 11 :se 1 - )|d' :- r' :- Id" :- t :- Id' :t d' :ri.nilfi -.r' d' - 111 :d' d' :t |1 :1 1 :se 1 :s 8 :f Ir :n li - 213. A discord of the Seventh can be succeeded by another discord of the Seventh, as may be seen in Mg. 112, meas. 4, and Fig. 113, meas. 3, and a aeries of discords of the Seventh may succeed in sequence (§ 110), as in the following example :— Fio. 114. =^feJ f I f p p , jiy- --y-°---i^g ^> rg J- J.J. m j-.^ J J j ''-' I '':'• ^E^ ^ -r Fig. 1 In' :ri 14. d' KEY C. :- It :- 1 ;_ Is |s :s s :f If :n n :r Ir Id' :t d' :r' |r' id' d> :t It Id :s 1 :r Is :d f :t, In - :1. :- f : :d - : :1 1 : :li r : f :- n - t| :l,.t, d - s :- s - S| :- d - It should be noted that in every other discord of this succession the 5th is necessarily omitted to save consecutive fifths. 214. As in a suspended discord, so in the discords of this class the dissonant note may leap to a consonant note of the chord before proceeding to its resolution. See example in Fig. 114, meas. 4. 215. The DiscoED or the Ninth is another that belongs to the class under consideration. It is formed by adding a 9th to the discord of the Seventh. The root may only be taken in the bass, and is therefore omitted in all the inversions. 216. The discord of the Ninth can be used in its first, second, and third "inversions, but not in its last inversion. The omission 104 TEXT BOOK OF HARMONY. of the root from the inversions gives the appearance of a discord of the Seventh; the first inversion of the Ninth corresponding to the root position of the Seventh, the second inversion of the Ninth to the first inversion of the Seventh, and the third inversion of the Ninth to the second inversion of the Seventh. But the one discord is to be distinguished from the other by the chord of resolution, whose root is a 4th above the root of the discord. i Fio. 116. 1 I , 5^ J L J J I J * * j j i i J. ^ I i r^^ 1 — r -m p. I I U I \ -^—i^-iir a m ^ r i rx-T-X 1 — I — r i 6 | ! I . 7| \ i±^ j l J ,1 I I 8| I ! -Tt-^ * • d rrrr^ i rr-f ff^ a I J^J-JJ-^-^ Fig. 115. kbt C. 1 2 ri :di It :t n :f |f :s t :1 |ri :r' d :f |r :n D "Di Pi' :ri s :s di :t d" :s 9 1 :s |di : f :s Is : di :di |1 : f :n In : di :ri |ri di n :r |n f s :s |s di d :t, jti li s t :s 8 :- ri :t S| :8 Idi ri In 1 It 1 Is f "Ld 6 n' :ni |r' :t s :f Is :s t :di |ri :r' 8 :1 It :8 di .Ti jr' :di n :r |n :f di :1 It :di 1 :f J8 :1 f :n' In' ri di - r :8 11 t d' - di :t |di fi ni - 1 :8 If ^TA S7EJ 8 d - PBEPABED CONSTITUENT BISOOBDS. 10b 217. The first and second inversions of the discord of the Ninth are also somewhat like discords of the Seventh in their treatment, in that the 7th to the root (corresponding to the 6th in the discord of the Seventh) needs neither preparation nor resolution, bee Fig. 115, meas. 6, 7, 8. But in the third inversion, the 7th in the bass must both be prepared and resolved as usual. See Fig 115, meas. 3, 4, 5, 8. 218. The interval oE the 9th brings another 5th into the combination, and if the original 6th be present, as is usual in the inversions, there will be some danger of proceeding in consecutive fifths in resolving the discord, especially if the 9th be in some part above that containing the 6th. To avoid the error the 5th of the discord can either ascend a degree, as in the third last chord of Fig. 115, or rise or fall to the 6th of next chord, as in measure 4, where the 5th of the Tonic in the tenor part rises to the 5th of the Sub-dominant to prevent, on the one hand the consecutive 5ths with the soprano that would have ensued had the root of the Sub-dominant been taken, and on the other hand the infringement of the rule in § 73 had the 3rd been taken. 219. It was said in § 156 that if to the quasi chord on the Mediant of the Minor the " altered seventh " were added for a 5th a discord would be produced. This discord of the Atjgmenteb Fifth is also included by some writers in the class of discords just described. The 5th, however, which is the dissonance, naturally resolves upwards just as in the suspension of the note as a 7th over the first inversion of the Tonic (§ 197) to which it bears resemblance. As a prepared con- stituent discord it is resolved on the chord of the Sub-mediant [JP]. The discord is available in the root position and first in- version. It is preferable to double the third rather than the root. Fig. 116. Pig. 116. Lah is A. :n n :1 se:se l:t 1 :t| n :d n :n d:r d :se se:l t :di Irse 11 1 d :f -Bb f :n 1 106 TEXT BOOK OF HARMONY. 220. The 7th can be added to the discord of the Mediant with the augmented 5th subject to the same conditions that applj to other discords of the Seventh, but the 5th must in all cases be prepared, and resolved on the 3rd of the following chord, which constitaent will necessarily be doubled. Fio. 117. rr^rrcfr ^ ^4^ai j it^ ! J ^ S :t=t ~P m r^ ii "1 r Fig. 117. LahisA. t :1 If I :n|.ri se:l |1 :se ni :di |ri :t d :f |r :n di :t 1 :se ni :ni 1 :n IMJ) di :di Ini :ri se:l |1 :n t :1 |1 :se n :f Id :ti 7BeJ)J di :di It :t n :f If :n.r se:l 11 :se t| :1| |r :n ''"Di 107 CHAPTER XV. DNPEBPAEBD CONSTITUENT DISCORDS OF THE DOMINANT 'NINTH, ELEVENTH, AND THIRTEENTH —ACCENTED PASSING-TONES— THE PEDAL. 221. The discord of bhe Dominant Seventh may be taken as the representative and model of the class of Unpuepabbd Constituemt DiscoiiDS that are now to be described. As will be seen, they are all founded upon the Dominant Seventh. 222. The Dominant Ninth is first in order. It consists of the Dominant) Seventh with the 9th added, which is naturally a major 9th in the'Major and a minor 9th in the Minor. This 9th, unlike all the others, may be taken without preparation. Its ordinary resolution, as in other oases, is by descent to the next scale note. The dissonance of the 9th can be resolved like a suspension while the rest of the chord remains, as in Fig. 118, meas. 1, or the discord as a whole can be at once resolved on the chord of the Tonic, as in Fig. 118i meas. 2, 3. This latter form of resolution is the more common, and in this direct form of resolution the discord is exhibited in all its available inversions in Fig. 118. The root, as in other oases of inversions of the Ninth, is necessarily omitted. Hence the discord of the Dominant Ninth in its inversions wears the appearance of a discord of the Seventh on the Leading-note. See measures 3 and 4 of the following example : — Fio. 118. * ^^^ r' m -^ d d ^XllA^LiA^l J=AMJ^^^J r-r^^n^g r r T7 ^^ 108 TEXT BOOK OF HARMONY. Eia.. ] * (:s 11 18. 8 KEY C. s :1* Is :di * * 1 :s Is' :f' n' :r' |d' :t d' ):n If f n :f In :n f :n is :1 s .1 Is :f n ):d' It t di :t Id' :di r> :s Id' :t d' :t |di :r' s ^ •■' .'4' S| si :si |d :1| t| :d |n :r om om n :f In :r '■'Sd om d 223. The.major 9tli on the Dominant may not be placed below the 3rd, or leading note. The last inversion, with the 9th in the bass, cannot therefore be used. 224. The minor 9th, though commonly placed above the 3rd when the discord is in its root position, may be placed below the 3rd, and therefore the last inversion can also be used. The discord of the Dominant Minor Ninth in its inversions is the same as that described in § 158 (and illustrated in Mg. 71) as the chord of the Diminished Seventh on the leading note, in which section it will be seen that the combination practically consists of a succession of minor 3rds. This is why the minor 9th can be placed in the bass. The following example exhibits the discord in its root position resolving directly on the Tonic, and also with the 9th resolving like a suspension in the root position and in two inversions of the discord. Fl8, * 119. f :ni se :1 r' :d' n :I Lah is A. * r' :n' |f' :n'.r' se:l |se :se ri :d' |r' :t t :d'.l|n :n It :t If :n |se :se |r :r :1 :n :di :li * I se : se :r :t :1 :di :1 225. Both the major and minor 9th can be resolved within the chord, not only upon the root, as already seen, but also upon the 3rd of the chord. In this case the 3rd may not be sounded with the 9th. The first inversion cannot therefore be used. Though UNPBEPABED CONSTITUENT DTSOOBDS. 109 the other inversions can be used, including that with the 9th in the bass, the discord with this form of resolution is but seldom found in other than the root position, especially in the Minor. 226. The 9th may either move up by a second or down by a 7fch to the 3rd of the chord. In the minor 9th the upward movement produces an augmented 2nd in melody, and this is one of the exceptions to its prohibited use referred to in § 146. But the downward movement produces the more pleasant interval of a diminished 7th. The irregular movement of the 9th no doubl owes its origin to the preference for the diminished 7th rather than the augmented 2nd, the movement in the Minor being afterwards imitated in the Major. Fis. 120.« LiiJHi ji Mil Lah is A. -j^^ 0.. m ^ .m ^ — K- f If r i r r F I I :n * f :se 1 :f * fi :se 1 :n r :r d :d r :r d :d> t -4 1 :1 t :t 1 :1 8 n :n f :f n :n 1 The upward movement of the 9th is shown in the figuring by a 3 following the 9 instead of an 8. The figures following' the Ninth cannot therefore appear in the regular order hitherto maintained of the higher figure being placed above the lower. In the inversions the upward resolution is shown by the arrange- ment of the figures. See Mg. 121, meas. 3. 227. When the 9th moves to the 3rd the 7th may be omitted for the nonce provided it be taken when the 9th is resolved and be approached from the root, by degree as in meas. 2 of the following example. The 9th also may, when resolving on the 3rd, stand at an interval of a 2nd from the root, as in measure 3. ^ Fig. 121.* , , * I * , , J V . Jl^^^ia^JJ ' "T r i M r ', 1 I I I J ^ ^1 J. T r. r,mT I? 'g 4 3 5 6 4 3 - ? a no TEXT BOOK OF HABMONY. FlO. 121. KEY C. 8 :di |1 :t n :s Is :s di :ni |fi :f' d :d |r :r 228. The interval of the 9th should not be approached by similar motion, especially when it stands in the extreme parts — Fio. 122. H : n KEY 0. :s 11 :t di di Is s :s If :- n f is f :ni |ri :— di di jri — :di Is :- I li Hi t, di * si 111 t d s -If — n si ni |ri — di n d Is, — d m 0z ?3i= s - 11 n - If di - It d - Is 229. Kor should the interval of a 7th be approached from an 8vB when one part moves only by a degree — Fio. 123. KEY di C. 1 s n — n r s f n — d 1< d — 230. The Discord of the Eleventh is next in order. It is formed by adding to the Dominant Ninth another 3rd, which gives an 11th from the root. The 11th is the same scale note as the 4th, a dissonance which it has been seen drives out and resolves upon the 3rd. With this resolution the discord of the Eleventh in its root position resembles a suspension of the 4th and 9th on the Dominant Seventh (§ 209), but differs from it in that the dissonances need no preparation, though some one or more of them usually receive it. In the root position the 9th is often omitted, as in the next example. The compound interval of the 11th is figured according to its simple form of a 4th, as in Fig. 124. The upward resolution of the 11th is shown by the arrangement of the figures, as in the case of the upward resolution of the Ninth (§ 226), see Pig. 125. UNTBEPABED 00N8TITUENT DISCORDS. Ill From Mendelssohn's " In the Forest." KEY S. * :ri di -It :-.d' d' — I — :f f -If :-.f n — 1— :r' r' -in :-.ri di — 1— :f t s -Is :-.s d — 1 — 331. When in the Eleventh the 9th rises to the 3rd (§ 225) the 11th may rise to the 5th. See Fig. 125. The 5th in this case may not be taken with the 11th except when the 5th is in the bass and descends to the root when the 11th is resolved. See Fig. 126. Fig. 125. From Sir A. Sullivan's " Hymn of the Home-laud. ■^\> ? F r ' r 'I " KEY £|;. n :d Id :r d - 1- si :si 111 :ti d - 1- d :n If :f n - 1- S| :S| |S| :si d - 1- "*S Fig. 126. From Sir G. Macpabben's " Sigh no more, ladies." * P i TfTT^ ' c/r T %= J. 1-^ ^ 1 J. ^^^ ^ I I =pz: 1 — r Fig. 126. key F .* r :r :n s -.f :n r — — d :— . — d :d :d d r :d d ti.li t| d :- — f :f :s 1 t :di 1 8 f n :— — f :f :n r 8, :1, fi S| — d :- — 112 TBXT BOOK OF BARMONY. 232. The discord in this form with the upward movement of the 11th and 9th is also used in the inversion with the 9th in the bass, as in the following excerpt : — Fig. 127. * From Henry Leslie's " gentle sleep." ^^ ^ i-J^ ^ It M KEY Bl;. f| r * |S| — 1- — n. Id r n 111 ti d 233. In all the foregoing cases there is no doubt about the discord being founded on the Dominant Seventh, the root being present and the 7th being resolved in the usual way. The pecu- liarity attaching to the theory of the Dominant Eleventh may be summed up in the statement that on the one hand it allows of the dissonance being taken without preparation and that on the other it allows of its being resolved upwards, or even dissolved in the consonance of another chord. The second last note of Pig. 124, for instance, would be accounted as an 11th by many theorists, although others, with whom the author agrees, would consider the note sufficiently accounted for as an "■ anticipation " (§ 118). Even the other cases in Figs. 124 and 127 could be accounted for otherwise than as " Elevenths." 