TH^^UNIVERSITY OF ILLINOIS LIBRARY 78/ Return this book on or before the Latest Date stamped below-. A charge is made on all overdue books. U. of I. Library fiaR30'36 OCT 2 7 19S8 RPR 1 OCT 02 1986 on 26 19SS MAR 0 8 lb82 ^ 8 Wfe 805 7-S ELEMENTS OF MUSIC, HARMONY, AND MUSICAL FORM. ELEMENTS OF MUSIC, HARMONY, AND MUSICAL FORM A COURSE OF STUDY FOR THE USE OF STUDENTS PREPARING FOR EX A MINA TIONS. BY M. I. RICHARDSON WITH AN INTRODUCTION BY GEORGE RISELEY Orcauist of Bristol Cathed>al, and io the Colston Hall Co., and Professor of the Organ at the Royal Academy of Music, RIVINGTON, PERCIVAL & Co, 34-. KING STREET, COVE NT GARDEN, LONDON 1893. ^0 Digitized by the Internet Archive in 2015 https://archive.org/details/elementsofmusichOOrich f INTRODUCTION T HAVE had very great pleasure in reading through i the following that occurred to me. - T sx X the following work, and in suggesting any additions The plan seems to me to be good, and well-worked out, and I think that the book is eminently adapted to answer the end for which it has been written, namely, the assistance of those who are preparing for examination. It only professes to be a careful compilation, with no attempt at originality, but it may be none the less useful on this account to those for whom it is intended. I feel sure that it will be found helpful, and I shall gladly take every opportunity of recommending it. georgp: riseley Bristol, November^ iSgj. 405333 PREFACE THIS work has been compiled with a special view to helping students who are preparing for examina- tion. The desire has been felt to explain everything necessary to this purpose in as simple words as possible, and to avoid confusing the student by the introduction of' any extraneous matter, or by a superabundance of technical terms. The book is in three parts. The First Part treats of the elements of music, and assumes no previous knowledge of the subject on the part of the reader. The Second Part is occupied with the consideration of the diatonic and chromatic concords and discords, suspen- sions, passing notes, pedals, etc., and, in fact, all that is generally placed under the head of " Harmony." It has been thought best to take all the diatonic chords first, and afterwards those which are chromatic. But if it is preferred, the two can, of course, be concurrently studied- Chapter XIII., for instance, being taken side by side with Chapters I. and II. The diatonic chords are presented in order of the addition of 3rds. Thus the chapters on the common chord are followed successively by those on chords of the 7th, 9th, nth, and 13th, the consideration of passing notes, sequences, etc., being delayed until later. It is hoped that this arrange- ment may tend to simplify matters to the student. Synony- mous words, such as " concord " and " common chord " are -viii PREFACE. interchangeably used, so that the student may become equally familiar with all. The rules given concerning the preparation of essential discords, modulation upon a pedal, etc., are intended as safe- guards to learners, to whom absolute freedom in these matters cannot be wisely accorded The study of Harmonics is beyond the scope of this work ; but a slight reference to the subject has been made, in the hope of awakening interest and stimulating to further research. At the end of each chapter, in the first two parts, there will be found a number of definitions and rules, being, in fact, a recapitulation of the work of the previous chapter, together with a paper of questions and exercises. The Third Part of the book contains short explanations of the various musical forms, both instrumental and vocal. In the selection of the musical illustrations, the aim has been to choose those which are simply set, avoiding, as much as possible, quoting any chord which has not as yet been learnt. It has not been always feasible to carry this out, but, as a rule, the surroundings of the examples will be found easy of comprehension. In conclusion, I wish to express my grateful thanks to my kind friend, Mr. George Riseley, to whom I am deeply indebted for his valuable advice and assistance, which have been so willingly given to me throughout my work. M. I. RICHARDSON. St. Regulus, St. Andrews, November^ jS^j. CONTENTS PART I. CHAPTER I.— Stave; Clefs; Notes; Rests; Dots page i Derivation of word Mzisic, i. Stave, 4. Ledger lines, 5, Score ; the great stave, 6. Various clefs, 7-1 1. Object of different clefs, 12. Voices and instruments for which treble clef is used, 13. Alto, 14. Tenor, 15. Bass, 16. Compass of voices, 17. Notes, 18, White keys of pianoforte, 18, 19. Time-name of notes, 20. Table of Relative Value of Notes, 20. Rests, 21. Dots, 22. CHAPTER n.— Sharps ; Flats ; and Natukals page 11 Inflexion, i. Sharp, 2. Flat, 3, Double sharp, 4. Double flat, 5. Natural, 6. Double natural, 7. Contradiction of inflecting signs, 8. Number of sounds pro- duced by inflexion on same degree of stave, 9. Black keys, 10-12. Enharmonic diesis, 13. Diatonic, chromatic, and enharmonic semitones, 14. CHAPTER HI.— Time page 15 Definition of rhythm, i. Bars, 2. Accent, 3. 'I'ime, 4-6. Time-Signature, 7. Examples of simple time, 7. Compound time and examples, 8. Breve time, 9. Table of Time-Signatures, 9, Arrangement of accents, 11. Triplets, 12. Dif- ferent grouping of notes, 13. Completing bars with rests, 14. Table of cor- responding Time-Signatures, 15. CHAPTER IV.— Marks of Performance ; Musical Terms page 26 Syncopation, i. Ties, 2. Dots and dashes, 3. Pause, 4. Double bars, 5. Appog- giaturas and acciaccaturas, 7. Embellishments, 8. Representation of very high or very low notes, 10. Abbreviations, 11. List of Musical Terms. CHAPTER v.— Intervals page 36 Interval, i. Consonant and dissonant intervals, 2. Perfect and imperfect consonances, 2. Major intervals, 3. Minor intervals, 4. Augmented and diminished intervals, and Table of Simple Intervals, 6. Inversion of intervals, 7. Table of Inversions, 8, 9. Rule for construction of perfect intervals, 10. Diatonic and chromatic intervals, 11. Compound intervals, 12, 13. ^ CONTENTS. ^ liaise 4'^ CHAPTER VI.— Diatonic j>cales ^ Signature 3- f-sseiuiai bna i ^ ^ ^^^,,^5 tXLs ;"'NLbIr o" i" signatures a chromatic .semi,o,« Stiii^nrt^r^^^^^^^^^ Sib^ic-r^arr^or-^^^^^^^^^^^ flats, i6. CHAPTER vn.— Chromatic Scales ^"-^^ 5^ rhrnmntir scalc I Arbitrary chromatic scale and intervals forming it, i. Harmonic '^'^'^XomaTc sea';, . Note's peculiar to chromatic scale. 3. Reasons u. favour of harmonic notation, 4. PART II CHAPTER I.— Diatonic Concords t'age 63 Melody and harmony, i. Triad : major, minor, augmented, diminished 2 Tna^s of t^Lnr ^nle Q Of minor scale, 4. Concords or common chords. 5. in major key?. 6 n Jiinor k?ys 7- Different positions of ---f J'^g^.^f f fio-ured bass 10 Exercise on Triads. 11. Consecutive ists. sths. and 8thb. 12. 13. grt n 'of kadingnote. X4. False relation. X5. "'^'^^I'^^^^^^^^^^^^ Similar, contrary, and oblique motion, 17. Cadences : full close, half close, lalse cc^ence ; Tierce de Picardie, x8. Rules of part-writmg, 19. CHAPTER n.— Inversions of Concords ^'^^^ ^3 Inversions of triad, i. Root of chord of the 6th, 2. Notes best to double in four Darts r Chords of the 6th in major and minor keys, 4. Succession of 6ths 8 gSond'imcrsion of triad, 6. Noies best to double, 7. Rules for treatment of the ^, 8, 9- CHAPTER III.— The Dominant 7TH ^^^^ 95 Fundamental and essential discords, x. The dominant 7th, 2. Resolutions of the chord, 3-7. Ornamental resolution, 8. CHAPTER IV.— Inversions of the Dominant 7TH P'l?^ io4 Aversions of dominant 7th. x. Resolutions 2. ^''''''o^r^^^^^T' sion, 3. Exceptional resolutions of the ^ and 4, 4. Ornamental lesotution. 5. CHAPTER v.— Essential Discords of the 7TI1 A'A''" ^^5 Essential discords of the 7th. x. Resolutions, x N-^^^^Jj';!^^^ chords can be taken. 2. Indeterminate as to key. 3- ^"^^f ^1°'^ ° ^ Table of sions.and resolutions. 5. Last inversions upon every note of a kt>, 6. laDlc 01 degrees upon which 7ths and their inversions may occur, 7. CONTENTS. x5 CHAPTER VI. —The Dominant qth page 123 Formation and intervals of chord, i, 2, Resolutions and exercises, 3. Inversions, 4. First inversion, major key, ' ' leading 7th " and resolution, 5. Second inversion and resolution, 6. Third, 7, Inversions in minor key: first, "diminished 7th," 8. Second, 9. Third, 10. Fourth and resolutions, 11. Notes which must rise or fall to their resolution, 12. f.icense in resolution of the 3rd inversion, 13. En- harmonic change of the diminished 7th, and possible keys to which it may resolve, 14-16. To find roots of fundamental discords, 17. CHAPTER VII.— Essential Discords of the 9TH fage 144 Intervals of chord, i. How distinguished from dominant Qths, i. Progression of the notes of the chord, 2. Inversions and their resolutions, 3. Degrees upon which chords of the 9th may be taken, 4. Upon which the inversions may be taken, 5. CHAPTER VIII.— The Dominant iith and 13TH page 150 Formation of chord of nth, I. Resolutions, 2. Inversions and resolutions, 3. Chords of nth upon supertonic and tonic, 4. Dominant 13th, 5. Inversions, 6. Reso- lutions of 13th, 7, 8. Resolutions of inversions, 8. Supertonic and tonic 13th, 9. CHAPTER IX.— Suspensions page 162 Definition and example of suspension, i. Preparation and position in bar, 2. Notes available as suspensions, 3. Rules for their use, 4. Suspended 9th, major keys, 5 Suspended 4th major keys, 6. Suspended 9th and 4th, minor keys, 7. Suspen- sion 7-8 ; rising suspensions, 8. Differences between suspensions and diatonic discords, 9. Rules for accompanying suspensions, 10, 11. Double and triple suspensions, 12. Delayed resolutions, 13. Ornamental resolutions, 14. CHAPTER X.— Pedal-Notes fage 179 Definition of pedal : notes available as pedals, i. Modulation during pedal passage, 2. Pedal as harmony note, 3. Examples of pedals, 4. Chief chords employed upon a pedal, 5. Major chord on submediant, 6. Inverted pedal, 7. Double pedal, 7. Figuring of pedal passage, 8. CHAPTER XI. — Unessential Discords page 188 Definition, i. Passing notes, 2. Rules for their use, 3-5. Figuring of passing notes, 6, Auxiliary notes, 7. Changing notes, 8. Anticipations, 9. Retardations, 10. Arpeggios, n. Ground bass, 12. CHAPTER XII.— Sequences page 203 Definition, " melodic " and "harmonic" sequences, i. Real and tonal sequences, 2. Licenses allowed in sequences, 3, Modulating sequence, 4. • CHAPTER XIII.— Chromatic Chords page 208 ■^hromatic chord, i. Chromatic concord on supertonic, 2. Chromatic concord of minor 2nd of key, and the "Neapolitan 6th," 3. Chromatic chords in major key, 4. xii CONTENTS. CHAPTER XIV.— Chromatic Fundamental Discords page 218 Supertonic 7th with inversions and resolutions, i. Tonic 7th, inversions and resolu- tions, 2, Supertonic and tonic 9th, inversions and resolutions, 3. Eleventh on supertonic and tonic, 4. Thirteenth on supertonic and tonic, 5. Chromatic chords of the dominant 9th and 13th, 6. Chromatic resolutions of dominant discords, 7. CHAPTER XV,— Thr Augmented 6th, and the Augmented 5TH ... page 239 Notes upon which the augmented 6th may be taken, and intervals of the chord, i. " Italian, French, and German" 6th, 2. Chord on minor 2nd of key, 3. Resolu- tions, 4, 5. Inversions, 6, Augmented triad inversions and resolutions, 7. CHAPTER XVI.— Modulation page 253. Modulation of three kinds, i. Natural or simple modulation, attendants of a key, 2. Chords commonly used in modulating, 3. Gradual and sudden modulation, 4. Chords approached as belonging to one root, and quitted as belonging to another, 5,6. Extraneous modulation, 7. Keys most easy of access. 8. Compound modula- tion, 9. Enharmonic modulation, 10. By means of the diminished 7th, 10. By various other chords, 11, 12. Notation of modulating chord and examples, 13. CHAPTER XVII.— Rhythm page 274 Disposition of accent, i. Periods, sections, phrases, and feet, 2, 3. Analogies in language, 4. PART III. MUSICAL FORMS • f'^S^ -77 PART I. ELEMENTS OF MUSIC. CHAPTER I. I The word music is of Greek origin {mousike, from mousa, a muse), and signifies the art in which sound is the principal element. 2. Musical sounds are produced by rapid and periodic vibrations of the air. Irregular vibrations result only in noise, and very slow vibrations are not heard. 3. In order to represent sound to the eye, it is necessary to have a system of musical notation. 4. Musical sounds or notes are named after the first seven letters of the alphabet : A, B, C, D, E, F, G; and these are represented by various characters, such as J J which are written upon and between five horizontal and parallel lines, called the stave or staff. 5. As this stave is not of itself sufficient for all requirements, ledger or light lines are added above and below it, for the repre- sentation of notes that are too high or too low to be written within it. The term ledger, or leger, is derived from the French word leger — light. B 2 PART I. — CHAPTER I. 6. In the present day two staves are employed for pianoforte music, each consisting of five hnes and four spaces. On the upper one is written the music for the right hand, and on the lower one that for the left hand. For organ music and for songs three staves are required. Pianoforte. Right f ^^^^^^^^^^^E^^^E Hand. Left 1 Hand. Organ. Voice. Right Hand. Pianoforte Accompaniment. Right Hand. Left Hand. Left Hand. Pedals. When more than three staves are employed, as in music for an orchestra, &c., a composition is said to be written in Full Score. Two staves constitute Short, or Compressed, Score. Instances are extant of a stave of four lines, used chiefly for church music, but it is now discarded. In former times a series of eleven lines was used, called the Great Stave ; but afterwards, for convenience' sake, the middle line was omitted, and the shorter five-line staves were employed instead. Stave of Eleven Lines. 7. Clefs.— A clef is a sign placed at the beginning of a stave, to fix the position and the alphabetical name of the notes. Without a clef, notes written on a stave bear no name and represent no sound. The clef is a key to the stave, and determines the position of one note, from which all the others are counted. ELEMENTS OF MUSIC. 3 The word is derived from the French clef, or cle, or the Latin davis^ meaning key. See Note.^ 8. The two clefs most in use are the treble or G clef, and the bass or F clef : — Treble clef. Bass clef. The treble clef fixes the position of G on the second line of the stave, which line is enclosed by the final curve of the clef This G is the first one above the C nearest the middle of the pianoforte. Example of the Notes on the Treble Stave. EFGABCDEF Lines. Spaces. EGBDF FACE The bass clef fixes the position of F on the fourth line of the stave, a dot being placed on each side of the line. This F is the first one below the C mentioned above. / Example of the Notes on the Bass Stave. ' G A B C D E F G A Lines. Spaces. 1 ^ 9 4» ' i , 1 ' 1 — J — ' GBDFAACEG 9. There is also the C clef, which is called soprano, alto, or tenor, according to its position on the stave. When placed on the first hne, it is the soprano clef ; when on the third, it is the alto clef • and when on the fourth, it is the tenor clef Examples. Soprano clef. Alto clef i i 3 Tenor clef -us- or' ^ From the Latin clavis {a key) are derived the words clavier and clavichord, meaning a keyed instrument. PART I.— CHAPTER Notes on the Lines and Spaces of the Soprano, Alto, and Tenor Clefs. Soprano clef. CDEFGABCD Lines. Spaces. FACEGGBDF Lines. Spaces. DFACEEGBD The position of " middle C " in all the clefs is shown below. See Note.^ (Except as a test of knowledge, the soprano clef is obsolete in England.) Alto. Tenor. ^g!' Treble. Soprano. C 10. The sections of the Great Stave of eleven lines used for the above clefs are as follows :— For the bass clef: the ist, 2nd, 3rd, 4 th, ^^d 5th lines For the tenor clef: the 3rd, 4th, 5th, 6 th, and 7 th Imes. Fo the alto clef : the 4th, 5th, 6th, 7th, and 8th lines. For the soprano clef: the 6th, 7th, 8th, 9th, and loth hne^^ For the treble clef: the 7th, 8th, 9th, loth, and nth lines. .Tenor stava. Alto stave. Soprano stave. Treble stave. Bass stave. hen. that the first ledger line below the Treble stave, and the Great Stave. .-Elements of music. !'he Great Stave (G, C, and FdeH m 1 For the sake of completeness, all the clefs have been explained in this place ; but it will generally be found desirable to defer the study of the C clef in its various positions until perfect facility in reading and writing in the treble and bass clefs has been acquired. II. When all the clefs have been thoroughly mastered, it will be found useful to write short passages, such as the following one, in the treble, alto, tenor, and bass clefs, taking care to represent exactly the same p'U/i (i.e., height or depth) throughout. The relative position of notes written in various clefs will thus be firmly impressed on the mind. m ^ — ^ 12. A few rules for guidance in the general application of the clefs may be found useful. It must be understood that the object of having various clefs is that music may be included as much as possible within the staves, thus avoiding an inconvenient number of ledger lines. 13. The Treble or G clef is used for the treble or soprano voice, which is the highest, and for the mezzo-soprano voice, which is the next highest voice of women ; for the violin, flute, piccolo, oboe, clarionet, horn, and trumpet ; and for the right-hand music of the pianoforte and the organ. In modern vocal scores this clef is also used for the treble, alto, and tenor voices, the music for the latter being sung an octave lower than it is written. PART I. — CHAPTER I. lA The Alto or C clef is used for the contralto, or lowest voice of women ; for the counter-tenor, or highest voice of men ; for the alto trombone and for the viola. m The Tenor or C clef is used for the tenor, or next highest voice of men ; for the tenor trombone, and for the higher notes of the violoncello and the bassoon. l6 The Bass or F clef is used for the baritone voice of men, which'is lower than the tenor voice and higher than the bass ; for the bass or lowest voice; for the violoncello the bassoon, the G trombone, the tympani, the left-hand music of the pianoforte and the organ, and for the pedal music of the organ. 17. The ordinary compass of the treble, the alto, the tenor, and the bass voice, is given below :— Treble voice. Alto voice. Tenor voice. Bass voice. 18 Notes —Every note has two names : a pitch-name and a time-n'ame The first is determined by its position on the stave ; the last by its shape. The pitch or alphabetical nanie is one of the first seven letters of the alphabet. A, B, C, D, E, F, G ; for under fh e names are comprised all musical sounds. The seven letters are represented by the natural or white keys of the pianoforte ; and it will be observed that the eighth key from any white note is always a repetition of the first, both in appearance and m sound whether higher or lower. This eighth sound is usually called the octave, from the Italian word ottava, eight. 10 There are five black keys on the pianoforte, divided into two ™ups*; one containing three, the other two The note A lies betweeA the two upper keys of the group of three The position of the other white notes can easily be learnt, remembering to reckon upwards, or to the right. Thus : B is the next note above A, &c. (For Black Keys, see Chap. II.) 20. The time-names of notes are as follows :— breve, semibreve, o; minim, J ; crotchet, J ; quaver, j""; semiquaver, 4 ; demiserniquaver, ^ ; semidemisemiquaver, In this list each note is worth half the preceding, and double the following one. 8 PART I. — CHAPTER I. The foregoing table should be learnt by heart, both as it stands and in the reverse way. Thus : two J'= one J^, &c. Example of Pitch (or Alphabetical) and Time-Names of Notes. G ABC D E F Pitch- names Quavers. Crotchet. Quavers. Crotchets. Semibreve. 21 Rests. These are signs used to indicate silence, the length of which is determined by the shape of the rest. There is a rest corresponding to the time-name of each kind of note. The breve rest is square, and fills the space between the third and fourth lines of the stave ; the semibreve rest is oblong, and is placed under the fourth Hne ; the minim rest is oblong, and is placed above the third line • the crotchet rest is an upright line, with one stroke to the right in the third space. A crotchet rest is also frequently represented thus : J. The quaver rest has one stroke to the left m the third space ; the semiquaver rest has two, the demisemiquaver rest three, and the semidemisemiquaver rest four strokes to the left, bee Example below : — Rests. Breve. Semibreve. Minim. Crotchet. Quaver. Semi- Demisemi- Semidemi- quaver. quaver, semiquaver. It is very important to realize fully that a rest represents the time-value of the note of the same name ; and that where a rest is seen, silence must continue for exactly so long as the note ot the same name would be sounded. 22 Dots —A dot placed after a note makes it half as long a-ain ' Therefore a dotted note is equal to the note itself and one of the notes next in value, or if/iree of the notes next in value. Ihus, a dotted semibreve is equal to a semibreve and a minim, or three 1 1 ' I minims :o-=o Gi ord d RECAPITULATION. 9 The value of a second dot is half that of the first. Therefore a double-dotted semibreve is equal to a semibreve, a minim, and a crotchet; or three minims and a crotchet: o-. =o J J or ! I i I . cJ tzi d S A third dot is very seldom seen : its value would be half that of the second dot. The value of the first dot then is half, that of the second a quarter, and that of the third an eighth, part of the note. The above rules apply equally to dots placed after rests. RECAPITULATION. Chapter I. 1. Music. — The art in which feelings and ideas are expressed through the medium of sound. 2. Notes. — Written representatives of musical sounds. 3. Stave. — The five horizontal and parallel lines on and between which notes are written. 4. Ledger Lines. — Extra or light lines added above and below the stave, used for the representation of notes which are be- yond its compass. 5. C/«?/jr.— Signs placed at the beginning of staves, to fix the po- sition and alphabetical name of the notes written thereon. 6. Pitch {or Alphabetical) Name of Notes. — One of the first seven letters of the alphabet. Determined by the clef employed, and by the position of the notes on the stave. 7. Time-Name of Notes. — Determined by their shape. 8. Rests. — Signs to denote silence, and corresponding to the time- names of notes. 9. Dots. — Signs which make the preceding note or rest half as long again. 10. Double Dots. — Where two dots follow a note or rest, the value of the second is half that of the first. jQ PART I. — CHAPTER I. EXAMINATION QUESTIONS. Chapter I. 1. How are musical sounds represented to the eye ? 2. What is the stave? Distinguish between Short Score and Full Score. 3. In what way can notes be expressed which are beyond the compass of the staves ? A Give the names of the notes on the first three ledger lines and spaces of the G and F clefs, above and below the stave. c Of what use are clefs? Give a short explanation of each of those named in the foregoing chapter, and show their relative pitch by the position of " middle C on eacn stave. 6. Name the notes on the lines and spaces of the four clefs. 7. Give the time-names of the various notes in general use, and show their relative value. 8 How many crotchets are contained in a double-dotted minim, a semibreve, a double-dotted crotchet, and a dotted quaver, collectively ? 9. Write the value of a double-dotted minim in demisemiquavers. 10. Express in quavers the value (i) of a dotted breve and (2) of a double-dotted semibreve. CHAPTER II. Sharps, Flats, and Naturals. 1. Inflexion is the alteration of a note on the keyboard, by substituting a higher or a lower one for the original note, without changing its position on the stave. The signs used to inflect notes are called sharps, flats, and naturals, and they must always be placed before the notes to which they refer. 2. A sharp, J, raises a note one semitone ; i.e.^ moves it one semitone to the right. A semitone is the smallest interval found on the pianoforte. An interval is the difference in pitch, i.e., height or depth, between any two musical sounds. 3. A flat, lowers a note one semitone; i.e., moves it one semitone to the left. 4. A double sharp, x, raises a note two semitones, or one tone. 5. A double flat, t?t?, lowers a note two semitones, or one tone. 6. A natural, t?,^ restores a note that has been sharpened or flattened to its original position. It therefore lowers a sharp one semitone, and raises a flat one semitone. 7. A double natural, corrects a double sharp or a double flat, lowering the former, and raising the latter, one tone. 8. When it is desired to take away one sign only of a note that has been made double sharp or double flat, it is done thus — Care should be taken to place the two signs in proper order, remembering that it is the sign nearest the note that affects it; so that in taking away one sign of a double sharp, for example, the sharp must be placed next the note, t||, or it will not effect its purpose. 9. By means of inflexion, we can produce five different sounds on the same degree of the stave. Ex. m G sharp. Gflat. ^ double G double ^ sharp. flat. ! ..J S 10. Black Keys.— All the black keys are sharps and flats. To take the group of three black keys upon the pianoforte. They lie one semitone higher, or to the right of the notes F, G, and A respectively; ^ The natural is a sign of comparatively modern appliance. Formerly the flat was used to lower a sharp one semitone, and the sharp to raise a flat one semitone. A. double sharp corrected a double flat, and vice versa. ,j PART I.— CHAPTER 11. therefore they are F*, Gf, and A* (see 2). They are also one emkone lower than the notes G, A, and B respectively ; therefore IhCT are AV, and ; therefore F| is the same note as G^ GitasAb, andAi;asB['(see3). at must be remembered that this is not true of stringed instru- ments where intervals smaller than a semitone can be obtamed.) The two remaining black keys are one seniitone ^.gher than the notes C and D, and they are therefore C$ and D|. ihey *e also one semitone lower Aan the notes D and E and they "e therefore DP and EP. So that C$ and Db are identical, as are D| and Eb. 11 But though all black keys are sharps and flats, all sharps and flats are not black keys. For the "e'ct note above B is the white key usually known as C ; therefore this key s also B| And because B is the next key below C, n is also C». For the same reason E# is a white key, as is also FP, Thus white as well as black keys can be sharps and flats. 12 They can also be double sharps and double flats. For instanieT As the note D is two semitones or one tone higher han C it must also be CX; and as it is one tone lower than E s EbP This white key then has three names for it is D, and it is rx and it is Ebb. Therefore it will have three positions on the ^4 for It can be written as D, or as CX, or as EbP ; and yet there will be no change of sound. 1-2 To write a note in a different place on the stave and yet to repreLTthl sLe key on the pianoforte, is called an " Enharmomc Diesis, or Change." enharmonic change; tor it is eitner ui , double sharp nor a double flat. A complete list of all the enharmonic changes possible upon the pianoforte is appended— RECAPITULATION. 13 14. It may here be explained that there are three kinds of semi- tone — diatonic, chromatic, and enharmonic. A diatonic semitone is expressed by two following letters, and is written on two degrees of the stave (a). A chromatic semitone is expressed by the same letter, and is written upon one degree of the stave (d). An enharmonic semitone is expressed by two following letters, and is written upon two degrees of the stave. It can be sung, or played upon stringed instruments, but not upon the pianoforte (c). (^) " ic) Diatonic semitone, Chromatic semitone, Enharmonic semitone, GtoAb. GtoG|:. G|toAt7. RECAPITULATION. Chapter II. 1. Infiexion. — The alteration of a note on the keyboard without changing its position on the stave. 2. Interval — The difference in height or depth between any two musical sounds. 3. Semitone. — The smallest interval found on the pianoforte. 4. Signs of Infiexion. — Sharps, flat^, and naturals. 5. Their position. — They must be placed before the notes to which they refer. 6. Sharp. — A sign which raises a note one semitone. 7. Flat. — A sign which lowers a note one semitone. 8. Natural. — A sign used to lower a sharp, or to raise a flat note, one semitone. 9. Double Sharp. — A sign which raises a note one whole tone. 10. Double Flat. — A sign which lowers a note one whole tone. 11. Double Natural. — A sign used to lower a double sharp, or to raise a double flat, one whole tone. 12. Enhar?7ionic Change. — A change of notation, but not of sound. 13. Diatonic Semitone. — One which is expressed by two following letters, and is written upon two degrees of the stave. PART 1. — CHAPTER II. Chromatic Semitone.— On^ which is expressed by one letter, and is written on one degree of the stave. Enharmonic Semitone.— One which is smaller than a chromatic semitone, and which, therefore, cannot be played upon the pianoforte. EXAMINATION QUESTIONS. Chapter II. How can a note be raised or lowered without altering its position on the stave ? How many different sounds maybe represented on one degree of the stave by means of inflexion ? Give an example. Give two names for every black key on the pianoforte. What is the smallest interval or distance obtainable on the pianoforte ? Give instances of sharps and flats, double sharps and double flats, occurring upon the white keys of the pianoforte. What is the name and effect of the following sign, i^? In former times, how was its purpose accomplished ? Where should all signs of inflexion be placed? When it is desired to take away one sign from a double sharp or double flat, how can this be done? Give an example. State what is an "Enharmonic Change," and illustrate your answer by examples. Write on a treble stave (i) the notes A and C. Change them to (a) double sharps, then (b) to naturals ; afterwards {c) to double flats, then {d) to naturals. Write on an alto stave (2) the note D ; change it {a) to a double sharp, {b) to a single sharp, and {c) to a natural. . Give examples of three kinds of semitone, with an explanation of each. . Point out the diatonic, chromatic, and enharmonic semitones in the following passage : — CHAPTER III. Rhythm, Bars, Accent, Time. 1. The subject of rhythm will receive fuller consideration here- after (see Chapter XVIL), and in this place it will only be explained so far as may be necessary to the clear understanding of the present chapter. " Rhythm, or metre, has to do with the symmetrical arrangement of music with regard to twie and accent — music being rhythmical when the accents recur periodically " (Banister). Music is arranged in phrases of varying length in somewhat the same way as language is presented to us in sentences-. Musical phrases are often divided from each other by rests; as are, sentences by stops. The rhythm of a piece should be carefully studied and strictly observed in performance. The word is derived from the Greek, ruthmos, measure, time. 2. Bars. — All musical compositions are divid'ed into small equal portions by means of upright lines placed across the stave. These lines are called Bars, and the music contained between two of them is termed a bar, or a measure of music. The value of every bar in a piece is the same, whether expressed by notes, rests, or both. 3. Accent. — In each bar of music there must be one or more notes more strongly brought out than the others. This stress is called accent, and it must recur at regular intervals throughout every musical composition. Accent must not be confounded with Emphasis, which is denoted by the marks, A, > , sf, rf, etc, placed over any note in order that special prominence may be given to it. The employment of emphasis in music may be compared to that of italics in language. 4. To make music intelligible, it must be written in some fixed form of time. Every bar of music can be separated into a certain number of equal parts termed beats ; the number and value of these beats show the kind of time in which the music is written. 5. Time. — There are two principal divisions of Time ; Even and Uneven. The first includes Duple and Quadruple Times (usually termed Common), the latter. Triple Time. Common Times have an even number of beats in a bar, such as 2 or 4 ; whilst Triple Time is uneven, having three beats m a bar. 6. Common and Triple Time are also subdivided into Simple and Compound Common, and Simple and Compound Triple. i6 PART I. — CHAPTER III. 7. The kind of time employed is indicated by the l^ime- Signature. This is placed at the beginning of every piece of music, and stands immediately after the Key-Signature (see Part 11. , Chap. II., 3). It consists of two figures, one above another, which together represent the fraction of a semibreve, the upper figure being the numerator, the lower one the denominator. The numerator shows the number of beats contained in each bar ; the denominator shows the value of each beat, or the number of parts into which the semibreve is divided. The semibreve is the standard of measure- ment for all modern music. Therefore the figures |, used as a time-signature, mean that the semibreve is divided into four parts, and that two of those parts are taken to form each bar. As the fourth part of a semibreve is a crotchet (see Table of Relative Value of Notes), then | means that two crotchets, or their equivalent in other notes or rests, are contained in each bar. The same reasoning will be found to apply to every other time-signature. The term "simple time," therefore, means that each beat is an equal part of a semibreve. The following are examples of Simple Time : — Two minims. ^ i i Two crotchets. Two quavers. ft: Three minims. Three crotchets. 1 Three quavers. Three semiquavers. _« it i Four minims. 1=F C5 ^ Four crotchets. 5 i^a 00 RHYTHM, BARS, ACCENT, TIME. 17 Four quavers. 1 .. ' — Four semiquavers. 8. Cojnpound Time is formed by the addition of a dot to each beat of simple time ; so that, whilst in the latter each beat is of the value of one note, in the former it is of the value of a dotted note. Thus the compound form of four crotchets in a bar is four dotted crotchets, and each beat represents a crotchet and a half — that is, a crotchet and a quaver, or three quavers. There are, therefore, four beats in the bar, each of the value of a dotted crotchet, and thus it is expressed by the time-signature All compound time signatures are formed in the same way ; for, as we cannot write figures to represent a dotted note, the figures of the time-signature show the number of notes next in value which are contained in each bar. Therefore, as is the compound form of % it is evident that in order to obtain the compound form of any simple time, it is only necessary to multiply the top figure by three, and the lower one by two. And in the same way, to obtain the simple form of any compound time, the top figure must be divided by three, and the lower one by two. Perhaps, at some future time, it may be thought well to add a dot to the lower figure of a time-signature, for the compound form of any simple time, which plan would obviate the present confusion. The compound form of \ would then be %, signifying four dotted crotchets. The following are examples of Compound Time : — Six minims, or two dotted semibreves. r3 — : — Q ' Six quavers, or two dotted crotchets, Six semiquavers, or two dotted quavers. PART I. — CHAPTER III. Nine crotchets, or three dotted minims. Nine quavers, or three dotted crotchets, ^ Nine semiquavers, or three dotted quavers. Twelve quavers, or four dotted crotchets. 0 1- '-^ Twelve semiqua vers, or four dotted quavers. s: o a. ■ I Twelve demisemiquavers, or four dotted semiqu.avers. Twenty-four semiquavers, or eight dotted quaver^_0 ^^^^^^^^^^ ^- 0 The simple form of this would be |, but it is n-ot in use. RHYTHM, BARS, ACCENT, TIME. 19 9. There are two exceptions to the rule that a time-signature must consist of two figures. Instead of the latter, we sometimes see C or (jj at the beginning of a piece of music. The first indicates a value of four crotchets in a bar, and this time is more frequently employed than any other.^ The half circle with the stroke through it represents the only kind of time in which the semibreve is not the standard of measurement. It is termed either a//a breve {a la breve) time, or tempo a capella^ church time. In this form of time, the breve is the standard of measurement ; and it is chiefly used for church music, having either four or eight minims in a bar. The breve signature does not necessarily mean a slow time, for it is generally played faster than the value of the notes would seem to indicate, the semibreve having but little more value than the ordinary minim, the minim than the crotchet, and so on. These two signa- tures, with examples, are given below — #— p — 1 0 0 & 1 — G>—^ — t ' Table of Time-Signatures. Simple Duple. Compound Duple. 2 1 2 2 2 2 2 4 8 16 Simple Triple. 2 32 6 6 6 6 6 2 4 8 16 32 Compound Triple. 3 1 3 3 3 3 2 4 8 16 3 32 9 9 9 9 9 2 4 8 16 32 Simple Quadruple. 4 32 Compound Quadruple. 4 1 4 4 4 4 2 4 8 16 12 12 12 12 lS 2 4 8 16 32 10. In all cases where the top figure of a signature is higher than four, the music is in compound time. 11. The arrangement of Accents. — In all kinds of time, the strongest accent must fall on the first beat in each bar, and wherever this rule renders it necessary, the music must begin with an incom- plete bar, which should be completed at the end of the movement. (See (d) in the next example.) In duple time there are two accents ; one strong, on the first beat, and the other weak, on the second beat {a, b). ^ The C represents a half-circle, and was formerly used as a symbol of incom- pleteness, representing common or imperfect time. Triple time was considered perfect, and so was indicated by a circle O? the symbol of completeness. In modern music the C is frequently replaced by ^; and the circle is quite obsolete. 0 Rarely or never seen. 20 PART I. — CHAPTER III. In triple time there are three accents; one strong, on the first beat, and two weak, on the second and third beats (c, d). In quadruple time there are four accents; two strong, on the first and third beats, and two weak, on the second and fourth beats {e, /). 12. Triplets.— A triplet is a group of three notes, played or sung in the time of two of the same value. They are often marked by a slur, and the figure 3 over them, but should these signs be omitted, the grouping of, for instance, three quavers to one crotchet, is sufficient to indicate the triplet ^ triplet may consist partly of notes and partly of rests, as in the example below :— 3^ 3 3 3 1 0 ^ — — * 1 — 1 i ■ — m — 1 p F H — r I There are also Quadruplets, i.e., four notes played in the time of RHYTHM, BARS, ACCENT, TIME. 2T three of the same value ; Quintuplets, five notes in the time of four ; and Sextuplets, six notes in the time of four. 13. In writing music, great care should be taken to group the notes correctly and according to the beat. For example, a bar may- contain six quavers, and yet may be in either of three kinds of time, except for the different arrangement and accenting of the notes. See the following examples : — Simple Triple. Compound Duple. ' Simple Duple Six quavers in a bar. ^ — r— I 1-1 r- | : [$ Twelve quavers in a bar. Simple Triple. Simple Quadruple. Compound Quadruple, 1 — ^ n m 2 — -g : : . ...-xi it 14. When it is required to fill up incomplete bars with notes or rests, each beat or division of the bar must be clearly defined. Except in quadruple time, notes or rests of greater value than one beat should not be used. A semibreve rest may, however, be used to denote silence during a whole bar, whatever the time signature may be. See (2) in the next example. 22 PART I. — CHAPTER III. Examples of Completing Bars with Rests. Complete the following bars with rests : — j Question. Answer. |' (2) Question. Answer. i Question. Answer. Question. Answer. ^ r j Question. Answer. 15. A Table of corresponding Time-Signatures is given below, showing what is the compound form of each simple time. Duple. Simple. Compound. Triple. Simple. Compound. Quadruple. Simple. Compound. 2 6 3 9 4 12 1 " ' 2 2 ■ ' 4 2 ■ 4 2 6 3 9 4 12 2 ' " 4 4 • 8 4 " ' 8 2 6 3 9 4 12 4 ■ ' 8 8 ■ 16 8 ' ' 16 2 6 3 9 4 12 8 ' ■ 16 16 ■ • 32 16 * " 32 2 6 16 ■ • 32 RECAPITULATION. Chapter III. Rhythm. — The symmetrical arrangement of musical ideas. Accent. — Regular stress. Emphasis. — Special stress, to bring a note into greater prominence. Bars. — Upright lines, placed across the stave to divide the music into equal portions. Time. — Arrangement of accents. Time- Signature. — Two figures, placed at the beginning of a composition immediately after the key-signature, represent- ing the fraction of a semibreve ; the upper figure showing the number of beats in a bar, the lower one the value of each beat. EXAMINATION QUESTIONS. 23 7. Divisio7is of Time. — Two. (i) Even, which includes both duple and quadruple times, usually called common, and (2) Uneven, which includes triple times. 8. Subdivisions. — Simple and compound common, and simple and compound triple. 9. Simple Time. — The value of each beat is that of an equal part of a semibreve. 0. Co77ipound Time.— The value of each beat is that of a dotted note, or the addition of a dot to each beat of simple time. 1. Alia breve. — According to the breve, i.e., time in which the breve is the standard of measurement. 2. 7h//^/.— Three notes played or sung in the time of two of the same value. 3. Position of Accents.— The strongest accent must fall on the first beat in each bar. 4. To fill up Incomplete Bars with Notes or Rests. — Each beat must be kept separate, and, except in quadruple time, notes or rests of greater value than one beat should not be used. EXAMINATION QUESTIONS. Chapter III. 1. Define Rhythm. Distinguish between Accent and Emphasis. 2. How many kinds of Time are there ? What are their sub- divisions ? 3. What is a Time-Signature ? and to what note has it reference ? 4. Explain the difference between Simple and Compound Time. 5. Give examples of the following times — simple duple, simple triple, compound triple, and compound quadruple. 6. Write two bars according to each of the following signatures :— - 2 3 4 12 0 2 2 4 8 16- 7. Write two bars, each containing twelve semiquavers, grouping them in three different ways, so as to represent three different kinds of time. Give the signatures. 8. Write a few bars according to the following signatures : — 2 4 i 16 ^4 8- Let the first bar consist of notes of the value of one beat, and in the others use dots and rests and notes of various value, including one or more examples of triplets. 2 4 PART I. — CHAPTER III. 9. Complete the following bars (i) with notes of the value of a beat, and (2) with rests. 10. Add bars and time-signature to the following passage : — i Re-write, Example 10 in notes and rests of half the value. Add bars and time-signature to the following passage : — 1 13. Re-write Example 12 in notes and rests of four times the value. 14. Explain the term alia dreve,'' and illustrate your answer. 15. Write tied notes to represent the value of five crotchets (i) in simple, and (2) in compound time. 16. Write two bars according to the following signatures: 4 || 4 f 4- Let each consist (i) of five notes, and (2) of four notes. Do not write two bars alike. 17. Show the possible time-signatures of a bar containing a minim, and of one containing a quaver and four semiquavers. 18. Write three bars consisting entirely of semiquavers. Let the first be in 4, the second in |, and the third in \q time. Group the notes according to the accent in each example. 19. Represent a sound of the length of five quavers in common time, completing the bar with rests. 20. Represent a sound of the length of five quavers in | time, com- pleting the bar with rests. 21. Write (i) in I time a bar beginning with a crotchet and com- pleted with rests ; (2) in | time, a bar beginning with a crotchet and completed with rests ; and (3) in common time, a bar beginning with rests and ending with a quaver, followed by a bar beginning with a crotchet and ending with rests. EXAMINATION QUESTIONS. 25 Add bars and time-signatures to the following melodies : — I i I t • p 1 " i ■sd — 4^ 3 • : k : 1 •hp — » • ll i :|i=p: — 1 — V- _! _N — 1 is — 1 , N . 3i=*=zl: 26 PART I. CHAPTER IV. CHAPTER IV. S3mcopation, Ties, Turns, Pauses, Abbreviations, and Musical Terms. I. It has been laid down as a general rule that the principal accent must fall on the first beat in each bar. Frequently, however, for variety or special effect, the accent is placed on the unaccented portion of the bar, and by means of a tie (see 2) is carried over the accented beat. This reversal of accent is called Syncopation. The word is derived from the Greek suncope, meaning cutting, or (in grammar) the omission of a letter or syllable in the middle of a word. Its application in music is not obvious, but it may possibly have reference to the omission of the regular or grammatical accents. Syncopated notes are brought into special prominence, and, in the example below, the last note of each of the triplets must receive the strongest accent. ^ ^ _Schumann. 3 Students are recommended to exercise themselves in finding examples of syncopation in musical compositions. 2. Ties. — A tie or bind, — ^, when used to connect two notes in the same position on the stave, and precisely similar, means that the first only is to be struck, and the second held on to its full value. Should the second note be altered by inflexion, or should it be on a different degree of the stave, the tie would be called a " slur,^^ and its use would be to enjoin smoothness and connectedness in performance, which is also indicated by the term legato, smooth. 3. The reverse of legato is denoted either by the term staccato, detached, disconnected, or by means of dots and dashes : J J A slur used with dots means that the notes are to be mezzo, or half- staccato: J J -^'--^ ABBREVIATIONS AND MUSICAL TERMS. 27 4. A pause, often emphasized by the words /unga J>ausa, indicates a prolonged stay on the notes or rests over which it is placed, beyond their ordinary time value. The letters G. P. (Grosse, or General Pause) are also used to signify a pause. 5. Double Bars. — A double bar with dots :[|: or :[|: signifies the repetition of portions of a composition. The dots i^e/ore the double bar refer to the preceding section ; those after it to the following one. The words jDa Capo, from the beginning, written D.C., are also used to denote a repetition. A double bar has no influence on the time ; and the latter should be strictly kept, so that no break can be heard when the repetition takes place. No marks of repe- tition are to be observed more than once. Double bars are always placed at the end of a composition or of an important section thereof. When an alteration of the concluding portion of a section is desired, it is signified thus : — 1 l7? la V olt 1. 1 2da volta. \ — ' Vf — ^— - 1 It will be understood that in the second time of playing the section, the portion marked seconda volta, second time, is to be played instead of that marked prima volta, first time. 6. The words Al Segno, to the sign, or Dal Segno, from the sign, written A.S. and D.S., refer to a mark from which the repeat is to be taken. 7. Small notes called appoggiaturas and acciacaturas are in frequent use. The appoggiatura (so called from the Italian word appoggiare, to lean) has the value of the note written, and takes so much time from the following essential or principal note. It should be leant upon, and brought into prominence, and should be written as played. Example : = j_ J_ . -^^ ^ ~ s s ^ The appoggiatura used to be of two kinds, superior and inferior : the former being written thus, ^J; the latter thus, p J. The first represented the appog- giatura as now understood ; and the second was equivalent to the modern acciacatura. 28 PART I. CHAPTER IV. The acciacatura (from the Itahan acciacare, to crush) is written thus : j', and takes practically no value from the principal note, but it is sometimes described as possessing that of a demisemi- demisemiquaver. , ri l^s:^M K\ .11 1 Example : S = S ^ S or -^s = S • - - d 8. Other embellishments are turns, trills, and shakes, which are shown in the following examples : — From this it will be seen that all marks of inflexion placed above the signs of turns and trills, refer to the next note above the principal one ; and those placed below, refer to the next note below. When a shake is placed over two or three notes in succession, it is usual to pass from one note to the next by means of a turn, and, as a general rule, the turn is used as a finish of a shake, as is seen below.'^ tr tr tr Played. 0 The turn is often indicated by two small notes on the stave, thus :— ABBREVIATIONS AND MUSICAL TERMS. 29 It is often best to begin a shake* with the upper note. This is sometimes indicated as follows : — tr Various other kinds of turns and trills, many of which are now obsolete, may be found in the works of Bach, Couperin, etc. 9. The terms crescendo [cres.) and diminuendo {dim.\ or de- crescendo {decres.), meaning a decrease or dying away of sound, are often indicated by the marks — 1113===- 10. In order to avoid an inconvenient number of ledger lines in representing very high or very low notes, the following signs are often used : 8ve- {ottava), meaning that a note or passage is to be played an octave higher than it is written ; and 8ve sotto or hassa (Italian — sotto, below ; bassa, low), meaning an. octave lower than it is written. The word loco (Italian— is generally written at the end of the mark ; but the termination of the line thus, — ^ is in itself sufficient to indicate the return to the written pitch. ^ Played. , -0- ^ - ^ r r f -^r r i 40 ' — a J 30 PART I. CHAPTER IV. II. A table of the abbreviations in most general use is appended, followed by a list of the Italian terms commonly used in music. I Written.! Played thus. | Written. | Played. | i Bis. I Played. * m \\ IT f 1 ITALIAN TERMS IN GENERAL USE. 31 ITALIAN TERMS IN GENERAL USE. For the Pace of a Composition. Grave Largo Lento Adagio ... Larghetto Andajite ... Ajidantino Moderato Allegro ... Allegretto Vivace . . . Veloce Pi-esto Prestissimo Literally. Grave Large, grand Idly Leisurely Diminutive of largo . Going Less going Moderately Gay, lively Diminutive of allegro Lively Rapidly Very fast Very fast Meaning in music. Very slow Very slow Slow Slow Not so slow as largo Slow Used by some writers to signify- less slowly than andante ; by others^ less quickly than andante. Moderately fast Quick Not quite so fast as allegro Quick Very fast As fast as possible For Slackening and Written. Rallentando ... Rail. ... Ritardando ... Rit. Ritenuto Rit en. . . . Meno niosso Allargando ... Allar. ... Piu mosso Accelerando ... Accel. ... Stringendo Piu stretto Increasing Speed. Meaning in music. .. Slackening It .. Literally less motion Literally enlarging, but used to signify getting slower .. Literally more motion, quicker .. Hastening .. Urging on the speed 35 51 35 For Tone. Written. Literally. Meaning in music. Mezzo pia7io . .. 17lp ... ... Half soft Rather soft Piano .. P ... .. PP ... ... Soft Soft Pia7iissiino . . . Very soft As soft as possible Sotto voce ... Under the voice Very soft Mezza voce . ... With half voice... With moderate power Una cor da ... One string The soft or left hand pedal istobelowered Tre corde ... Three strings ... The soft pedal is to be raised Mezzo forte . .. mf ... ... Half loud Rather loud Forte ... . .. / ... ... Loud ... Loud Fortissimo .. ff ... ... Very loud As loud as possible 32 PART I. CHAPTER IV. Written. Literally. Crescendo . Cres. Increasing ... Sforzando ■ sf Forcing Forzato . > Forced Riiiforzando .. . Pinf, r/z, rf Re-inforcing Decrescendo . . . Decres. . . . Decreasing Diminuendo . . . . Dim. Diminishing Perdendosi . . . Perdeji. . . . Losing itself Mancando Failing, waning Morendo Dying away Smorzando . . Smorz. . . . Smotheringly , Calando Falling away . Molto Poco Poco a poco . . . Ma non troppo Assai Co7i moto Comodo Non tanto ... Quasi Sempre For Increasing and Diminishing Tone. f Meaning in music. Increasing intone Strong emphasis Decreasing in tone Diminishing in tone Getting softer Gradually beinghushed Lessening both in time and tone intensified or modified by as Allegro molto „ Poco piu fnosso „ Foco a poco rit. „ Adagio 7na non troppo „ Presto assai „ Andante con moto „ Allegro comodo „ Allegretto 7ion tanto „ Allegretto quasi allegro (rather faster than alle- gretto^ almost allegro') „ Sempre accelerajido Many of the foregoing terms are often the following words : — Very Little Little by little, gradually... But not too much Lit. enough, but usually signifying decidedly^ very With motion Easily, not hastily Not so much As if : almost Always Sometimes the word glissando, gliding, is seen written over a run : its signification is that the passage should be played by one finger as rapidly as possible, gliding from one key to another. Arpeggio, or Arpeggiando, when written over a chord, means that the notes of that chord are to be played in succession instead of in combination ; this is illustrated in the example of an arpeggio placed amongst the abbreviations. The word is derived from the Italian a7pa, a harp ; the effect of chords played on the harp is aimed at in arpeggi. Tre?Jiolo placed over chords or notes signifies that they are to be repeated as quickly as possible, so as to produce the trembling effect only perfectly attained by stringed instruments. Portamento, gliding from one note to another, applied to vocal and orchestral music. MISCELLANEOUS TERMS AND WORDS. 33 MISCELLANEOUS -4, means at, by, with, etc. A piacere, at pleasure. A battuta, with the beat : this last term being used to denote the return to strict time after hastening or slackening the speed. Da Capo, D.C., from the beginning. Dal Segno, D.S., from the sign. At Segno, A.S., to the sign. Senza replica, without repeat. Senza replica sino, or at fin, without repeat to the end. Volti Subito, V.S., turn quickly. Simile, in a like manner. Ad libitum, at pleasure, freely, with- out strict regard to time. Colla parte, with the solo part. Colla voce, with the voice part. Come sopra, as above. Come prima, as before. ColP arco, with the bow : used in music for strings, indicating the return to the use of the bow after 2i pizzicato passage, i.e., touching (lit. pinching) the strings with the fingers. Una volta, once : lit. one time. Due volte, twice. LHstesso tempo, the same time : meaning that each beat must occupy the same length of time as before, whether the value of it be increased or lessened. Prima volta, first time. Seconda volta, second time. Poi, then. E or ed, and. Ben, well : e.g., ben marcato, well marked. Con sordini, with mutes. In or- chestral music this signifies the placing of small instruments, made of wood or brass, on the bridge of the violins, to deaden the sound. In pianoforte music, it means that the soft pedal is to be lowered. Senza sordini. Orchestral music — the removal of the mutes. Pianoforte music — the lowering of the right hand pedal. "ERMS AND WORDS. Mano destra, M.D., right hand. Mano sinistra, M.S., left hand. French — Main droite, M.D., right hand. Main gauche, M.G., left hand. Ossia, or else ; used when there is a choice of two ways of perform- ing a passage. Latin — Opus, op., work. Tempo rubato, lit. robbed time : ap- plied to a certain free style of playing, taking part of the time value from one note and giving it to another ; hastening or slack- ening for the sake of expression, or special effect. Segue, it follows : meaning that the next movement is to be immedi- ately begun. Attacca, is used for the same pur- pose. Semplice, without embellishment. Tictti, all : meaning that all the voices of a chorus, or all the in- struments of an orchestra, are to perform— used after a solo part, or when only a few persons have been performing. Solo, a part performed by a single voice or instrument. Duet, Duo, 2l piece performed by two voices or instruments. Trio, a piece performed by three voices or instruments. Quartett,Quatuor, a piece performed by four voices or instruments. Quintett, Quintuor, a piece per- formed by five voices or instru- ments. Sestett, Sextuor, a piece performed by six voices or instruments. Septeit, Septuor, a piece performed by seven voices or instruments. Octett, a piece performed by eight voices or instruments. Tacet, be silent : used when a voice or instrument is not to perform during a movement. D 34 PART I. — CHAPTER IV, Manner of Performance. Affettuoso Agitato ... Animato Appassionato Arioso Brillante Brioso Calmato Cantabile or Cantando Capriccioso . . . Con aniore . . . Con anima . . . Con bravura . . . Con brio Con deiicatezza Con dolcezza . . . Con dolore . . . Con espressione Con felicitd ... Con forza Con fuoco Con grazia . . . Con gusto Con leggerezza Con maestd ... Con passione . . . Con spirit o . . . Con tenerezza Deciso Delicato, Deli- catainetite^ Dolce ... ... Dolente Doloroso Affectionately Agitated Animated Passionate In a singing man- ner Brilliant Briskly, energet- ically Calmly In a singing man- ner Capriciously Inalovingmanner With soul, ex- pressively Lit. with bravery- with spirit With energy, life With delicacy With softness, gentleness With sadness With expression In a happy man- ner With force With fire, energy With grace With taste With lightness In a stately man- ner With passion With spirit With tenderness Decidedly Delicately Softly, sweetly Plaintively Sadly Espressivo . . . Giocoso Giojoso Grandioso Grazioso Gustoso Lacrinioso or lagrimoso ... Legato Leggiero Lusingando ... Maestoso Mar cat 0 Martellato ... Marziale — alia 7narcia Mesto Ondeggiante . . . Pes ante Piacevole Placida^nente Poniposo Rapidamente Risoluto ..: Scherzando . . . Serioso Soave Sostenuto spirit oso Staccato ... . . . Strepitoso Te7npo giusto Tenerainente . . . Tenuto Tranquillo . . . Vibrato Expressively Jocosely Joyously Grandly Gracefully Tastefully Mournfully Smooth Light _ Caressing Majestic [ner In a marked man- lit. hammered — signifying the rapid repetition of a note or chord Martial ; ' like a march Pensively In an undulating, waving manner Heavy In a pleasing way Placidly Pompous Rapidly Resolute Playfully Seriously Sweetly, gently Sustained In a spirited man- ner Crisply, detached Boisterously In exact time Tenderly Held Tranquil A tremulous qual- ity of tone ^ The addition of niente to an adjective changes it into an adverb, being there- fore equivalent to the English syllable /y— thus : delicato, delicate, dehcatamentc, delicately. EXAMINATION QUESTIONS. ^5 EXAMINATION QUESTIONS. Chapter IV. 1. What is syncopation? Give an example. 