234. The non-necessity to prepare, or to resolve the dissoimnce in the usual way serves as a convenience to explain irregularities with regard to other combinations which are termed inversions of the Dominant Eleventh, but which are not so obvious as the cases already shown. The discord of the 7th on the Supertonio when- ever the dissonance is unpsrepared as at a, or resolved upwards as at h in the following example, is termed the Dominant Eleventh, the root being omitted. Fig. 128 UNPBEPABED CONSTTTUENT DIS00BD8. 113 Fio. 128 d' :t Lahis A. 1 :se 1 :se 1 :- i d' d> r' n' n :n n :n f :n n :— s f f p) 1 :se 1 :t t :r' di :- s 1 t d' 1. :t| d :n r :n li :- n r S| d 235. The Supertonio Seventh when followed by the second inversion of the Tonio, as described and shown in § 81 and Fig. 35, is also accounted for as the Dominant Eleventh, the omission of the root allowing the original 7th {i.e., the 3rd to the Supertonic) to be treated as a consonance. So also is the same combination of notes when used as in the following example, claimed as an instance of the Dominant Eleventh. Pig. 129. j^ From Henby Smabt's anthem, " What are these." m 3= ^ ^^ , Fig. 129. kbi * d :- :r li :- :1. f :- :f f G. PI 8| n — — n n — :— — : : 1 — ; • ■ ^ )d :— :d k :- :fi d di d d| — : — -\:- ■■ The theory of the " added sixth " referred to in § 81 and rejected in the case in Fig. 35 certainly applies here with more reason than that of the Dominant Eleventh. The chord in the ear is the Bub- dominant, the cadence being Flagal, and the note in the melody is a mere passing-tone in the Sub-dominant chord. ' 236. The Discord of the Thirteenth is the last of the series based on the Dominant Seventh. It is formed by adding to the Dominant Eleventh another 3rd, which gives a 13th to the I 114 TEXT BOOK OF HARMONY. root. This is naturally a minor 13th in the Minor and a major 13th in the Major. Of course all the seven constituents cannot be talcen together, even if the score consisted of a sufficient number of parts to represent them. The essential constituents are the root, 3rd, 7th, and 13th, those which are found in the common oases of the discord. In by far the greater number of these common cases the 13th (as a compound 6th to the root) is resolved like a suspension on the 5th, which it displaces. In very many cases, too, the dissonance is prepared like a suspension. Instances of the discord in this form are of frequent occurrence in a close where the second inversion of the Tonic has heretofore been employed. Fia. 130.i|c i -i- zs=t: I W- J- A J. J. J. ^^ ^ I 6 5 7 - FlO. 130. KEY C. 6 5 s 7 - |:s l:s * ri di * d' t 1 ni * ri di — f — n se — 1 s f — n — t — di ri — d> di t — di — s 'S 'S 1 n ^M f a 6 8 'S 'S d — 237. The 13th, however, needs no preparation, and both 13th and 7th, which dissonate with one another, may be taken together without preparation as in the following example. But the 13th must in all cases be above the 7th. Fio. 131. I From the close of Menoblbsohh's." The Primrose." * KEY A. :|C ^ J--fr jc± m s d In - .r d — S| — It, s. S| — n 8 If — n — d "l Is, — d — UNPSEPABED CONSTITUENT DI8G0BDS. 115 The 13th is figured according to the simple form of the interval, a 6. But the 6 is placed above the 7 to show the relative position of those intervals in the arrangements of the parts. 238. The discord of the Thirteenth, both in Major and Minor, with the same constitution as that mentioned in § 236, is also resolved as a whole direct upon the chord of the Tonic or upon the Sub-mediant. Neither chord, however, allows of the 13th being regularly resolved. Instead of the dissonance falling a degree as in ordinary resolution it falls a 3rd. With this resolution the discord is always at the unaccented part of the measure or of the beat, and the 13th is invariably in the air. It is precisely of the nature of the indirect anticipation tone described in § 119. See the following examples. Fio. 132. fct P 1^ From the close of Sib J. Benedict's " Old May Day." I , * 3=t -C7- S^ FlQ. 132. KEY A. n d :- Is ;- I- :- I- fi :- ti :- si :— s, :— * d :- 1- :- — :— :— d :- - :- S| :— — :— d, : :- — :— i Fig. 133. From Barney's " The Wind." Lah is Gr. t| .,d :1, sei.,Bei:l| r .,r :d pii .,ni :1| 239. The discord in the form of constitution already shown, with either form of resolution, can be employed in the first inversion and in the third inversion, and the treatment will be the 16 TEXT BOOK OF HARMONY. flame as in the root position. The following excerpts; exhibiting the first inversion of the discord in both Major and Minor with both forms of resolution, will sufBce. Fig. 134. From Pinsuti's " In this hour of softened splendour." i ^ '' — — ^ ■» . ^EEr ■» m m » jL I 4^44 J. ^rrgT'gT^ -^ Fio. 134. 8 t KEY C. :ri.si:ri.ni ri d' :s.s :s .8 8 — :fi.fi:fi.f' ni — :t.t .-t .t di — rl :t.ni:t id' n :n .n :pi .pi :ri.r':r'.r' 86 :se.se:se.se: The two passages agree in the Major and Minor, except that in the Major the D [r'] in air is interpolated between the 13th and the resolution on the Tonic. This interpolated note may be regarded as an indirectly prepared 9th, or as an accented " passing-tone,'" to be presently described. 240. The 7th with either form of resolution of the 13th may be omitted, provided that in the one case the 7th be included when the 13th moves to the 5th, and that in the other the 7th be included in the Dominant before the 13th is taken. See the following examples. From Sir Stekndalb Benneti's " God is a Spirit." KEY £!|7.'9|E .n n.d :n r d :- — .d d.d:t| ti d :- — .8 s.n :s f n :— — .d S|.8|:8| S| d :- ~ UNPBEPABBID QONSTITUENT DISOOltDS. 117 Fio. 136. ^ From Mendelssohn's "Hunting Song." LahisB. - * .di 1 - .se 1 - .ni di - .n 1, - In the case in Fig. 136 the 7th is interrupted in its resolution. In both cases the part having the 7th moves in the interval of 6ths to the part having the 13th, In both cases, too, the discord of the l3th has the appearance of a first inversion of the chord of the Mediant, but the context shows the difBerenoe. 241 A less common form of constitution of the discord is that which includes the 9th. This constituent resolves upwards upon the 3rd (for which it is substituted) in contrary motion to the resolution of the 13th. As the 13th is invariably in the top part the 9th could not resolve on the 8th at the same time as the 13th resolved on the 5th without making consecutive Sths. See the following example. Fig. 137. From H. Leslie's " Te Mariners of England.' p^m^FM ^j^A. 4 4 ^^ tead KEY : d.n — In r d S|.d - 11, ti d n.s - If f n S| - Is, — d 242. A less common resolution of the 13th is that upon the 7th^ • upwards. In this case the 7th is necessarily omitted, and the constitution of the discord is root, 3rd, and 13th, as in the following examp e. ^^^ ^^^ ^^^^ ^^ ^ Macfakben's " The Three Fishers." gi :P=P= '/. '/. ^^. S > I ka^^L^ ^p ::g= I 118 TEXT BOOK OF EABMONY. Fia. 138. Lah is F. * d .r :n .f |t| :d .r li :1|.1| |1| :sei.sei li.t|:d .r In :pi .n li;t|:d .r jn :pt| jr\\ - I- - I- 243. The discord of the Dominant Thirteenth, like tbat of the Eleventh, is made a convenience of to explain combinations that are not obviously founded upon the Dominant. In each of the following examples, at the place marked with An asterisk, is a dissonance of a 7th on the sub-dominant of the scale. From Macpabren's " What went ye out," in St, John the Baptist. T.ah is G. * li :-.l,|l, di :-.filfi li :-.r Id :sei :t, 1. n, d fi :-.r,|r, :ni U I- From Bennett's " Abide with me," in Woman of Samaria. Lah is Gs. * * ^ i ni:di - :t di.,t :d' se:l f :se 1 .,se:l t :d' 1 :ri di.,ri :di n :-.l| r :n 1 :li It has been seen (§ 211) that a Discord of the Seventh on the Sub-dominant chord is unavailable in its root position, and that in a first inversion of the Supertonip Ninth, which gives the same combination (Fig. 115), the dissonance which is 7th to the bass needs preparation. In the example. Fig. 139, the 7th is unpre- pared, and though in Fig. 140 it gets preparation, the contralto part there moves by an augmented interval, a movement that was forbidden in § 146 in progressing from one chord to another. Hotb oases are therefore termed inversions of the Dominant imPBEPABEB CONSTITUENT DIS00BD8. 119 Thirteenth, the root, 3rd, and 5th being omitted. This accounts for the non-preparation of the 7th to the bass (the 13th) in Fig. 139 and for the augmented interval in Fig. 140, Trhich as a 9th to the root is allowed to rise to the 3rd, as seen in § 226 and Fig. 120. 244. Accented Fassing-tones are those which in § 122 were alluded to as occurring simultaneously with the stroke of the chord. They are dissonances which are like suspensions in that they form no part of the chord in which they are introduced, but are unlike them in that they are not prepared and are not restricted to any particular dissonance. They are ornaments of melody rather than of harmony, and correspond to the apjpogia-. twras. There are no definite rules that obtain in regard to the employment of accented passing-tones, but their use often saves a too frequent change of chord, and is a convenience when the unaccented note allows of a chord that is in good harmonic relation to the context. 245. The most common form is that in which the dissonance is approached by degree and proceeds in direct scalewise motion. An example of this has already been incidentally referred to in Fig. 134 a. Two parts may have accented passing-tones simultaneously, provided they are consonant with one another, as in the following example — Fig 141 ♦ From Mendelssohn's " In the forest." I as FlO. 141. KEY D. s d' It :ni.ri d> — n - If :f n — d> - |r' :d'.t d' — 8 - |8 :s d — 120 TEXT BOOK OF HARMONY. or an accented passing-tone may be associated with a suspension, as in the following — Fio. 142-. ^ From Eeay's " The joys of Spring." KEY S. :s ni * -:dMt - 1 s :- - :f n -:s Is - f n :- - :t di - :d' |di - d' di;- - :si d -:n If - 1 d':- - 246. A less common form of the accented passing-tone is that in which the dissonance returns' to the same scale note as that from which it was approached, as in the following example. Fio. 143. From the Chorus of Shepherds in Schubert's Rosamunde. * I KEY A.^C S|.d :t|,d n :si nil .Til. til n. :rii S| :g|.S| S| :si d| :d|.d| d, :d, V V \ I This form is more ofeen employed when there are two parts moving in passing-tones. The tenor and bass in Fig. 127 at the third beat may be considpred as accented passing-tones. 247. A more irregular form is that in which the dissonance is approached by leap, and this is more used than the form just described. The leap may be by any interval, even an augmented interval, but the more common leap is by a 3rd, and when the dissonance is single it is often a note that belongs to the previous chord, as in the following example — Fio. 144. From Sir G. Macparben's " Orpheus with his lute." KEY F. I £ * pz fT m ^d^^( :n s f In :r d :- It, - :d d - Hc- fi:-.fi|fi - :g 1 - if :- r :-.r |r - Ir, :-.ri s,.:- 1- - DNPREPABEB CONSTITUENT DISCORDS. 121 When the dissonance approached by leap is not contained in the previous chord it is often accompanied by another (in Birds or 6ths), thus — Fio. 145. From H. Smart's "Days of Darkness." KEY BIj. 248. But in the following example the dissonance, though single, approached by leap of a 6th, and foreign to the previous chord, ia of great beauty. From the Chorus " Hail, tright abode," Fio. 146. 4c in 'Wagnbii'b Tannhaiiser, i « H ^^ i: i^ I :§= ?=: f ■r^ pezpL - >-El[' !' \ rr.r r - fea ejt^. riv^^^^^ m^ F 8 [O. 146. -In KEY -.,d B. d * -Is f d -id -•.1. 1, -11, n -Id -.,n n -|r -j di — hi -.,1. li -If, ■ n :-.d |n„r:d.,t| d s n s. :-.S||s| :si :-n|f :f :-.d|t, :r :-.S||S| :si d .--Is, IS, : ,d^' Id. : 249. TsE Pedal is the 'last form of dissonance that remains to be noticed. The term originates in organ music : the tonic or the dominant being often held down on the Pedal irrespective! of the chords and progressions that are sounded at the same time on the manuals. This explains the nature of the Pedal. The music above the Pedal tone is quite independent of it, except .that it is in the key of which the pedal is the tonic or the dominant. In a pedal passage the harmony above the pedal tone is therefore complete in itself, having its own bass. The Tonic Pedal is 122 TEXT BOOK OP HABMONT. commonly used, not " only used," as Sir Grore-Oaseley says, " by way of protracting the final cadence." The Dominant Pedal is mostly used somewhere towards the close, often to give point to the re-introduction of the opening or other principal theme ; or, as in a fugue, to intensify the final exposition of the subject. 250. In the application of the Pedal to other than organ music it need not be a sustained tone, but may be a repeated tone, may be interspersed with short rests, and its ootave may be changed. 