2. Explain the difference between a tie and a slur. 3. What are Double Bars? Give the meaning of D.C., D.S., and 5. Give examples of appoggiaturas and acciacaturas, together with the derivation of the terms. 6. Explain the terms ^oco piu mosso, sempre crescendo, 7neno / fz, con grazia, con forza, ben marcato, gltssando, coUa parte, con sordini, senza sordini, meno mosso. 7. Write as many terms as you can remember relating to pace, putting them in proper order. ' 8. What terms are used (i) for increasing tone, and (2) for lessen- ing it ? 9. Give the meaning in music of staccato, legato, sostenuto, leggiero, scherzando, soave, mesto, maestoso, a piacere, con brio, con dolore, con tenerezza, con gusto, Vistesso tempo, accelerando. CHAPTER V. Intervals. . I An interval is the difference in pitch, i.e., height or depth, between any two sounds. Intervals are reckoned (i) alphabetically, (2) inclusively, and (3) upwards. Alphabetically : that is, by the number of letters employed : e.g. from C to F is a 4th, because four letters are used. Inclusively : that is, reckoning both the first and the last letter. Upwards : that is, from the lowest note to the highest, unless ex- pressly stated to the contrary— 3rd. 4th. 5tli. 6th. 7th. 8th. 9th. 1st, or Unison 2nd. 2. Intervals are divided into two classes ; consonant and dissonant. To the first class belong all perfect intervals, together with major and minor 3rds and 6ths. . To the second class belong all 2nds and yths, together with all augmented and diminished intervals. Consonant intervals are subdivided into perfect and imperfect. The perfect consonances are the 4th, the 5th, and the 8th. (The I St or unison is also perfect, but as it contains no distance, or difference in pitch, it can hardly be called an interval.) The imperfect consonances are major and minor 3rds and 6ths. r-^^c^.,o^f Dissonant. 1 Per act. Impf rfect. All ists or unisons 4ths, 5ths, and 8ths. Major and minor 3rds. Major and minor 6ths. 2nds and yths and all augmented and diminished intervals. 3 There are four major or greater intervals : the 2nd, 3rd, 6th, and 7 th. These are a semitone greater than minor, and a semitone less than augmented. Major intervals may be augmented. INTERVALS. 37 4. There are four minor or lesser intervals; the 2nd, 3rd, 6th, and 7th. These are a semitone less than major, and a semitone greater than diminished. Minor intervals may be diminished. 5. Perfect intervals may be both augmented and diminished. 6. Augmented intervals are a semitone greater than major, or than perfect; and diminished intervals are a semitone less than minor, or than perfect. A table of all simple intervals, i.e., those within the compass of an octave, is appended. /- — Unison, Perfect. 1 Minor. Seconds. Major. Augmented. v=\ i=i — n Thirds. Diminished. Minor. Major. Fourths. Diminished. Perfect. Augmented. Fifths. | Diminished. Perfect. Augmented.] Minor. Sixths. Major. Augmented. X The diminished 2nd would be an interval less than a chromatic semitone— as, for example, from A to Bt>'7 — and is therefore not available. Other intervals not employed in harmony are the aug- mented unison, 3rd, and 7th, and the diminished 6th and 8th. 7. Inversion of Intervals.— To invert an interval is to change the relative position of the two notes by placing the lower one in the upper part, or the upper one in the lower part. Example : Original interval. Inversion. 38 PART I. CHAPTER V. Ill the second chords at (a) and (^) the lower note of the first chord is placed in the upper part, and the reverse is seen at (c) and {d). A 5 th becomes a 4th. A 6th becomes a 3rd. A 7th becomes a 2nd. An 8th becomes a ist. 8. By inversion, /A ist becomes an 8th. A 2nd becomes a 7th. A 3rd becomes a 6th. A 4th becomes a 5th. It will be seen by the foregoing table that the cardinal number of any interval, together with that of its inversion, make 9. Therefore, in order to find an inversion of an interval, subtract the number of the original interval from 9, and the remainder is the answer. Again, there are twelve semitones in a perfect octave. Therefore, to find the number of semitones contained in the inversion of any interval, subtract the number contained in the original interval from 12, and the remainder is the answer. This fact may be verified by reference to the following table of intervals and their inversions. 9. When inverted, Major intervals become minor. Minor become major. Augmented become diminished. Diminished become augmented. Perfect remain perfect. N.B. — In all cases where intervals are augmented or diminished, the semitones employed are chromatic. TABLE SHOWING THE Unison. INVERSIONS OF INTERVALS. Seconds. Major 2nd. Minor 2nd. Augmented 2nd. 2 sen\itones. i semitone. 3 semitones. Inversions. Perfect octave. 12 semitones. Minor 7th. 10 semitones. Major 7th. II semitones. Diminished 7th. 9 semitones. i Major 3rd. 4 semitones. Thirds. Minor 3rd. 3 semitones. Diminished 3rd. 2 semitones. Minor 6th. 5 semitones. Major 6th. 9 semitones. Augmented 6th. 10 semitones. INTERVALS. 39 Inversions. Perfect 4th. 5 semitones. Perfect 5th, 7 semitones. Fourths. Augmented 4th. ^ 6 semitones. Diminished 5th. 6 semitones. 22: Diminished 4th. 4 semitones. Augmented 5th. 8 semitones. /n versions. Perfect 5th. 7 semitones. Perfect 4th. 5 semitones. Fifths. Augmented 5th. 8 semitones. Diminished 4th. 4 serni-tones. Diminished 5th. 6 semitones. Augmented 4th. 6 semitones. Inversions. '$ Major 6th. 9 semitones. Minor 3rd. 3 semitones. Sixths. Minor 6th. 8 semitones. Major 3rd. 4 semitones. Augmented 6th. 10 semitones. Diminished 3rd. 2 semitones. Inversions. m Major 7th. II semitones Sevenths. Minor 7th. 10 semitones. Diminished 7th. 9 semitones. Minor 2nd. I semitone. Major 2nd. 2 semitones. Augmented 2nd. 3 semitones. * The names " tritone 4th" and "imperfect 5th" are often applied to the" augmented 4th and diminished 5th when they are diatonic in a key. 40 PART I. CHAPTER V. 10. Both the notes of a perfect interval must be of the same quab"ty ; i.e., both sharp, both flat, or both natural. Thus perfect 5ths are contained between the notes D and A, G$ and D J, Ct? and Gt? ; and perfect 4ths between the notes Ct and F#, and Db, Ex and Ax. The exceptions to this rule are found in the intervals formed by the notes B and F, and are shown in the following example : — Perfect 5th. Perfect 4th. Perfect 5th. Perfect 4th. 1 1 ^ 11. All major, minor, and perfect intervals are diatonic, and all augmented and diminished intervals are chromatic. Perfect intervals cannot be made either major or minor, and can only be either augmented or diminished. Therefore, a perfect in- terval, when altered by inflexion, loses its diatonic character, and becomes a chromatic interval. 12. Compound Intervals.— All intervals beyond the octave are termed compound intervals. These are the 9th, loth, nth, 12th, 13th, 14th, and 15th. The 15th is called a "double octave." The compound intervals are, with the exception of the 9th, the nth, and the 13th, considered as repetitions, and as the compound forms of those simple intervals to which they correspond. With the one exception of the 9th, compound intervals are figured as simple ones. To find the simple form of any compound interval, it is only necessary to subtract 7 from the number of the compound interval, and the remainder is the answer. Thus, A 9th = a compound 2nd. A ioth = a compound 3rd. An iith = a compound 4th. A 1 2th = a compound 5th. A 1 3th = a compound 6th. A 14th = a compound 7th. A 1 5th = a compound 8th. It is obvious then that the addition of the number 7 to any simple interval will give the compound form of such interval. Thus the compound form of a 3rd is a loth, of a 5th a 12th, etc. Simple Compound - Interval. Form. 2nd. 9th. -o- -©>- -o- -G^ 3rd. loth. , 4tli- nth- 5th- 1 2th. i 6th. 13th. 7th. 14th. 8th. 15th. RECAPITULATION. 41 13. Those compound intervals which are considered as identical v/ith the corresponding simple ones, are treated in precisely the same way as these latter, being either major, minor, perfect, augmented, or diminished, as are the simple intervals. But those intervals which are considered independent are differently treated. A 9th may be major or minor. An nth is always perfect. A 13th may be either major or minor. Major 9th. Minor 9th. Perfect 1 1 th. Major 13th. Minor 13th. RECAPITULATION. Chapter V. 1. Intervals. — The difference in pitch, i.e., height or depth, between any two musical sounds. 2. Simple Intervals. — Those within the compass of an octave. 3. Perfect Consonances. — The 4th, 5th, and octave. 4. Imperfect Consonances. — Major and minor 3rds and 6ths. 5. Dissonances. — All 2nds and yths, and all augmented and dimin- ished intervals. 6. Major Interval. — Greater than minor, and less than augmented, by one semitone. 7. Minor Interval. — Less than major, and greater than diminished, by one semitone. 8. Augmented Interval. — One semitone greater than major, or than perfect. 9. Diminished Interval. — One semitone less than minor, or than perfect. 10. Perfect Interval. — One which, when inverted, remains perfect, and when altered by inflexion, becomes either augmented or diminished. 11. Inversion. — The placing of the lower note of an interval in the upper part, or vice versa, 12. Compound Intervals. — Those beyond the compass of an octave. 13. Compound Intervals which are identical with the corresponding simple ones. — The roth, 12th, 14th, and 15th or "double octave." 14. Compound Intervals which are independently treated. —The 9th, II th, and 13th. PART I. CHAPTER V. EXAMINATION QUESTIONS. Chapter V. T. In what three ways are intervals reckoned? 2. Which intervals are consonant, and which are dissonant ? 3. Distinguish between perfect and imperfect consonances. 4. What are the intervals which may be both augmented and diminished ? 5. Explain the terms, " simple interval," and " inversion." 6. How many major, and how many minor intervals are there ? 7. Give examples of the alteration by inflexion both of major, and of minor intervals. 8. How many semitones are contained in (i) a diminished 3rd, (2) an augmented 5th, (3) a major 7th, (4) a minor 6th, and (5) a perfect octave ? 9. Give the perfect 5th to the following notes, A, Ef, B\>, Gbb, Fx. 0. What does (i) a major, (2) a minor, (3) an augmented, and (4) a diminished interval become by inversion ? 1 . State the distinguishing characteristics of a perfect interval. 2. Name some exceptions to the rule that "the two notes of a per- fect interval must be of the same quality." 3. Give the inversions of the intervals mentioned in Question 9. 4. Write the major 3rd above the notes Git, aJ, D#, Bt?, Fb, E, ebb, Cx, using the tenor clef. 5. Give the inversions of the intervals mentioned in Question 14, using the tenor clef. 6. Write perfect 4ths above all the notes on the lines of the soprano clef. 7. Give five examples of diminished 7ths, with their inversions, using the alto clef. 8. Convert the minor 7ths contained between the notes D and C, E and D, F and E?, G and F, into diminished 7ths, in two different ways. 9. Explain the term " compound interval," and give two examples, o. Augment the perfect 5ths contained between the notes A and E, Bb and F, F and C, G|: and D|:, in two different ways. Use the alto clef. I CHAPTER VI. Major and Minor Scales. 1. A Scale is a succession of sounds ascending and descending by single degrees. There are three kinds of Scales : Diatonic, Chromatic, and En- harmonic. The Diatonic Scale is composed of a series of tones and semitones, arranged in alphabetical order, from any note to its octave. (Derivation oi diatonic : Greek, dia^ through; tonos^ a tone.) The Chromatic Scale proceeds by semitones only, from any note to its octave. (Derivation of chromatic: Greek, chroma^ colour.) The Enharmonic Scale includes intervals smaller than a chromatic semitone, and therefore cannot be played upon keyed instruments. It can, however, be sung, or played upon stringed instruments. 2. The Diatonic Scale has two Modes or Forms, the Major and the Minor, which are distinguished from each other by the position of the semitofies. In the Major Mode, these lie from the 3rd to the 4th, and from the 7th to the 8th degrees of the scale. All major scales must be form.ed upon the model of the NormaP Scale of C major, given below, and must contain the same intervals, sharps or fiats being added as required. Perfect Major Major Perfect Perfect Major Major Perfect 1st. 2nd. 3rd. 4th. 5th. 6th. 7th. 8th. Semitone. Semitone. i : ^ 1 f_ Therefore, all the intervals of a major scale ard either major or perfect. In the scale of C major, the semitones occur in the required places, without the introduction of any sharp or flat, but, in starting from any other note than C, this is not the case, and some alteration is necessary, C being the only scale formed entirely of white or natural notes, and therefore requiring no Key- Signature. 3. Key-Signature is the term used for those sharps or flats which are placed immediately after the clef, and which inflect the notes whose position they occupy upon the stave, throughout the piece. These sharps or flats are called Essential, because they belong to the key in which the movement is written. All other sharps, flats, ^ Normal, i.e., unaltered by inflexion. 44 PART I. — CHAPTER VI. or naturals which occur during the movement are called Accidentals^ and their effect lasts only throughout the bar in which they appear, unless it be carried on by a tie (see Part I., Chap. IV., 2) into the next bar. 4. The technical names of the degrees of the scale are as follows : 1st note. — Tonic or key-note. 2nd note. — Supertonic (above the tonic). 3rd note. — Mediant (midway between the tonic and the dominant). 4th note. — Subdominant (under the dominant, holding the same position under the tonic as the dominant above it). 5th note. — Dominant (ruling note). 6th note. — Submediant (midway between the subdominant and the tonic, being in the same position under the tonic as the mediant is above it). Also occasionally termed Super- dominant (over or above the dominant). 7 th note. — Leading-note (leading to the tonic). Also termed " sub- semitone," and " la note sensible 8th note, — Octave. N.B. — This table should be committed to memory. 5. Tetrachords. — To construct a major scale upon any key of the pianoforte, let us refer to the example given of C major. It will be \ seen that this scale can be divided into two precisely similar halves, ) each consisting of the interval of a perfect 4th (that is, of two tones J and one semitone), the first beginning on the tonic and ending on the subdominant, the second beginning on the dominant, and ending on the upper tonic, or octave ; the two halves therefore being separated from each other by the interval of a tone. These series of four notes are called tetrachords, from the Greek words, tetra, four, and chorde, string. In major scales the notes always occur in the same order, i.e., the two tones precede the semitone. ) 6. Major Scales with sharps succeed each other in perfect ' 5ths upwards, so that the second half of each scale is the first half of the next, and the dominant of every scale thus becomes the tonic of the next. Example : ^ ^ G major. i 2nd tetrachord. 1st tetrachord. Semitone, 1st tetrachord. 2nd tetrachord. C major. ^ Also occasionally termed Non-csscntial, MAJOR AND MINOR SCALES. 45 The second tetrachord of each new scale will be found to need * the addition of a sharp, in order that the semitone may occur in the right places For example, beginning on G, the dominant of C, we find that the first tetrachord is correct, but in the second, the semitone lies from the 2nd to the 3rd, instead of from the 3rd to the 4th degrees. Therefore we must move the third note one semitone to the right, i.e., substitute F# for F (as is seen in the previous example), and the tetrachord is correct. F sharp is therefore the key-signature of the scale of G major. Again ; starting from D, the dominant of G, and retaining the F sharp of the key of G, we find that the first tetrachord is correct, but that the third note of the second tetrachord requires to be raised, and that C sharp must be substituted for C. F sharp and C sharp, then, form the key-signature of the scale of D major. The sharps of the key-signature must always be placed in the order in which they are added, ^ the last one being always the leading-note of the scale. Major scales are arranged in order of addition of sharps, and not according to alphabetical position (thus, A is not the first scale, B the second, etc.). TABLE OF MAJOR SCALES WITH SHARPS. C major. No key-signature. 1 - ^ \ \ 1 ^ . \ -J — 0 — «— ' • m — ^ — d — ^- ^ — ^ \ — \ — t * — • — ^- G major. Key-signature, F|1 — I. =d_H D major. Key-signature, FJ and C|:— 2. 0— - A major. ^ \ \ ' i i ' ' * ' Key-signature, F|;, C|;, and G|;— j. ' — li ^ E maj — h or. K ey-signature, F|;, C|;, GJ, and D|;— 4. -it—' I — 0—\\ 1 The sharps or flats of a key-signature must be kept within the stave, and to this end must succeed each other either in fifths upwards or in fourths downwards. 46 PART I. — CHAPTER VI. TABLE OF MAJOR SCALES WITH SKARYS— confirmed. B major. Key-signature, F|;, C|:, G^, D|;, and A|;— 5, i \ . F|; major. Key-signature, .•=1 1- ' '-^J J i I-. ., g|,d|,a|:, andE|--c. C# major. Key-signature, F^, C|, 0$, Djf, A#, E#, and B|:-7. 7. Major Scales with Flats. — These scales, like those with sharps, proceed by order of addition of flats. Thus we begin with the scale of F, with one flat, and end with that of Cb, with seven flats. Whereas, in major scales with sharps, each succeeding scale is formed by the addition of a tetrachord to the second tetrachord of the preceding scale ; in those with flats, the order is reversed, and each new scale is formed by placing a tetrachord l?efore the first tetra- chord of the preceding scale. Consequently, major scales with flats proceed by perfect fifths dowmvards. We again start from C, using the first tetrachord of that scale as the last one of the new scale, and preceding it with a complete tetra- chord, beginning on F. But, using the natural notes only, we find that there is no semitone in the tetrachord, and that it consists of three whole tones, or an augmented 4th ; therefore we must lower the fourth note of the tetrachord, 2>, substitute B flat for B, and the tetrachord is correct, the 4th is perfect, and we have the scale of F major, with the key-signature of B b . To construct the next scale, we place a tetrachord before the first tetrachord of the scale of F, having again to flatten the fourth note, and we obtain the scale of B flat, with the key-signature of BP and Eb. Thus the key-note of each succeeding scale is the subdominant of the former one, and the subdominant of the new scale is always the note requiring to be flattened. Therefore the last flat of the key- signature is the subdominant, and the last flat but one is the tonic of the scale. TABLE OF MAJOR SCALES WITH FLATS. F major. Key-signature, Bb — i. MAJOR AND MINOR SCALES. 47 Bj? major. Key-signature, Bb and E[7 — 2. Eb major. Key-signature, Bj?, EQ, and A,'' — 3. Ab major. Key- signature, Bb, Eb, Ab, and Db— 4. 1 — 0 — ( „ — « — P — F — ~ — * — . 1 1 11 Db major. Key-signature, Bb, Eb, Ab, Db, and Gb — 5- — \ 1 1 Gb major. Key-signature, Bb, Eb, Ab, Db, Gb, and Cp — 6. « ' « 1 i — ' — 1 1 — Cb major. Key-signature, Bb, Ebi Ab, Db, Gb, Cb, and Fb — 7- -#Jtb-b : ^ i t 1 — i 1 1 ^ — 1 1 — -] 8. The three last scales of the foregoing table, (DP, Gb, and Cb) represent the same keys on the pianoforte as the scales of C^, F$, and B, respectively. The key of Dj7 is often preferred to that of C #, because it contains fewer inflected notes, having only five flats, whereas has seven sharps, and therefore any further change or modulation would necessitate the use of double sharps. E is preferred to cb for the same reason. Gb and Fif contain the same number of signs, the one having six flats, the other six sharps, and the two scales are used impartially. 9. The number of signs contained in the key-signatures of two major scales a chromatic semitone apart, is always seven. Thus, D has two sharps, Db has five flats, Bb has two flats, B has five sharps, etc. 10. Scales with Double Sharps and Double Flats. — These scales are not in ordinary use, but a knowledge of them is sometimes required. The scales of Cf and Cb have every note sharpened or flattened. Therefore we can proceed no farther in the addition of signs without the aid of double sharps or of double flats. These occur in the same order as single sharps and flats, beginning in the first case with Fx and ending with Bx, and, in the second, with BPP, and 48 PART I. — CHAPTER VI. ending with FbP. The key-signatures and tonics of these scales are given below, together with those of the scales which are their enhar- monic substitutes in general use. SCALES WITH DOUBLE SHARPS. ^ — ; N I G sharp ; 8 signs. A flat ; 4 signs. I D sharp ; 9 signs. E flat ; 3 signs. | A sharp ; 10 signs. B flat ; 2 signs. ! E sharp ; 11 signs. F ; i sign. B sharp ; 12 signs. C : none. F double sharp; 13 signs. G ; i sign. 1 I C double sharp ; 14 signs. D ; 2 signs. SCALES WITH DOUBLE FLATS. F flat ; 8 signs. E ; 4 signs. '^B double flat ; 9 signs. A ; 3 signs. E double flat ; 10 signs. D ; 2 signs. A double flat ; 1 1 signs. G ; i sign. | D double flat ; 12 signs. C ; none. G double flat ; 13 signs. F ; i sign. I D double flat ; 12 signs. C ; none. G ' 1 C double flat ; 14 signs. B flat ; 2 signs. In these scales, the last double sharp of the key-signature is the leading-note of the scale, and the last double flat of the signature is the subdorainant of the scale. MAJOR AND MINOR SCALES. 49 11. The foregoing table shows that the number of signs contained in the key-signature of any scale, together with that of its enharmonic change, amounts to 12, until we come to scales in which the number of signs of the key-signature exceeds 12, after which the signs increase by two in each successive scale. For example, contains 9 sharps, and its enharmonic change El?, contains 3 flats : 9-1-3 = 12. F double sharp contains 13 sharps, G has one: 134-1 = 14. The next scale, C double sharp, has 14 sharps, D has two, i4-f 2 = 16. 12. Diatonic Minor Scales. — There are two forms of minor scale in use at the present day ; the ^^armonic, and the Melodic or Arbitrary.^ In the Harmonic form, semitones lie from the 2nd to the 3rd, the 5th to the 6th, and the 7th to the 8th degrees of the scale, both in ascending and in descending. In the Melodic or Arbitrary form, semitones lie from the 2nd to the 3rd, and from the 7th to the 8th degrees in ascending, and from the 6th to the 5th, and from the 3rd to the 2nd degrees in descending. An example of each form is appended. Minor Scale of C. Perfect Major Minor Perf. 1st. 2nd. 3rd. 4th. Perf. Min. 5th. 6th. Maj. 7th. Perf. Oct. Harmonic Form. — : , _ _ _ 1 ' « « 1 ! \~ Melodic or Arbitrary Form. Perfect Maj. Min. Perf. Perf. Major Maj. Perf. Minor 1st. 2nd. 3rd. 4th. 5th. 6th. 7th. 8th. 7th. . ^ . \ -J , ^ ' ■ ^f— ^ — rr^s r— Minor Perf. Perf. Min. Maj. Perf. 6th. 5th. 4th. 3rd. 2nd. I St,. ^ The Harmonic is the truest and most natural form of minor scale; but as the interval of an augmented 2nd, which occurs between the 6th and the 7 th degrees, is more than a tone, and is moreover, a chromatic ^ The minor scale has undergone various changes. The following are two of the older forms, the first being the "^olian " : — 5° PART I. CHAPTER VI. interval/ the scale was on this account considered by many authorities to have lost its diatonic character, and the melodic form was therefore adopted. The effect of this latter form in ascending is, with the ex- ception of the minor 3rd, entirely that of a major scale, and to obviate this, the 7th and 6th are flattened in descending. The intervals of a minor scale are either major, minor, or perfect. The chief characteristics of the minor scale are the minor 3rd and the minor 6th. All minor scales are formed in the same way as the scale of C minor, given above. 13. The terms " relative minor " and " relative major " are applied to a minor and a major scale having the same key-signature. The tonic or keynote of a relative minor is always a minor 3rd below that of its relative major. Therefore the tonic of a relative major must always be a minor 3rd above that of its relative minor. Thus E minor is the relative minor to G major, E being a minor 3rd below G, and the key-signatures of the two scales being the same, namely, F sharp. The harmonic minor scale has six notes in common with its relative majop, i.e., all but the leading-note. The melodic minor scale has the first five notes of the scale in common with its relative major in ascending, and every note in common in descending. 14. A minor scale beginning on the same key-note as the major scale of the same name, is termed its " tonic " minor. Thus C minor is the tonic minor of C major, D minor of D major, etc. ^ In the harmonic minor scale, the 3rds and 6ths must be mnior, but otherwise the notes of a major scale and of its tonic mmor m the harmonic form are identical, the two scales thus havmg five notes in common. In the melodic minor scale the 3rd must be minor, the ascencjing scale being otherwise identical with the tonic major scale ; but m descending, the 6th and 7th are lowered, and there are therefore but four notes in common with the tonic major. But it is clear that the key-signatures of the two scales will not be the same, because every minor scale has the same key-signature as the major scale a minor 3rd above it (see 13 " relative minor "). Therefore there is a difference of three signs between the signatures of any major scale and its tonic minor. For C major has no sharps nor flats, and C minor has three flats ; D major has two sharps, D minor has no sharps, but has one flat ; E major has four sharps, E minor has one sharp, etc. So that three notes are lowered m the ^ See Chapter V., 11. MINOR SCALES. 5^ tonic minors of major scales, either by losing sharps, or by gaining flats, or by both. The notes thus lowered are the 3rd, 6th, and 7 th; but the last is raised by means of an accidental, in order to form the leading-note. 15. Minor scales with sharps proceed by perfect fifths upwards, and minor scales with flats proceed by perfect fifths downwards. The last sharp of the key-signature is the 2nd note, or supertonic of the scale, and the last flat of the key-signature is the 6th note, or sub- mediant of the scale. TABLE OF MINOR SCALES WITH SHARPS. Relative tt • tt A minor. Tonic Major. H armomcForm. ^ ^J !^:^ ^ _ ^ , ^ Major. m jL jL major. i Melodic Form. \ ■ R. M. „ H. F. E m^nor. m T M. PES M. F. J - ! I m R.M. ^ H. F. B minor. — , — \ — ^- T. M. 4^ M. F. -:ir-*- H. F. M. F. I** T. M. TABLE OF MINOR SCALES WITH FLATS. R. M. H. F MINOR SCALES. G minor. 53 T. M. R. M. H. F. C minor. T. M. M. F. i R. M. H. F. Jib ! iiu'lb i =F F minor T. M. 1^ M. F. R. M. H. F. .l?b . ik^b B7 minor. T. M. II Jib . . ^ — 1 1 \ r— EH— 1 v\> \ J ^0 1 0 * R. M. H. F. El? minor. T. M. S5 M. F. 1 ^ 11^' ^ — — 1 ^# " " ^ TT T- Ab minor. M. F. Ik'lbi, II 'i i — 54 PART -CHAPTER VI, l6 A knowledge of minor scales with double sharps and double flats is occasionally required, and a table of their signatures and tomes is appended, together with those of their enharmonic substitutes. The last double sharp 'of the key-signature is the supertonic of the scale; and the last double flat of the signature is the submediant ot the scale. MINOR SCALES WITH DOUBLE SHARPS. E sharp minor 8 sharps. F minor 4 flats. B sharp minor 9 sharps. C minor ; 3 flats. F double sharp minor ; lo sharps. G minor 2 flats. C double sharp minor II sharps. D minor I flat. G double sharp minor ; A minor ; 12 sharps. none. D double sharp mmor 13 sharps. ^ — E minor ; I sharp. A double sharp minor. 14 sharps. B minor. 2 sharps. MINOR SCALES WITH DOUBLE FLATS. RECAPITULATION. 55 B double flat minor ; A niinor ; 12 flats. none. E double flat minor ; D minor ; 13 flats. I flat. A double flat minor ; G minor 14 flats. 2 flats. RECAPITULATION. Chapter VI. 1. Scale. — A succession of sounds, ascending and descending by single degrees. 2. Diatonic Scale. — A acale consisting of tones and semitones, ar- ranged in alphabetical order. 3. Chromatic Scale. — A scale consisting of semitones only. 4. Enharmonic Scale. — A scale containing intervals smaller than a chromatic semitone. 5. Major Diatonic Scale. — A scale in which semitones lie from the 3rd to the 4th, and from the 7th to the 8th degrees. 6. Key- Signature. — Sharps or flats placed immediately after the clef. 7. Essential Sharps or Flats. — Those of the key-signature. 8. Accidentals. — Sharps, flats, or naturals which are not in the key- signature, and whose effect lasts only throughout the bar in which they appear, except when carried on into the next bar by a tie. 9. Key of C, G, etc. — When the music is written according to the scale of C or G. TO. Order of addition of Sharps. — By perfect fifths upwards. 11. Order of addition of Flats. — By perfect fifths downwards. 12. Tetrachord. — A series of four notes, together forming the interval of a perfect fourth, the two tones preceding the semitone. 13. To construct successive Major Scales with Sharps. — Add a tetra- chord to the last one of the preceding scale. 14. To construct successive Major Scales with Flats. — Place a tetra- chord before the first one of the preceding scale. PART I. CHAPTER VI To find the Key-note of a Major Scale with Sharps.— li is a semi- tone above the last sharp of the signature. To find the Key-note of a Major Scale with Flats.— li is the last flat but one of the signature. 3Iinor Diatonic Scale, Harmonic Form.-Y^h^n semitones lie from the 2nd to the 3rd, from the 5th to the 6th, and from the 7th to the 8th degrees, both in ascendmg and m descending. Minor Diatonic Scale, Melodic i^^r;//. -When semitones lie from the 2nd to the 3rd, and from the 7th to the 8th degrees m ascending, and from the 6th to the 5th, and from the 3rd to the 2nd degrees, in descending. Relative Minor.— The minor scale whose key-note is a minor 3rd below that of the major scale with the same key-signature. Tonic Minor.— The minor scale beginning on the same key-note as the major scale of the same name. Notes cofnmon to a Harmofiic Minor Scale and its Relative Major.— Six, namely, all but the leading-note. Notes common to a Melodic Minor Scale and its Relative Major. In ascending, the first five notes, in descendmg, every note. Notes common to a Harmonic Minor Scale a?td its T onic Major.— Five, namely, all but the 3rd and the 6th. Notes common to a Melodic Minor Scale and its Tonic Major.- In ascending, all but the 3rd ; in descending, four notes. Diatonic— KQ.(iox^mg to the key-signature. C^r^.;.^//..-Contrary to the key-signature, but inducing no mod- ulation, or change of key. Enharmonic.-\^\.e^^^\^ smaller than a chromatic semitone. In pianoforte music a change of name but not of sound. EXAMINATION QUESTIONS. Chapter VI. I. What is a scale ? How many kinds of scales are there ? 2* Describe the formation of a Diatonic, a Chromatic, and an En- harmonic Scale. 3 Give the derivation of the words " diatonic " and " chromatic." 4. What are the two forms of the Diatonic Scale ? Give a descrip- tion of each. EXAMINATION QUESTIONS. - 57 5. Explain the terms "Key-signature," "Essential," and "non- essential " or " accidental " signs of inflexion. 6. Give the technical names of the degrees of the scale. 7. What is a " tetrachord " ? Give the rules for the employment of tetra chords in the construction of successive major scales with sharps and flats. 8. Name the rules for finding the key-note of a major, and of a minor scale, with sharps or flats. 9. What is the order of the addition of sharps, and of flats, in suc- cessive diatonic scales ? 0. Explain the terms " relative minor " and " tonic minor." 1. Write out the relative minors of A, F^, D ?, and Bb major, in both the harmonic and melodic forms. 2. W^rite out the tonic minors of E, B, Et?, and Al7 major in both harmonic and melodic forms. 3. How many notes are common to (i) a harmonic minor scale and its relative major, and (2) to a melodic minor scale and its relative major? 4. Give the rules for finding the key-notes of scales with double sharps and double flats. 5. Name the scales in which both sharps and flats occur. 6. Give the technical names of the notes common to a harmonic minor scale, and its tonic major. 7. How many signs are contained in the key-signatures of two major scales, a chromatic semitone apart ? Give illustrations. 8. Write out the scales of A|f, E#, and Bbb major, together with those scales which are their enharmonic substitutes in general use. 9. Write this note ^ and the major 3rd above it. Change the name of the upper note by enharmonic diesis ; say what interval is thus produced, and to which minor key the two notes belong. CHAPTER VII. The Chromatic Scale. I. The definition of a Chromatic Scale, together with the deriva- tion of the term, has been given in the foregoing chapter. Necessarily, there is but one form of the Chromatic Scale, for it both ascends and descends by semitones. There are, however, differences in its notation. Formerly, it was customary to ascend by sharps, and to descend by flats, because this method required fewer accidentals than any other. This is generally called the Arbitrary Chromatic Scale. The intervals of the scale are then as shown in the following example :— The scale here consists of perfect, major, and augmented intervals in ascending, and of perfect, major, minor, and diminished mtervals in descending. 2 But it is now generally considered that a chromatic scale should be written, as far as possible, according to the key-signature of its tonic, and that it should therefore consist of the notes of the major scale of the same name, and of those of its tonic minor m both forms (both ascending and descending) together with the two notes which are not contained in either of the three scales. This is called the Harmonic Chromatic Scale, and its chief characteristic is that such notes as are influenced by the key-signature remain un- changed. This is exemplified in the following chromatic scale of D :— THE CHROMATIC SCALE. 59 _0 jlJ I 4-'— 4 *—. D major. D minor. Harmonic Form, 1 I.J J. 1 Uh= Ot-^ — - M J ^ 1 — — ^ * -tt^ \ — ^ — ^ — ^ D minor. Melodic Form. Q , 1 i u. . ^ — # — « : f- 1 J . ^/ * ' ! ' ' ' 1 3. The minor 2nd and the augmented 4th (marked x) are there- fore the only notes peculiar to the chromatic scale. Most authorities agree in preferring the use of the augmented 4th in ascending, what- ever form of notation be employed ; the reason for this being that, as the leading-note of the key of the dominant, it is more closely allied to the key than the diminished 5th. The minor 2nd, too, considered as the minor 9th of the tonic, is more nearly related to the key than the chromatically raised key-note, and its use is therefore preferred. 4. Another reason for the employment of the Harmonic notation is that all the notes of the scale are then contained in the three fundamental chords of the minor 9th, derived from the dominant, the supertonic, and the tonic. (See Part IL, Chapter VI., 17.) This will be more clearly understood when the chords of the 9th have been learnt, but an illustration is given below, in the key of C, and it may easily be seen, by reference to the appended list of chro- matic scales, that every note of the chromatic scale of C is to be found in one or other of the three following chords. Fundamental Chords of the Minor Ninth. — Intervals of each chord (reckoned from lowest note), — major 3rd, perfect 5th, 6o PART I. CHAPTER VII. minor 7th, and minor 9th. The first chord is on the dominant the key, the second on the supertonic, and the third on the tonic. 1 , TABLE OF TWELVE CHROMATIC SCALES, which the harmonic notation is observed. CHROMATIC SCALES. 6 1 1 1 1 mm T 1 ^ — ^ — ^ — I |,J []J » — ^ — hp — ! 1 — r^i- h — — \ — 1 — 1 — \ — 1 •--iv i=^5 , 1 l=i • — f-i^ 1 1— T 62 PART I. — CHAPTER VII. RECAPITULATION. Chapter VII. 1. Old Form of Notation^ or Arbitrary Chromatic Scale. — Ascending by sharps, and descending by flats. 2. Modern^ or Harmonic Form. — Combination of a major scale and its tonic minor, the latter in both forms, together with the two notes not contained therein. 3. The two notes not contained in the above three scales. — The minor 2nd and the augmented 4th. EXAMINATION QUESTIONS. Chapter VII. 1. Write a chromatic scale, from A to its octave, in two different ways. 2. Explain the reasons for the employment of these different no- tations. 3. What are the intervals of a Harmonic Chromatic scale ? 4. Exemplify your answer to Question 3, by the chromatic scales of Cj, Dt QxV, and G#. Do not write the key-signatures. 5. What augmented interval is always preferred in the chromatic scale to its diminished equivalent ? 6. Which are the notes of the chromatic scale which are not con- tained in the major and minor scales having the same tonic? 7. Point out the diatonic and chromatic semitones in the chromatic scale of F|. PART II. CHAPTER I. Triads and Concords, or Common Chords. I. We are now to learn to understand chords, and to write them. Melody and Harmony are the two great essentials in the writing of music. Melody is a succession of single sounds, such as may be sung by one voice. Ex. r r 1 4 r r 1 1 ' ^ 1 It will be seen that the sounds must be varied; the repeated sounding of one note would not produce melody. Harmony is a succession of sounds in combination ; that is, formed by the singing or playing of two or more notes at the same time. A chord is the combination of two or more notes ; therefore, harmony is a succession of chords. Ex. , ^ — ^1 ^. > i 1 1 i J. ^^ 1 , 1 , ^^r r i 1 1 -4 -4 1 1 1 ! 1 2. The first chord to be learnt is that of the ^n'ad. A triad is the combination of a note with its third and fifth ; consisting, therefore, as its name implies, of three notes. Triads are of four kinds ; major, minor, augmented, and diminished. A major triad consists' of a note with its major third and perfect fifth. A minor triad consists of a note with its minor third and perfect fifth. An augmented triad consists of a note with its major third and augmented fifth. 64 PART II. T— CHAPTER I. A diminished triad consists of a note with its minor third and diminished or imperfect fifth. Major. Minor. Augmented. Diminished. The lowest, or bass note, is called the root of the triad, for it is the fundamental note of the chord, and from it the mtervals are reckoned. 3. If we use the notes of a major scale, and form a triad upon each degree, the result is as follows :— Ex. Major. Minor. Minor. Major. Major. Minor. Diminished. The scale used above is that of C major, in which all the notes of the triads will be found. 1 -n ^ As all major scales are formed alike, the followmg rule will apply equally to scales with sharps and with flats :— . • The tonic the subdominant, and the dominant bear major triads, the supertonic, the mediant, and the submediant bear minor triads, and the leading-note bears a diminished triad 4 The Harmonic minor scale is considered as the foundation of harmony in the minor key, and the notes of all the diatonic chords of the minor key which are most frequently seen will be found m this form of the minor scale. The triads of a minor key are then as follows : Minor Diminished Augmented. Minor. Major. Major. Diminished. fc=== ^ ^^=^=:g i We see that the key-note and the subdominant bear minor triads, the dominant and the submediant bear major triads, and the super- tonic and the leading-note diminished triads ; the mediant alone bears an augmented triad, having an augmented 5th between its root (the minor 3rd of the key) and its 5th (the leadmg-note). It will be observed that all triads on the dominant are major, because the third from the dominant is the leading-note of the scale, and is a major third both in major and minor scales, being accident- ally raised in the latter case. C major. C mmor. Triad on Dominant. TRIADS AND CONCORDS, OR COMMON CHORDS. 65 5. Major and minor triads are also termed Concords, or Common Chords. The bass note or root of a common chord is always the key-note of a diatonic scale, which is major or minor according to the third of the chord. It is evident, then, that augmented and diminished triads cannot be common chords, because they contain an interval which does not occur in any diatonic scale having the root of the chord for its key- note. For instance : the diminished triad on the leading-note of major and minor scales cannot be a common chord, for the 5th is diminished, and the 5th from the key-note of every diatonic scale is perfect. For this reason, too, the augmented triad on the mediant of minor scales cannot be a concord, or common chord, for the 5 th from the key-note would then be augmented instead of perfect, and an augmented 5th does not occur in either the major or the minor scale having the root of the chord for its key-note. This is illustrated in the following examples. C major. Diminished triad SCALE OF B MAJOR. SCALE OF B MiNOR. on leading-note. X X C minor. Augmented triad SCALE OF E f>. MAJOR. SCALE OF Ei?- MiNOR. on mediant. v^u'l uJ H=^ X X X 0 The roots and the 3rds of the triads above are marked x in the scales, the 5ths in the scales are marked ■0-, and it will be seen that they do not correspond with those of the triads. 6. There are then six Concords or Common Chords in a major key, of which those of the tonic, the subdominant, and the dominant are major, and those of the supertonic, the mediant, and the sub- mediant are minor. The chord of the mediant is less often used than the others, as it has a somewhat harsh effect, and unless care- fully treated, is hardly available as a concord. Many authorities deny this chord a place amongst the other concords, thus reducing the number of common chords in a major key to five. 7. There are four Concords or Common Chords in a minor key, of which those of the tonic and the subdominant are minor, and those of the dominant and the submediant are major. 8. Some writers object to the term " common chord " unless four parts are used. The additional part is generally the octave to the root, and this is called " doubling the root." The 5th may also be F 66 PART II. — CHAPTER I. doubled, or the minor 3rd, but the doubHng of the major 3rd has not a good effect. The chord can also be written in three positions, for it consists of three different notes, either of which may be placed at the top. See example : — Chord of C Major. | Chord of A Minor. Root doubled. m-^ — — IS 1 5th doubled. ^ 5-e> 1 Root doubled. 8- 1 5-<5> ' 3rd doubled. 5th doubled. tJQ Chord of G Major. | Chord of D, in 3 positions. | ' 5-?:5 ' — rc? " ^"8 Root doubled, fntt'^^oodf doubled. 3rd at top. 5th at top. 8th at top. -8-0- 12:22: p Chord of D Minor. | 1 Z^^h- — Bad. Bad. 5-e>- Bad. -s-^s*— It is not good to have large and unequal distances between the parts, as in the three last chords above ; as a general rule, it is best to place the widest gap between the two lowest parts. We have already learnt that compound intervals are figured as simple ones,' with the exception of the 9th. Thus, in the last chord above, though the top note is at a distance of two octaves and a 5th from the root, and the next note is at a distance of two octaves and a 3rd from the root, yet they are simply figured 5 and 3. In whatever position a common chord may be therefore, it is always figured 3. o. Concords or common chords may be written in what is called "close position," or "extended position." Tl;\e first is when the 1 See Part I., Chapter V., 12. TRIADS AND CONCORDS, OR COMMON CHORDS. 67 parts lie near together, the second is when they are widely separated. 1 — \ — s — ^—w Close positions. (&\, ? r r=f r i 1^ Extended. |" ^ — & €^ S> O The student should now write the common chords of various keys (Al?, B!? minor, Ef?, minor, etc.) in three positions, doubling alternately the root, the 5th, and the minor 3rd, and using both close and extended positions. 10. In progressions of chords with a figured bass, all unfigured bass notes are understood to bear triads or concords, major or minor according to the note on which they are built. When a |:, t^, or is placed above or below a bass note, it signifies that the 3rd from such note is to be inflected accordingly, and when placed before the figure 5, it signifies the raised or lowered 5th. A note is also often raised a semitone by a stroke through the figure, as ^, i^, % i A r This applies to all figures of a figured bass. Wherever an acci- dental is placed before a figure, the corresponding note must be inflected according to the sign. See example below. JI b7 jf6 X w be J5 J7 x6 II. Complete the following chords, using four parts, and state in each case what kind of triad is indicated. t>5 ff5 Jt5 55 J5 X S « 12. Before proceeding to write chords in succession the following rules must be mastered. 68 PART II. — CHAPTER I. It is forbidden for any two parts to move either in perfect ists or unisons, perfect 5ths, or perfect 8ths or octaves with each other. These faults are shown below. But two parts may repeat the same unison, 5th, or 8th, as at {d) : — At {a) there are consecutive unisons between the treble and alto parts ; at {b) consecutive 5ths between the alto and bass parts, and at {c) consecutive octaves between the treble and bass parts. But there may be perfect unisons, 5ths, or 8ths in two successive chords, provided they do not occur between the same two parts. {a) , . (^) , (^) , . i r r-j ^ r ^ f 1 1 — At {a) there is a perfect 5th between the bass and tenor in the first chord, and between the bass and alto in the second ; at {b) the tenor and alto are in unison in the first chord, and the bass and tenor in the second ; at {c) there is a perfect 8th between the bass and alto in the first chord, and between the bass and treble in the second. These are all correct. Consecutive 5ths are allowed when one of them is an imperfect or diminished 5 th, though this is not desirable between outside parts. Allowed. Not good. Consecutive perfect 5ths and 8ths are also occasionally permitted by contrary motion, but they should be avoided in the earlier stages of part-writing. It is not gpod to proceed in the extreme parts by similar motion to a perfect concord, this giving rise to what are termed hidden consecutives, i.e., consecutive perfect 5ths or 8ths are passed over. TRIADS AND CONCORDS, OR COMMON CHORDS. 69 Example i 8 Therefore, as a general rule, a perfect concord should be approached in the outside parts by contrary or oblique motion. The exceptions to this rule are when the highest part moves a 2nd, and the lowest skips a 4th or a 5th ; and when the harmony moves from dominant to tonic ((2), or vice versa {b) ; or from tonic to subdominant (<:), or vice versa (d) : — {a) {b) [c) (d) 13. The rule forbidding consecutive unisons and octaves does not apply to the singing or playing of whole passages in unisons or octaves, as in the following extract from Beethoven's Choral Sym- phony. The orchestra first plays the passage in octaves, and the voices then sing in unisons and octaves. Voices. r 4—^ — [- I I Alto. Tenor. BA£ ! I I 1 I -t — r -J- -J- - 1 fj gZ ^ v->^S> i Q Z> 70 PART II. CHAPTER I. 14. The leading-note, which occurs in dominant triads, is free to rise or fall when the following chord is some other than that of the tonic. It usually, however, rises by preference, and it should not be doubled. 15. When the two notes of a chromatic semitone occur in two successive chords, in different parts, as at (a), this is a false relation, and is forbidden, on account of its bad effect. But when the two notes are given to the same part, as at {h\ the progression is correct. If one of the notes be doubled, the other must only appear in one of the parts, {d\ or consecutive octaves will result, as at {c). [a) , {b) (^)8 8 8 (^) Correct. Most modern authorities, however, do not consider that false relation exists when the 3rd of the first chord is either the root or the 5th of the second, as at {a) {b) ; nor when the chromatically altered note is part of a fundamental discord (see Chapter III.), as at (i>) • 1 H 1 5 1 i The last rule, with the examples at {c) and (d), will be found applicable in later chapters, when fundamental discords have been explained. 16. As has been said before, equidistance between the parts is desirable, and large skips, with the exception of that of the octave, should be avoided. Where it is practicable, conjunct movement is to be preferred, i.e., movement by single degrees. There are also certain harsh intervals of melody which are for- bidden. These include all augmented and diminished intervals, with the exception of the diminished 5th, the augmented 2nd, and its inversion, the diminished 7th. The first of these may freely be used, provided that it return to some note within the interval {a). The augmented 2nd is more usually found in instrumental than in vocal TRIADS AND CONCORDS, OR COMMON CHORDS. 71 music, and is better avoided in the early stages of part-writing. Whenever used, it must rise. The diminished 7th may be allowed, if it return to some note within the interval {b). The major 7th and intervals beyond the octave are forbidden. Harsh Intervals of Melody. ^1 ,^_ir -^J' ^ {a) Correct. Bad. (3) Correct. Bad. 1 ^ m m ^ The augmented 2nd is sometimes met with in choral works, as in the following passage from Mendelssohn's " Elijah." Two examples of the use of the augmented 4th from the same composer's oratorio, "St. Paul," are added, but the student must avoid writing this interval. m 0 f ^. \ \ 1?' r ^ » g" He went by a whirl - wind to heaven. Stone him to death ! Stone him to death ! His ways are past our un - der stand ing. 17. There are three kinds of motion : similar, contrary, and obhque. Similar motion is when two or more parts move in the same direction (also termed Direct or Parallel motion). Contrary motion is when parts move in opposite directions (also termed Indirect motion). Oblique motion is when one part remains stationary, while another moves. Similar motion Contrary motion between the in all the parts. bass and the other parts. Oblique motion in various parts. ) \ i 72 PART II. CHAPTER I. In progressions of common chords, contrary and oblique motion are preferable to similar, as the latter often results in consecutive 5ths and 8ths. See {a) above. l8. Cadences. — We are next to consider the various kinds of Cadence in general use. A Cadence is the close of a musical phrase, or sentence, or of a rhythmical period. The word is derived from the Latin, cadere, to fall. There are three kinds of Cadence or Close : the Perfect or Full Close, the Imperfect or Half Close, and the Interrupted, Deceptive, or False Cadence. The Full Close has two forms, the Authentic and the Plagal. When the chord of the dominant is followed by that of the tonic, this is the authentic form of the full close, and is generally meant when the term "perfect cadence" is used. When the chord of the subdominant is followed by that of the tonic, this is a Plagal Cadence. When the chord of the tonic is followed by that of the dominant, this is an Imperfect Cadence, or Half Close. When the chord of the dominant is followed by the chord of the submediant, or by some other chord than that of the tonic, this is an Interrupted, Deceptive, or False Cadence. Full Close. Authentic Cadence. Plagal Cadence. i Imperfect Cadence or Half Close. Jk , Interrupted or False Cadence. f -8- I The Full Close, in either form, is final, but the plagal cadence is less indicative of the key than the authentic or perfect cadence. It is often used in addition to the authentic cadence with good effect, and is so frequently employed in church music that it has been termed the Church Cadence.^ In writing the authentic cadence it is indispensable that the leading-note should rise to the tonic. ^ See example above. 1 The Plagal Cadence frequently appears at the end of Handel's choruses, such as, for example, " And the glory of the Lord," the "Hallelujah," etc. 2 Many examples may be quoted in which composers cause the leading-note to fall in a final cadence, so as to end with a complete chord ; but students are rccom- mended to make all leading-notes ascend. TRIADS AND CONCORDS, OR COMMON CHORDS. 73 When a composition is written in the minor key, the final chord is sometimes made accidentally major, by raising the 3rd of the tonic. This is a very frequent device in church music, and is more often seen after the plagal, than after the authentic form of the full close. It is called the " Tierce (3rd) de Picardie." The Half Close, or Imperfect Cadence, is used for the close of a section of a movement, but it is not final; and though it appears sometimes at the end of a movement, this is only when such move- ment is introductory to the next, without any break. It is essential that the last bass note of a composition should be that of the tonic. Examples of the different kinds of Cadence are appended, taken from well-known hymn tunes, of which the chords throughout consist chiefly of concords in their original position ; i.e., with the root in the bass. The tune, " Victory," is entirely composed of common chords with the root in the bass, with the exception of the two chords marked x, where the chord is in its first inversion (see next Chapter). In this and in subsequent chapters, specimens of the chords treated of, will be given in as simple forms as possible, and the student should search for similar examples, first taking chants and hymn tunes, as being the easiest, and afterwards looking into other works. It is also strongly recommended to analyse chords in music, going carefully over all the chords in a selected passage, writing below the names of those which are known, and omitting the unknown ones. This is done in the following examples, where all the common chords are marked. The student will thus obtain familiarity with the ap- pearance of chords, and will be able to distinguish those which have been learnt, at a glance. Plagal Cadence. 0 ■ i J Plagal Cac ence. 1 ^, 1 =1 Q . p & |S>— J A \ ! -r^—f^ 1 1 — 1 1 1 ^ 1 1 1 — \ — Common chord of EA EEEA EXE E "London New." Half-Close, or H \ & ^— 1 ! ^ p— r f r - D C U Bmi. D G D A TRIADS AND CONCORDS, OR COMMON CHORDS. 75 "Winchester Old." 1st line. Plagal Cadence. ! 1 1 1 H i : i m C Dmi. Btr B,^ Windsor." 1st line. X Half Close. P -p p- i 1 m G mi. G mi. " Swabia." G mi. D D ■ ^ ^ 1 ^ 1 —y-i & ~ ^ ' p p -p • — s> — — & D ^ y D G X A B mi. RULES OF PART-WRITING. 