251. The Pedal may begin with any chord of which it is a constituent. It may terminate in consonance or dissonance with the harmony above it, but the dissonance must, of course, be resolved. Any of the chords or discords that have already been mentioned, and any of the chromatic chords or discords yet to be mentioned, can be used above the Pedal. Sometimes the Pedal will be a constituent of the harmony above it, in which case the Pedal will be the bass ; and sometimes the Pedal will be entirely, foreign to the harmony above it, in which case the part next above the Pedal must act as the bass. See the following example, which immediately precedes the close of the chorus. Fio. 147. From " Hy soul, praise the Lord," in Macfakken's St. John the Baptist, $ ^ ^ ^ m f0 ^^^ J L tr ii Y^ zrr a -H - UNPEBPABJED CONSTITUENT DISGOBBS. 123 Fio. 147. KEY B|7 8| d :d :r f. ni.fi:si :li f d.r :ii :f S| d, :- :— n :— :s r :r n f : t, :l,.t,:d.ti li.s,:l, ti d : 8 :f.s:n f.n:f s 1 : - :d :d d :- — — • n :n :f t,.l,:d.ti:l| s.f :l.s:f d, :- :- - :1 t|.d:r.d s.l:f di :d| r :n •d r t| ;d 8| — t,.l,:s, :l|.si fi S|.f,:ni ri — s.f :pi :f .n r n .r :d r — — :— :d d - .d :d d t. 252, The Tonic pedal is not only used in the close, but also at the very commencement of a composition. Mendelssohn fre- quently opens his part-songs with a passage that has for its bass the k^-note dissonating more or less with the other parts, which cannot be regarded otherwise than as a pedal. The following is an instance : — Fio. 148. =tf ^m From Mendblssohn's " Praise of Spring." ^ — J J^ . /n j. ^ • m ^f^^^^^f^ ! >V ^'^l-l -^Jj.- j .-j'i:^ ... . - Fio. 148. KEY A. Id :-,r n ■ In :-f Is, :-.d d |8| :-.li In :-.f 8 Is :-.f Id :-.d d Id :-.d 8 : Is :-.l ta,: |ta,:-.tai n : In :-.n d : Id :-.d s.f: f.f : d.d: f :-.s n tl :-.t, d r :-.r 8 d :-.d d 253. Though the primary object of the pedal is to confirm the key of which it is the tonic or dominant, the harmony above a tonio pedal may contain brief changes — (1) into the Sub-dominant key 124i TEXT BOOK OF HARMONY. which will convert the pedal momentarily into one on the dominant of that key (see Eig. 148, meas. 3, 4,) ; or (2) into the Dominant key, which will convert the pedal for the time into one on the suh-dominant of that key. Similarly the harmony above a Dominant pedal may contain a brief passage into the Domin'anti key, converting the pedal :into one on the tonic of that key. Also' above the Dominant pedal in the Major may be taken a brief change into the Relative Minor of the Sub-dominant. See the following example : — Fib. 149. From " Hallelujah," in Beethoven's ^0!««< o/,Ofiws, Pig. 149. key C. S It 1 :- de< :1 Id' :r ' |ri :di f :f In ;n 1 .s :1 .t Idi.ri :ni.fei s :s Is :s - I- But in all capes the;ti'anBition: to another key must be foUowsd by harmony that will re-establish the ori^mal key, as in measure 3 of this example, and meas. 4 of Fig. 148. 254. A double pedal is sometimes employed of the tonic and dominant combined, as in the following example : — UNPBEPABEB CONSTITUENT DISGOBDS. 125 Fig. 150. From the opening of Smart's " The Curfew." ^^^ IE =F?^ -^Cr -^ -^ > > f ^ a- i "P- ^ ^ J- JU- FlO. 160. KBT G. d, :- / / I n.f :s n .r :d n :s .s d.d :d d .si :si S| :d .li d.r :n s.f :pi d :n .f s: . d, ;i; iS r : n .f t| : d .r s :s :si :d, s s d .r :n .d li :t|.li S| n r d .ti :d .8| f. :f, .f. n. d> t 1 :s .n f :r .t| d s: — d| :d| di - ', 255. Either the tonic or dominant may be sustained in an upper part as in the lowest part independently of the prevailing harmony, in which case it is called an Invbeted Pedai. Unmis- takable cases may be easily found in Handel's oratorios, such as in the choruses " Ah ! wretched Israel " and " Tune your harps " of his Judas MaccabcBug. It will be more to the purpose to quote here a shorter example of a case which the tyro might fail to recognise. TEXT BOOK OF HABMONY. Fio. 151. From a Te Deiun in F, by H. Shabt. I J ! N N ^3 I ^ ^1 ?2= Fig. ISl. KEV B|j. Is, :- 1| :t| Id :r |S| :- S| :si |S| :8, Id :- d :f |n :r hi :- fi :si Hi :t| The contralto in the second measure can only be accounted for as a short inverted pedal, the first and third chords of the measure being clearly the Sub-dominant and Sub-mediant respectively. n :s If :n.n r - 1- - d - 8| :si Id :d.ti li - Is, f| n. - d :r Id :d.d d - It, - d - d :t| Hi :S|.S| fi - Is, - di - 127 CHAPTER XVI. OHEOMATIO DISCORDS ON SUPBRTONIO, TONIC, AND DOMINANT ROOTS— CHROMATIC CONCORDS— DIS- CORDS OF AUGMENTED SIXTHS— CHROMATIC PASS- ING-TONES. 256. Tlie distinguisTiing features of chrom atic progression have already been sKown in Chapter X, §§ 134, 135. The common cases of the major chord of the Supertonic and of the Supertonic Seventh resolving on the Dominant Seventh and upon inversions of the Tonic were there illustrated in the Major. It will be convenient to resume the subject of chromatics by illustrating that chord and discord in the Minor. They are the same in constitution as in the Majoir, and have the same progressions, but as shown in § 168, where the chord was used transitionally, there are two " altered notes," and as this made the transition somewhat rare, the chromatic use of the chord and discord is also proportionately less common in the Minor than in the Major. The following exhibits, the chord in its root position and the discord in all its positions resolving on the Dominant and on the Tonic in the regular way already shown in the Major in Pigs 58-60, and in the exceptional ways named in the following sections, which apply equally in Major and Minor. Fio. 152. ^ *3 ¥^ — ■=- * i it^i^i i m f^fT 128 TEXT BOOK OF HARMONY. FiQ. 152. Lah. is A. 1 * 2 * 1 :1 II ' :di It :t \:1 |fe :n ) :ni Ire' :i' :sei rl \:li Iti ferey n :re |n di :fe II li :t, Id 7fere2' 6* * * 1 re t t. se:l |1 :1 r :d |r :t, t rl.sjf :fe n :f |r :re di :t Id' :fi \ n :n |n :1 1 :se II :di n :-.r|d :1 fei:ni Ire' :ri 1 :1 11 :t t :di It :rf re :n |fe :se di :ni |?ei :r' 8 d' . 1 :n |fe.t|:n n : n' :d' It :t 1 : 1 :1 11 :se 1 : 1 11 :se If re In :r d t Idi :t 1 feln :n li 6 * n' ;n' |re':n' t :1 |1 :1 t :di II :di se:l |fe :n 257. In the (major) Supertonic Seventh the dissonance may be doubled — (1) when the root is omitted, see meas. 5 ; (2) when the 7th . remains in one part to be the root of the Tonic chord, in which case the other 7th is nnrestricted in its progression. But this is rare in less than five parts. 258. When the 6th moves to the root of the Tonic chord the 7th may leap to the 3rd (see meas. 3), the root of the discord then moves to the 5th of the Tonic. 239. When the 3rd falls to the 7th of the Dominant chord the 7th of the Supertonic may rise by a degree provided that the 5th rise with it by a degree, see meas. 6. This is a very rare exception. 260. The 9th added to the Superfx)nic Seventh makes the discord of the Sttpeetonic Ninth. This 9th is naturally major in the Major and minor in the Minor. But the minor 9th is also used in the Major. The 9th may, as in the Dominant Ninth, be unpreparedi and may resolve upon the root or 3rd of its own chord, or the discord may resolve as a whole upon a Dominant discord or upon the Tonic chord. The direct resolution is the more common. The discord of GHBOMATIG GONGOBDS AND DISGORBS. 129 the Supertonio Ninth in the Major with the direct resolution is exhibited in the folio-wing example in its root position and several inversions. The major 9th, as in the Dominant Ninth, should not be belo-w the 3rd. The discord in the Minor is less used, especially in the root position, where the minor 9th is a very harsh dissonance to the root. In the inversions the root is of course omitted, as in other cases. i Fig. 153. J ,^J i J L f a Vj ^ .4 i a m tim ^ rm AA±A. i -JS_t :lu zi: ^ ■■¥=^ m 1. >^' ', i J- J -P2= f-r Fi a. 153. *1 n' :r' KBY C :di 2* di :t :d' 3* pi' * 4 ri : :s fe :f :n 1 :s s.n 1 s :fe s — : :di di :t :di n' :r' di di - :di di t : :d S7 r :s :l.s fe :f n.s fe '•EJ s :1 97teKo s — : d< n di d.t,; 5* fe d' ■Jl' -.ri:di.ni s :n .s - .t :di s, :d 6* n' fe 1 d :n' :n :s :d 7* ni fe d> r 130 TEXT BOOK OF HARMONY. 261. When the discord is resolved upon the Tonic the minor 9th in the Minor or the major 9th in the Major can only be resolved like the 7th by remaining to be a constituent of the next chord. See meas. 3, 5, and 7 of last example. But it is similarly resolved when it remains to be the 13th of a Dominant discord. See the following example :— ; Fio. 164. From " The Hunt's up," iu Sir G. Maoparren's May Day. * KEY C. n\ n' ni — — r' di — fe f — — f n — di t — — t di — 1 s — — S| d — 262. The minor 9th on the Supertonic, which is itself a chromatic note, is more used in the Major than the major 9th, especially when the discord is in an inversion ; the inversion of the discord of a minor 9th produces, as has been seen in § 224, a chord of the Diminished Seventh, which is only "partially" dissonant. The minor 9th on the Supertonic, when employed in the Major, is resolved upon the Tonic chord by rising a chromatic semitone. See the following example, meas. 5. Fio. 155.* .1 I I 1 ,1 2 I * 3 4 I * , fet ri- yf ' rVrr'rr -i=P= ^ I I J I I Be K^ ^^m $ qZG =t=^ ^ -£±1 -3=iz rt*PT-#r- =P2= r I I III -m- -m- -»* \ — m 1 *■ 'M -ri- ict S m ~-rr CHBOMATIO OONCOBDS AND BISCOBDS. 131 1 lO. 155. KEY C. * na':r' Ir' :n' 2 di -11 :- 3 S - |di :t 4 * di .— I-] :s fe :— If :— n — |na:r S d.r|n :f s :fe|s / :d> di :-|di :t d< -|di :t di -|-:s s il Is ( :d n < :r' r >* na' -Is -jr." :di 1 6 S 8 |fe:f inaFE * * fe|s :di n 7 di : -|-:r -It :- n :re |n ] m.pEd di:-|-|| :1 1 -Is :s n re In :re n : -If :- n — 1 — :ri di -id' :di di 1 Is :fe s : -Is :- s — 1 — :f nL fe »FE -Is :n d m -|-:li 'FEc "n^FI f- -Is, :- d — I — 263. When as in meas. 4 and 6 the minor 9th resolving upon the 3rd of the Tonic is also approached by the 3rd of the Tonic it is customary to write the 9th as a chromatic semitone above the root. The substitution of Dj( in the bass of meas. 4 and in the contralto of meas. 6 for El? [re for na] is termed an Enharmonic change. The change transforms the whole chord in appearance, and it looks like the Supertonic Ninth of the relative minor, but the resolution shows that the apparent 3rd of a Ninth in the Minor is the 9th in the Major written with a conveniently false notation. 264. The discord which is used to efEeot a transition. to the Sub- dominant key (§ 137), viz., the Tonic Seventh, is also employed with chromatic progression within the key. The 7th (which is minor) is the altered note in the Major, but the 3rd is the altered note in the Minor. S lez: Ig-- ta d taD S n de> 1 265. The Tonic Seventh resolves upon the Discords of the Dominant or Supertonic. The 7th in other cases always falls to the note below. In this case it cannot do so when the resolution is upon the Dominant discord. The 7th of the Tonic therefore rises to the 3rd of the Dominant, and the 3rd rises to the 7th of the Dominant, as in the following example :— 132 TEXT BOOK OF HARMONY. fio. 156. i i: §§ U^r^^^UM -» — li- ^ i^rr i-f-r !•- "P -^ ¥■ J - -,,^-g-ir^i^,-;^ J-J-*U §^ p ' I — ^ — \ — I— T- FiG. 156. Lah is A. ( 1 |di :dei n |n :n di 11 :s '\ 1 111 :li 74.i ri :di 11 :t n :n Is :se se :1 |n' :n' t| :d |de:r li^Lb 1 :di II :t 1 :n |n :n pi' id" |de':r' d :1 Is :se * n :1 Is :se n :d jde :r di :1 II :t 1 :d [n :n Examples of this resolution in the Major are shown in Fig, 158 measures 1 and 4. 296. "When the resolution of the Tonic Seventh is upon the Supertonio discord the 7th faUs, and the 3rd rises in the ordinary ' way, but by a whole tone, to the 3rd of the Supertonic. See this resolution of the discord in the Minor in Fig. 157, and in the Major in Kg. 158, meas. 2. Fio. 157. 1 « 2 ^^m 4* q=^ ^^S :gi— r -W I I iA^ ^u^ M j^^^^^^^mm I I Fio. 157. key C. 1 4c 2 * 1 :1 Is :fe II :1 |d :de In :s III :li re :n |n :t| fe:n |1 :1 t| :d |de :re n :-|l :1 d :t| |n :n 1 :se|l :di n :-|d :1 4* 1 :1 Idi :t n :1 11 :se de':re'|n' :r' s :fe |n :n CHROMATIO CONCORDS AND DISCORDS. 133 Fio. 158. 1 , * 2 . * 3 * 4 * J i j4-^.^ ;j j, j J i m m i ?B=?C ^ I I Fig. li 1 * |d> :ta )8. SET C. 2 * t :d> |ta:l 3 * s :1 Is :fe 4 * f :n In :r In :n f :s \n :fe s :d Id :d t| :d |ta,:t, Is :s 8 :d> |di :di d< :1 |ta:l 8 :s Is :f Id :d taD r :n Id :r t»D n :f in :na t«D4 r :d |si :si 267. The 3rd of the Tonic discord may fall a chromatic semitone to the minor 9th of the Supertonio as in meas. 3 of Fig. 158, and more exceptionally the 3rd may fall a whole tone to the 5th of the Dominant discord when the 5th falls with it to the 7th of the Dominant, as in the close of Fig 158, where the discord is exhibited with the root omitted. The 7th in the Tonic discord even with the root omitted cannot be doubled as in the cases of the Dominant and Supertonic Serenth. 268. The 9th added to the Tonic Seventh makes the discord of the ToNio Ninth. In both Major and Minor the 9th ux this discord is naturally Major, and the 9th maybe resolved, like the Dominant Ninth, upon the root or 3rd of its own chord. Whether the discord be resolved on the Dominant or, Supertonio discords the major 9th of the Tonic receives but stationary resolution-^it remains to be the 5th of the Dominant (see Fig. 159, meas. 1) or the root of the Supertonic. 