19. The faults which are immediately to be explained will not occur in writing successions of concords in their root position, so that the following rules apply chiefly to subsequent chapters^ but they are given here for the sake of convenience. 1. Consecutive 2nds and yths between any two parts are for- bidden. 2. No part may proceed in consecutive 4ths with the bass, or lowest part, except when the second is an augmented 4th. 3. Should a chord be sounded in various positions, or should one or more parts move in arpeggio (see Part I., Chapter IV.), when the 3rd of the chord is quitted by one part, another part must at once take it, the 3rd being a necessary note of the chord. 76 PART II. — CHAPTER I. No two parts, which are at the distance of a 7th apart, may proceed by similar motion to an octave. The interval of a 9th should not be approached by similar motion. The tendency of the two notes which form an augmented interval is to diverge; i.e., to proceed to notes outside the interval. The tendency of the two notes which form a diminished interval is to contract ; i.e., to return to notes within the interval. pi', 1 ^ 1 j • ^ 1 \ 1 1 s J ' ^ 1 X XX w — — g^' — ? ^■'11 - -f^T 1 1 -f 1 1 1 1 At (i) are shown consecutive 2nds in close and extended pos- itions, and consecutive 7ths ; at (2) there are consecutive perfect 4ths between the two lowest parts ; at (3) is shown the takmg up of the 3rd by various parts when chords are played in arpeggio ; at (4) 7ths proceed by similar motion to octaves; at (5) Qths are ap- proached by similar motion ; at (6) in the second chord there is an augmented 2nd between the two upper parts, and an augmented 4th between the upper and lower, and both these intervals diverge ; at X there is a diminished 7th between the outside parts, and a diminished 5th between the two lower parts, both of which intervals contract ; and at XX there is a diminished 5th which contracts. 20. At the end of the chapter there will be found a number of exercises on common chords. In those in three parts, where the 3rd is given, supply either the 5th or 8th, as is most convenient. Where no 3rd is given, supply it. RECAPITULATION. 77 When writing a Full Close in three parts, the 3rd may be omitted in the last chord, when its insertion would cause the leading-note I. {a) 1 1 (^) 1=1? ^ 1 Bad ^ r ( J fL. 1 i S3 It Add alto and tenor parts (the alto must be above the tenor, except when the two parts sound the same note, which must not occur in two successive chords) : — L I I I I Single Chant. Tallis. i —iS> — G (S> 1 ^ — H — 1 — r r ' CHAPTER IL Inversions of the Triad. I. Hitherto we have studied triads in their original positions, with the root in the bass. We are now to place one of the other notes in the bass, thus inverting the chord. As there are two other notes of a triad besides the root, there must be two inversions, for either the 3rd or the 5th may be taken as the bass note. The same notes are used, but the intervals of the chord are changed. For, when the 3rd is placed in the bass, the root becomes the 6th, and the 5 th becomes the 3rd, to the bass note. To take the first inversion of the triad of C. We place E, the 3rd of the chord, in the bass, and C, the root, is then a minor 6th above E, instead of being a major 3rd below it, and G, the original 5th, is a minor 3rd above E. This is the first inversion of the common chord of C, and it is called the " chord of the 6th " (or sometimes the chord of the 6th and 3rd). It is figured | or simply 6. i In three parts ^^'^"^"^^ chord of C. 1st inversion ; 3rd in P ■ Root in bass. Chord of the 6th. Root. In four parts. K 0 \ Chord of C. Root in bass. z~& Chord of the 6th. 3rd in bass. 6-(5>- H— (The guide or direct av signifies the root. ) 2. The root of a chord of the 6th is a major or a minor 3rd below the bass note, according as the chord is the inversion of a major or a minor triad. If the 6th be minor, the fundamental chord is major, and if the 6th be major, the fundamental chord is minor. 84 PART II. — CHAPTER II. The reason of this is obvious, for the inversion of a major 3: produces a minor 6th, and vice versa. -i When writing in four parts, it is best to double the 6th, if possible (the root of the chord) ; and the 3rd may also be doubled ; but the doubling of the bass note is undesirable when the funda- mental chord is major, because the doubling of a major 3rd is seldom admissible ; but when the fundamental chord is minor, the bass note of its first inversion may freely be doubled. In a succession of chords of the 6th, however, it is often necessary to double the major 3rd to the root. See 5 {h) on following page. ^ Not so good. Bass note doubled. Good. 6th doubled. 3rd doubled Good. 4 Every note of a major scale may bear a chord of the 6th There are therefore seven first inversions in a major key, For, though the leading-note bears a diminished triad, and not a common chord yet Its first inversion, the chord of the 6th upon the supertonic of the key, is available as a concord. Q > >■ o .5 .Stj o c 00 ^^^^^^^^ D major. D minor. INVERSIONS OF THE TRIAD. 85 . A first inversion may be taken upon every note of the minor scale, except upon the dominant. Here the 3rd, being the inversion of the augmented 5 th in the mediant triad, is dissonant, requiring preparation and resolution, and cannot, therefore, be used as a con- cord. But the 6th and 8th may be taken on the dominant ; and in four-part writing, either may be doubled. The chord is generally figured Q to distinguish it from ordinary first inversions. (See above (a).) What has just been stated applies equally to both forms of the minor scale. 5. When writing a succession of 6ths in four parts, the 6th and die 3rd, as at (a) below, or the 6th and the 8th, as at (^), should be alternately doubled, in order to avoid the consecutive perfect 5ths and 8ths which result from doubling either the 6th, 3rd, or 8th con- tinuously (c). (^) , 1 I (^) . J L ' i =^ ,^ - — fr^ r~ — h 5 — " I I 1 1 1 - ^- J J - r 6 ~l 1 6 6 6 \ \ ' 6 6 6 6 — f 6 6 6 6 6 6 6 6. The second inversion of the triad has the 5th in the bass. The root then becomes the 4th, and the 3rd the 6th, to the bass note. This is called the "chord of the 6th and 4th," and it is figured %, 3: The three triads which are most frequently taken in their second inversions, both in major and in minor keys, are those of the tonic, the subdominant, and the dominant. The second inversion of the tonic triad is the 4 on the dominant {a), the second inversion of the subdominant triad is the % on the tonic {b) and the second inversion of the dominant triad is the % on the supertonic (c). Dom. 2nd inversion, triad. {a) $ triad. 1- on tonic. I on supertonic. Chords of the 4 are sometimes found upon other degrees of the scale than the three here mentioned ; but students are advised only to use them as shown above. 86 PART II. — CHAPTER II. 7. In four parts it is always best to double the bass note (the 5th to the root) if possible. When this is not practicable, either of the other notes may be doubled ; but when the 6th is minor, it is generally doubled in preference to the 4th. Care is requisite both in approaching and quitting a ^. The reason of this is that the 4th sounded with the bass note produces an incomplete effect, and needs resolution ; and therefore it is that, though the 4th is the root, it is not the best note to double. In this a I differs from a | and a |, for in both these last cases it is best, if possible, to double the root. - 8. Any 2 may be preceded and followed by chords on proximate bass notes {a). A ^ may be approached and quitted by leap from another position of the same chord (b), (c). It may be approached by leap from another chord in its original or root position {d) ; but may only be approached by step from the inversion of another chord {e). The 2 on the dominant is generally followed by a | on the same bass note ; the 6th falling to the 5th, and the 4th to the 3rd. The % must then be figured {d), ie). This is called a " cadential " 4, as it usually occurs at the end of a phrase. It must then be at a more accented portion of the bar than the chord which follows it. But when it is both preceded and followed by a chord on the same bass note, this restriction does not apply (/)• The 4 on the supertonic is generally both preceded and followed by the tonic chord or its first inversion — see {a). The 6th in this chord is always major, for it is the leading-note of the scale. In minor keys it is accidentally raised {g). The 4 on the tonic is commonly followed by a | on the same bass note {h). It will be observed that the bass note is doubled in all the following examples : — INVERSIONS OF THE TRIAD. 87 1 II -x * 1 ] 1 — ^ — n 1 I 1 1 J j — r ' -8- " 1 ■ 1 — 0 1 — ' 1 1 _mL - rj <• Q . 1 1 ' ' — 1 — A ! 1 — ' ft K i V- 1— (/) 1— 1 1 —4-. 1 ^ 1 i — ^ \ 1 i 1 1 1 1 1 1 1 -0- — -. 4 •^^ 1 1 1 1 1 i 1 -- ^ L — ^ \ i— 5> 1 6 — 4— 6 5 4 3 (or-. ^ ' < rJ i ^ , 6 , 1 \ ^ — G> — 6 ©>— 4 -.-! 1 ~^ — 1 — r — ' 6 5 4 3 J J ry— 5 6 & — ■ 1 ^ ^ 6 6 92 PART II. — CHAPTER II. Double Chant. 1 h- —G — O \ i 6 6 — 1 r r ^ ' 6 6 1 ' , — «s> 6 ' ^ — H- ^ ^ — 1 — & -7. P — — ^ & — -\ \— 6 S6 6 5 6 5 4 3 I Hymn Tunes. — - i 1- 1 — ' — ' — ' — h kS* M— LJ ^ 1 \ 6 6 — sJ — &—ri Tf- ^ 1— ^ — f — 1 h — ^ — ^ — t h — \ — p 11-^ 1 __| M 1 i M — ' h — ^^-1 — ^— ^ 1 ^c^-^ 1—^^ — ^ — — EXAMINATION QUESTIONS. 93 ■1 I- 1 ! 1 1 -& & 1 1 J ! 1 =11 y ^-^ ' — e:> — r ^ ■ - — ^ G — Gi— 6 -& — i 1^ =}=:-H- \ ! 1 ^ -G> ^ — Q i 1 ' 6 -A^ — « h \ ' -J- J 1 7 6 h — \ — 6 5 4 3 8. It is necessary that the student should clearly understand the difference between the dominant 7th on a note, and in the key ^/such note ; as on A, and in the key of A. The first means that A is the root, that is, the note upon which the chord is built, and that A is the dominant of the key we are in ; therefore we are in the key of D, or of D minor {a). The second means that the chord is built upon the note E, for E is the dominant of A, and we are to form a dominant 7th in the key of A {b). Dominant 7th on A; Dominant 7th («) 1 r ^ Almost every chant and hymn tune will be found to contain examples of the resolutions of the dominant 7th. Several tunes consist entirely of common chords and their inversions, with the dominant 7th, and these may now be analysed throughout. The H 98 PART II. — CHAPTER III. following are examples of the different resolutions of the dominant 7th :— Resolutions of the Dominant 7th. (i) to the submediant chord ; (2) to the tonic chord ; (3) to a ^ on the same Beethoven. Concerto in E flat. (I) Mendelssohn. Concerto in G minor. (3) 9. It is allowable for the dominant 7th to proceed first to some other note of the chord before taking its proper note of resolution. This is called an ornamental resolution. In the following extracts the 7th resolves ornamentally, rising to the root before falHng to the 3rd of the next chord. Handel. ' ' Jephtha. " X u— ^-^ — — 0 — ^ 9 '1 ' — m -=\ « ; ' r' / TP Handel. Messiah." THE DOMINANT SEVENTH. 99 10. Add inner parts to the following well-known chants and hymns, according to the figures : — Single Chants. , — ^ — ^1 ~^ — ^ 1 1 r> 1 — o & — — ^ ^ — h- -1 ' hH 6 6 1 — — <5» — —Gh— k-, 1 1 — (S» — 1 — — 1 — i*^? — , -& in — — 1 -^^t? i =r=F= S» — 6 5 Double Chants. 1 1 —©J —& — & — -f^ — 6 6 ^3 SB S6 6 3 4 6 7 3—4 3 ^1 1 1 1 ,J , ^ — ^- — ^k^- — G> ^-p- ©> - C^- . — r- 6 r.J 1 6 ^ TTT- 1 1 3 4 6 1 1 —f^ & i f^- 5 6 r—& 1- P U-i "■•[■ ' 1 ^ 6 8 7 4 3 — TOO PART II. CHAPTER III. Hymn Tunes. " Bridehead." 1 1 1 ^ ' J J J- —r^ — & — ^ — -r^- o rj — i p— ' r p ■-t 1 ' ! ^ ^ 1 ^^-1 LJ 1 1 , . 6 6 6 i ! I 1 =F 1 r 6 5 6 Dundee." mm J J J-^ 1 — ^ \ D — h 1 ^ — 1 — M > d .J 1 1 1 — r-" <^ p — ^ — j 1 u 6 S 4 S RECAPITULATION. Chapter III. 1. Fundamental Discord. — A dissonant combination derived either from the dominant, the tonic, or the supertonic, and need- ing no preparation. 2. Essefitial Discord. — A chord in which the dissonant note is a necessary part of the harmony, which may be derived from any root, and which should be prepared as well as resolved. 3. Dominant Seventh. — A major triad on the dominant, with the addition of a minor 7th. RECAPITULATION. 10 1 4. Difference in the chord in major and minor keys. — In the latter, the 3rd of the chord is accidentally raised. 5. Dissonant note. — The seventh. 6. Resolution of yth. — It must fall a minor 2nd in major keys, and a major 2nd in minor keys, or remain to be a note of the next chord. 7. Progression of the jrd. — Being always a leading-note, it must rise. 8. Notes which are free in their progression. — The root and the 5 th. 9. Common Resolutions of the dominant yth. — (i) To the tonic con- cord; (2) to the submediant concord; (3) to a 4 on the same bass note ; (4) to one of its own inversions. EXAMINATION QUESTIONS Chapter III. 1. What is a " Dominant Seventh "? Give an example. 2. Distinguish between a " fundamental " and an "essential " discord. 3. What difference is there between a dominant 7th in the major, and one in a minor key ? 4. Which notes of the chord have a fixed progression, and which are free? 5. Which notes are indispensable, and which may be omitted at will? 6. Name three resolutions of the chord, and illustrate your answer in the key of F. 7. What forms of Cadence may be recognised in some of these resolutions ? 8. Write and resolve chords of the dominant 7th in the keys of B major, B minor, E major, E minor, Cf major, and C f minor. Do not write the key-signatures, but place accidentals before the notes requiring them. 9. Give an example of a resolution of the dominant 7th that is only occasionally seen. — :=t ^ — r -11 Take the six notes above as roots, and form a chord of the dom- inant 7th upon each of them, resolving them into either a major or a minor key. Write the signatures, and figure the bass. I02 PART II. — CHAPTER III. 1 1 . Distinguish between a dominant 7th on G and in G, and between one on B flat and in B flat. Illustrate your answer, give key-signatures and resolutions, and figure the bass. 12. Complete the following exercises : — I I ^3 6 6 5 6 6 5 4 3 6 5 4 3 6 T 4 3 1 ! 1 — 0 1 t — ^ — & — 1 1— - 6 6 6 C6 6 6 6 7 6 6 4 Q 4 Si 4 q 06 6 6 6 7 6 5 4 4 Q 4 C 6 6 Jf6 6 5 6 4 * 6 8 7 W3 6 8 7 6 6 5 6 4 3 6 5 6 6 7 4 ,J 4 3 — 0- 1 -^55> 1 .1 6 7 6 6 7 8 3 EXAMINATION QUESTIONS. Add alto, tenor, and bass parts below the following :- A 103 2:± $ i i P ^ m ■ ^ ^ 1 -J i ' ' ' p — 1 1 1- ^ ■ h- I'll "L-Z^ CHAPTER IV. Inversions of the Dominant Seventh. I. There are three inversions of the dominant 7th, which occur upon the 3rd, the 5th, and the 7th of the chord. The first inversion is the chord of the i, and occurs upon the 3rd of the chord, this being the leading-note of the scale. The second inversion is the chord of the 4, and occurs upon the 5th of the chord, this being the supertonic of the scale. The third inversion is the chord of the 4, and occurs upon the 7 th of the chord, this being the subdominant of the scale. These chords are all shown below, in the keys of G major and G minor. 6 4 4 • • ^ ^ 2 Dominant 7th. 1st inversion. 2nd inversion. 3rd inversion. Root in bass. 3rd in bass. 5th in bass. 7th in bass. Si -0-5- :e:±2: 6 «4 2. The foregoing chords all resolve either upon the common chord of the tonic, or upon its first inversion. 6 The 5 resolves upon the common chord of the tonic. o 6 The 4 resolves either upon the common chord of the tonic, or upon its first inversion, INVERSIONS OF THE DOMINANT SEVENTH. 105 6 The 4 resolves upon the first inversion of the common chord of the tonic. It must be remembered that the 7th to the root is the dissonant note, and whether it appear as the 7th in the original position of the 6 6 chord, as the 5th in the 5, as the 3rd in the. 4, or as the bass note in 6 3 3 the 4, it must be resolved. Wherever the root, and the 5th to the root, appear, their progression is free. The 3rd to the root, being the leading-note, should rise. The three inversions of the dominant 7th are usually figured 5, 3, and 2) respectively ; but the student should remember that 5 implies a 3, 3 implies a 6, and 2 implies a 6. G major. A 1 ! J 1 */ 1 I i ' ' 1 , I A JL 1 ^ J — Kv= ) ) 6 5 4 3 1 6 4 6 2 G minor. 1 ' 1 1 1~ A A A A 1 — ^ — 1 A 1 — — — 1 — 1 1 6 5 4 3 Jf6 6 4 3 6 6 2 3. The following licenses are permitted in the resolution of the second inversion of the dominant 7th : — (1) When the 3 resolves upon the first inversion of the tonic triad, the 3rd (which is the original 7th) may rise^ in order to avoid the doubling of the bass note which is otherwise inevitable. See {a) in the previous example. This doubling of the bass note is especially undesirable in a major key, for it necessitates having two major thirds from the root, and we have already learnt that in four parts this should generally be avoided. See la) below. In a minor key, the bass note of the chord of resolution may be doubled ; but it is more usual to make the 7 th rise, as at {b). (2) The root may be omitted in the 4, and the 3rd (the 7th to 3 the root) may be doubled, as at {c), but in this case one of the 3rds Io6 PART II. CHAPTER IV. must rise, and the other must fall, in order to avoid the consecutive 8ths seen at {d). 1 G> 1 8 1 8 j A. A, 111." r ^^^m — — [ hAV^ — 1 4 6 56 4 6 4 6 3 4 3 3 4. An occasional resolution of the 2 is to a | on the note below ; I.e., the second inversion of the submediant triad. A 3 is also sometimes resolved on a chord of the 6th on the note below. An example of each of these exceptional progressions is appended, taken from Mendelssohn's " St. Paul." =1 > j- 1 i 1 ' '. J_ -J- 1 i I— \ 1 1 1 1 -4- /I — f— t 4 6 6 6 7 6 2 4 4 8 4 4 6 4 6 2 3 The dominant 7th and its three inversions may all be taken in succession, provided the last chord be resolved. Beethoven. Mass in C. 1 -111 \ ^ 1 m -1 N — ^ 1 i± — 0 1 ^^-^ 4 ' 4 2 3 - ^ -J 6 7 5 3 INVERSIONS OF THE DOMINANT SEVENTH. 107 Students are recommended to copy the bass parts of simple hymn tunes, containing only common chords and their inversions, the dominant 7th and its inversions ; to figure the bass according to the chords ; then to shut the book, and to fill in the three other parts according to the figures, afterwards comparing the result with the original. The following hymn tune contains examples of all the inversions of the dominant 7th and their resolutions. 1st inversion (a) ; 2nd inversion (3) ; 3rd inversion {c). .4 ■ ■ --8-- Mm I I I (a) 6 6 4 6 1 6 5 —J . 1 1 4 2 1 1 1 1 6 1 1 6 5 4 3 —J — ! n W f-T~T~T ... . J 1 1 (S) S>— * Arm. 1 1 A J y ? .t^fj^M — — \ — i ^ j,,. 1.,,., t-w-^ ?ir- 1 8 7 5 — 8 7 3 — 5. In the inversions of the dominant 7th, the 7th may resolve ornamentally, as below. Handel. ''Messiah." X X Ornamental resolutions are also practicable in the case of all other discords hereafter to be described. The following consideration of Harmonics need not necessarily be studied in this place. It can, if preferred, be taken later, or even omitted altogether. It is written independently of the rest of the work, and what is absolutely needful for the student to know, is therefore repeated in another place (Chap. VI. 17). PART II. — CHAPTER IV. Harmonics. Harmonics are those sounds which are produced by the vibration of strings, or of columns of air. When a- stretched string which is fastened at both ends, is made to vibrate, the whole length vibrates alone only for a very short time ; afterwards the natural divisions of the string begm to vibrate also, and other sounds are heard, as well as the first one. The primary single sound is called the Fundamental Generator, or Prime, the other sounds all being derived from the principal one. The vibration of half the string produces the 8ve to the first sound, of a quarter, the 8ve to the second sound, of an eighth, the 8ve to the third sound. i w But a string will also vibrate in other aliquot parts, as 3rds, 6ths, etc. The vibration of a 3rd part of the string produces the perfect 5th to the second octave ; of a 6th part, the octave above the 5th ; and of a 12th part, the octave above the second 5th. i The vibrations increase in number in proportion as the length of string decreases, and the more rapid the vibrations, the higher in pitch is the sound. The octave above any note is produced by the vibrations being doubled in number. Thus slow vibrations produce deep sounds, whilst rapid ones produce high sounds. There are various kinds of harmonics : as primary, secondary, tertiary, etc. We shall here only concern ourselves with the first of these. Briefly, then, the primary harmonics of any generator are the major 3rd, perfect 5th, minor 7th, and minor 9th. They are written below in close positions, for the sake of compactness. Thus the primary harmonics of the tonic furnish us with five of the twelve notes of the key. HARMONICS. 109 To obtain the other seven, we turn to the first new note generated by C (other than the repetition of C in various octaves), which is G. This gives us the following notes : — Again, D is the first new note generated from G, and its primary harmonics are as follows : — If we look again at the three chords we shall see that all the twelve notes of the key of C are contained therein. Scale of C. — U-, 91 0 Thus it is clear that all the notes of any key are referable to the tonic, the dominant, and the supertonic. These three notes then are the three generators of a key. It may just be stated that the major 9th, the nth, and the major and minor 13th are secondary harmonics. They may all be taken upon the three generators of the key. This will be seen when the chords of the nth and 13th are explained. 6. Add two inner parts to the following : — Double Chants. -H r- ^— ^ 1 ? L — e> -P P- 6 & — 1^ ' 0 — r H \ ^ 4 6 5 3 4 3 ^ ^ rj r TT-] -1 — ^ ^ r r ^ — u I I I e 6 6 7 4 3 IlO PART II. — CHAPTER IV. INVERSIONS OF THE DOMINANT SEVENTH. Ill Hymn Tunes. m — 1 1 1 , — — CJ r-4 1 1 — — — e> ^1 56 J r-n ! 1 1 — >o Q 4 6 2 tS> O- ?2: 4-1- Z2: 1^ r'f p ' 1 6 «6l ( i h- 6 5 4 S 6 4 4 2 S ffl{4 6 jf6 2 RECAPITULATION. Chapter IV. 1. Inversions of the Dominant yth. — Three in number; viz., the 6 6 6 chords of the 5, the 4, and the 4. 3' 3' 2 6 2. Their positions in the key. — The 5 occurs on the leading-note, the 3 6 6 4 on the supertonic, and the 4 on the subdominant. 3. Dissonant note in each Inversion. — The 5th in the |, the 3rd in the 1 and the bass note in the 1 112 PART II. — CHAPTER IV. 4. Resolution of the dissonant note. — It must fall a 2nd, save in exceptional cases. 5. Notes free in their progression—The root, and the 5 th to the root. 6. Note which should always rise. — The 3rd to the root. 7. Resolutio7is of the Inversions.— | resolves on the tonic con- cord, the ^ on the tonic concord or its first inversion, the J on the first inversion of the tonic concord. 8. Licenses peculiar to the 3.— (i) The 7th to the root may rise, in order to avoid doubling the bass note of the chord of resolution, and (2) the root may be omitted, and the 7th to the root may be doubled, provided that one rise and the other fall, to avoid consecutive 8ths in the resolution. EXAMINATION QUESTIONS. Chapter IV. I.. State the number and the names of the inversions of the dominant 7th. Upon which degrees of the scale do they occur ? 2. How do the inversions resolve, and which is the dissonant note in each ? 3. Write the chord of the dominant 7th and its inversions in the keys of D major and D minor. Give resolutions, and figure the bass. 4. Say what licenses are permitted in the resolution of the |, and give examples in the key of F. 5. Write the chord of the dominant 7th and its inversions in the key of A. Resolve the chords in various ways, give the roots, and figure the bass. 6 Write the chord of the dominant 7th on FJ, with its inversions and resolutions. Do not write the key-signature, but give the roots and figure the bass. 7. Convert the following chords into chords of the dominant 7th, or one of its inversions, in some major key, by the addition of one accidental in each chord. Give roots and resolutions, and figure the bass : — EXAMINATION QUESTIONS. 8. Convert the following chords into chords of the dominant 7th, or one of its inversions, in some minor key. Add one accidental in each chord, give roots and resolutions, and figure the bass : — • n 1 n ^ J ; 1 U , t " P Y — *P r : u 1 U , IJ 9. Use the following notes as roots, and form chords of the dom- inant 7 th upon each of them. Write the inversions also, and resolve the chords into major and minor keys. Give key-signatures and roots, and figure the bass : — 10. Use the four notes given in Question 9 as the bass notes of each of the three inversions of a dominant 7th in either major or minor keys. Resolve the twelve chords, give key-signatures, roots, and figure the bass. 11. Complete the following exercises : — Add alto and te nor parts : — 1 1 1 ii — 1 1 J ^ P 1 - 6 ~i 1 ' 4 6 2 =!= 1 :i — 6 6 6 5 4 4 3 2 1 1 . 11. 6 4 6 3 0 1 6 6 '7 4 3 $6 4 3 6 56 6 7 5 4 5 5 3 — U — Lh 6 7 6 6 4 5 04 2 6 6 6 4— P 6 I 114 PART II. — CHAPTER IV. Add three parts above :- =t==t 4 6446 66546446 66 7 3 532 432 235 56 6 6 84 6 {6 4 • 2 4 3 3 i 1 — \ V 8 7 % - b 4 I ' I i 6 4 6 6 8 6 4 3 4 5 2 6 7 4 3 ^^^^ 0 — 1 • — 1 1 6766Q6 6 Q a 34 4 2 3 Add three parts below 1 — ^ k F ^ ^ 1 1 1 r ^- ~9 ^ m • ^ lU — ^ CHAPTER V. Diatonic or Essential Discords of the Seventh. I. Diatonic chords of the yth, formed upon other degrees of the scale than the dominant, are often distinguished by the terms non- dominant or secondary yths. They are essential discords ; and though they consist of a triad, with the addition of a 7 th, they differ from dominant yths in the following particulars : — {a) The absence of the combination of the major 3rd and minor yth, which is the distinctive feature of a dominant yth. {b) The yth should be prepared as well as resolved — that is, the dissonant note should appear as a consonant note in the preceding chord. {c) They do not invariably determine the key. {d) They have only one resolution, viz., to a chord on the 4th above the root of the yth — in other words, the bass of the discord must rise a 4th. {e) They have only two available inversions, taken on the 3rd and 6 6 yth of the chord, the 5 and the 4. ' '32 Many instances may be met with in the works of both the early and modern composers of the use of essential discords without pre- paration ; but students are strongly advised always to prepare them. Example of Chords of the yxH. in O. •00 ■5 "J'S 0-3 S' u eg , > ^ From the foregoing chords it is seen that a non-dominant yth may contain either a major 3rd and a major yth or a minor 3rd and a minor yth. The same note that resolves one yth may prepare the next, as at (a). The yth must in all cases resolve by falling to the 3rd of the next chord. Ii6 PART II. — CHAPTER V. 2. Essential discords of the 7th may be taken upon any note of a scale, provided they can be correctly resolved. There can be no 7th upon the subdominant (except in a sequence^ see Chapter XV.), because there is no common chord upon the leading-note, where it should resolve. There can be no 7th upon the leading-note, because of the harsh efifect of its resolution upon the mediant triad in a major key, and because the mediant of the minor key bears an augmented triad. The best position for an essential discord of the 7th is upon the supertonic, when it resolves upon the dominant. This is seen at {a) in the previous example. Chords of the 7th are also freely employed upon the tonic, the mediant, and the submediant. 3. That an essential discord of the 7th does not determine the key like a dominant 7th is shown in the following chords. The first may be either in C, or in G, or in F ; the second may be either in C, or in G, or in D : and the third mav be either in C, or in F, or in B flat :— The first of these chords is shown below in each of the three keys, C, G, and F ; the other chords may be similarly worked out by the student : — ! 1 1 \ d— —ry---^ 1 I ' 1 J « ^ d- 1 1 1 ^ m » 1 i 1 JS_ . ^ 1 - — [- 1 , 1 1 1 1 6 7 6 7' 7 6 4. Chords of the 7th are often taken in succession, the bass rising in 4ths, as seen in the next example. It is not necessary that a 7th should always resolve upon a common chord, though this is perhaps the most usual resolution ; but it may resolve upon another chord of the 7th, provided that the root of the second chord be a 4th above that of the first. DIATONIC OR ESSENTIAL DISCORDS OF THE SEVENTH. II7 5. It has been said that there are only two available inversions of non-dominant 7ths, the first and the third. The second inversion, taken on the 5th of the chord, is not used. The 5 resolves upon a concord on the note above its bass 3 6 note, and the 4 on a chord of the 6th on the note below its bass 2 note : — \ 1- -I— 1 '1 ^ t \ ! r^v 1 — 1 J 1 r \ -J- -J- -UvH — ' 1 =4=: 5 2 The I very frequently precedes a cadence, as above, resolving either upon a common chord or a dominant 7th : — 4—. j — \ A — . — 1 r i 1 i J. « J -1 — ^ 6 6 7 5 6. Though there can be no chord of the 7th upon the subdom- inant, because the leading-note does not bear a concord, yet because the first inversion of the diminished triad upon the leading-note is available as a concord (being the chord of the 6th upon the super- tonic), the 3rd inversion of a subdominant 7th may be taken upon the mediant, and resolved upon a chord of the 6th upon the super- tonic. See example below (a). Though there can be no chord of the 7th upon the leading-note (see 2), yet because the first inversion of the mediant triad in a major key is freely used as a concord, the last inversion of a 7th on the leading-note may be taken upon the submediant, and resolved upon the 6th on the dominant. See {b) : — Ot. ..'"' 1,1 ! , J ..it,,'^'. n " * " « ff 6 ' ' 2 5 Il8 PART II. — CHAPTER V. Notes on which 7ths and their Inversions may be taken in a Major Key. 7. A chord of the 7th may be taken on the tonic, the supertonic, the mediant, and the submediant. A I may be taken on the tonic, the mediant, the subdominant, and the dominant. A 2 may be taken upon every note of the scale. In a minor key a 7th may be taken upon the supertonic and the mediant. A I may be taken upon the subdominant and the dominant. A ^ may be taken on the tonic, the supertonic, the mediant, the subdominant, the dominant, and the minor 7th, Students should exercise themselves in distinguishing between dominant and non-dominant 7ths and their inversions, selecting for this purpose hymn-tunes or other simple passages of music. The following passages furnish examples of sequences (see Chapter XV.) of essential discords of the 7th and their inversions, with resolutions. Where a dominant 7th or one of its inversions occurs, it is marked x : — 7ths in root position. Handel. " Israel in Egypt." 1 1 1 , — ^ _J J 1 X X X 1 J, 1 ^bV^' J " 1 • -U 1 1 J. S. Bach. i .111 •! al al ; X ' » 9 ^ ~£=? — 1=— 1«— 7 "7 T "r DIATONIC OR ESSENTIAL DISCORDS OF THE SEVENTH. II9 T. S. Bach. Or^an Fujnie in D major. 1st inversions. •' « 3rd inversions. i J. S. Bach. Organ Fugue in D major. X i i -Ji- -S- J- Y ^ , 1 u— i — J — \ — L- I r ' I 6 4 6 4 2 2 ' I I I r 6 4 6 4 6 4 6 2 2 2 3rd inversions, in three parts. J. S. Bach. Organ Fugue in D major. -m- -m- RECAPITULATION. Chapter V. . Essential discords of the 'jth^ or non-dominant yths. — Chords of the 7 th formed on other degrees of the scale than the dominant, and not containing the combination of the major 3rd and minor 7 th. I. Intervals of non-dominant yths. — A major 3rd, perfect 5th, and major 7th; or a minor 3rd, perfect 5th, and minor 7th. ;. Preparation of dissonant note. — The 7 th, both in the original chord and in its inversions, should appear as a consonant note in the preceding chord. I20 PART II. — CHAPTER V. 4. Progression of the intervals of the chord. —The 7 th must fall ; the 5 th and the 3rd are free, the latter not being a leading-note. 5. Resolution of a non-domiriant yth. — To a common chord, or a chord of the 7th, on the note a 4th above the root of the 7 th. 6. — Inversions— Ty^o available ; the i on the ^rd above the root. 6 3 ' and the 4 on the 7 th above the root. 7. Resolutions of inversions.— The i resolves on a common chord a 2nd above its bass note ; the 4 resolves on a chord of the 6th a 2nd below its bass note. ^ 8. Degrees of the scale upon which chords of the '/th are undesirable. — The subdominant and the leading-note. EXAMINATION QUESTIONS. Chapter V. I. What are non-dominant 7ths ? To what class of discords do they belong? 9.. Explain the particulars in which they differ from dominant 7ths. 3. Upon what degrees of the major scale may 7ths be formed? Give examples in the key of F. Resolve each chord. 4. Give some examples of chords of the 7th and their resolutions in a minor key. 5. What are the available inversions of non-dominant 7ths ? How do they resolve ? 6. Which is the dissonant note in each of the inversions, and what progression must it take ? 7. Show one position in which chords of the 7th upon the sub- dominant and the leading-note may be freely used. Write in the key of A. 8. Resolve the following chords, and say what three major keys they may each be in : — EXAMINATION QUESTIONS. 121 9. Complete the following exercises : — J J J 1 1— ^ — ^^T^ 6 6 7 5 » 6 5 4 3 1 ' 1 1 1 1 r 8 6 6 7 4 54 2 6 7 8 \P i 1 1 il — • 2 J 1 ! 1 ^ 1 • 1 <« T— l-j ^ ^ 1 ' — r^i — r^i"^ 7 7 (iii^^^'i r r r- ^ 1 1 1 ' r r r r r 5 86 1 Jf4 6 4 2 3 — J 6 J J p 1 — ^ — 1 7 4 6 2 r r ^ 4 6 6 2 =^-^ - ' 1 4 2 6 7 7 J J J \ ' 6 6 6 7 4 3 p 1 J * 3 6 5 """^^ ^ ^ ^ 4 6 2 -1 — r ' 4 6 6 2 7 7 7 — f— 1^ =b _ 6 6 5 1 ^g^H'^ r ri 4 6 2 a * 4 6 2 1 \— 6 6 6 5 — I* f- ^ J 0 -* 1« — ^— 1 f_ 6 ^ r p n 777 6 6 -] I ^ * 6 6 5 5 I22 PART II.— CHAl'TER V. 1 ' J Mil * ^ r 1 ' 6 7 1 1 ' r 6 6 5 6 4 5 3 ' 4 2 1 J -J I ! J . ^-^i^* ■mr\r\^ ^ r— « ] 6 4 ' 3 M— -1 — 6 4 6 2 -J- k -| ^-"-^ 6 6 6 4 \ \ 1- 8 P J 7 1 6 6 5 i ^ — r Q= 2 6 tje 4 3 6 «— ^ 4 6 6 2 1 * 1 1 ^ 13 — 4 2 67B— 46 6 66.87 2 5 C - Add three parts below : — CHAPTER VI. The Dominant Ninth. 1. The chord of the dominant 9th is formed by the addition of a 3rd to the chord of the dominant 7th ; this 3rd being the 9th to the root, and being major in a major key, and minor in a minor key. The 9th, like the 7th, is a dissonance, and must fall to its resolution. Being also a fundamental discord, it requires no pre- paration. The treatment of the other notes of the chord is precisely the same as in the dominant 7th. 2. The chord of the dominant 9th consists of five notes ; and in four-part writing the 5th is omitted, and the 9th, 7th, and 3rd are retained. In major keys the 3rd should be kept below the 9th, on account of the harsh effect caused by the proximity of the two notes ; but this does not apply to minor keys. The 9th should not be contracted to a 2nd. The chord of the dominant 9th in D major and D minor is given below : — i-o- '1 ' I 7 Resolutions of the- Dominant 9TH. 3. The 9th frequently passes to an 8th, whilst the other parts are stationary, as at id) ; the chord then becomes a dominant 7 th, and is so treated. The other resolutions are — to the common chord of the key- note (b) ; to its second inversion (^) ; to the third on the san>e bass note (d) ; and to one of its own inversions (e). In five-part writing the 5th is employed, and care must be taken when the 5th and the 9th move at the same time that the 5th should rise ; for if not, consecutive 5ths will result, as at (/). Should the 5th be placed above the 9th, the consecutives would be avoided ; 124 PART II. — CHAPTER VI. but a major 9th should, if possible, be kept in the upper part. In minor keys this does not apply. i l(«) I %4- ^ 6 9 8 i - i l(^), [c) I II I I I I ! ' I I I I I I I I 9 6 7 7 4 3 4 S 1 J J , ^ji p — 1 — » g ^ H — I— --f-^ 1 u — 1 — " Before going on to the inversions it will be well to complete the following exercises : — 126 PART II. — CHAPTER VI. u —J 1- — V- 1 ^ — H — 0— P • - 1 4^ — }- 7 $ 2 f — u 1 e » — L 1 6 j — 9 -1 — < r 1 =4=: _! ^ ±^ 6 5 6 7 4 S — \ 1 S4 2 =i= 6 -1 i 9 8 84 7 — 2 -r^ 1 : 6 J6 4 f 6 5 9 7 11 9 1 6 4 2 6 6 9 7 $ 8 1 p • - 1 1 6 6 •9 7 % — ^ 8 7 - — 6 — 1 7 7 4 F 4 6 2 =1= s 11 4 2 6 ^ 1 6 5 1 I Inversions. 4. There are four inversions of the dominant 9th, of which the last is available only in a minor key. The root is omitted in all the inversions of the chord. 5. Inversions and Resolutions in a Major Key. — The first inversion is the 5 upon the 3rd of the chord, this being the leading- note of the key. It consists of a diminished triad and a minor 7th, and it is often called the "chord of the leading 7th." It resolves generally upon the tonic triad. The dissonant notes are the 7 th and the 5th (the original 9th and 7th), and these must fall ; while the 3rd (the original 5th) must rise, in order to avoid proceeding in consecutive 5ths with the 9th {a). The 7th frequently passes to a 6th, whilst the other notes of the chord remain, as at {b). In this case the 3rd may fall. The leading THE DOMINANT NINTH. 127 7th also sometimes resolves upon a J on the key-note, the 7th and 5th then remaining to be consonant notes of the next chord {c). See also Chapter IX., 13. I I: (^) {c) 1 1 1 — 1 1 r±- 1 & — 1 1 _ ^■ The intervals of the leading 7th are identical with those of the non-dominant 7th, which may occur upon the leading-note of the scale in a sequence (see Chapter XII.) ; and the two chords are distinct from each other by the facts that the leading 7 th needs no preparation, and that it is often resolved upon the tonic triad; whereas the non-dominant 7 th should be prepared, and it resolves upon either a triad or a prepared discord a 4th above its bass note, i.e., upon the mediant. 6. The second inversion is the 5 upon the 5th of the chord, this 3 being the supertonic of the scale. It resolves upon the first inversion of the tonic triad, i.e., the chord of the 6th upon the mediant. The 5 th and 3rd are the original 9th and 7 th, and must fall ; while the 6th (the leading-note) and the bass note rise. The 5th frequently resolves before the rest of the chord, as at {a) : — (2>J_4 \- „ & — ~ * # Gf 1 i^^—hv* 1 5 4 3 — 7. The third inversion is the 4 upon the 7th of the chord, this 3 being the subdominant of the scale. It resolves upon the first inversion of the tonic triad. Here the 3rd and the bass notes are the dissonant notes, whilst the 4th (the leading-note) must rise ; and the 6th (the original 5th) must also rise, to avoid consecutives. But if the 3rd (the original 9th) resolve first, the 5th to the root may fall, 128 PART II. — CHAPTER VI. which obviates the necessity of doubling the bass note of a first inversion of a major concord. See (a) : — i (a) I T2: 6 — 4 — 3 2 8. Inversions and Resolutions in a Minor Key. — The first inversion is the 5 upon the 3rd of the chord, this being the leading- 3 note of the scale. It consists of a diminished triad and a diminished 7th, and is termed the chord of the diminished 7th." Its chief resolution is to the tonic triad, when the 7th and 5th, being the dissonant notes (the 9th and 7th to the root), must fall : whilst the 3rd (the 5th to the root) should rise, because it is better to double the minor 3rd of the tonic triad than to have consecutive 5ths, even though the first is a diminished 5 th. When the 7th resolves first, the 3rd may fall, if preferred (a). The diminished 7th may also resolve upon a § on the tonic, when the 7th and 5th remain to be consonant notes of the next chord. (Refer to Chap. IX., 13, and to Chap. XIV., 7.) 9. The second inversion is the i upon the 5th of the chord, this 3 being the supertonic of the scale. It resolves upon the first inversion of the tonic triad. The 5th and 3rd are the 9th and 7th to the root, and must fall ; while the 6th (the leading-note) and the bass note rise. The 5th may resolve first, as at (d). 10. The third inversion is the 4 upon the 7th of the chord, this being the subdominant of the scale. It resolves upon the first inversion of the tonic triad. The bass note and the 3rd are the 7th and 9th to the root, and must fall ; the 4th, being the leading-note, must rise ; the 6th is the original 5th, and should rise ; though if the 9th resolve first, it may fall — {c). II. The fourth inversion is the 4 upon the 9th itself, this being the submediant of the scale. It resolves upon the second inversion THE DOMINANT NINTH. 129 of the tonic triad. The bass note and the 6th, being the dissonant notes, must fall, and the 2nd and 4th must rise — the latter, because no part should proceed in consecutive 4ths with the bass, this being productive of bad effect. When the bass note resolves first, the 4th may fall {d). The chord then becomes a simple dominant 7th, and is so treated. Resolutions of the Inversions of the Dominant qth in a Minor Key. ^^^^^^ J 1 1 : 1 J. A. 1 J. A — P ^ r— r r u 'a. 7 5 5 — 5 Av 1 '■'W r 86—6 6 6 5 4 54 3 — 3 — |— :|--W»- - 6—6 jf4 - 3 2 I 4th inversion, {d) 1 n -J- r 4 82 6 7 4 5 82 3 12. The dissonant notes in the inversions of the dominant 9th, which must fall to their resolution, or remain to be consonant notes of the next chord, are as follows : — In the first inversion, the 7 th and 5th ; in the second inversion, the 5th and 3rd ; in the third inversion, the 3rd and bass note ; in the fourth inversion (minor keys only), the bass note and 6th. Noks which must rise :— In the first inversion, the bass note and 3rd ; in the secona inversion, the 6th and bass note ; in the third inversion, the 4th and 6th ; in the fourth inversion (minor keys only), the 2nd and 4th, g. 130 PART II. — CHAPTER VI. 13. In the third inversion of the dominant 9th it is allowable for the bass note, which is the 7th to the root, to leap to the key-note, instead of proceeding by step to the note below. See the following examples : — Mendelssohn. Op. 7, No. 7. if ^ Si^ ^ — U ^--f^n ^ ; 1 g- Gade. Novelletten, for Piano, Viol., & 'Cello. -J 1- Mendelssohn. "Lorelei." J 1 P^-J^- i~Q :c 14. The diminished 7th is often called the " enharmonic chord," on account of its peculiar susceptibility to enharmonic change ; for, without changing the bass note, every chord of the diminished 7th may be referred to four roots, as is shown in the following example. Treating the four chords as inversions of dominant minor 9ths in a minor key, the first is in the key of G minor, the second in E minor, the third in C sharp minor, and the fourth in A sharp minor. Some- times it is desirable to enharmonically change the bass note, as at {e), THE DOMINANT NINTH. I3I to avoid an inconvenient number of sharps or flats. The key at {e) will then be B flat minor, instead of A sharp minor, as at {d) :— u'j <*i J '\aU '"hu '-Lit^ b7 IJ S6 6 56 Jt6 S6 56 5 5 54 5 64 54 3 3 x2 — H— 1 ! b6 be 4 t)4 2 or |- 1 The four roots of the diminished 7th given above are then D, B, GJt, and Ej. Looking again at the chord, we see that D is a semitone below El?, the 7th of the chord ; B is a semitone below C, the 5th of the chord ; GJ is a semitone below A, the 3rd ; and E# is a semitone below FJ, the bass note of the chord. Thus the four roots of a chord of the diminished 7 th are the four diatonic semitones b^low the four notes of the chord. It will be observed that the notes of the chord given at (^3;) are enharmonically changed in succession, in order to obtain the new roots. For at {b) the 7th is changed ; at (4 the 5th ; and at {d) the 3rd. Thus one note of the chord is altered for every fresh root, the enharmonic change of each note being retained in the following chords. For instance, the D # at {b) is retained at {c) and {d) and the B J at (c) is retained at {d). 15. Hitherto we have considered all diminished 7ths as inver- sions of diatonic fundamental discords, and what is about to be explained will not be clearly understood unless reference is made tO' the chromatic fundamental discords w^hich are given in Chap. XIV. ; though, for the sake of completeness, it is given in this place. We have already learnt that any chord of the diminished 7th may be in one of four minor keys. But as the dominant minor 9th and its inversions may be taken as chromatic chords in the major key (see Chap. XIV., 6), then each of the four chords given above may be in the tonic major of those minor keys to which they are resolved, i.e., in G major, E major, C J major (or D 1? major), and A{ major (or B r> major). Therefore a chord of the diminished 7th may be in one of eight keys. 16. Again : Either of the foregoing chords may be an inversion of a supertonic minor 9th or of a tonic minor 9th (see Chap. XIV.,, 3, 4). 132 PART II. — CHAPTER VI. And because supertonic and tonic minor Qths may be taken in both major and minor keys, therefore each of the four chords given above may be in one of four other keys, thus making sixteen new keys. Therefore, by enharmonic change, a chord of the diminished 7th may be in any one of the twenty-four keys, and may be derived from any one of twenty-four roots. We have seen that the first chord at (a) in the previous example may be either in G minor or G major, and it is given below, resolved into four other keys, making six keys in all. The other three chords at (d), (c), and (d), or {e), may be similarly worked out by the student, each fresh notation producing six new keys, thus comprising the twenty-four keys. -I- 1st inversion of a chord of the super- tonic minor 9th in C minor. Do. in C major. 1st inversion of a chord of the tonic minor 9th in D minor. Do. in D major. The value of these enharmonic changes will be seen when we come to treat of Modulation^ i.e., passing from one key to another. The diminished 7th is sometimes termed "the modulating chord." To Find Roots of Fundamental Discords. 17. Fundamental discords are derived from one of three roots in a key — either from the dominant, the supertonic, or the tonic. The root of a fundamental discord will give the following intervals : major 3id, perfect 5th, minor 7th, major or minor 9th, perfect nth, and major or minor 13th. The supertonic and tonic chords are chromatic, and will be found in the chapter upon Chromatic Chords (see Chap. XIV.). The added intervals of the nth and T3th will also be explained in a subsequent chapter. It must be remembered that though the 9th and the 13th may be either major or minor, the 3rd, 5th, and 7th never vary ; so that should the root of a chord give either a minor 3rd, a diminished 5th, or a major 7th, it may at once be decided that such chord is not a fundamental discord. A few examples of the inversions of the fundamental discord of the minor 9th, taken from the opening phrases of Beethoven's THE DOMINANT NINTH. Sonata, No. 8 (" Pathetique "), are subjoined. The roots will all be found to bear major 3rds, perfect 5ths, and minor yths :— a 6 Chord of 4 ; 2 Chord in last inver. Chord in original of minor 9th original position, on G. position. Chord of dim. 7th; 1st inver.. of minor 9th on D. Chord in original position. Chord of 4 ; 2 last inver. of minor 9th on D. 177 5 Chord of 4 ; 3 3rd inver. of minor 9th on Original G. position. Chord of 4 ; 3 3rd inver. of minor 9th on Original D. position. Chord of 5 : 3 2nd inver. of minor 9th on G. Original position. i in P 4* b5 A simple general rule to find the root of a fundamental discord is the following : Take the sharpest note of the chord, and the root is a major 3rd below it. This sharpest note is that one which will naturally rise a semitone, and which thus gives the impression of a leading-note. In the examples above, F $ is evidently the sharpest note in those chords in which it appears, and B in the remaining chords ; there- fore the roots are D and G. When there are two sharps in a chord which both rise a semitone to their resolution, as at (l) in Paragraph 13 — that which is last in the order of addition of sharps is a major 3rd above the root ; therefore the root of the chord is B. Examples of Ninths. Major 9th (X) ; root position. , Schubert. Mass in F. 134 PART II. — CHAPTER VI. Minor 9th (X). Spohr. " The Last Judgment." =1 . - — .^±^^.^ — i -1= Minor (X) and major (^) 9th. Chopin. Valse. ] h::^— 1 1— J- T — -1*— / ,N . ■ • Beethoven. Minor 9th (X) ; 1st inversion m concerto in C minor. Schumann. Minor 9th (X) resolvmg on another root. Requiem 3: -=l-~ Major 9th (X). Mendelssohn. " Hymn of Praise." 1 " 1 THE DOMINANT NINTH. Schumann. "An den Sonnenschein." :^ ^ ^ 1st inversion of major 9th, the " leading 7th" (X) ; 3rd inversion (^). Beethoven. Symphony, No. 5* ^ X ^ X 1st inversion, the "leading 7th." Sterndale Bennett. " Woman of Samaria." 2nd (X) and 3rd (0) inversions. Brahms. Requiem. :1: 1 J J-, 1 \ 1 1 1 r r rH^ ^-'--^ 1 . J. 1 — 1 ^1 36 j 3rd inversion. IS PART II. CHAPTER VI. Sterndaie Bennett. " Woman of Samaria. " -A U-J— J ' 1 I 1 — r 2nd (X) and 3rd (O) inversions of major 9th. ^ Schumann. Paradise and the Peri. 1, — . 1 * 1»" \ '1 fc l-_JiL_il|^-_ ?BEE :t=t I , I 1 I I I -I ' I I 3rd (X) and 4th (•^) inversions of minor 9th. Sterndale Bennett. "Woman of Samaria. i, I It: Showing chords of the 9th on the dominant, the tonic, and the supertonic. Dominant 9th, 3rd inversion (X) ; tonic 9th, 3rd inversion (^) ; supertonic 9th, 3rd inversion (*) ; dominant 9th, 2nd inversion {^). Beethoven Sonata, Op. 10, No. 3. s XI THE DOMINANT NINTH. C(^y±.. 1 — \- -'|s> — : 2nd inversion, minor 9th (x)- x J. S. Bach. Fugue in G minor. X „ i I .^J- i A -J - - M-'T-j-j - Minor 9th resolving on 3rd (X). Mendelssohn. 1 2nd (X) and 4th (0) inversions of minor 9th. Bach. Prelude 22. J^' I r;]^ * — 1 4th inversion, minor 9th (X). Bach. Fugue 22. SI I3S PART II. — CHAPTER VI. 2nd (X), 3rd (^), and 4th {^) inversions of minor 9th. Beethoven. Sonata, Op. 10, No. 3. RECAPITULATION. Chapter VI. 1. Ckord of the Dominant gth. — Formed by the addition of a 3rd to the chord of the dominant 7th, such 3rd bemg major or minor, according to the key. 2. Dissonant notes. — The 9th and the 7th. 3. Their progression. — They must either fall or remain as consonant notes of the next chord. 4. Position of the 3rd and its progression. — Below the 9th, when the latter is major. It must rise. 5. Notes omitted in four-part writing. — The root and the 5 th. 6. Progression of the in five-part writing. — ^When below the 9th it must rise, to avoid proceeding in consecutive 5ths with the 9th. When the latter resolves first, the 5 th is free. 7. Resolutions of the chord. — The 9th may resolve first, while the other notes remain, passing to an 8th or a 3rd on the same bass note. It may also resolve upon the tonic triad or its second inversion, a 4 on the same bass note. 8. Inversions. — Three in the major key, four in the minor : the 5 6 6 7 (leading 7th), 5, and 4 in major keys; the 5 (diminished 7th\ 6 6 6.33 3 5, 4, and 4 m mmor keys. 3' 3' 2 9. Position of the gth in the inversions. — In major keys it is best at the top ; but in minor keys there is no restriction. 10. Resolutions of ifiversions. — The 5 to the tonic concord, the | 6 6 and 4 to its first inversion, the 4 (in the minor key) to its 3 2 second inversion. In all the inversions the 9th may resolve on the root while the other notes are stationary, in which case the chord becomes a dominant 7th or one of its inversions, and is so treated. EXAMINATION QUESTIONS. 139 11. Progression of the dissonant Wherever the 9th and 7th appear they must fall, or remain as consonant notes of the next chord. 12. Note omitted in all the inversions. — The root. EXAMINATION QUESTIONS Chapter VI. 1. What is a " dominant 9th " ? Give an example (i) in the key of A, and (2) on A. Give key-signatures. 2. Of what quality is the 9th ? 3. Describe the progression of the notes composing this chord. 4. Which is the note that is omitted in four-part writing, and that, when employed in five-part writing, has a fixed progression ? 5. Name the resolutions of the dominant 9th, and write them in the key of E flat. 6. How many inversions are there (i) in a major and (2) in a minor key ? 7. What note is omitted in all the inversions ? 8. AVrite and resolve each inversion in the key of G major and G minor. Give roots and key-signatures, and figure the bass. 9. Name the dissonant notes in each inversion and state their pro- gression. 10. What interval does the 3rd to the root form in each inversion and what progression must it take ? ti. State the cases in which the 5th to the root is free to rise or fall? 12. What is the best position for a major 9th? and which note of the chord should always he written below the 9th ? 13. Change each of the following chords into a chord of the domi- nant 9th or one of its inversions in a major key, by the addition of one accidental to each chord. Give roots, resolutions, and key-signatures, and figure the bass : — I40 PART II. — CHAPTER VI. 14. Give the names usually applied to the first inversions of the dominant major and minor 9ths. 15. Change each of the following chords into a chord of the domi- nant 9th or one of its inversions in a minor key. Add one accidental to each chord. Give roots, resolutions, and key- signatures, and figure the bass : — 1 i 1 : z=t: 16. Complete the following chords, according to the figures. Give key-signatures and roots : — 9 177 7 (79 be 6 b7 5 5 b7 5 .4 S 3 17. By enharmonic changes resolve the two following chords of the diminished 7th into eight different keys. Regard each chord as an inversion of a dominant minor 9th : — I I b7 7 5 5 1 ^^^^ 1 ^ G 5 7 6 6 — 6 4 6 4 5 3 EXAMINATION QUESTIONS. 1 L4. ^ m 1 1 1 -0- 1 6 98767 6 G 46 '987 76543 5 5 2 7 — 3 4 3 =1 1 i G> \^ 0 M- r— S> i ^ ^= 1 1 7 6 4 5 4 3 6 — 7 5 6 7 3 4 5 6 4 5 2 6 142 PART II. — CHAPTER VI. 1 1 1 J - 1 — p 4 —G>—. 6 ^ 4 i 6 6 5 __ ^ — 6 4 5 h 1 [— 6 \1 i 5 7 -1= The student should now take the treble part of hymn-tunes, such as those quoted in previous chapters, and harmonize them, com- paring the result with the book. It will be found excellent practice also to select simple melodies, of which the following may serve as specimens ; and to add alto, tenor, and bass parts, all in their proper clefs, figuring the bass : — " Drink to me only with thine eye -. ^ — m- -4- ^ l^J — V — V — N 'w — "The Vicar c )f Bray." =^ ) ^ h =^ ^ A — \ • ^ « —s * ]^ =:q=l_ 1 — \ — -A -=1 - —HI _=:*: -=]: — 0 — — --^r^ ^^-^1 4 3 r(^):,b4 P -h-H 4 — 3 2 ^ 1- ^ r 6 6 4 -^=^ -r 9 7 ti 1 ft 8 1 -r - 6 — 6 5 4 S — 6 6 5 9 8 7 6 S 4 if4 2 « 6 6 9 5 7 6 b7 t|6 5 D5 5 1 7 5 7 6 S 5 — — 6 1 G 9 5 7 — 1— ^ — 0 — u 8 ==t= I _ 4- 6 4 2 — 6 6 4 2 4 2 — »—- m — G 6 -*-it:i 0 ^ 4 4 $ 2 3 2 6 7 7 7 7 4 6 13 2 — ^ — • 7 6 9 6 5 7 S — 1 \ 8 EXAMINATION QUESTIONS. 149 Essential Discords of the Ninth— Major Keys. -4-^ 1 1 r*^^ 1 ^ -4— -# — J 0 — ^x:r^ f 1 1 1* r * ' LLj 1 ^ 6 — 46 66 7 987 66 2 5 5 7 6 5 5 3 4 3 1 [N *" — 1 — —i-^-0- 1 — 0 — 0 ^ — 6 5 6 5 6 6 5 — - 6 5 f- ^ 1 6 4 3 — k 0 ; 'r^ 9 8 7 7 — 5 TTS * 1 1 — 1- 6 — 1= 7 4 2 — j 1 r 6 7 7 # 6 4 #— 5 3 7 6 6 5 7 -^- 6 6 4 # 5 7 6 5 — H ~r— — & — 6 5 -i-^t^ ' ! _L 1 L_z ^1 4 67 4667687 3 5 2 5 H — ' ^ 657 7 7 6 46 4 3 5 2 ynt)', ^ 0 1— — 1— s>— -^^=^ - |S> — Resolved on the 3rd. With the 9th. -H — r —Gt ^ -- 'ithout the Qtl 1 G =3 =1- -Gh- jS> 11 3 7 — 1 11 3 9 « 7 — 1 THE DOMINANT ELEVENTH AND THIRTEENTH. When the 9th is major it resolves with -the iith (x). Resolved on the 5th. With the root. When the nth resolves on the 5th, and is accompanied by the 9th, the latter usually also rises (x). 3. As there are six notes of the chord, there are five inversions, of which the first is hardly ever seen. The four in use are taken on the 5th, 7th, 9th, and nth of the chord, and are shown below with their resolutions. The intervals of these inversions will be recog- nised as identical with those of the essential discord of the 7th with which we have become familiar, and from which they are distin- guished by their needing no preparation, and by their different resolution. The fourth resolution can only be taken when the 9th is minor, as in the following example. The third inversion is often termed the " chord of the added 6th," and is frequently used in cadences. 2nd inversion, taken on 3rd inversion, 4th inversion, the 5th of the chord. on the 7th. on the minor 9th. — h ' I — — iS>— ' 1 —G>— - p 1 ' 1 ' 1 ' 1 1 G 1 1 1 -0- >P & 6 ^ ■ 7 6 6-w- — — e*— H-^ 5 4 C 3 2 5th inversion, on the nth. \ 1 , — P — & ] — 1 —\ Major 13TH. THE DOMINANT ELEVENTH AND THIRTEENTH. Resolved 011 the 5th ; on the 7th on a tonic concord. :=) - f 1 — ' [^=^ 1 — Minor 13TH. I 7 (13)6 (13) 6 7 s - (13)6 — 1 =]. . — -r -r -- 6 — 5 — 4 3 4 — 2 3 7-W-6 4 ^ 4th inversion. 5 th inversion =4 j 6th inversion. 7-W-— 6 5 5-W-6 3 4 2 3 9. Chords of the 13th may also be taken upon the tonic and the supertonic ; but they are of much rarer occurrence upon these degrees than upon the dominant. Examples of Chords of the iith and 13TH. Dominant nth (x). Chopin. Impromptu in G [?. =1: 154 PART II. CHAPTER VIII. 2nd inversion (x). Mendelssohn, Sonata, Op. 6. ^^^^ -^-^ — ^ 3rd inversion (x). Mendelssohn. " Midsummer Night's Dream." : 5 5 . 3 ^ 5th inversion (x) ; 3rd inversion (^). Mendelssohn. Italian S>TTtphony. -d- -4- 5th inversion (x) ; ist position (0). Mozart. Sonata 13. THE DOMINANT ELEVENTH AND THIRTEENTH. 