269. The minor 9th on the Tonic though not a natural note in either Major or Minor is more used, doubtless because the discord of the Tonic Minor Ninth inverted becoming, as in the other cases, a Diminished Seventh is less dissonant. The miuM: 9th on the Tonic in resolving upon the Dominant discord rises a chromatic semitone, as in Fig. 159, meas. 2, 4 ; and in resolving upon the iSupertonio discord either rises a chromatic semitone, or, as in meas. 3, falls a (diatonic) sranitone. The progression of the several notes in each case is the same in all the other inversions. 134 TBXT BOOK OF HARMONY. Fia. 159. 1 « 2 ^^^s^^^^P I I I I J-iJ-^-J- -»-# j^ AilUtLfeUj: SI ^ I T P : Fh«=#F 3^^ -fe=M'- r"r I 1 ' I Fio. 159. LahisA. 1 * 1 It :t 2 * 1 :1 |ta:t 3 * 1 :t |ta:l i * se:l |ta:t 1 Is :se 1 :n |n :n n :se |s :fe f :n.l|s :se di |dei:ri di :1 Is :se 1 :piI IrI :rei ri :di |dei:ri 1 11 :n f :d |de:r d :n.r|de :d t| :d.l||n :n 270. The minor 9th of the Tonic in the Major is sometimes written, as in the case of the minor 9th on the Supertonic, as a chromatic semitone above the root. This false notation of the 9th, like that in the other case, transforms the appearance of the discord, which looks like a tome minor ninth of the relative Minor. See the following excerpt, where Qfl is written in the bass for AJ? [de for ra]. Fio. 160. From J. Barney's "A "Wife's Song." #t-j-l i .. . 1 ^ -FT -j pt^.' i^ -^-i-H 1 rrrr 1 1 J 1 1 -p- ?-■ ^ i- ^^ J. * -m — FlO. 160. KEY G. 4- * -t :i= ' :r r :de |r :de r — In :-.n s -.f In :r d ):li s, :si Is, :si s. — jta, :-.ta. ti -.t,|t. :t. d i:f f :n If :n f - Is :-.s f -.lis :f n [ d t, :le, It, :le, t, — |de :-.de r s. Is, :si 1, CHROMATIG CONCORDS AND DISCORDS. 135 Sometimes even the minor 7th of the discord is written as a sharp 6th to the root. Hence the 3rd and 5th chords would be claimed by theorists as examples of the Tonic Minor Ninth. 271 . To complete the series of discords founded on the Supertonio and Tonic roots it should be stated that the minor and major 13th can be taken on the Supertonic in both the Major and Minor, the minor 13th on the Tonic in both Major and Minor, and also the major 13th op the Tonic in the Major only. AH these are, how- ever, extremely rare, and many of the quotations from musical works that are adduced as examples are quite as intelligibly to be accx)unted for in other ways. The following examples wiU suffice. The example Eig. 161 illustrates the Supertonic Major Thirteenth, and Fig. 162 the Tonic Minor Thirteenth. Fig. 161. From Sir J. Benedict's "The wreath." Fio. S 161. * t KEY S. :-.l It :-.l n na :-.nalna :-.pia s fe :-.fe |fe :-.fe d d :-.d id :-.d :- I Fig. 162. m ^^ -rtr From Sir Cteo. Macfakren's Chriatmaa. a =g=^ =f -^ =F2= i i I =g= 1B6 TEXT BOOK OF SABMONY. Fio. * n 162. KEY ( - In :- 3. f :- |f d - Id :- r :- |r la - Ila.- la:- Is d - Id :- t,:- It laD :- n - 1- :n ;- d - 1- :d :- la - 1- :1a :- d - 1- :d f :s Is d :r 1 :t d :d 272. It is next in order to notice chords and discords which in the Minor are natural harmonies, but -which in the Major become chromatio harmonies. It ■will be convenient to foUow with the discords first. 273. The minor 9th on the Dominant can be used in the Major in the same way that the major 9th was used and with the same resolutions that were described in §§ 222, 226, 226, 227. Each of the major 9ths in Mgs. 118 and 121 can be made minor, and no futher illustration wiU. be needed here. 274. The minor 13th on the Dominant can also be used in the Major. It has, however, but a very hmited use, and has a different resolution from the major 13th. The minor 13th cannot resolve on the 5th within the chord, but the discord resolves as a whole direct on the Tonic chord, and the minor 13th rises to the 3rd of the Tonic. On account of this upward resolution the minor 13th is habitually written as an augmented Sth to the root. See the following example : — Fio. 163. 4 mt rrom Mendelssohn's " Happy lover." I G. s :- d :- s :- n :- - It, If :n :ri |si :- :si Ir :- :f - :ti n :- S| :- n :- d :- It may be noted that when the 7th is included, as is usual, a doubled 3rd is a necessity in the Tonic chord. OHBOMATIG 00NG01iD3 AND DISCORDS. 137 275. The chromatic concords in the Major that remain to be noticed are all formed from the chords peculiar to the Minor. 276. The Sub-dominant-may have its 3rd chromatically altered to a minor 3rd, and may be used in aU the positions and places of the major chord. It is principally employed for effect in approach to a close, sometimes following the chord in its major form, and sometimes approached direct from some other chord by which the chromatic 3rd of the Sub-dominant is either approached by a diatonic semitone or by a leap. The Sub-dominant in the close of either Fig. 28 or 29 could be made minor without other alteration. The chromatic minor chord is also used in a Flagal cadence. See the following : — I Fig. 164. Il From Sir John Goss' anthem, " If we believe." ^ m ^ -H 1- -y g'-^— * 0- =e±: "P — P" ! I ggj- w I I d=t: I I I I I -Ji=3t=j±. 3± M. -^=X±i -m- :|=t: -tTt Fio. 164. KEY D. * :d.d la -.la:la.la la :s :f — n r n :— — :d.d d -.d :d .d d :d :d — d — d :- — :d.d f -.f :f .f d :d :f »F : d — j- :d d : d — 1- :si la, : n d — |- :n na : |na. Id I la, |na Id jla. .d' di d la, f f f. I- :d' :d :1a, :f :d I 280. A chromatic concord in both Major and Minor is formed on the flattened supertonic. The 5th is in the Major also a chromatio note. The chord is nsed in the root position and fii'st inversion. Its progression is not restricted to any particular chord, but it mostly proceeds to the Dominant or Tonic. The following example of the chord in both its positions in Major is very striking. A Dominant pedal passage immediately precedes the chromatio chord. i Fig. 167. From Sir Geo. Macfakben's " What went ye St. John the £aptist. out," ^ JSlAJS^V •pgr Wc ^=S -Ui^ I ! ^M ^e =s=p; ^^ FlO. 167. KET C f :- I- la:- I— ra':— | — f :-|- i»EA4 |d> :ni In :1 II :di Is :b rai Ifi :- ri.t:di.ri|f :- n la |la:- s.f :n.r |r :— d ra' |ra': - .ri.ri:di.t|t :- d> f .nalra :d t,.r :n.f Ir :— n i«RA 140 TUXT BOOK OF HARMONY. 281. This chord in its first inversion as it first appears in the previous example, or as in the following example in Miaor, is often called the chord of the Neapolitan Sixth. The passages a and h show two resolntionss Fig. 168. a B^^SE ff From the " Dies Irse " of Mozart's Eeqtdem Mast. =P=P=P2= 1 V- I I A ^P^ :^ jL iJ. .^ A. ./ W==W=-X^ t=F= =t F ta G. 168. -11 T,ah f -Ife — f -Id' — r TA -Ire 5 — 1 :se| n :n I di :t I n :n I * * |ri :-.ri ri :di It — 1 If :-.f n ;n |n — n ta|ta:-.l se:l 11 SB 1 r |r :r n :1 |n — li 282. The same chord as the last in the Minor is occasionally used in the relative Major in which the root stands on the flat seventh of the scale. The foUo-wing, in which the chromatic chord stands between the Tonic and Dominant Seventh, is a clear instance. Fig. 169. From Sir Geo. Maofakben's " 'Welcome all," Christmas. w 3zE3E :t 5= — r- =t=t 1^ :Ez3: -^-P— ^- 6^ J. ^ -•: ■ J J. -^ Fig. 169. key C. n' :- s :- di :- d' :- fi ; ta ; ta : TJ - I- r f :- t :- r' :- s :- ^EHEJ GHBOMATIO 00N00BD8 AND BI8G0BD8. 141 :- - r' :- - Is' - - ni - 1 :- -■ di :- - It - - di - 1 :- fi s' :- - in - - ml - 1 :- - s :- - Is - - d - 1 Id' :- |pi' id' 283. Even the chord of the Tonic in the Major ia chromatically altered to a minor chord. But it must he in a context that is characteristic of the original key to prevent the effect of a change into the " Minor of the same Tonic." An example may be seen in Fig. 173, meas. 3. Discords of the Augmented Sixth. 284. A chromatic discord remains to be noticed which diners in its formation from all others. The element of dissonance in it is an augmented 6th, an interval that contains the same number of semitones as a minor 7th. The most common instances of such a Discord are formed upon the minor sLsth of the scale, a note which is natural in the minor, but chromatic in the major. The prime constituents of the combination may be said to be the two notes fOTming the interval of the augmented 6th and the 3rd to the lower note of that interval. Other notes may be added, but these define the chord. The two notes of the augmented interval may be taken without any preparation, but are mostly both approached by step, or one is prepared, as in the second and third cases in the next example. The regular resolution of the dissonant interval is for the upper to rise a semitone, and the lower to fall a semitone, producing an octave in the next chord. In the Minor the discord constituted, as shown above, is frequently used in a Dominant cadence, as in the second case of the following example. Js>- -SS.Z re' fe' 1 d' f la Fig. 170 142 TEXT BOOK OF HARMONY. Fio. 170. Hi di It :1 Lah is A. * se :1 |ri ire' 3 :fi |ni :di 1 :*' |di :t T ) n |n :re n :n |1 :1 se:se|l :n re :re |n :r d \ 1 It :t t :di 11 :1 t :t |di :i> di :1 11 :se 1 f 1 Is .-f 4roJ? n :d If :f n :n.r|d :l.s fe :f In :n li In this form, of constitution, wMch is seen also in the Major in the first case of the next example, the discord is known as an Italiait Sixth. The chord of resolution may be the Dominant, or the second inversion of the Tonic. 285. The next common form of the discord has a perfect 5th as well as a 3rd to the lower note of the augmented interval, and thus constituted the discord is termed a Q-EasiAM' Sixth. In this form it cannot resolve on the Dominant, as consecutive Sths would ensue with the bass. It is resolved upon the second inversion of the Tonic, and is in frequent use in approach to a tonic close, as in the third case of both the previous and following examples. Fi8. 171 :|s I * ^ i=t ^zzitzzM: i ir=r^ -ri r Jr - J- J -J. J- J- M- ^- J. ^ ^ eI ic4z^_ r-r Fio. 171. KEY C. 4: (is :s \|n :r.n )|di :ri ' Id' :t di :di |r' :ri f :fe|s :fe d' :di It :di 1 :1a Is :1a n' :r' s :— di :t is :s |s :n |di :di "LA ««LA :-|n :d di :di |di :t f :fe Is :f d' :pia' In' :r' li :lai |si :si The 5th, which in the Major is the flattened third of the scale [na] is sometimes written a sharpened second [re]. 286. The least common and somewhat harsh form of the discord has a (pluperfect) 4th to the lower note of the augmented interval, and thus constituted the discord is termed a Fbench Sixth. It can resolve on the Dominant, as in the first case of Fig. 170, or on OSROMATIG CONCORDS AND DISCORDS. 143 the second inversion of the Tonic, as in the the second case of Fig. 171. 267. It is often asked " what is the root of these Augmented Sixths ? " but no entirely satisfactory answer has yet been given. Some have considered that the root is a 3rd below the bass, and that the upper note of the augmented interval is the raised or sharpened octave to that root, but this does not account for either the 4th to the bass in the French form or the 5th in the German form. In the German form there is a complete major chord independently of the augmented 6th to the bass, and on the whole it would be more satisfactory to regard the lowest note of the combination as the root. But modern theorists ascribe the combination to two roots. The lowest note is said to be the minor 9th of the Dominant, and all the upper notes are said to belong to the chromatic chord or discord of the Supertonio. This accounts for the inversion of the Supertonic Ninth in Fig 170, meas. 4 not resolving directly in the way here- tofore noticed. 288. The cases already noticed are samples of the common resolution of the Augmented Sixth — ^the two notes of the augmented interval move sunultaneously. But occasionally while one note falls or rises a chromatic semitone the other remains to be a con- stituent of the next chord or discord. See the following excerpt : — Fig. 172. From the "Lacrymosa" of Moz^ri' a Sequiem Mass, * l^rr^pp^ ^^i 4uyMMMy -r- ^1 mz F 1 [Q. 172. -Is X btF. -Ife:- * -Ife:-:- fe -:-|s -:-|l:- -|s - - na - -|na - - |na:- - |na:- ;- r -:-|r -:-lr:- -|S| - - d' - -Id' - -|d' :- -Id' :-:- di -:-lt -:-|t:- -Id' - - fe - -Is - -lla:- -|la:-:- 1 -:-|s -:-|f:- -In - -- 289. The chord of the Augmented Sixth is usually found, as in the preceding examples, in its original position. Inversions of the combination are occasionally met with. The inversion which M4 TEXT BOOK OF HARMONY. has the upper note of the augmented interval in the bass is that which is most seldom used — it is the inversion that is in some treatises entirely forbidden. In the best instances of the use of this inversion the bass and the part having the other note of the augmented interval proceed in contrary motion, and often the original position of the discord is in the context, as in the following example : — Fio. 173. From PiNSUTi's "The Crusadera." i^s=^^^ i^ ICfc r ¥ 4 ^- irpN ■ _ -&- :?3i: m: ^ -'I ^-. m ZZ2Z T3~ -E; \ Fig. 173. key F. d Id :d li llaiilai d Id :d fei'.fei fi \i -If I- -I- &-'- d d :- S| fe,:- na na:— S| la,:- 290. A discord of the Augmented Sixth formed on the flat- tened second of the scale is also occasionally used, the leading note being the upper note of the augmented interval; The same variations in the entire constitution of the discord occur as in that of the other Augmented Sixth. In this case the lowest note is OHBOMATIO G0NG0BB8 AND DISC0BD8. 145 said to be the minor 9th of the Tonio, and the upper notes are said to belong to the Dominant discord. See the following example — Fio. 174. From "Woe unto ub" in Sir M. Costa's Mi. I I *' i g^ dfciiz :j&- l 1- itzt f=rr=F^ / ! I ^ I I J-- -J> ! ^ y£2~ _ca_ 3=P= =!^=t 5t=ti =tz=t: Fio. 174. key I s :-.s|d> :d> PI :-.n \n :n -dMs :s -.did :d t :-|- f :-|- s :-|- ra : — | f :-.f If :f n :-!- - tl :-.t, |t| :t, d :-|- ^ s :-.s Is :s s :-|- — ra :-,ra|ra :ra d :-|- — Chromatic FASsiNG-TOD'iis. 291. All the chromatic notes thus far noticed have formed constituents of the chord or discord, but chromatic notes are often used that form no part of the chord or discord in which they are introduced. These are called OnaoMATio Passkg-tones. Like the other passing-tones they may occur after the chord is struck as unaccented passing-tones, or they may occur simultaneously with the stroke of the chord as accented passing-tones. They may occur singly or in couples according to all the rules for the diatonic passing-tones, which apply equally to the chromatic passing-tones. The sharpened notes of the third and fifth chords of Fig. ICO may be taken as examples of chromatic passing-tones. The only additional rules required are the foUowiag : — 292. "Wlien the root, 5th, or 7th of a chord is approached by a passing-tone taken by leap the passing-tone must be a semitone below those respectiye chord constituents. -^, J J,J- I J„ I '^Ttrf ^a 146 TEXT BOOK OF HARMONY. Fio. 176. LahisA. * re .n d 1 n n' t, n se 1 n d * de'.r' :n' n se de'.r' :n' 1 :1 1 :1 f :d :se .1 :f :1 .•r d' t 1 PI - .r d 1 se 1 n n li Chromatic passing-tones do not produce any false relation to the constituents of the previous and following chords. 293. If a chromatic passing-tone be succeeded by a diatonic passing-tone the passage must proceed in semitones till a constituent of a chord or discord be reached, as at a, not as at h. Fio. 176.' a ^^s^ma:^ . ^ ^ m d^—^ i :?2^ f^ a I d' PI '10. r t.ta re. n 1.1a ET C s r — : — b d' PI t.ta 1 s :— r ;— — s d ~~' s t. , . s d _ s :— ti :- I 294 A chromatic passing-tone when moving upyrards, may be taken at the same time as the diatonic note of the same degree, and the two notes may be even at the distance of only the semitone between the inflected note and the diatonic note. See the following example : — OHBOMATIO C0NG0BD8 AND DISCORDS. 147 Fio. 177. ^ J, n,^j jm From Sir A. Sullivan's " Joy to the Victors." KEY C. 3|C ^ S d s I ^ s 1 .8 |fe :8 s f f .f If :f n t t.t It :t di r S|.S||r :s, d 295. The minor sixth and the major seventh of the Minor scale may succeed each other as passing-tones, either ascending or descending, especially in the chord of the Dominant, as in the f oUowing e3[ample : — Fig. 178. P ^^^^=1,4*^ i ^ m ^ ^L. #f ^y^y r Fio. 178. LahisA. t .di |r' .ni se .1 n r' t :li sei.f : :n n : :d' t : :1 n : n" .r' |d' — m - II f< .sei t r se 148 CHAPTER XVII. TRANSITION TO UNEELATED KEYS. 296. The essentials of a transition to a new key and the means by which changes are made to closely related keys hare been shown in Chsipters X and XI. The means by which changes are made into more distant keys may now be mentioned in conclusion, 297.' Any major chord, diatonic or chromatic, may be regarded as the Tonic or Dominant of any other key. Thus the Dominant of a Minor key may become the Tonic of a Major [^Mmaj become D] as in the following example : — i Fig. 179, From No. 20 of Br. Stainbr's St. Mary Magdalen. ■I* iiS- 55: fe k $ei: m i^=ipi ixpni^ 1 — T -r- I m^^M ^iSL. V33L '^^^^ ip~bp~ -fe&- Fio. 179. LaH is G| D|.t.in.l.r, d :r m di :(?! 4i i\- ni :- ri :- d' : 1 n, :1, ™in -.m f -fe %■- s : — s :— n : d :1, t|8 -.s f -fe 8 '. — di :- t :- di : li :fi ''id :ta\ l\ '.la\ «i :— s :— S| :— d : • The transition in this example is from GS minor to D( major, hut the notation of Ej^ is used for Dt for conTenisnce. The small notes show the instrumental interlude. TRANSITION TO UNRELATED KEYS. 149 or a chromatic chord, as, for instance, the minor Sub-mediant of the Major key, may be taken for the Tonic in another key as in the next example. Fio. 180. Fiom No. 9 of Ba. Stainek's St. Maty Magdalen. $ 3= I *= i^ t=:t T -&rr w^- ;=if^=s rx I I - P j g - |t>,Q l| I I 1 iA=A SI ^- zai ^ ^^=P^ "m Fio. 180. kby F. r.8.d.f.I>b. {\l r :— — d : dn n d.,d:f .n r d. ^:d d :- t| S| : ••.d d d.,d:d.d ti d. i:f f :— — n : nag s \^.;!^ :1 .s f n. (:ri 8| :— — becomea J r f , \ becomes ; r t, hi t' *,r, / 'ila. Roots. \ S / \ "M / I "M, / I s 299. As each of these can be treated as belonging to a Tonic, Dominant, or Supertonio root a transition can be made into twelve different Major keys and into the same number of Minor 160 TEXT BOOK OF 3ABM0N7. keys. The following is an instance of a change of key effected by the enharmonic alteration of the chord of the Diminished Seventh. Fio. 182. D minor. From No. 13 of Sir M. Costa's SU. Fio. 182. Lah is D. E.t.m.l.r.s. t :- t :— 1 :- 1 ; — «la:- — : — s ; — f :- f :- f :- f ; — "f :- — : — n :— r :— r :— r :— r : — : der :— — : — n :— r sei :— sei :— li :- li :1. I'lt, :- ti :t, d :— Here the last inversion of the Tonic minor ninth in D Minor be- comes the first inversion of the Dominant minor ninth in B Major. 300. The interval of the augmented 6th it was seen in § 284 was practically the same As a minor 7th, and the German form of ihe chord of the Augmented Sixth has practically the same intervals as a Dominant Seventh. This discord can therefore be treated as the other, and a change efEeoted into a new key that will have five sharps more in the signature. Every note of the original Dominant Seventh takes a different progression, and the resolution, especially of the interval of the 7th, which becomes the augmented 6th and moves a chromatic semitone each way into the octave, contributes to an effect that is exceedingly fine. The following excellent illustration of this change will form an appropriate conclusion to this treatise. The chord marked * is at once the Dominant Seventh of the key of D|7 and the Augmented Sixth on the minor sixth of C. Fig. 183. From No. 6, Part II of Gounod's JRedemptim. TRANSITION TO UNBBLATBD KEYS. 151 Pio 1S3. KEY Db. n> :n' .,n'|n'.ni:di .ni 8> — Ir' s :s .,s |s .s :n .8 t — It n' di :n' .,ni|n'.n':d' :d> .,di|di.di:s .n' .d' 8' r' — Ir' It s d :s .,s Is .8 :n :d .,d Id .d :d .8 .d t 8 — Is IS ..n' .,d' ■.n' .,d' .,8 .,8 :|EC.t.m.l.T.B. f'fe' td' "fe' rl|Ta' td' "la - I- - I- - i- d' In' :s' 8 Id' :n' d' 8 In' Id' :8' :n' n Is :d' : .,r' n' : : .,t d' : : .,r' : .,t n' : d' : : .,8 : .,8 s : 8 : .,fe' .4' .,fe; .,na' .,1a d' 8' n' I- I- I— n' :- ir' — d' :- 1- : d' :— It — d' :— 1- : n' :- If d' :- ir' — n') , d'J ■" 1- : 8 :- Is — lil- 1- : 1S3 GRADED EXERCISES. CHAPTEE I. 1. (a) State aboye each interral formed by the following two parts, its name and quality, as major, minor, perfect, or imperfect ; (6) and under each interval specify the name and qlialitv of the inversion. 3^S r8=t f^^TTTT . Q J | ,^. I ! J nJ— J— J I T'! I ! n r r Ms :n |r :-|-:d |1 : :t |1 :s If :— 11 :- 1 (\a :— I— :t, 111 :— |— :t| d :- if :-|r :n |r :d ] I KKT C. II r' :- It :- t, :s |-:f -:d' |fi :- n :— II :t — :n" |r' :d" d' :s |f :n -:t |di :- r :— Id :— CHAPTEE II. 2. Place Eoman figures (I for Tonic, V for Dominant, IV for Sub- dominant) [capital letters D, S, F] under each note of the scale to show in which chord or chords it is found. ^^^^^M I* "■'■>' » 164 TEXT BOOK OF HARMONT. CHAPTEE m. ? 23-34. 3. Fill in the Contralto and Tenor parts, using only the Tonic and Dominant chords. j=i fefeE -it — *- -ri- m rrrrTT pzqc ipzz T — r T-"-r I KEY C. s :di ri :ni di -.r' In' :— Is :di t :d' d :d si :d d :si |d :— id :d s :d § S7. 4. Fill in the inner parts, using only the Tonic, Dominant, and Sub' dominant chords. !l di :t Id' :- d :si |d :— i =t I ^^i^feS^ :t=t m^ *=p: f^^=^ -ipf:- — i — r KEY C. n :n If :n d :d f :d r I W n :r d :s n :— d :- s :s d :d 1 :s f :d d' :t d :si d' :- d :- § 38-40. 6. Fill in the inner parts, using only the same chords as in £z. 4. i fa=^: t=X » ?^ I I KEY G. n :r n :s d :s, d :d f :r n :— d :1, si :d d :t| d :- fi :si d| :— di :fi d| :d, fi :si d, :- GRADED EXERCISES. 155 _6. Write Soprano, Contralto, and Tenor parte to the following Basa, the whole making chords of whiqh the basa notes shall be the roots. mi -i»— (t 33= t=M:. S KET C. ||d :d |s :d |f -.a |d :-|d> :f |s :d |f :s |d CHAPTER rv. 7. Fill in the inner parts, using Dominant Seventh [7S] twice. f^rjPUZi-^ mi m mh t=m- =PC=p: =pc=P= ^^ 1 — T KBT C. -I — r |8 :n 1 :8 Is :f n :— Is :d' r' :'n' |f' :r' d' :— Id :d f :d Id :si d :-|d :d s :d-|f :s d :— 8. "Write the three upper parts, Soprano, Contralto, and Tenor, to the following Bass of chords in their root positions, introducing the 7th into the Dominant in each cadence. KEY Ejj. |:d |f, :d Id :s, |d :- |- :d [s :d |f :8 |d :-|-| CHAPTER V. 9. Give in order the names of the cadences, as Tonic [D], Dominant [S], Plagal, or Sub-dominant [F] in Fig. 28. .156 TEXT BOOK OF HABMONT. CHAPTEE VI. §§ 55-59. r. 10. Figure the Basa of Figs. 28, 29, 30, 31. The root positions, ex- cept in such a case as that named in § 64, may be left unfigured. Place also against each inverted chord Bomaa figures, as in Ex. 2, to show ■whether the chord is Tonic, Dominant, or Sub-dominant. [Write under the Bass of Pigs. 28, 29, 30, 31, the names of the chords in capital letters, and tiieir positions in small italic letters, as Jib, Sc, &c. The a position may be understood.] {§ 61, 62. 11. Fill in the inner ports, and figure * the Bass [name the chords] as in Ex. 10. I li*Ei -J — ^- ■S=Mz ^—' 1- zizzt -it—»- «fe t-t-t-u^^=m =1 KEY A. In :s |d :n, f :n |r :d fi :d Jti :d tl :- id :r n :f Hi :t, d :-- S| :- Id :t, d :1, If, :8, d, :- 12. Fill in the inner parts. 1*=^ — t" — t- -J- =^=lq =3= 4 ^= =i^=if^ =^ myrp — -*- -• ■ =— Yp ■■ ■-_■■ ^ -|S— — f— =fq fF= • a— f A L±z- :^ 4= 1 =F=y -1 — -1— ■ ' — *! — — KEY Id :si |d| :pi, Bb li :r In :d fi :tj |d| :n, t, :- Id :f s, :- Id :1, r :n |f :r t| :d jf, :si d :- di :- * This is to be nnderatood as required in all future ezerciBt». GRADED EXERCISES. 157 . }?• Y^^ *^® t'l^o iiPPer parts to the following Bass, usine the chords indicated. 6 B r i I 5 6 7 m KEY E. pd :s |n :f |1, :d Is, :- |n :t| Id in. If, :s, id :-| D S D4 P F4 D S — DJ 'S4 D D4 F 'S D - §§ 63, 64. 14. Fill in the inner pEurts. Mif~r~7 ^^ ?3= :P=?t ^Ef^ KET G. In :r s :f In :r n :-|f :r . n :d Id :t, Id :s, n, :f, Is, :8, d :-|l, :t, d :ni |si :s. 63, 64, 70. 15. Fill in the inner parts. i fe 1^ ^ rstiTt. N — *— a^- p^g =«»=F S! I * I * KET Af;. |n :r Id :t, |d :n Id :ti |d :8| In, :d, n :r |d :r 8, :— |n, :8| n :f |n :r d :1, Is, :8, d :- d :- 158 TEXT BOOK OF HARMONY. $ 65. 16. Add the three upper parts to the following Bass. ?a^ mz -m ■- *=t: f- 6 6 4 3 KE7 C. :d If :n |r :d |8 D F Di 'Sc D S l-:d |r :n |f :s Id :-|-| — D S« D4 F 'S n 65, 69, 71. 17. Fill in the inner parte. i I*ZZt gg .T"r"r w^ .izzp_ :|=t: KBT Ejj. In :d r :n |f :1 s :-|l :f s :d> |di :t d> Id :n t, :d 11, :f, d :-lf :r n :d |g| :si d 18. Harmonise the following air for S.C.T.B., using the second inver- sion of Dominant Seventh ['Scl the second inversion of Dominant [So], and the second inversion of Tonic [Do]. Malce a Sub-dominant cadence for the first section. i q=4: =t= J L I I ■I^L,g_ J L -^— *- itzt zi: =i=*==^ KEY C. I Is :1 |t :di |ri :n' |fi :- |n' :r' |di id' |d' :t |di :-|| Note. — The rules in §§ 35 and 36 should now be observed, and followed In all future exercises. GBABED EXEBOISEa. 159 § 66. 19. Add the three upper parts to the following Bass. s ^ f - =1=1; ■i=P- t=t: 6 6 4 3 =t:t e 8 4 3 KBT F. =p=i; =P=t=::t =»=:p:tt '. • I i s "H Id :r |n :t, |d :r |d :-|l, :t| Id :r |n :f Is :- i D 8e D4 'SA D Sc , D — F4 S« D 'Sc Di F S — }|n :r |d :n, |1, :f, Id :- |d :d Id :1, |S| ;s, Id :-l| D4 '&! D D4 F4 F Fc D D Fc D F4 D<; 'S D — f 67. 20. Fill in the inner parts. P tP* 7J- IfcE a ?=t= =p — 0- 1 — r ?2-^ t I rt%3= -:^ — u— -^ — U — *- =^ —^ -r — 1 - 1 -i -»- -r p r, • — m — J- ~1 ^ # f 1 — 1 — -t=d T — p- T- =^= -F- 1-^ ^= — \ KEY E. :d |r :n |f :s :d |t, :d |1, rs. :s If :s :n !r :n II :s If :d 1 :- f. :- |-:s |-:ni f :n If :r fi :s, |1, :t, n :-| d :-| f :- |-:1 |-:fr s :f In :r Hi :lt |si :si d :-| d :-| 160 TEXT BOOK OF HARMONY. §§ 68, 73. 21. Add the three upper parts to the following Bass. ma JT w t=t: ffi i: ^=r^ S ^ ?= Z3Z ;^^ 6 J KEY E|7. « 8 4 6 8 4 2 Ud :n Is :f |ri :r Id- .— |ri :d II, :s, |f, :1, |s, :- | D Di S 'Srf DJ 'So B — D4 D F* D(! P P4 S — J In :r Id :n |s :f In :— js :d If -.n |s .-s. Id :— [| D* So D D« S 'Srf Di — S D 'S |t :1 jl :se |1 § 154. 60. Add the three upper parts to the following Bass. ^g F f=F= pa ^ ^ ji Lah is G. Ill :t| |d :sei |1| :pii |f| : L "Me Lb ''•'Mb L ^"M F I » In, :1| If, :ri It^ :ni Vk •'M L W S ■>T'"'M L § 155. 61. Harmonise the following, using in first section the first inversion of le minor chord of the Dominant [MV] inversion of the Supertonic chord [TS] the minor chord of the Dominant [^i1, and in the second section the first ^^HJ^^4p=^^^V[-^J Lah is C. ||d' :1 |se:l jn :1 |se:- |1 :t |d' :t |1 :se |1 :-| GRADED EXERGISE8. 