1 55 Sterndale Bennett. " Woman of Samaria." 4th (x) and 5th (^) inversions. 5* invers ion, Min or I3tli. ^ 0 ^ X —m ^ — ^ 4th inversion ; nth (x). Sterndale Bennett. " The Lake. 1 X ^ 1 1 1 i r= 4- — »- _ J. S. Bach. Prelude 8. Last inversion of nth (x). . 1 Js r— ' p 3 ^ — R -« 1 Q jS> ' PART II. CHAPTER VIII, Dominant minor 13th (x). Schubert. Sonata, No, 4. -p- ^1 X^ i 1 1 — « * #- V- 0 1 -j-tjf — nth and 13th ; 3rd inversion (x). Mendelssohn. Violin Concerto. 3rd inversion of minor 131)1 (x) ; 2nd inversion of lltfi {%) ; 1st inversion of minor 13th m. q^^^^ ^^^^^ p^^^_ J ft I I 1 — r RECAPITULATION. I 5 7 3rd inversion ; major 13th (x). Goetz. 147th Psalm. 3 3rd inversion of 13th and iith (x). Gade. Novelletten. i ^6 1 I... 1 — ^ — — • — ■ 1 i 1 ! -4- 1 1 1 1 ' — 1 1 '1 -1 h ' 1— — ■ ■ i ^— f — ' \ Last inversion of major 13th (x) Schubert. Sonata, No. 6, __;==JS; ^ fa^ ? V ^ ^ RECAPITULATION. Chapter VIII. 1. Chord of the dominant iith. — The addition of a perfect nth from the root to the dominant |. 2. Figuring, — The nth appears as a 4th. PART II. — CHAPTER VIII. 3. Resolutions. — To the 3rd or to the 5th of the root ; to a tonic -concord ; or to a supertonic discord. 4. Progression of the nth.— It either falls to the 3rd, rises to the 5th, or remains to be a note of the next chord. 5. Notes of the chord omitted and retained. — In four parts the 3rd and 5th are usually omitted, and the nth, 9th, and 7th retained. The note on which the nth resolves must not be sounded with it. 6. Inversions. — Four available, taken on the 5th, 7th, 9th, and nth of the chord. The 3rd inversion is only available when the 9th is minor. 7. Resolutions.— ThQ nth generally resolves first on the 3rd or the 5 th of the chord ; after which there remains a chord of 7 or 7, or one of their inversions, to be treated in the usual way. 8. Distinguished from essential discords. — By needing no prepara- tion, and by their resolution. 9. Other chords of the nth. — These may be taken upon the tonic and the supertonic, and resolved on the same root, or on a chord with another root. 10. The dominant 13th. — The addition of a major or minor 13th from the root, to a chord of the nth, 9th, or 7th on the dominant. 11. Figuring. — The 13th appears as a 6th. 1 2. Inversions. — Six in number ; of which the 5th is but rarely seen. They are taken upon the 3rd, 5th, 7th, 9th, nth, and 13th of the chord. 13. Notes generally retained in four parts. — The root, 3rd, 7th, and 13th. 14. Resolutions. — The 13th resolves upon the 5th or 7th of the root while the other notes remain ; or upon a tonic concord. 15. Position of the 13th. — Below the 7th, except in the last inversion. 16. Other diatonic chords of the 13th. — These may be taken upon the tonic and the supertonic, and resolved on the same root ; or (more often) on a chord with another root. 17. Resolutions. — The major 13th frequently resolves alone; after which the remaining notes of the chord are treated in the usual way. The minor 13th often resolves on a chord with another root. EXAMINATION QUESTIONS. EXAMINATION QUESTIONS. Chapter VIIL 1. How do you form a chord of the dominant nth, and how is it figured ? 2. Of what character is the nth, and to what class of discords does the chord belong ? 3. In four part writing, which notes of the chord are generally omitted, and which are retained ? 4. Write a chord of the dominant nth in the key of E flat, and resolve it in four ways. 5. What notes should never be sounded with the nth ? 6. Distinguish between an inversion of the dominant nth and an essential discord of the 7 th, and illustrate your answer. 7. Write the inversions of the dominant nth in the key of D, and resolve them. 8. What is a "dominant 13th," and how is it figured? Give an example in a major and in a minor key, using all the notes of the combination. 9. Which notes of the chord are generally retained in four parts ? 10. What note should never be sounded with the 13th; and what note should always be below the latter, except in the last inversion ? 11. Resolve a dominant 13th in three ways in the key of D minor 12. Write and resolve the six inversions of the dominant 13th in the key of C minor. 13. Complete the following exercises : — The Dominant Eleventh. :|— ^- h 5 3 6 5 4 3 ^ — 6 6 4 6 5 3 6 6 — 5 4 3 2 =^-^-' 5 7 5 3 « — ' 9 6 4 6 — 7 6 9 8 7 — 4 3 4 6 7 ■2 -pi— +-p ' — 1 — 4 6 2' 1 — 1 — L_ 4 6 2 a — m. — 0 ^ _ 4 6 4 2 3 7 6 6 6 — 6 7 5 i6o PART II. — CHAPTER VJII. 22: ^^^^ 6 j; 54 6 7 f6 6 6 9 S 6 50 t?7 5 2 4— $4 7— 175 5 3 - 3 2 - 6 9S "46 560 56 6 o 7—3 05 3 — 0 : - 5 jf4 6 5 6 4 3 54 6 — 6 5 3 12 4 G 4 4 — 9 0 0 — 4 5:4 0—0 8 :2 a 4 D 4 0 . 0 it 2 -2 5—7 3 — 4 The Dominant Thirteenth. 9 6 7 7 4 3 7 6 5 4 3 EXAMINATION QUESTIONS. l6l # . 0 — 5 3 4 5 7 — 6 5 4 3 6 7 5 4 6 7 SEC J : (— :pz=:p?: 7—569 6 5 3 4 7 it - lf2 If if6 — 6 7 — 5 4 6 5 3 - 5 _ B^4 »5 ' 1 9 & =^1 Jf4 6 Jf6 »4 5 9 8 7 — — 8 6 5 — 3 ^ pN-^ » • * -^-J— i L:j— 6 7 6 J( _ 6 7 5 5 5 ' r i i ■ 6 7 if 7 if —6 6 5 3 5 e> |S> o 7 7 987—4987 7 — 5 Jf 7_65 67 — 5 65 4 5 if - 4 If - - if - ME CHAPTER IX. Suspensions. I. A suspension is the prolonging of a note of one chord during the following chord, of which this note forms no part. This is called a " discord by suspension." The note must appear in the same part in the two chords, and must proceed to the note, either one degree higher or lower, which it has delayed. The appearance of the note in the first chord is the preparation of the discord, the suspension is the discord, and the progression to the note it had suspended is the resolution of the discord. Example : Without suspension. With suspension. Kb) -S: Here neither the C at {a\ nor the A at {b) belongs to the common chord of G, and they only delay the B and the G. 2. When the two notes are tied, as above, the preparation must be of at least equal length with the suspension, but when the sus- pended note is sounded again, this rule is not so stringent. The suspension should be on a strong beat of the bar, such as the first and third beats of common time, and the first (and occasionally the second) of triple time. The preparation may be on a strong beat, but in no case must it be on a stronger beat than the suspension. The resolution should be on a weaker beat than the suspension. SUSPENSIONS. 3. The notes available as suspensions are the 9th and the 4th of any root, and the 5ths of the 3rd and 7th degrees of both major and minor keys. The octave of the key-note is also suspended by a 7 th, this progression being used generally at the end of a section. (See Chapter XVII.) The note of resolution must not appear in any part at the same time as the suspension, with the exception of the 9th with the root in the bass, as above. (There are also other occasional exceptions, when the note of resolution is sounded with the suspension at the distance of at least an octave below it ; but students are advised to adhere to the rule just given.) 4. Faulty progressions are not justified by the introduction of sus- pensions ; as for instance, the following consecutive 5ths and 8ths. With suspensions. 5 I Without suspensions. Without suspensions. Therefore gths cannot be prepared by 8ths, nor 5ths by 6ths Suspensions in Major Keys. 5. The suspension of the 9th may be taken upon any note of the key which bears a common chord. It is accompanied with the 3rd and 5th, and resolves upon the root {a). Its first inversion, upon the 3rd of the chord, can be taken upon every note of the key, and is accompanied with the 3rd doubled, or with the 3rd and root ib). The second inversion, upon the 5th of the chord, may be taken upon those notes which bear the second inversion of concords. It is accompanied with the 6th and the octave to the bass note ic). The third inversion, having the 9th in the bass, may be taken wherever the resolution can be made to a common chord. It is accompanied with the 3rd and 5th to the root, one of these notes being doubled. * It is allowed to have the root in an upper part, 164 PART II. CHAPTER IX. approached by conjunct movement, but the doubUng of either the 3rd or 5th is preferred (d). Suspended 9th. CI4- 1st inversion. (^) 1^ I I I I 1^ I 7 6 1 1 1 1 — ' — ^1 !— r r 1 ^2 ^ 1 ! 1 J 1 1 1 J . .. 1 1 r 1 ^ — r — (S> — Lt.-1 -t 4- " i 2nd inversion. J — 1- I 1 1 I® 6—6 5 4 6—6 5 4 3rd inversion. ! 1 -Gi —J 1 0^ -— 0- l 1 J- J- p 1 1 1 - ri 6 4 — 6 2 6 ^-v- — ^ / 6 6 / 6 / 17 6. The suspended 4th can be taken upon every degree of the scale which bears a common chord {a). Its first inversion can be taken upon every note {b). Its second inversion can be taken upon those notes of the key which bear the second inversion of concords {c). The last inversion, having the 4th in the bass, can be taken upon every note {d). The resolution of a suspension may be delayed by its proceeding first to a consonant note of the next chord, and afterwards taking its proper note of resolution [e). SUSPENSIONS. 165 The mark y under a bass note signifies that it is to be accom- panied with the chord of the following note, as at {d). ^ 1 1 l' -^1 1 r ■1 1 -0- r 1, 1 — H A 1 1 J- r r 1 1 ' 1- U 4 3 6 4 3 5 4 3 — 1 — 1^ ^ — _1 ^ < J 1 1 4 ■ 'j V \ — 1 — ^ 1^ ! 1 j-^l ^ m J 7 6 4 — 7 6 7 4 — 4 8 i66 PART II. — CHAPTER IX. Suspensions in Minor Keys. 7. The use of suspensions is far more restricted in minor than in major keys, both because the minor scale bears fewer common chords, and because in several instances, an augmented interval would occur in the resolution of the suspension. Thus — The suspension 9 8 can only be taken on the tonic, subdominant, and dominant. The first inversion 7 6 on every note but the tonic. The second inversion I4 on the tonic, supertonic, and dominant. The third inversion 2 on the supertonic, dominant, and submediant. The suspension 4 3 can be taken on the tonic, dominant, and submediant. The first inversion 1 1 on the first five degrees. The second inversion 7 6 on the supertonic and dominant. The third inversion | on the first five degrees. Suspension 9 8. ^ • ■ ^ 1st inversion. 2nd inversion ^ \^ i68 PART II. — CHAPTER IX. 8. The suspension 7 to 8 on the key-note is given below in both a major and a minor key {a). The 5th of the 3rd and 7th degrees of both major and minor keys may be suspended, and resolved on the same bass note c, d, e). On any other notes of the key than the 3rd and 7th, the 5th may either rise to the 6th, or proceed to any other note. The diminished 5th of the second degree of the minor scale could only resolve by an augmented interval (/). These rising suspensions are by some writers termed retardations. \ 1 [a) I 1 1^ (0 I I (a) -r-t- 1 . 1 1 rji- i u 1 ' : 1 -1 - -^^ J^?h « |C2 — (^) 1 1 . (.) ' • ' (/) :=^-— : 6 1 U-i 1 — Ut U_i y_ $5 6 6 5 6 6 4 5 Jt6 9. One of the chief difficulties in learning suspensions Hes in the fact that their figuring so closely resembles that of diatonic discords of the 7th, 9th, nth, and 13th. They may be distinguished from the latter by the following points : (1) A discord by suspension does not belong to the chord in which it appears. (2) It must be introduced on an accented beat. (3) It invariably needs preparation. (4) It must in all cases resolve on the same root. Whereas : (1) A diatonic discord is an essential part of the chord in which it appears. (2) It may appear at any part of the bar. (3) It often (as in the case of fundamental discords) needs no preparation. (4) It frequently resolves upon another root. These differences may all be verified by reference to the foregoing chapters on diatonic discords. SUSPENSIONS. 10. When therefore we see the figures 9 8, they signify a common chord with the octave to the root delayed. A chord of the 9th would be accompanied with a 7th, or the 7th would certainly appear when the 9th resolved on the root. Again, the figures 7 6, 4 3, only denote inversions of diatonic discords when some other note charac- teristic of the chord is present, showing that the discord is an essential part of the combination ; and when, also, the resolution accords with the rules laid down for the resolution of diatonic discords. 11. Therefore it is clear that the chord of the suspension is accompanied in the same way as the chord of resolution ; from which follows the rule : " When figures indicating a suspension occur, accompany the first figures with the notes belonging to the last." Thus, when 9 8 is seen, add a 5th and 3rd, because these notes would naturally accompany an 8th. When 7 6 is seen, add two 3rds or a 3rd and 8th, because a chord of the 6th is so accompanied when the 6th cannot be doubled. To 4 3 add a 5 th and 8th, for these notes accompany a 3rd. To |1 add a 3rd. To \1 add an 8th. To f 4 add an 8th. To 1 3 (suspension in the bass) add a 6th or 3rd. To 2 3 (suspension in the bass) add a 5th or 3rd. Double and Triple Suspensions. 12. The 9th and 4th may be suspended together, when each receives the same treatment as when employed separately. General rules for accompanying double suspensions : To II add a 5th. To f I add a 3rd. To ^ 2 add an 8th. To 1^ (suspension in the bass) add a 3rd or 8th. To 3"^ (suspension in the bass) add a 5th. Sometimes it may not be possible to adhere strictly to the rules in the above tables, but, taken as general guides, they may be found useful. When the leading-note is the 9th or the 4th, it must fall. Triple Suspensions are formed when three notes of one chord are retained while the bass note of a second chord is sounded. This may only be done when the root of the second chord is a 4th above that of the first, and when, also, the notes dissonant to the second bass note move by conjunct movement, i.e.^ by step of a 2nd. PART II. — CHAPTER IX. Example of Double and Triple Suspensions ; — 1^ ri — ' — ^ — 1 — -w * o - ^1 1 -Vl 1 tf-r -^1 1 1 ^ i 6 6 0 6 2—2 6 6 6 6 2—2 I t 7 8 5 — 2 3 , 13. The resolution of any discord may be delayed by part, or the whole, of the chord being suspended over the following bass note, provided that the root of the second chord is a 4th above that of the first, and that all dissonant notes move by step. The following three examples are taken from Bach's Organ Fan- tasia in G minor. At {a) the root of the first chord is G, and of the second C. At {b) the root of the first chord is F$, and of the second B, and at {c) the root of the first chord is C, and of the second F. SUSPENSIONS. 14. Any suspension may, like the 7th, be ornamentally resolved, i.e , it may, previous to its resolution, proceed to some other con- sonant note of the chord, either by leap or by step, provided that it return to its proper note of resolution before the harmony changes. An example of ornamental resolutions is given below, taken from Fugue 35 of Bach's 48 Preludes and Fugues, one which contains a great number and variety of suspensions. Auxiliary notes are also often interposed between a suspension and its resolution, as at 1 ^ -1 , 1 ^ -J- — 0— ^ — * — ^ -1 r 2 is> r \ 1 r r r The following passage also is a good illustration of the inter- position of auxiliary notes between suspensions and their resolutions. (Refer to Chapter XI., 7, Auxiliary Notes.) Dr. Hubert Parry. Blest Pair of Sirens. m 3f if 4— L f 5 T72 PART II. CHAPTER IX. The following are examples of suspension : — Haydn. Sonata in E i?, No. 6. 5^ i m — f J. S. Bach. Prelude 36. _T. S. Bach. Prelude 36. iy4 PART II. CHAPTER IX. Mendelssohn. Organ Sonata No. i. — & — — H =-1 r M4fce= ■ RECAPITULATION. Chapter IX. 1. Suspension.— Th.Q retaining of a note of one chord during part of a succeeding one, to which this note does not belong. 2. Preparation. — The appearance of the suspension as a consonant note in the previous chord. 3. Percussion or RefejiHon.—Tho. retaining of the note in the second chord, to which it is dissonant. 4. Resolution.— ThQ passing of the suspension to the note, one degree higher or lower, whose appearance it has delayed. 5. Position in the bar of the three Preparation : on any beat. Suspension : on a strong beat. Resolution : on a weaker beat than the suspension. 6. Length of preparation.— Vlm^X. at least equal that of the suspen- sion when the two notes are tied. 7. Notes available as suspensions. — The 9th and 4th of any root ; the 5th of the 3rd and 7th degrees of the scale ; and the major 7th of the tonic. 8. Notes which must ?iot be sounded with suspeiisions. — Those on which they resolve, except the 9th with the root in the bass. 9. Rule for accompany i?ig figures indicating suspensio?is. — Accom- pany the first with the notes belonging to the last. 10. Double Suspensions.— When two notes of a chord are suspended. 11. Rule for their treatment. — Each note is treated in the same way as in single suspensions. 12. Triple Suspensions. — When three notes of a chord are suspended. 13. Rule for their treatment.— 'Ed.ch root must be a 4th above the last ; and all notes dissonant to the chord of resolution must move by step of a 2nd. EXAMINATION QUESTIONS. EXAMINATION QUESTIONS Chapter IX. 1. What is a discord by suspension ? 2. Describe the three processes necessary to a suspension. 3. At what portions of a bar should a suspension and its resolution be placed? 4. What are the notes available as suspensions ? Give an example of each in a major and a minor key. 5. On what degrees of (i) a major and (2) a minor scale can a suspended 9th and a suspended 4th be taken ? 6. On what degrees can their inversions be taken in a major key ? 7. Illustrate the following rule: "The introduction of suspensions does not justify a bad progression." 8. What is the reason that the use of suspensions is more Hmited in the minor than the major key ? 9. Give an example (i) of a double and (2) of a triple suspension, with rules for their treatment. 10. Complete the following exercises : — On Single Suspensions. r-G> H — 4 3 -h- 6 / 6 m — I— -0- 6 7 6 7 4 3 6 ^ P -I 1^ 5 6 6 -/^ 9 8 4 3 J p: — — ap — 'i i ^ = f-t 5 6 4 3 7 V— • -r -1 1 m 6 6 6—4 5 4 2 / 6 4 3 9 8 6 — 4 2 1 / 6 6 6 — 5 4 « 7 6 7 4 3 6 4 2 i — 6 -0 A 1 ! i k 4—6 566 766 5 — 6 56 78 2 - 2 - 176 PART II. CHAPTER IX. ^ iS^^G a - / / B6 fl5 56 4 q P 04 2 fi'^ 6 9 3 6 5 — 9 2 8 7 a =] i ■ — — & 1 — u- — «o ^ — 1 ' 6 98 7 56S5 6 56 /6 98 J 0 « =4= * 5—5 2 fo — 0 — a 2 — 2 — 2 7 57 4 5 » - Double and Triple Suspensions. 1 f- 6 9 8 / 6 / 7 6 5 4 9 S 9 S 6 5 6 6 — 7 b 5 4 4 — 4 — 9 S 3 3 3 3 4 3 9 8 4 3 8 7 6 7 5 5 4 J 3 — 7 (> 6 9 8 Jf(5 J Jf5 6 7 0 4 S 3 1=F — 4 — 6 1^1 / J6 6 5 S 3 56 8 S — 5 — 3 EXAMINATION QUESTIONS. 177 — & ^ — t3i> — 7 8 5 7 — 4 3 Q5 6 4 Q 5/6 8 3 8 6 5 4 D 11 / 6 / 6 / p6 9 8 7 6 7 9 3 tl 37 8 4 3 r— 0 =1 F 9 8 6 7 fi 6—6 5 4 5 6 7 7 8 4 3 / 6 7—9 8 4 3 7 8 4 S DEFERRED Resolutions of Suspensions. P • 7 3 6 5 5 2 2 9 S 9 3 8 4 3 ' — 1 — \ — ^ 1 , 7 3 6 — —G> 1— i— <^ • L-(S» 4/66 784 5 6. J 98 2 4 5 6 0 6— — ^ 7 8 CHAPTER X. Pedal Notes. 1. A pedal note, or point, is a note sustained in the bass during a succession of chords, of which this note may or may not form a part. The notes available as pedals are the tonic and the dominant. These may be held on together, forming a double pedal (The subdominant is, very occasionally, used as a pedal, and sometimes, by modulation, becomes a tonic pedal.) The term " pedal " originated with organ music, where the tonic or dominant is sustained on the pedals, whilst the chords are played on the manuals. Pedal notes were formerly often called " organ points." 2. In the works of the older masters, modulation during a pedal passage is not common, except, during a tonic pedal, to the key of the subdominant, when the pedal becomes a dominant pedal to the new key ; and, during a dominant pedal, to the key of the dominant, when the' pedal becomes the tonic of the new key. In modern works free modulation is often met with in the course of a pedal passage. 3. A pedal usually, though not invariably, both begins and ends as a harmony note. Formerly it was considered indispensable that it should form an essential part of the chord when quitted, but modern practice does not acknowledge this necessity. 4. When the pedal note does not belong to the harmony, the part next above it is considered as the bass, and it is subject to the rules for the progression of bass parts. The chords then proceed as if th^ pedal were not present. Examples of dominant and tonic pedals are appended : — Mendelssohn. Organ Prelude, No. 2. Tonic Pedal. i8o PART II. — CHAPTER X. f r- 1 ? ^ r * Dominant Pedal, ' ^ — — * — ^ — i — S> ; 1 1 1 J J 1 - Tf f r i " 1 r Tonic Pedal. ^ — 1 — ?-^^F^r= **f1 ^ ^ — ^ © h — r- 1 -1 ^ b-^^ rJi^ '^t- ° — f 1 P ' i 1 bp o - . fir- — 1 '\-: ' :! tg^il-^pti — ^ji 1 L_ j 1 1 ^ ^ 1^1— ridj « ■ I Mendelssohn. Organ Sonata, No. 2. 1 = 1 Dom inant Pedal . l82 PART II. — CHAPTER X. "Of 1 /* — 1 1 r p (^) ' 1 — — = — =4= ^1 In the above example modulation is made to the key of the subdominant, and the C is introduced as a dominant pedal of the new key, becoming a tonic pedal at (d). J. S. Bach. Prelude 22 ("48 Preludes and Fugues"). Tonic Pedal. J. Brahms, Schicksalslied. Tonic Pedal. I -J J 1 I II "a 5. The dominant 7th and its inversions, and the leading and diminished yths with their inversions, are some of the chief chords 7 7 employed upon a tonic pedal. They are figured 4 and 4 when four 2 2 parts are written above the pedal. When only three parts are used, the 5th or 2nd is omitted in the dominant 7th, and the 2nd in the leading and diminished 7ths. PEDAL NOTES. 183 6. The major chord on the submediant, and the fundamental discords derived from that root, may be taken upon a dommant pedal. These chords are foreign to the key, and must resolve upon some chord containing the 7 th of the dominant. Mendelssohn. " Hymn of Praise." I- ^ 7. Sometimes the pedal is placed in an upper part, when it is termed an " inverted pedal." The rules for its treatment are the same as when it is in its original position, except that the lowest note of the chord must form a correct bass part, and not the part 7texf the pedal. Mendelssohn. Organ Sonata, No. 2. RECAPITULATION. Example of Double Pedal. 185 Sullivan. " The Golden Legend. 8. The chords of a pedal passage may be figured according to their distance from the pedal note or from the part next above it, which is often considered as the real bass. (See 4.) The first method presents the most difficulty to the student, because quite simple and familiar chords appear new and complicated when reckoned from a note which frequently forms no part of the har- mony. In long and elaborate passages it is very common to write the figures above the pedal, as thereby confusion is avoided. In organ pedal passages the words " Tasto solo " are often seen, meaning that the bass is simply to be held on whilst the chords are sounded by other instruments or voices. RECAPITULATION. Chapter X. 1. Pedal note or point.— K note sustained in the bass during a succession of chords, to which it may or may not belong, 2. Notes available as pedals— Th^ tonic and the dominant. 86 PART II. — CHAPTER X. 3. Double pedal. — When the tonic and the dominant are sustained together. 4. Pedal as har?nony note. — It generally forms part of the chord both when taken and quitted. 5. Rule for part above pedal. — Considered as the bass part, when the pedal does not form part of the harmony. 6. Most usual modulations employed on a pedal. — To the key of the subdominant during a tonic pedal, and to the key of the dominant during a dominant pedal. 7. Inverted P^al. — When the sustained note is in an upper part. EXAMINATION QUESTIONS. Chapter X. 1. What is a pedal note or point, and what is the origin of the term ? 2. Which degrees of the scale are available as pedals ? 3. What are the modulations most frequently met with during a pedal passage ? 4. Give a reason for the former restriction of modulation when pedals were used. 5. When is it usual that a pedal should form part of the harmony? 6. Name some of the chords most frequently employed during a pedal passage. 7. Explain the terms " Double pedal " and " Inverted pedal." 8. When the pedal is not an essential note, which part is considered the bass ? and which is the bass part during an inverted pedal passage? 9. State the difficulties which may occur in figuring a pedal bass. How may they be obviated ? 0. What is meant by the words " Tasto solo " ? 1. Describe the following passages : — Beethoven. (I) EXAMINATION QUESTIONS. (2) 187 Beethoven. 4=g & j--^ ^- -gr: 1 If IT ir -p- -r -p- F f ir IT IT I I I I I I I Beethoven. (4) --1^1 r- -J — ^- J — ^ ^ ^ — T^. B CHAPTER XL Unessential Discords. I. Besides the essential discords with which we have become famihar, there is a large class of unessential discords. These are notes which are not essential to the harmony, and which form no portion of it. They are classified thus : i. Passing notes ; 2. AuxiHary notes ; 3. Anticipations; 4. Retardations. Passing Notes. j 2. These are notes which ascend or descend between two yessential notes, which last may be either consonant or dissonant. A When passing notes proceed according to the key in which the passage is written, they are diatonic (see (a) below). When they proceed by semitones only, they are chromatic {b). Passing notes are often called "discords by transition." They do not change the key, and they may occur either in one part, or in several parts at the same time. {a) The passing notes are marked x X Schubert. Impromptu in El?. •f-r ^ 2 ^ — — -, ' Handel. " Israel in Egypt. j fe^i gz^S j : ^ -S- ' ^^^^ &c. UNESSENTIAL DISCORDS. 1S9 Spohr. " The Last Judgment." ^ — ^ 3. When passing notes occur on the weaker beats, they are termed regular ; those on strong beats are irregular. The former are, the most usual. As with suspensions, a passage which is wrong without passing notes, is wrong with them. Therefore the following progressions at n (a) and (d) are inadmissible, because of the consecutive 8ths and 5ths. At (c) the progression is correct, but^ that at {d ) is not good, on account of the oblique motion to the unison. 1 H — ' ^3 Fd-3— q 4. When a chromatic note is taken as a passing note, the passage : must continue to proceed by semitones until a harmony note is/ reached. Example : / NOT— « 0 g - □ e> i g 5. The 6th and 7th of the melodic minor scale are frequently used as passing notes, both in ascending and descending. Example : 6. In slow time, passing notes are sometimes indicated in the figuring, and when this is the case, care must be taken to accompany them in the same manner as the essential notes which they follow. See (a). 190 PART II. — CHAPTER XI. When they occur in the bass, the horizontal dash is often used to denote the holding on of the other parts {b). i J. J- .c± i , I.I 1 6 5 3^ 4 6 3 b I 1 I ! ' 1 I I I 3 b 6 5 55 The following are examples of diatonic passing notes in more than one part at once. Beethoven. Mass in C. ^ .M^* m ^ -4 -3 Mendelssohn. " Hymn of Praise." I UNESSENTIAL DISCORDS, T9I Auxiliary Notes. 7 Auxiliary notes are notes which precede or follow essential notes' at the distance of a 2nd above or below them. They do not always fill up the distance between two essential notes, as do passing notes but they may return to the note from which they proceeded. They' may be approached, but not quitted, by skip, except in very rare cases. They may appear in more than one part at once, pro- vided that sufficient notes of the harmony remain to indicate the chord. An auxiliary note is seldom more than a semitone below essential note, unless the latter be the major 3rd of the key m which case the auxiliary note may be either a tone or a semitone below it. Schubert. Impromptu m 192 PART II. — CHAPTER XI 1 — ^ — ^ -1 1 1— w « ^- =]: 4: 1: 1 m 1 'W -0- Auxiliary Notes approached by Skip. Mendelssohn. Concerto in G minor. a 1 7^sp^1t% -^-^ - — ^ r-n —^-4 1 — ■ p ^— 1 1 I ^^^^ S3£ Auxiliary Notes in Two Parts. Mozart. "Requiem.' 1 -| — r 8. It is allowed for an auxiliary note to leap a 3rd to the note on the other side of the harmony note, on which it must afterwards resolve. When so treated it is called a " changing note." Example : UNESSENTIAL DISCORDS. Changing Notes in Two Parts, 193 Handel. " Alexander's Feast." i Appoggiaturas and acciacaturas are two very common forms of auxiliary notes (Part I., Chap. IV. 7). Anticipations. 9. When one note of a chord is sounded before the others, and during a preceding chord, to which it does not belong, it is termed an anticipation. Example : (a) X id) ^ Here the notes marked x evidently do not belong to the chords in which they are found, but to the following chords. The D of the chord of G, and the E of the chord of C, are therefore anticipated in the preceding chords. At {b) the chords are shown without the anticipations. The following example of anticipations is from Men- delssohn's "St. Paul." ^—0-0 194 PART II.