171 § 167. 62. Add the three upper parts to the following Bass. ^^ E£ ^ ^ f= l« § Lahis B. ||1 :1| ]t, :d |sei:l| |f, :- |1, :d |t, :1| |r :n [l. z z p Lb '"'Mb L F — L Lb L • :- |d :-| D SJ *L L F* F E T4 Di F *De Do *S 'S 'd — 06. Add the three upper parts to the following Bass. =Et=E -i=p- :^=t "i^t W I '6 Lah is A. I Hi :d In :- |d :1 |-:s |- :f In :- |r :n |1| :-|| §§ 195, 199. 97. Add the three upper parts to the following Bass. -*s> r:; — > — ^ ^S B =^E( 7 8 '9 8 r 9 8 ^g ^ ?az !E r^= =P=zt '6~^^ '- • ^ « ■« I 4-1 3 KEY AI7. j|d :-|l, :t, Id :-|l, :f, jm :- lf| :- |ri :- isi :-.iij D — Fi Si 9D D L Ea 'D* D4 ^F F E — »S S'Srf J im :ri j- :d| |d :- |t| :- |d if, |si :- |g, :- Id :- || m Sc 9I>» D LJ — 9Sa SJ D E4 "Do Dc *'S 'S D — om om om See Appendix for additional exercises. |si :-.fi GRADED EXEBOISES. 179 98. Harmonise the following air, iising suspended discords in every ueasure 1>ut the first complete measure. i 4 1- ■Msj=3iz -ri - i ^^ znti Lahis A. |:1 |di :r" :n" |ni :r' :r' |d' :— :t.l|se :— | :n' In' Id' :— :t It :1 :8e II :— \\ 197, 198. 99. Add the three upper parts to the following Bass. f-l i: 5 6 S :t:3P=^: 5 6 7 6 S \ |7 8 Lah is B, HI, :r Id .— Ir :-|sei:-|l, :d If :- |n :- |1, :-|| 100. Harmonise the following, using measure but the first. ^ suspended discords in every ^^ ■» ^ - rt=X i # it=^ EE^ -ri- ^ KBY Bh. , , i Ijs, :1, :t| |- :d :n |- :r :d |- :t, \Y :- :d 111 :- :t, Id :- :- 180 TEXT BOOK OF HARMONY. § 202. 101. Harmonise the following, using suspended discords with inter- rupted resolution at each of the place? marked with an asterisk. fr-j li d I ^ ^^=j: i ^ =J=T: KEY Bh. :n If :r I- .s, :d I- .r :t| J- .d :1| I- .r :s, |d :- 1- .t|,li:ti .r |d §j 204-206. 102. Harmonise the following, using combined suspensions where the syncopations occur. I nj • i fc^ J — ^ ^- -id r—»- - *'— i^ jtl-jL $ fe -i — P4 ^-^l :t -JC^ ^*E2 s 1< — *- •*— 1< - KET A|7. i In :r |— :d |f :n |— :r |s :f I— :n |s :1 In :f I— :8 In :s I— :f |r :f 1— :n If :r j— :d § 207 103. Add the three upper parts to the following Bass. Mi ii 8 a «^ f i i f= r~~r~f ■ 6_ 1 .9 8 }7 8 4 3 Lah is B. pi, :r |d :- |-;t| [1, :- |-:si |- :f| |n, :n |1, :- L '"Md '•'Lb Lb '*SSe SMb *"L L *Me Mb '*Se Sb "M — "»Z L GRADED EXEROISEB. 181 104. Add the three upper parts to the following (unfigured) Baas, using suspensions, single or combined, at each of tlie places marked *. * if * * * "^^^ :t ?= ^^ [^ ^ r :?2= =P= ||d :- |r :t, |d Hd, :- Id :se,|l, ||1, :t, Id :-|n, :- |8| Hi if If ■|1, :- If, :-|n, :- In :|G if, |r :— jd :— jn, :sei|l| |li :-.s,|f; :si If, :-|J :- |-:-|d| :- |- § 208. 105. Harmonise the following, using suspensions of complete chord at the first heat of every measure. ^-1 J_J_^^^ h-JP-J-J- i feiii *?* 3 ^ I*=3t g" *- KEY A. iin :s I— :1 |s :f |r :— |d :n |— :f |n :r |— :n 106. Add the three upper parts to the following Bass. mx 1=1^ E£ ^ % r Lah is A ill -.1, Ir :- In :- Id :- |1, :f |r :- |n :-|l, :-j| L Z 'TS n "M — '"Lb Lb L F ^Tb Tb '"Jf — *"i L 182 TEXT BOOK OF HARMONY. CHAPTEE XIV. §§ 210, 211. 107. Add the three upper parte to the following Sa8s. :p=t ^. t=t It -X 3 2 = 1 ^^ =P=F e^ -p— e- -•— P- 1 — r KEY C. C 8 * 6 6 2 5 5:d In :r |d :f |— :n I— :r |1 :— Is :f |n :f Is | D D* Sc 'D F 4De DJ 'Frf T4 L 'Trf MJ E* D* JE4 S |:d |t| :-|li :t, |d :!, jr :d It, :s I- :f |s :s, Id 11 D Si 'Dd F« S* D 'L E W S4 MJ'Lrf'EJ S 'S D § 212. 108. Add the three upper parte to the foUowing Bass. [^^=^'^ f^f^T^-^I^Xf" Lah ia G, Hi :t, |1, :si |-:f, |ni :- Ir, rd, |-:t, jd, :n, llj .— L SEb L Mb ••Ld Rb "M ' JK Tb Lb ''M SM Lb '"Jf i — § 213, 214. 109. Harmonise the following, using a sequence of 7ths after the pattern of the opening measure. -TJ- ^ P4- HE^feE^ ^ zMzit I I I I m^ r KEY Bb. :s — d f - ti n — li r — S| d - r ti d — :si d — d :n n — f :d li — r See Appendix for Additional Exercises on discards of the Seventh. GRADED EXERCISES. 183 §§ 215-218. 110. Add the three upper parts to the following Bass. ^ r— r fe ?E E^ =1= 5 I -^ =pa:; KEY A. II d| :n, 3 Bb s |d :f, 9'D F :8i {1| :t, Mi "Be Si :d |r :ri :ni I D "T* It 9'DJ ilf, :8, :1, I- :s, :f, ' F — F4 "Trf MJ "EJ |8| :— :si S Be 'S Idi Sp 111. Hannonise the following, using discords of the Kinth at all the places marked *. J_^J_J 4-^J ^ J-rJ— J !- is^ ^ # |:n' |-:ri |— :di |— :s |— :d' :d' I— :t Idi :- §§ 219, 220. 112. Add the three upper parts to the following Bass. Lah is A. HI :n"|d':f |r rt. Id :r \n :n If :- |d :i [n .- | ' L •'M»D F n SEb Lb S "M "Db F — Li "OT "Jf — jjf :r in :d |f :n ir :d jd :t It, :li It, :n.|l, :-| SFi^-DdFi lyMj/ L — 184 TEXT BOOK OF HARMONY. 113. Complete the following. m- ^m ^^- 3= i &fc -m^^^t- i I I A '^ ?^!^ KEY B|j. :s r :— :ti :si :d t. :— :ni :n, n li — :r S| PI, — :sei ti d — :r d| 1, fi 1. :t, d r : :n 1. fi : :ti n — t, : r :— Sl — 1, — : :si GRADED EXERCISES. 185 CHAPTER XV. §§ 2M-223. 114. Add the three upper parts to the following Bass. m^ :?2= .-•-!■- iz=t g=t: 7 6 5 - ^ ^; ^ ^ =P^t: =P=t =t=|tt: 87 KEY £|7. J:d Is,:-!!, :-|s, :d |l|.t,:d It, :- |d :£, |s, D 97S 7S L — "S B F4 D "S* 'S4 D F S 'ti ilt, :d If :r In :r |d :f In :f.rls :si |d :- 1- || »'SA D F s'Sc m Ti D ^&d DJ E4E Dc S'S D — — § 224. 115. Add the three upper parts to the following Bass. ^te =t==t= ?* =t=3 ■¥=&- 1 — r ii I 1 7 6 5 - t^S ^^E=E^ » I 14 - 6 }6 - «3 2 5 4 ^^^ =P-*- =1=^ H L (. I '.,S Lahis G. 1:1, In, :1| Id :1| In, in, |fi :li |sei:sei|l| :si |-:fi |ni | ' L ""Jf 1. Lb L ^"M Le Sb L«"'mi-MbL Mb *Se Sb •'M om 1:1, |r, :-ldi :- lta :- l^i :-.ri|d, :t, |1, :d, |fi :ni |1, || ' r«„u^7«i/ir.* -""Jfo7"ifiz4 — Zb SM L Zb^o'Mer-'ML IviKMd^-ildLb —'""Mc^-MeZb 186 TEXT BOOK OF HABMONY. §§ 225-227. 116. Add the three upper parts to the following Bass. » :fe ^ 9 is 7 *- IT-T-^ Ifi Wf =|t=f. =t:=P ^ Lah is B. U :-|n e 7 4 7 4 2 ^ f n 111 :-|r :- |d :t, |1, :ti |d :r L —«M'"'ML —^Md'"'MdLh''McL — lb M p |r :n If :se |1 :d Ir :n |f :seijl| :d |n :n ll| :— n Lc«M.e'"'MhL Lb R Lc 'Mei^Mb^^L Lb «M ''•'M L — 117. Complete the harmomes to the following. 4- =ibJ=J iki=J= =i mr. '■^ -•— p- 9 3 7 - 7 - S 6 4 — 3 - i -J — u -i^ — » - j=^ m. ¥=^ =P=t: 1 — r- 9 4 8 - 7 7 5 4 - KEY F. S.B. :s 11 :t |di :n If :— |n :s 11 :t |di :1 : Is, :- I : 1, :t, | : r :- j : WS 'S «Se ■'Sb wSc 'Sc n :r |d :t. :s 1 :t. Id :n S :s Is :f : s,~ :f| 1 »s ■'Sd ; : 111 :t, 'Se ISb s :- - d :-|- GRADED EXERCISES. 187 §§ 230-233. 118. Write the three upper parts to the following Baas. m^ t=t % § 9 4 8 2 i 6 '3 7 ^^ 7 I r r i ~r 433 Fi KEY B|j. ||d| :ni js, :s, |8, :f| In, :- |f, :- In, : D D4 Dc S "8 'Srf D4 — '"Srf'SdDi I |d, :ni |ri :Sj Id, \% ll^ -.t^ \\^ :t, ld| :ni D D4 «*Sc 'S D SJ L Dc ^*Se 'S4 D DJ - |r, Is, 974S IS' 'S D — :sj 119. "Write the three upper parts to the foUowing Bass. imi =t: =l==i 2 *- r I ' - Lah is A. :li In :-|f :n |r :— |d :1, |f :Be,|l, :d |r :n |1, i iiM'"'M F Le*'Md'"'M:dLh L '''*Mef«>Mb L WTbl^M L §§ 236-240. 120. Add the tiiree upper parts to the following Bass. KEY Or. Hd :r Is, - Hi 'S L :-|ti :8, Id :1, |n, :- |f, :- |s, F* "Si 'S D F4 D4 — B4 — S } If, :-]n, :- Hi :-|s, :fi !n, :f, {s, :- Is, :- |d :-|| ' |8- :- |- :- 1- :- l-:-l-:f' I"' :r' |d' :-l| 190 TEXT BOOK OF HARMONY. CHAPTER XVI. § 256. 129. Add the three upper parts to the following Bass. m m^ ■■^^ =t=iE i^ r r 6 b5 le Lah is Gr. Ill :d Iti :t| Ui :rei|ni :— |U :di |ri :tj |ni in, |lj :- L Lh'"'T'"'McL'^Tb Lc"!^ L Lb S t^^T Lci^M L — 8 5 §§ 266-269. 130. Add the three upper parts to the following Bass. s -•-^= =F rf=^rF -i — r T 4 5 If 16 E^t El^ M ptr^F^ r In : t Lah is B. I 111 :r Id :ti n re Ir ^d |ti :1| |d :r In :— L ■'"Md Lb ■n»"T'"'M F Lc'"^Tb ^"MdLb SM L Lb "li "M ||li :1 Ir :n |fe:sell :— |1, :1| |sei:l| |r :n |1, :- L L '' Tb ''M'"«"Tc''"Mb L — i'fc"ZK'"ifii Ti ?"Jf L - 131. Harmonise the following, using the (major) Supertonic Seventh at the places marked *. . . I I i # 4=^^ i i -U-U J=± }=i::Ft:^ -^-*- S :*=t* zi; Xj9.1i IB JV. 4e ilC A HI :t |d' :fi jn' :rei|ni :— jr' :di It :1 |1 :1 jd' :t | )|d' :r' |ni :- jd' :1 11 rse II :1 11 :1 |di :t 11 :-| GRABEB EXEBGI8B8. 191 §§ 260, 261. 132. Add the three upper parts to the foUowing Bass. ^ t^ r " n''^ =ff^ 1^1 KSY G. I Id :1, |r -.8, II, :s, |fei:f| In, :r, |d, :— |d :fei|si :— I D ^LWfeRrs L DoW'HJ'Srf D4 T4 D' — I)»''MDo S I Id :-|d :t, jd :!, js, :fe, |f, :n, jl, :- |s, :- |d, :-| 133. Add the three upper parts to the following Bass. ^jJEgEJ^ mm e* -pc^S: Frztfi:. t2 6 *2 » s i^tEE -^ -}| -•-rP-- fe= ll 12 8 |J|~?« « f ^ 87 liah is F|. Hli :sei|l| :f| |n, :re,|ri :d| jlj :l|.s,|fei:— jf, :n, jr, :— | L •'-Mb L Rb Lc'"'REn»MdLb L L "i^REb — ^SEd Le E — ||1, :1| |se,:- |1| :- |d :— It, :d |r :- jn in, |1, ; L''*'REc'"'Mb'"'lIb L —3>'REd—''SEb Lb R —^WW"!! L 192 TEXT BOOK OF SABMONY. 134. Harmonise the following, using the Supertonio Ninth in the seveial inversions indicated by the given bass notes, lesolving each discord upon the chord of the Tonic. i^^ I J — u i5 m |fe^' SE ^^m m^ m It Lah is C [\n :1 I 1 :se |1 :di : I : di :t Id' :t 11 :di |t :1 re :— I : : I :re si'r n :f |fe:l : Id : se:— 11 :- : II, : di :- |-:t :fe I : 1 :se 1 :- §§ 262, 263. 135. Add the three upper parts to the following Bass. m^^ ■m m — • — » n — F^— I — H T m =t=a::^t q - "FT i i E»S^ ^^ * - L^l— I =?-• =i==t: r b7 i KBY ASj. n I ^7 3 j :d| jta :d| Ir, :ri |si :— jli :1| |si :ni jf, :fei|S| :— D WSJ D m»7ieii 7ieK 7S — L FE4 Do D4 F ■"■?£ Do — ||— :t||d :d |d :ni |si :feilf| -.nLrildi :1| js, :si |d| :- S SJ D">^FEcD DSDc'^FE''SrfD* D^'FEADo'S D — GRADED EXEBCISES. 193 §} 264, 265. 136. Harmonise the following, naing the Tonic Seventh ['^i] in all its positions lesoMng upon the Dominant Seventh. ^^^^ S^ ^-F^^=i=^- •Gh-r- LahisG, i :n Id :de |r :n Id :ti |li :in In :n \n :n In :— |— j |:t| jd :r |n :d |de :r jd :ti |1, :1. |1, :t| |1, :-l-|| § 266. 187.4< Add the three upper parts to the following Bass. ^M^ ^m "F I % a=.^_ =«r=F=^ 'W- ?= S 5 S * t if* Lah is £. I \ \ «l If 3 8-87 3 4 4 t HI, :se,ll( :li It, :d Ir :- |1| :t, |d :- jde :re |n :- | Lb -Ji-Lb^t^Tb Le "M \ Id :li Isj :— |fei:- in, :rei Ini :ni |fei — |n, :— |1| :— | §§ 265-267. 188. Harmonise the fallowing, using the Tonic Seventh ['•D] m its root position, first inversion, second inversion, and twice in its third inversion wilii different resolutions. Un :d Id :n If :f jn :r |d :n |8 :r jn :fe|8 :— | ||8 :n |fe:s Id :pi |f :n |r :f |n :- |- :r jd i-|| ' See Appendix tor additional exercises. 194 TMXT BOOK OF EABMONY. §§ 268, 269. 139. Add the three upper parts to the following Bass. i1 'I, b'3 6 w a^ i » 2 y 5 3 8 7 Lah is D. |11, :r |t, :d H, .-n, |1, :f, In, :rei|ri :d, |1, :f, In, :- | Hli :d jde :r |d :1| |S| :sei |1| :tai|t| :d.r|n :ni |1| :— I L Lb^'DM''«'Md Lb L^I)Ea'M'"'ML — §§ 269, 270. 140. Add the three upper parts to the following Bass. ^^^P^^ m. r^ 6 6 4 1,8 1 i>7 b inr • % ^m '^f E^ KEY c. jra) |d' :s |n :d |d :si |d :— In :d |;de5:r |n :fe|s :— I Id :t| |d :f |n :na|r :si |d ita,!!, :1| |s, :si Id :— 11 D 'S* D F»t»M'»»FEd'S(! 'S D""«Mc7fcE(!m»pj;«Dc'S D — 6 5 4 3 \ GRADED EXEBCI8E8. 195 } 273. 141. Add the three upper parts to the following unfigured Bass, using the Dominant Minor Ninth p^S] in its root position and all its inversions with the 9th resolving on the root. :^St: m —f^ ^^ ^^ T ;-|d, :- In, :- |r, :- Id, :f, {s, :- 1- :f, KEY Bb- ||d :- |8i H"' =- ' fi :— Ini :— |ta :— Idr :si |lai:si Idt :— |— :— I 142. Harmonise the following, using the Dominant Minor Ninth in all its positions resolving direct upon the Tonic. ^^j^^^^-jjsL-jjfeLifeL^ ^ ^^^i^E^^^^^^Si KEY A. y.A \n :f |s -.1 |la :-|s :fe|f. :n |r :d |d :- |t, | j:r |s :f In :s [la:- [s :f |f :n |r :n |d :-|-|| 196 TEXT BOOK OF HARMONY. § 274. 143. Add the three upper parts to the following Bass, the Soprano to be the same in the third section as the first. M^ \ tl 8 - 4 - 3 - ?3= P=pc: !^ 73- 6 S 4 3 KEY A. 6 5 4 I - ^ ■« -7 S ' Hd :— jsi :1, |t, :si Id :— |d| :— Ir, :rei hi :.f| |si :— | D — S — »S«»'S D — D — 'Sff'^'Se Di EJ Be S pi, :-|t| :- \U :-|d, :- |fi :- |n, :r, Is, :s, Id, :- L — Si _ r.S4i.r.x'D — «'Srf— DJ 'E Dc 'S D - § 276. 144. Add the three upper parts to the following Bass. E^i ^^ 6 5 e »8 5 4 3 4 3 4 6 4 2 3 US 4 3 KEY O. |:d |1, :si If, :fe,|si :— |la, :s, |f, :n,.r,|d, :la,|8, :— | D Ti Dc E* >°'FE De S >»Fi Dc ••Tc D4 D "Fi Dc — H-:t, |d :-|s, :f, In, :r, |d, :s, |n, :-|f, :-ld, :-|-|| S SJ '•Fe D S 'Srf Di 'Sc D S DJ — F i-p «d _ j) ' GBABED EXEBGISES. 197 §§ 277, 278. 145. Add the tiiree upper parts to the following Bass. WFTT- P^F^^^F? ^ ''-' ' l> 4 3 2 e %>V ' f^ w bs 4 s I. 3 « S !» KEY At;. ||d :1, In, :f, |s, :- |- :f, \n, :f| |n, :ri |d, :- 1- :- | D F* DJ >>EJ De — S 'Sd D4 "EJ Di TJ D — 11 d :ni If, :ri |S| :— D DJ P '■•E De — l-:n, |lai:s, If, :f, |d, :-|-:-|) S D* ^Tb De i»F '"»F D — — — §§ 279-283. 146. Add the three upper parts to the following Bass. bg S i '« I 55 '4 a t, r^ # KET A. )ld :s, |i| :n, If, :fi |s, :- In, :d, Ira,:!, In, :fi |d, :- | D '.S L D4 F "EA* De S Di D >»EA 'Se D* ""F D — I Id :d |t| :d |tai:s, [la,:- |la,:fi |8| :lai Ib, :s, |d :-| D-^lAiSJ D TA'S ">»LA- >*Fi'*F">*De"LADe'S D - 198 TEXT BOOK OF HARMONY. §§ 284-286. 147. Complete the followiag. '-T •h ^ 1 E=^fcE=-_J^ 4 (P'):,\> L |»-ha— 4 1 1* rP m m -1— . ^by r ^1 — ^ ^^=-^ "!•'■ —ids ^ ^ r ^^ — ^ -1 ^— -f— - ^by-f^ — ^t^i^-'riT^ ^ p^ LahisF. '1 il :re :1. :1 1 :r 1 :ta, 1 :f d : 1 ll re 1 (ill sei 1, 8| fi :f. Hi r, |d, :taj Hi :ni fi f. ni - i [1 :re : 1 ta : se :1 : II )l :t, |r : :d )l :1 If : :re [|d li n, f, n, :ri di - Ii 1 :ni 1. :f. n, n. li — 148. Add the three upper parts to the following Bass. ^ P=fe 5=FlSi=i: -^x ¥—-^ ^ =t=t ?ciz t«= t- 6 5 6 6 4 3 5 4 '^ m^ 3 ?i:36K S ?=- -, - 4 « ^4 4 2 3 GRADED EXIIB0I8E8. 199 KEY B|l. I Id, :ni |f, :s, |1, :lai|S| :— |fe,:8| |lai:si.f||ni :r, Id, :— j D D4 F M4 L "LA. Do S w»fi4 D(!««LAS'SrfDJ Td D — I In, :d| |lai:8| |f, :n, |f, :— In, :d| 11, :1a, js, :s. Id, :-|| DJ D«"LADi!'Srf D4 F — D4 D rj'«™LAD(! 'S D — 149. Add the three upper parts to the following unfigured Bass, illus- tratiBg all three forms of the Augmented Sixth on the minor sixth of the scale. ©fc ~W » f r^ 3==;: fdr» I r r l ^f r rT v-f^— I- t=^ KBT F. I Id :t, |1, :s. If, :s, |la,:si |d in, |f, :s, jl, :la,|s, :- | ||d :1| |f :ra |r :n |r :d |t, :d |lai:la, js, :s, |d :-|| §§ 291, 292. 160. Harmonise the following, treating aU the altered notes as Chro- matic Passing-tones. Introduce companion passing-tones in the inner paits to those in the first score. KBT Ely. j:s |fe.8:i |s :n |re.in:f In :d |r.de:r |n :1 |s :- 1— | |:f lre.n:f |n :n jde.r:n jr :8 |1 :8e.l|t :r' |d' :-|-|, 200 TEXT BOOK OF HABMONT. § 295. 151. Harmonise the following, treating all the altered notes (except the seventh of the scale) as in preyious exercise. Introduce other passing-tones, diatonic and chromatic, in the inner parts and bass. P 4=q= ^nA ^^Uu^JE^ fei 1^ -jd--»- Lah is £. :li.ti|d :n |de.r:n.b|se.,l:se.f|n :re.n|f :n lr.,de:r.re|n :— |— ( :tr|d :n |r :d.n|l.,de:r.n|f :t| |d :n |r.n :f.se|l :-|— 11 CHAPTER XVII. Transitions to distant keys, of which this chapter treats, form suhjects for an almost boundless number of exercises. To give many exercises of a set form would, however, only limit their value as such, and would fetter the invention of the student. Exercises should be constructed exemplifying the transitions that are indicated in the text of the chapter ; to illustrate a diatonic or chromatic chord of one key becoming a Tonic or Dominant of another — ^to illustrate various transitions by means of the enharmonic alter- ation of the chord of the Diminished Seventh — ^to illustrate transition by enharmonic conversion of a Dominant Seventh to an Augmented Sixth, and to illustrate transition by enharmonic alteration of the Dominant Minor Thirteenth constituted with root, 3rd, and 13th only. A few exercises as models will be found on p. 205. 201 APPENDIX. CHAPTER VI. Second Inteksions §67 (2).— The second inversion of the Tonic chord is also used in an ascending stepwise bass quitted hy chromatic semitone, as in the common harmony of the second phrase of the National Anthem. Pig. 184. KEY A. PI n :f n -.r :d S| 1, :1. 8| -.fi :n, d d :d d -.t| :d d li :fr * -.sei:l, (3) The second inversion of the Sab-dominant chord is found less commonly than the others approached and quitted stepwise as in the following example — Fig. 185. KBT G. £ — r — n 1, d r ti d f 1 s — s r d * ti S| d (4) The second inversion of the Tonic and Sub-dominant chords preceded by other chords on the same bass, and quitted by step may be seen in the following examples, where the second inversion of the Tonic in Fig. 186 is followed by the note above, and the second inversion of the Sub-dominant in Fig. 187 is followed by the note below. Fig. 186. t^ -I- ^ 202 TEXT-BOOK OF HABMONT. :d |:si l:n :d Fig. 186. KEY F Fig. 187 r r 8 d t, t, d d f f n n S| S| 4' S| d :r d :si n :s 1, :ti Fig. 187 KEY A. n :n f — r :— d _ 8| :si 1, - si :— Sr — 1 d :d d - r :f n — I d :d d - t, :- d — (6) The second inversion preceded and followed by another note of its own chord in a direct succession through the tones of the ehord, finds illustration in the chords of the Tonic and the Dominant in the second part of the l^ational Anthem. Fig. 188. J ) J ! N I ** 5l=d= m iprrip: =^=F=^ 1 — I- ^^ J_J_:^JL_£j_Xi-iil^ ^ I ' * Fig. 188. KEY A, s :s :s :d :n :d :n :S| s -.f :n f :f f f - .n :r d -.t|:d t, :r ti t, -.d:t, n -.r:d r :s s s - .8 :8 d -.d:d S| :t, r S| -.si:s, In the following example the second inversion of the Tonic is also in arpeggio as in Fig. 188, but as it does not proceed to its root it is quitted stepwise according to the rule. Fig. 189. P mi =1= I te ^r T T fr^ - ^ Fig KEY A 189. :n •Is :n :si Is, :si :d Id ;d :d, |ni :si * d :d In :r ni :ni lsi :f| d :d Id :t| li :1| |S| :8| APPENDIX. 203 (7) Second inTersions of chords are also sometimes used in alternation with the root positions for a kind of bass play that is yery common in march and valtz movements, thus — Fig. 190. i i=g=d- ^-- 4- IcC A A A trT I ^ Fig. 1 In :- 90. f KEY G. :-|n :- 1 -Is :- Id :- ti :-|d :- d -Id :- Is :- s :-|s :- f -In :- Id :s, r :s, Id :si d d, Id :8, s :-|r :- n — r :t| |si :t| d — r :-|f :- n — t| :si |r :bi d — In this may he noticed other apparent cases of second inversions in consecution. But the chords which most appeal to the ear are those at the accents, and the progressions are practically the same as if the accented hass notes were each two pulses in length. CHAPTEE XIII. SusPBKsiONS § 190. — ^Exceptionally a suspended dissonance is sometimes resolved on a chord whose root is a third below that in which the suspension appears, as in the following sequential passage from the " Dona Nobis " of Mozart's (?) Twelfth Service. Fig. 191. ^ U^ I A 4 .r^- s' f f n' n' r' r' d' di t di d'.di d* r' t di 1 t s 1 1 8 s s'.gi 1' — s> — fi — rf — r' — pii ni.n' f r' n' d' r' t d< 1 f S d 204, ADDITIONAL EXERCISES. CHAPTER XIII. 152. (To follow Ex. 95.) Harmonise the following, using suspended fourths in root position of Tonic, Dominant, .and Suh-dominant chords. p,i 2 TTJ^ m f-^t-^ i ?= 3: rt ^ ^ Un, :— :d Id :t| :r Is :d :f If :n :8 i|di ;— :t |t :1 :b Is :r :f jf :n :— 153. (To follow Ex. 96.) Harmonise the following, using suspended fourths at the places marked with the asterisk, either in the root position of the chord or in its second inversion, or in the position in which the fourth itself is in the bass. ff^f =P==pe ^m t=-- KEY D. 4c :|s :s |d> :1 :ri |r< :di :& It :d> |d> :t * * * :r' Is :— :d' jl :— :r' Id" :— :t Id' :- APPENDIX. 205 154. (To follow Ex. 97.) HarmoQise the following, using suspended ninths at the places marked oy the asterisk,' either in the root position, first inyeision, or second inversian of the chord, or in the position in which the ninth itself is in the bass, as may be available. i ±: -l F i ( :r In :s :1a Is :n :d If :n :r In :— ) r |f :n :r |r :d :d |n :r :d |d :t| | s :1a Is f :n |r ;n :f In :— :r jd :— 163. (To follow 146.) Harmonise the following, introducing all the chromatic chords found in Ez. 146. ' 33?*= IQZ ?a- tz=b^=!!=)i ^^ KEY Q. I :n Ir :- d If :— :1a js :— :f In :r |"_J£ j :t| Id :r :f In :na :r I s :f :r Id :— The following will serve as models of the exercises referred to on p. 200 that should be wiitten on the subject of Chapter XYII. 164. Write an exercise commencing in the key of C major. Through its Sub-dominant pass into £ minor, modulate from this into Gr major, and through its Tonic pass into C minor, thence through an inversion of the Dominant minor Ninth of this into Al; major, and through the first inversion of its Sub-dominant back to the original key. APPENDIX. 209 165. Write an exercise commenciDg in the key of D major. Through an inveraion of its Supertonic minor Ninth pass into A minor, thence through an inversion of the Supertonic minor Ninth of this into Gr minor, from which modulate to Bjt major, and through the Tonic of this return to the original key. 166. Write an exercise commencing in the key of E major. Through its Tonic pass into A minor, modulate from this into the key of C major, thence through an inversion of its Supertonic minor Ninth into D minor, and hy an inversion of the Dominant minor Ninth of this return to the original key. 167. Write an exercise commencing in the key of A major. Through an inversion of its Supertonic minor Ninth pass into Cjt minor, modulate from this into E major, thence through an inversion of tBe Dominant minor Ninth of this pass into C major, and through an inversion of the Minor Ninth on the Tonic of this pass into D miuor, returning through its Tonic to the original key. 168. Write an exercise commencing in the key of Ej? major. Through an inversion of its Dominant Minor Ninth pass to Aj; major, through the Tonic of this into C major, thence through an inversion of its Supertonic Minor Ninth into E major, and through the first inversion of the Tonic of this return to the original key. 169. Write an exercise commencing in the key of Gr major. Through an inversion of its Dominant minor Ninth pass into E major, through an inversion of the Dominant minor Ninth of this into A minor, from which make a modulation to (J major, thence through the (major) chord on the minor sixth of this scale pass into the key of A7 major, and through the Dominant Seventh of this return to the original key. 170. Write an exercise commencing in D minor. Through the chord of the augmented fifth on the Mediant | considered as the Dominant Minor ThirteentSi) pass into F£ minor, through an inversion of the Supertonic Minor Ninth of this into the key of G major, thence through the chord on the minor Suh-mediant of this scale to the key of Bl^ major, and through the first inversion of the Dominant Minor Thirteenth of this return to D minor. aio INDEX. The numbers refer to the sections. Accented FasBing^tones II 244^248 Accidentals, Figuring of 133 Added Sixth, Chord of 81, 278 Anticipation Tone 118 Appoggiatnraa 64, 244 Attendant Keys 124 Augmented Fifth, Discord of 219 - Intervals 12 - Interval in Melody ... 146, 226, 243 Sixth, Chords of the. Auxiliary Keys 124 By-tones Ill Cadences 27, 48, BO, 61, 88, 91 Chords, Definition of 16 Constituents 17 Distribution 26, 26 Chords common to two Keys 127 common to two Modes 164 Chorda! Passing-tone 115 Chromatic Concords... 134, 266, 276-277, 279-283 Intervals 11,12 Passing-tones 291-296 Supertonic Chord 134, 256 Semitones 10 Church dose 50 Combined Suspensions 204-209 Pedal 264 Compass of voices 33 tkmiplete Chord 17 Compound Intervals 7 Concord 14 Consecutive Fifths 31 5th and 8ves. Bules to avoid ...30, 38, 39, 46, 90, 213, 218, 241 Fourths 72, 168, 184 Octaves 31 Passing-tones 121 Thirds in Two-part writing 179,180 Consecutives, Implied 114, 199 Consecutives and Incidentals... !{ Hi, 114 Consonance .. ■, fi Continuation Line 87 Contrary Motion 30 Crossing of Farts 34 Degree 2 Delayed Besolution 81, 201 Diatonic Intervals 9 Semitones 10 Diminished Intervals 12 Seventh, Choids of the ... 168, 224, 262, 269 Intervals in melody 40,147 Discord, Definition of 13, 41 ' of the Eleventh 230-235, 278 of the Thirteenth 236-242, 274 Discords by Suspension 190-239 of the Ninth 215-217 of the Seventh 211-213,220 of the Augmented Fifth 219 Dissonance 5,6 Distribution of Chord 25,26 Dominant Chord and its progres- sion 19, 28, 146 Chord, Second inversion of... 65, 67 Cadence 4& 49 Fourth 83-86 Key, Transition to 123, 135 Ninth 222-227, 273 Seventh 42,160 Seventh, Exceptional resolu- tion of 69 Seventh, Inversions of .. 66,63,66,68 Seventh, Besolution of .44-45, 150 Thirteenth 236-243,274 Thirteenth and Mediant dis- tinguished 240 Double Pedal 254 Thirds 73,77, 96, 148, 219 Doubling of Chord Constituents 2^ INDEX. 211 Elements of Tiansition {{ 125, 126 Eleventh, Discord of 230-235, 278 Enharmonic Change 263, 297-300 Exceptional ConsecutiTes 70, 71 doubling of 3rd 73, 77, 148 resolutions 69,267-269, 287 False Cadence (see Interrupted close) 88, 154 Notation 263, 2?0, 297, 300 Delation 132 Belation, Exceptions to ... 170, 292 Faulty Movement of parts 35 Fifths badly approached 36, 182 in Two-part writing 181-183 Figured Basses ... 56-58, 87, 116, 133, 195, 208, 226, 230, 237 First Inversions of Chords, Uses of. . . 62 Flattened Seventh, Choid of 282 Supertonic, Chord of 280, 281 Foundation Chords 20, 144 Fourths in Two-patt writing 184 French Sixth, Chord of 286 German Sixth, Chord of 285 Half-Close, The 48, 49 Transition in the 130 Imperfect Chord and its progression 16, 97-102 Consonances 6 Fifth, Interval of 6 - in Harmony 43, 44, 70, 71, 158 in Melody 40, 147, 167 in Two-part ^fftiting 183 Implied Consecutives 114, 199 Incidental Tones U2-121 Incomplete Cadences 63 Indirect Anticipation Tone 119 Interrupted Close 88,164 Besolution 202, 203, 214, 240 Interval 1 Inversions of Chords 66 of Intervals 8 Inverted Chords, Uses of 61-68 Pedal 255 Italian Sixth, Discord of. 284 Leading-note descending 89,95 Chord of, and its pragieBBian...97- 102, 107, 157 Major Chord, DeJlnitio]\ of 16 Chords of Major key 19 Mediant Chord and its progression 74, 63-96, 107, 156 Chromatic chord of, in Minor 166, 219 Minor Chord, Definition of 16 Chords of Major key 74 . Dominant 155 Second,Chromatic chord on,280,281 Modem Minor Scale and its chords, 140- 158 Modulation (Transition) ... 123-132, 136- 139, 168, 169 (change of mode) 162-169 Neapolitan Sixth. Chord of 281 Ninth, Badly approached 228 .Discords of the ...216-217,222-227 Ninth, Dissonance of, as a second ... 3 227 and Sevenths distinguished ... 216 Note in common 21,22 Oblique Motion 30 Stroke in Figuring 133, 195 Octaves, Badly approached 36, 186 in Two-part writing 186, 186 Omission of chord constituents 24, 83, 172-174 Ornamentation of Suspensions 202 Passing-tones, Accented 244-248 Chromatic 291-295 Unaccented 113-121, 159, 160 Pedal, The 249-255 Perfect Consonances 5 Cadence 27 Phrases 52 Flagal Cadence 50 Pluperfect Fourth 6 Position of Chords, Belative value of 60 Prepared Constituent Discords ... 210-220 Preparation of Dissonance 47 Progression of Chords ... 22, 28, 29, 37, 38 of Parts ... 30-36, 39,40, 69. 73, 112, 114, 132, 170, 199, 228, 229 Relation of Cadences 53 of Chords 21,37,38 of Sections 64 Belative Keys 124 Minor 141 Besolution of Dissonance 44 Delayed 81, 201 Interrupted 202, 203, 214, 240 Betardations 197 Bules of Part-writing..,29-40. 69-73, 132, 170, 171-189, 199, 200, 228, 229 Second Inversions of Chords, Bul<^s for 63-67, 16b Sections 52 Semitone 2 Sequence , 103-110, 121, 213 of Sevenths 213 Seventh, Discords of tki 80-82, 153, 211-213, 220 Badly approached 229 and Ninl^ distinguished 216* SimilEir Motion 30 Simple Intervals 7 Sharpened Fourth 134, 136 Sixth of Minor scale 160, 161 Short Score 26 Step 2 Sub-dominant Cadence 61 Chord, Second inversion of... 66, 67 Chord and its progression.,, 19, S', 38, 146 , Chromatic Chord of Minor ... 276 Key, Transition to 136-139 Suh-mediant Chord and its progres- sion 74, 88-92, 154 , Chromatic Chord- of Minor .. 279 Cadence 88, 91, 164 Supertomc Chord and its progres- sion 74-76, 78, 163 Ninth 260-2ia 212 INDEX. Bapertonic Thirteentli { 271 Seventh, Ohromatic discord of 135, 266-259 Seventh, Discord of Minor.. 80-82, 163 , Chromatic Chord of Minor 277,278 , Chromatic Chord of Major 134,266 Surprise Cadence 88, 151 Suspensions, Discords of 190-207 of the Fourth 190-194 — . — of the Ninth 195, 196 of the Seventh 197, 198 of complete Chords 208 Thirds in Two-part ^vriting 179, 180 Thirteenth,Bi«cards of the,236-243,271,274 Three-part Writing 171-176 Tierce ae Hcardie 151 Tonal Sequence 104 Tone i Tonic Cadence {27 Chord 19, 14* , Chromatic Minor Chord of... 283 Chord, Second inversion of... 64. 67 Minor 142 Ninth 268.270 Seventh 264,267 Thirteenth 271 Transition 123-lSS, 186-139, 166-169. 296-300 to unrelated keys 296-300 Tritone g in Harmony 43, 44, 72, 168 -— — in Melody 40, 108, 147, 157 Two-part ■Writing 177-189 Unison in Two-part Writlnff 187 Unprepared Constituent Discords 221-243 Upwaw resolution of dissonance 69, 197, 208, 219, 226, 231, 242, 259, 262, 265,269 J. ODBWEN AND SONS, MnSlO PRINTEBS, PLAI8T0W. LONDON B BT IKE SAME AUTBOM. TEXT BOOK OP eOUNTERPOINT. SEVEITTH EDITIOIT, ENLABOED. Contaiimig ovei One Hundred Examples. Intended for the use of Candidates for Musical Examinations, and for other Students. Oontaios clear and succinct rules amply illustrated by consistent examples. FEOM THE PREFACE. The success of the work as issued in its original form has far exceeded the most sanguine expectations ever entertained by the Author when it was first published. The concise form of the informa- tion which has proved so acceptable in the past editions is retained, as far as possible, in this. It will be found, however, that the rules are mostly amplified, and that in several cases they are supplemented by paragraphs in smaller type, that contain explanations of the general or special application of the rules. Besides the enlargement of the text, the number of examples is considerably increased for more ample illustration of all the various species in two, three, and four parts, and of combined counterpoints. There are also now included specimens, for which there was formerly no room, of counterpoints in triple and in compound times, and of five, six, seven, and eight-part couut^oint. " Mr. Oakey is the author of one of the best practical treatises on Counterpoint ever written ; the great merit of the book is that it is a small book containing the fundamental principles of t^ls art, and not overloaded with an immense number of rules." — ^ OrcAettra and Musical Eeview, Frioe TWO SHIIiIilNGS, Cloth. •,• AU the musical examples are in both notations. J. OURWEN & SONS. 8 & 9 WARWICK LANE, E.G. BY THE SAME AUTHOR. TEXT BOOK OF MUSICAL ELEMENTS. " Mr. Oakey haa given so much of the theory of music aa is necessary for the vocalist or instrumentalist before entering upon the study of the higher branches of music. In leas than a hundred pages he deals with the notation of tune and time, accent and measure, the major, minor, and chromatic scales, enharmonic change, expression, intervals, and harmony. One of the most valuable parts of thia little manual ia the series of 250 questions which are arranged according to chapters, and thus enable the pupil to test his progress at each stage." — The School Guardian. " Mr. Oakey is quite right in aaying that the information given in thia book ought to be in the poaseasion of all practical musicians, whether vocal or instrumental. He has compiled it to assist students preparing for the examinations of the musical institutions that are gradually growing up. In performing this task, he haa combined the apirit of an artist with the clear and incisive language of a scholar, and with the patient industry of a con- scientious artisan. How difficult it ia to write a musical grammar in lucid and elegant English no man can tell who has not made the attempt. The clumsy and inaccurate terms which have so long prevailed in the musical art are here avoided whenever this is poasible ; and while care is taken that terms that have a received, but no etymological meaning, shall be explained, the more senseful terms which have recently succeeded them are sanctioned and perpetuated. Everything is analysed and clearly explained. The illustrations to the book, abort as they are, are mostly taken &om classical compositions, both ancient and recent. The statements ai'e given in 313 separate paragraphs, all numbered^ On these 250 questions are given. Any student who can answer all theae must have a sound elementary knowledge of music, and to answer them he need only study what is given in the state- ments." — Lady. " Mr Geo. Oakey's ' Text Book of Musical Elements ' is an excellent little book, well calculated to be useful to those who desire to be informed on the matter with which it treats, either by self-tuition or with the aid of a maater. . . . Those who have been sdl along familiar with the elements of music in other methods and who desire to know more, or to formulate that information which they have already acquired, Mr. Oakey's book will be found most useful " — Monthly Musical Record. " It contains a full explanation of the rudiments of music, every term and definition being fully analysed, and it condudea with a chapter on the elementa of harmony aa far aa the chord ot the dominant aeventh. For young pianists and others who have not yet made the science of music a refruUr study it may prove useful." — Mum Trades Review. 2 ■* This book is designed chiefiy for the use of instrumental students, especially those studying the pianoforte. It is full of information, and perfectly clear. We can thoroughly recommend it to the notice of students. We would draw special attention to the scheme of keys, p. 26, and chap. XIV., which contains explanations of many subjects rarely explained in elementary books, and very rarely understood. We are glad to see a short sketch of Harmony. A pianist becomes a better player and reader when he knows something of Harmony. The examples are well chosen, and an exhaustive series of questions is appended." — Schoolmmter. " Mr. G. Oakey, Mus. Bac, is the author of a ' Text Book of Musical Elements,' in which he explains tune, time, notation, accent, measure, the scales and key-signatures, accidentals, enharmonic change, and, in his con- cluding chapter, the rudiments of harmony. Mr. Oakey shows good knowledge of his subject and a considerable faculty of lucid exposition." — Scoitman. " This is an excellent little text-book, containing a large amount of interesting and well-arranged matter, with a valuable collection of Questions and Exercises. Mr. Oakey has had considerable experience in teaching, and is, therefore, able to anticipate the beginner's difficulties, and to make prominent all those points which need special attention. The general ■ get up ' of the book is all that could be desired, and the language and style are, as a rule, forcible and dear." — Practical Teacher. " Mr. Oakey is to be congratulated on the excellence and accuracy of this little text-book, which, like his text-books on harmony and counterpoint, is admirably arranged. Special attention is given to notation first, pure and simple, that which is merely ornamental receiving careful explanation in separate chapters later on. There is a very useful section on ' Harmony,' followed by 250 excellent questions and exercises at the end, which add very greatly to the value of the book, which is worthy of a place in every musical student's library. We have very carefully read through the book, and pronounce it exceptionally good." — Teacher'a Aid. " This text-book, which is most exhaustive, whilst starting from the simplest elements, carries the student by progressive degrees to the ' Elements of Harmony.' The questions and exercises at the end are very useful, and form a noteworthy part of this volume. We can cordially commend this to the attention of heads of schools and colleges." — The Oraphic. " Mr. Oakey's ' Text Book of Musical Elements ' is intended for students of a more advanced inteUectiial order, and it goes so &r as to land its readers within the realm of harmony." — Mutical World. " To those who do not yet possess a needed text-book, Mr. Oakey's 'Text Book of Musical Elements ' will supply a clear and trustworthy one."— School Board Chronicle. iOXfRTH EDITION BEVISEI). Price One ShiUing, Paper ; One ShiUing and Sixpence, Cloth. J. CUEWEN & SONS, 8 & 9 Warwick Lane, London, E.O. BY THE SAME AUTHOR. FIGUEED BASS From, the Preface. The design of this short treatise on Eigui^d Bass is not only to explain the main features of tite system, but to show its amplication in all the various combinatioiis and devices found in modem harmony. While this is the main subject, this ■work will also serve as an epitome of harmony, and its examples will furnish supplementary illus- trations to the existing works that deal exclusively with this subject. From the "Musical Standard." "Mx. Oakey's Text Books on Harmony and Countej^oint have long been accepted as models of their order ; and this latest work from his pen is a welcome addition to the limited number of really good books for students. Mr. Oakey treats his subject with the student's needs ever before him, and this little book, though small in compass, deals with, a difficult subject in a broad and comprehensive fashion. A readable and workable book on %ured Bass was much needed, and this work supplies that need fully and well. It is just what a text book on a by no means easy theme should be, dear, lucid, and simple, and yet so oomiplete as to altogether cover the ground. From the "Music Trades Beview." Not only are the rules of figuring clearly given, but many interesting remarks are made respecting the complex^pes of figuring modem harmony. This treatise gives inultu'ii in parvo. From the Nonconforizxist Musical Journal. The subject is treated in a simple and plain manner, which students will fully apprecialje. Price, limp cloth, One Shilling. *j(^* All the musical exampUs are given in both notations. BY TME 8AME AUTEOM. nehi sped wmw exeqgises. [% Complete Courae.) Contains 250 exercises in all, including specimens of those set for University d^rees, and for the examinations of the E..G.O., and other institutions. From the Preface. The primary object of these exerciser is to furnish an additional set, alternative and advanced, to those in the author's " Text Book of Harmony." But they will also serve as a complete ^aded course to be used in connection with any other modem text-book QTX the subject. The earlier exercises are chiefiy designed to suit the needs of the very many students who, in order to consolidate their knowledge, find it desirable or necessary to go over the groundwork again in a fresh course. This first portion contains an mcreased number of three-part exercises, including those of the kind often set in examinations— every chord to be complete. The other exercises comprised in the ^eater half of the set are not only alternate but advanced in character to those iu "Text Book," Mid contain more ample developments of all the modem discords, chromatics, and changes of tonality. Price Two 5hillingr5, cloth. LONDON: J. CTTRWEN & SONS, 8 & 9 WABWICK LANE, E.G.