— CHAPTER XI. Retardations. 10. A retardation is the delaying of the appearance of a note of one chord by prolonging one of the previous chord. It is distinct from a suspension by the fact that it need not be prepared, and may proceed by skip, instead of by one degree. These retardations are often termed syncopated or driving notes (see Part I., Chap. IV. i). At {a) retardations are introduced, and at ifi) the passage is shown without them. Arpeggios. II. The nature of an arpeggio has been explained, and the derivation of the term given in Part I., Chap. IV. Arpeggios are used as an embellishment and admit of great variety of treatment. A few examples are appended. Mendelssohn. Prelude in E minor. Mendelssohn. Concerto in G minor. 1 ' 1^ ^ P- 1 p. ^ ^— p — - *-M ^ — ^ 1 — Z 1^— Schubert. Impromptu, No. 4. Arpeggios must not be used to disguise a bad progression. Therefore the following passages are objectionable, because the chords which they represent are forbidden. •o*.^ 5 5 1 5 1 H i -1 i --^^^ = 8 r Ground Bass 12. A progression in the bass is sometimes repeated several times, with different accompaniments : it is then termed a Ground Bass, or Ground. The following passage is an example. Handel. " The many rend the skies," "Alexander's Feast." 1^ r-l =^ — f*3rM J J J J . -4—/ -t ^ PART II. CHAPTER XI. 1 1 1 J 1 — \—^-m-^ — H 1 — H~" - ^ J_i_ ■r f t — ^ — w r - — m m. The ground bass continues throughout the whole of the Andante movement of this chorus : the first three sections only are quoted here. The following example contains both passing, auxiliary, and changing notes. The auxiliary notes are frequently quitted by leap, Handel. -Samson" UNESSENTIAL DISCORDS. 197 The following extract shows passing notes in one and more parts upon a dominant pedal, retardations, and arpeggios. J. S. Bach. Organ Fugue in A. i4 -rT — ^r*^ --f 1 =^ ^^==^ - « ^ ■ I r -J J — , — rj^ :g ?5= 1 1 n # 4 u ^^ ^ -H — — P— -- H- 1 1 i — # 1 • * 1 J- t-^ 1 — p-^ — rhi-p : 1 ! rrrf L ^— 1 J 4— *i r- r -< -•»— - « • — : 1 It is very common to employ passing notes in one or more parts upon a pedal. In the first example below there is first an inverted dominant pedal, and then an inverted tonic pedal, each having iq8 PART II. CHAPTER XI. passing notes in two parts below them. In the second there is an inverted tonic pedal, with passing notes in three parts below. Haydn. Symphony in C, No. i. mm rrr~r , ,r -Fr r , ~i — i — — \ — ^p- ^ — p — 1 - Ltt t i ttlt it " ^'~r^ " i PS Beethoven. Sonata, Op. 2, No. 3. (1^ RECAPITULATION. 199 Melodies which contain passing notes, such as, for example, " Cherry Ripe " and " Where the bee sucks," may now be harmonized by the student. Except in cases of unusual aptitude, the harmonizing of a given treble is found difficult, and a great deal of practice in this department is therefore needful. It is unnecessary to quote other melodies here or in subsequent chapters, as numbers can easily be found well adapted to the purpose amongst the National Songs of Great Britain and Ireland. The student will do well to select one or two at the end of the work of each chapter, and to harmonize them, and in this way freedom in the application of the knowledge gained of the various chords, will be quickly acquired. RECAPITULATION. Chapter XI. 1. Unessential discords, or discords by transition. — Passing notes, auxihary notes, anticipations, and retardations. 2. Passifig notes, — Unessential notes, ascending or descending between two essential notes. 3. ThezT character. — Diatonic when they belong to the major or minor scale, chromatic when they do not. 4. Regular or irregular. — Regular when on an unaccented beat, irregular when on an accented one. 5. Rule for their use. — Only admissible when the passage is correct without them, 6. Auxiliary note. — An unessential note, at the distance of a 2nd above or below an essential note. 7. Progression. — To an essential note a 2nd above or below it. 8. Changing note. — An auxiliary note which, by skipping a 3rd, passes to the note on the other side of that harmony note on which it afterwards resolves. 9. Anticipation. — The sounding of one note of a chord before the others. 10. Retardation. — The delaying of one note of a chord until after the others are sounded. 11. Arpeggio. — The sounding of the notes of a chord in succession. 12. Ground Bass. — A bass which is repeated several times, with varied accompaniment. '200 PART II.— CHAPTER XI. - EXAMINATION QUESTIONS. Chapter XL 1. What are unessential discords, or discords by transition ? 2. Distinguish between (i) diatonic and chromatic, and (2) regular and irregular passing notes, and give an example of each. 3. Correct the following passage, altering the passing notes as required. What rule do they infringe ? 4. Point out the faults in the following passage, and write it cor- rectly : — 1 1 ' n — — f^-l 1— 3 — - ^ — <9 — 1 f 1 — -» 4 0 1 ■ TT rn ^-^ — & I t ° 5. Give examples of passing notes in two, three, and four parts. 6. What is an auxiliary note, and wherein does it differ from a passing note ? 7. Write one or more examples of " changing notes," and explain the term. 8. Give the names and derivations of two kinds of notes which are very frequently employed as auxiliary notes. 9. Introduce passing and auxiliary notes, with some examples of changing notes, into the following passage : — EXAMINATION QUESTIONS. I , I i . 201 -i — r I I ' o 10. Explain the terms "anticipation" and "retardation," and give illustrations. 11. Give another term for "retardation." How may a retardation be distinguished from a suspension ? 12. Write examples of various kinds of arpeggio, and give the meaning and derivation of the term. 13. Give an explanation of the term " ground bass." 14. Complete the following exercises : — Diatonic and Chromatic Passing Notes, Auxiliary Notes, Anticipations, and Retardations. ■ 1 rTTi n~ri 1 - -(<^.-r4=-i—m » - -hK-r* 6 ' P i 6 6 6 4 3 t 6 6 5 0 f3-^ 6 - •ff*>^, — - • - - 1^ 1 ©> J6 6 «4 7 CHAPTER XII. Sequences. I. A sequence is the repetition of a progression of single notes, or of chords, upon other degrees of the scale. A sequence composed of single notes is called a "melodic sequence." Example : — A sequence composed of chords is called a "harmonic sequence. Example : — I J- I J , 1 . I . 1 rr 1 — ^ 2. When every interval is major or minor according to its char- acter in the original pattern, this is a Real sequence. But when the intervals are changed, and become major or minor according to the key in which the passage is written, this is a Tonal sequence. The above is a tonal sequence, for the 3rd in the treble is major in the first bar (D to FJ) and minor in the second (E to CJ). The 3rd in the 'bass is major in the first bar (D to Fj), and minor in the second (CJ to F). 3. In the original progression, all the rules of part-writing must be observed, but in the course of the sequence, many things are permitted which are usually forbidden. Thus, for the preservation of the sequence, the leading note may be doubled ; skips of augmented intervals may occur, either in the melody, or in any of the parts; and the dissonant triads may be used. The second inversion of concords is not available in a sequence 204 PART II. — CHAPTER XII. 4. When a sequence passes into other related keys,* such as the relative major or minor, the dominant, or the subdominant, the passage is called a " modulating " sequence. The following are examples of sequences : — Cherubini. Mass in D minor !T 3 J-^EE 1 I— u 1 # < 1 — 1 « ^--^^ p| — 1 — -i — Ef=tES ,-S=S=5h=IS— 1 — s — " — 1 1 ^ 1 1 1 1 [III -d ' • LI T 1 i 1 1 1 ■ =1 ^ * • ^ V 4 1 -rr ^ — ^ r Mozart. Requiem ^lass. I'T 'f d "-^ — ^ See Chapter XVI. 2. RECAPITULATION. 20? Dvorak. rhe Spectre's Bride.' « — — - r ^^b|i A J- -S> G>— ' 1 RECAPITULATION. Chapter XII. 1. Sequence. — The repetition of melodic or harmonic progressions with different notes. 2. Real Sequence. — When every interval is exactly the same as in the original pattern. 3. Tonal or Diatonic Sequence. — When the intervals are major or minor according to the key in which the passage is written. 206 PART II. — CHAPTER XII. 4. Permitted Licenses.— TYie doubling of the leading note, skips of augmented intervals in any of the parts, and the use of dissonant triads. 5. Modulating Sequence. — A sequence which passes into other related keys. EXAMINATION QUESTIONS. Chapter XII. 1. What is a sequence ? 2. Distinguish between a real, and a tonal or diatonic sequence. 3. Name some rules of part-writing which may be disregarded in a sequence. 4. What chord is unavailable in sequences ? 5. Continue the following passage sequentially : — 6. What is a modulating sequence ? Sequences. — m — -p r 1^1 1 UH — 6 7 6 4 3 4 — EXAMINATION QUESTIONS. 207 CHAPTER XIIL Chromatic Chords. 1. A chromatic chord is understood as one in which at least one note of a diatonic chord is chromatically altered. It does not necessarily contain a chromatic interval (see Part I., Chap. V., on Intervals). Thus in many of the following examples of chromatic chords, all the intervals are diatonic, and yet the chords are chromatic, because they contain a chromatically altered note. Chromatic chords need no preparation, and they induce no modulation. They are therefore either in the key of the preceding, or of the following passage; and, should these two keys be identical, the chromatic notes, though foreign to the key, have evidently not changed it. Chromatic notes may either rise or fall to their resolution. Chromatic Concords. 2. There are two chromatic concords which are common to both major and minor keys. These are the major chords on the super- tonic and on the minor 2nd of the key. In the major chord on the supertonic, both the 3rd and the 5th are chromatic in a minor key, and the 3rd is chromatic in a major key. The 3rd of the chord must not be doubled, and must either rise or fall a semitone to its resolution. In order to avoid modulating to the key of the dominant, the supertonic major chord should be followed by some form of the tonic chord or of the dominant seventh, or by some chord character- istic of the key. Mendelssohn. Concerto in G minor. CHROMATIC CHORDS. 209 Gade. " The Erl King's Daughter." !S_J ^ Mendelssohn. 13th Psalm. Beethoven. Sonata, Op. 7. X ft- ^-^m^ ^ ' L-i y M Mendelssohn. Concerto in G minor. =3 s=5=s^ -* ?|- 1 1 1 — 1 — -|— • \—m — ^ 0 mm— =t=t- , — h 3. The major chord on the minor 2nd of the scale is more often used in minor than in major keys. The root is a chromatic note, and in major keys the 5th is chromatic. The chord is often seen in its root position, but it is seldom taken in its second inversion. 210 PART II.— CHAPTER XIII. The first inversion is by far the most common form of this chord, and is generally known as "The Neapolitan Sixth." This chord consists of a minor 3rd and a minor 6th, and is taken upon the subdominant of the scale. It may be followed m various ways, and its intervals are free to rise or fall. This also apphes to the other positions of the chord. Chord in root positi^ (x) ; ist inversion (^). ^^^^^^^^^ Impromptu, No. i. 1st inversion (x) Beethoven. Sonata, Op. 31, No. 2. - ' feet -J- U J 1 I 1 I ! . I Mendelssohn. "Elijah." 1 i CHROMATIC CHORDS. 211 J. S. Bach. Dr. Crotch. " Palestine," 212 PART II. — CHAPTER XIII. 4. Those concords which are peculiar to the minor key, with their inversions, may be freely used as chromatic chords in the major key, excepting only the tonic minor chord, and its two inversions, which are but rarely seen. They are as follows : — (1) The minor common chord of the subdominant with its two inversions (a, c). (2) The diminished triad on the supertonic, with its first inversion {d, e). (3) The major common chord on the minor 6th of the scale, and its first inversion (/, g). The second inversion of this last chord is rare, though it is seen taken in arpeggio at ih). All these chords are shown in the following examples, with their ordinary resolutions. Mendelssohn. "Midsummer Night's Dream." Mendelssohn. " Lorelei." kh) {a) {b) {a) ! I ,11 CHROMATIC CHORDS. 213 P ^ fij Mendelssohn. Capriccio, Op. 22. I r^-i ^- m -J- i :3:zie: Mendelssohn. " Midsummer Night's Dream." 4- i (/) Schubert. Mass in A flat. , iS I I I I I £=e: ^^^^ PART II. — CHAPTER XIII. Rossini. *' Stabat Mater." Rossini. ' ' Stabat Mater. RECAPITULATION^ Chapter XIII. 1. Chromatic Chord. — A chord in which at least one note is chro- matically altered. 2. Treatment of Chromatic notes. — They need no preparation and, as a general rule, they may either rise or fall to their reso- lution. They should not be doubled. 3. Chromatic Concords common to both major and minor keys. — The major common chords on the supertonic, and on the minor 2nd of the key, with their inversions. 4. Their resolution. — The supertonic chords resolve generally either on tonic harmony, or a dominant discord ; those on the minor 2nd of the key are free. 5. Neapolitan 6th.— K chord of the 6th taken on the subdominant, consisting of a minor 6th and a minor 3rd. 6. Its Resolution. — Being the first inversion of the major chord on the minor 2nd of the key, its resolution is free EXAMINATION QUESTIONS. 215 7. Chromatic Concords peculiar to the major hey.^(i) The minor common chord on the subdominant, with its two inver- sions ; (2) the diminished triad on the supertonic, with its first inversion ; (3) the major chord on the minor 6th of the scale and its first inversion. 8. Resolutions. — Various ; but those to tonic or dominant harmony most usual. EXAMINATION QUESTIONS. Chapter XIII. 1. Explain the term " chromatic chord." 2. Give some rules for the treatment of chromatic notes. 3. In the key of E flat and its tonic minor give examples of those chromatic concords which are common to both major and minor keys. Add inversions and resolutions. 4. What is the technical name for the first inversion of the major concord on the minor 2nd of the key ? Write a phrase of four bars, introducing this chord. Figure the bass. 5. Write a phrase of four bars in the key of A, giving examples of the chromatic concords of the supertonic and of the minor 2nd of the key. Figure the bass. 6. Give examples of those chromatic concords which are peculiar to the major key, with inversions and resolutions. 7. Write a few bars in the key of B, and introduce the major chords of the minor 2nd and the minor 6th of the key. Figure the bass. 8. Complete the following exercises : — On the major chord of the supertonic. 135 , 07 % D5 Jf4 6 2 tl5 7 9 8 It »7 8 4 S 2l6 PART II. — CHAPTER XIII. 86 6 56 4 4 3 3 4 6 5 6 C 2 6 6 Jf4 6 S5 8 2 8 85 - 137 8 - 6 84 6667 98 8 2 5 4 8 8i' 8 4 3 On the major chord on the minor 2nd of the key, and the " Neapolitan 6th.' v~i~w — 1 — A i 1 1 1 ' ! 6 7 6 5 S76 6 Q4 6 4 2 tre 8 7 tl - ^ — ^{-^ — h — h- 6 fl6 4 3 ^— ir-r~ 6 be 6 Q4 6 — 4 2 176 — 6 7 4 t — 1 t[7=t- 1 4 6 3 6 7 4 6 C6 4 5 2 h— s — ri:^=^^ 9 S 6 t>6 3 b — 0 6 S 4 3 -1— t 7 Hi 6 0 t)5 86 C 4 6 b6 177 qe 8 7 0 175 42 543 — — ' -4 ^ - G 6 5 fi S Gb6 65 84 686 4 8 ^ Q 4 8 2 4 ■^^^ — ^-^'-^ — 1 7 be 6 7 4 8 4 3 EXAMINATION QUESTIONS. On the minor chord of the subdominant and its inversions. 217 The 1st inversion of the diminished triad on the supertonic. S3: 6 7 4 5 6—6 654 64 ffG 3b5432 3 4 B 4 7 6 7 5 - 5 6 1? 5 - 2 1? The major chord on the mmor 6th. 1 9 * imp ^ — 1 — r-^^^r- 6 6 6 5 6 bs b5 6 4 3 — 6 5 6 be — 8 7 b - 4 b5 6 5 6 7 4 3 2 3 CHAPTER XIV. Chromatic Fundamental Discords. I. Chromatic chords of the 7th may be taken upon the supertonic and the tonic in both major and minor keys. The Supertonic 7th. This chord consists of the major supertonic chromatic concord, with the addition of a minor 7th from the root. The intervals are then precisely the same as those of the dominant 7th ; and therefore, in order to avoid modulating into the key of the dominant, the super- tonic 7th, like the major concord on the same note, must be followed by some form of tonic harmony or by some chord characteristic of the key. The 7th either falls a 2nd or remains to be a note of the next chord. In the last case it may be doubled {a). Example :— fefe {a) J- U Q7 C!7 7 6 7 4 S s 57 The inversions of this chord may be taken and resolved ac- cording to the rules just given. 1st inversion. 2nd inversion. , " ! „ 1 \ I 1 ■! I w "^rd inversion. 1 4 3 The supertonic 7th and its inversions are in very frequent use. A few examples are appended : — CHROMATIC FUNDAMENTAL DISCORDS. 219 Mendelssohn. "LaudaSion." 1st inversion. ^ n *^ -sl- X - X -iS — -tf—m- Cj f— y:i -g-^-g- 1 — u 8 L-S) — 8 — ^ * Mendelssohn. "St. Paul." 2nd inversion. -f- ^ ^ -i^- -5 - • I Mendelssohn. 114th Psalm. 2nd inversion. • 1 1 i 1st inversion (x). H— 4- Schumann. "Blondel's Song." Supertonic 7th. ^ It — :t Spohr. " Last Judgment. J 1- J I N , I I 1 — r S I 220 PART 11. CHAPTER XIV. The Tonic 7th. 2. A chromatic chord of the yth may be taken upon the tonic in both major and minor keys. It is formed by adding a minor yth to the major tonic concord. In major keys the yth is chromatic ; and both 3rd and yth are chromatic in minor keys. The intervals are identical with those of the dominant yth ; and therefore, in order to avoid modulating into the key of the subdomi- nant, the tonic yth should be followed by a dominant or a supertonic discord. Example : — Resolved upon a Dominant Discord. Minor key. „ (a) Major key. -J- ' I 'I — G7 Resolved upon a Supertonic Discord. id) Maj or cey. 1 I Minor 1 1 Hub J 1 key. , ] 1 1 .C3L — 'i^ - r> P 1 1 1 i G> -g ^ 1 1 s> <5> 1 0 ■ I 13 7 7 6 7 7 D9 S fi 4 n Co 3" — 545 The yth may either rise a chromatic semitone, as at (a), or fall a 2nd, as at (d). The 3rd may rise a minor 2nd, as at (a), or a major 2nd, as at (^) ; or it may fall a chromatic semitone— but it must not be doubled. The inversions of the chord may be taken and resolved as- follows : — Resolved upon Dominant Discords. Major key. 1st inversion. 2nd inversion. CHROMATIC FUNDAMENTAL DISCORDS. 2nd inversion, without the root. 3rd inversion. I: '1 '1 A -«s>- Resolved upon Su-pertonic Discords. 1st inversion. 1st inversion, Minor key. -=1 ^- -- D7 S6 4 3 2nd inversion, without the root. A few extracts are appended, showing the employment of the tonic 7th : — 1 Schumann. " Paradise and the Peri -I— -P- H — r r ' 222 PART II. CHAPTER XIV. J. S. Bach. Prelude i. Tonic 7th. G 1 s> G 1 — — & Tonic 7th (X) ; ist inversion, supertonic 9th (0). J. S. Bach. Prelude i. i X Mendelssohn. Concerto in G minor. X ivi J. H-n^ — ^ ^ i 1 T ' ''-n ■ m^m^-^ — — ^ — . _ Jl =C_^ ^ • -r r r r-T^ -t= — X The passage is in the key of B ; the chord niarked X is therefore a tonic 7th, first inversion. J. S. Bach. "The Passion " (S. Matthew) f=E3 r7\ 1- X Though the last inversion of the tonic 7th, seen at X, resolves on the chord of E flat, there is no modulation, and the whole passage is evidently in the key of B flat. CHROMATIC FUNDAMENTAL DISCORDS. 223 The following example shows a supertonic 7th (X) and a tonic 7th (^) : — DussEK. Sonata in Et>. 1 w 1 ^ — ■ — r 1 1 i *- - Tonic 7th, 2nd inversion (X). Beethoven. Sonata, Op. 81. Tonic 7th ; ist position (X). Mendelssohn. •'' Elijah. \ ^ ■ 1 ' 1 1 1 c ^ — m — r r r 1 1^ =ti — 1 P =» 1 Tonic 7th ; last inversion (x). Mendelssohn. " Athalie." I S 1 1 , . 224 PART II. — CHAPTER XIV. Chromatic Chords of the qth. 3. A major or minor 9th may be added to the chromatic chords of the supertonic 7th and the tonic 7th. In a major key the 9th may be either major or minor ; but in a minor key it must be minor.. The intervals of the chord are the same as those of the dominant 9th ; and the 9th may either resolve on the same root or on a chord with another root. The other notes of the chord resolve as shown in the foregoing chromatic chords of the 7th. The chords of the 9th may be taken both in their root positions and in their inversions. The supertonic gths resolve either upon tonic harmony or upon a dominant discord. The tonic 9ths resolve either upon a dominant discord or upon a supertonic discord. Resolutions of the Supertonic qth. Major key. Resolved upon tonic harmony. Resolved upon a dominant discord. ^. .-^-^^ -4— n f^V:-tr 1 V r — 1 1 — '1 "7 u £6 b7 4 -r 1 1 b9 8 i - X)1 - -r— ^ 1st inversion. -fe ^ — 1 ' n ^ J & m — ^ 1 — 0— — ^ • 1 i ^ • t>7 cs b7 5 4 Minor key. 3rd inversion resolved on 2nd inversion resolved on tonic discord. dominant discord. CHROMATIC FUNDAMENTAL DISCORDS. 225 , , . 1 Ath inversion resolved on Major key. " dominant chord. ^^^^ In the foregoing examples the 9th either rises a chromatic semi- tone, as at ia) ; or falls a 2nd, as at {b) ; or remains to be a note of the next chord, as at ( 1 — * < 1st inversion, supertonic major 9th (x). Brahms. "Requiem." r 1st inversion, supertonic major 9th (x). ^ G. A, Macfarren. " May-Day. 4^ J- J- 1st inversion, supertonic minor 9th (x). Schumann. " Paradise and the Peri." ^ ff-^^^ — ^ u ^- - — I 2nd inversion, supertonic minor 9th (x). Schumann. " Paradise and the Peri. x 228 PART II. CHAPTER XIV. Examples of the tonic 9th X SroHR. " Last Judgment. i I Gounod. " The Redemption. " Mozart. X "Don Giovanni." ft*H.-r. 1 d « J « w — *l 1 . j^^; — -3 p 1 - 4. The nth may be added to the chromatic fundamental dis- cords in both major and minor keys. The nth is not a chromatic note, being the dominant of the key in the supertonic chord and the subdominant in the tonic chord. The supertonic and tonic nth may, Hke the dominant nth, resolve either upon the 3rd or the 5th whilst the other notes of the chord remain, or upon a chord with another root. This also applies to the inversions. The nth upon the tonic is very seldom used, and it is even rarer upon the super- CHROMATIC FUNDAMENTAL DISCORDS. 229 tonic, and it is not therefore needful to do more than refer to the chords. They are shown in their root-positions below : — Supertonic iith, with the 7th resolved Tonic lith, with the 7th resolved on on the 3rd. the 3rd. tH — i n-'i 1 — ih _j_ ^ A- A. A. A A,. =e EE 6 11 5 6 6 — 6 11 3 S4 6 7 - 05 P5Q7 q7 - 2 Supertonic iith, with the 7th and 9th Tonic nth, with the 7th and 9th resolved on the 5th. resolved on the 5th. 1 1 •? • J _^ \^4- u J. 6 11 5 C7 7 — t|7 11 5 S6 9 3 4 07 — 3 6 5. The major or minor 13th may be added to the supertonic or the tonic discords of the 7th or 9th. In a major key the 13th may be either major or minor ; in a minor key it must be minor. The 9th is often omitted when the 13th is employed ; and the 3rd and 7th are generally retained, or the 3rd and the root. With the major 13th. With the minor 13th. =1 : 1 1 ^ J i 1 1 1 ^ 1 I ■ Tonic maj • — 6 or I I. -1— 7 — 6 5 0 - 3th. -J ^ 1?7 4 1*" 6 Tonic f^^ ^ ' r 1 7 - Q6 be 5 4 B - b minor 13th. 1 9 — s> 1 1 1 1 — Q . 1 1 J- 1? 1 - S 5 3 - - £ 6 4 8 H \ 7 6 a — — 7 5 0 Chromatic Chords of the Dominant qth and 13TH. 6. Though the chords of the dominant major 9th and 1 3th are not available as chromatic chords in the minor key, yet those of the dominant minor 9th and 13th may be freely used as chromatic chords in the major key. The minor 9th and 13th are chromatic notes. Examples : — Dominant minor 9th re- solved on same root. Dominant minor 13th. 1 r—f-^ 1 1 I I 1 1 -r— ^ bo 8 7 — 6 7 — !?6 5 7 6 5 4 3 Dominant minor 9th resolved on another root. Minor 13th resolved on another root. 1 - m & i ■^1 -< ■ i(S>— —G> 1 , ' 1 J 1 1 A .i p f— - 6 l79 4 7 3 \ [— (5 7 The inversions and their resolutions are the same as those given in the chapters on the dominant minor 9th and 13th. The student should now refer to the resolutions of the diminished 7th given in Chapter VI. They will be found quite clear and simple when once the chromatic chords of the 9th have been mastered. CHROMATIC FUNDAMENTAL DISCORDS. 23I The following passage shows the employment of the dominant minor 9th in a major key : — Schumann. Novelletten, No. 4. 1 -1 i-^m—^ — ^ IT- m 1 -» 1 1 — These remarks apply also to the chords of the dominant minor 9th and 13th, and examples of each are added. The 9th and the 13th may, as in the diatonic resolutions, either resolve first, on the same bass note, or on another root, with the other notes of the chord. When the 9th resolves on the same root, there remains a chord of the dominant 7th to be resolved. The chords may be taken in their inversions. It is obvious that the supertonic or tonic discords, upon which the dominant discords resolve, must afterwards themselves be re- solved, according to the rules prescribed for their treatment. Dominant major 9th (x) resolved on a supertonic discord. -A - ^ 1 r 1 ^. ^, ^ if f> -|»- 1 ^ J- -j- 1 1 1 . 4 3 6 4 5 2 -1= tiz 6 4 3 Dominant minor 9th (x) resolved as a Dominant major 9th (^) resolved supertonic discord. upon a tonic discord. X ! 1- 1 1 1 1 r 1 1 ^ 1 1 1 J 1 1 9 8 6 {4 7—5 2 t - fl 6 J6 4 3 1 6 6- 5 4 3 — 6 Jf4 Q5 2 6 7 232 PART II. CHAPTER XIV. Major 13th, resolved on a supertonic discord. Minor 13th, resolved on a supertonic discord. 7 26 6 7 J6 6 79S 64 I'd 64 ;5 57 — 3 S3 S - Dominant major 13th, resolved on a tonic discord. jNIinor 13th, resolved on a tonic discord. — h thh i n ; — 1 1 1 m 1 1 1 1 *| 1 J ' J 1 1 1 1 1 1 — ^ 7 6 4 6 '4 1 " r r — 17 6 if4 6 56 i 4 4 — ; 2 — 2 3 6 5 C5 2 8 - 3 Chromatic Resolutions of the Chords of the Dominant 7TH, 9TH, and 13TH. 7. Besides the various diatonic resolutions of the chord of the dominant 7th, given in Chapter III., there are. certain chromatic resolutions which are often employed, of svhich the chief are — (i) the resolution to a supertonic discord; and (2) that to a tonic discord. The chords may be taken either in their original positions or in their inversions. For example, at (a) below, both the dominant 7th and the supertonic discord are in their first inversions ; while at {d) the dominant 7th appears in the third inversion. In chromatic resolutions the 7th may rise a chromatic semitone. See X below : — 3 55 543 D54 The 3rd may also fall a semitone to its resolution, as may be seen in some of the next examples. See CHROMATIC FUNDAMENTAL DISCORDS. The following examples show some chromatic resolutions of dominant discords : — Mendelssohn. "Athalie." Mendelssohn. " Athalie.' irp=c _£2_ "t — ^1 Spohr. " The Last Judgment." The following passage is interesting as showing four different resolutions of the same chord of the diminished 7th derived from the supertonic : — r >v J. S. Bach. Prelude 5. L (a) ' (^) 1 S3E RECAPITULATION. Chapter XIV. 1. Super tonic '^th. — A chord having the same intervals as a domi- nant yth, taken upon the supertonic of the key. 2. Inversions. — Three ; taken upon the 3rd, the 5th, and the yth of the chord. 3. Resolutions of supertonic 7th and its inversions. — To some form of tonic or dominant harmony ; or to some chord character- istic of the key. 4. Tonic '/til. — A chord containing the same intervals as the domi- nant yth, taken upon the tonic. EXAMINATION QUESTIONS. 5. Inversions. — The same as those of the supertonic 7th. 6. Resolutions. — To a dominant or a supertonic discord. 7. Supertonic gth. — The addition of a major or minor 9th to the supertonic 7th. In minor keys the 9th must be minor. 8. Inversions. — Four when the 9th is minor, taken upon the 3rd, 5th, 7th, and 9th of the chord. The last inversion is unavailable when the 9th is major. 9. Resolutions. — The same as those of the supertonic 7th. 0. Tonic gth. — The addition of a major or minor 9th to the tonic 7th. In minor keys the 9th must be minor. 1. Inversions. — The same as at 8. 2. Resolutions. — The same as those of the tonic 7th. 3. Supertonic and tonic nth. — The addition of a perfect nth to the supertonic or tonic 7th or 9th. 4. Resolutions. — Either upon the same root or upon a chord with another root. 5. Supertonic and tonic ijth. — A major or minor 13th may be added to the supertonic or tonic 9th, and resolved first or with the rest of the chord. In minor keys the 13th must be minor. 6. Chromatic chords of the dominant minor gth and ijth. — These chords may be taken upon the dominant of major keys, when their inversions and resolutions are the same as those of the diatonic minor 9th and 13th. 7. Chromatic resolutions of diatonic discords. — The chords of the dominant 7th, 9th, nth, and 13th, with their inversions, may resolve chromatically upon either tonic or supertonic discords. EXAMINATION QUESTIONS. Chapter XIV. 1. Describe the chord of the supertonic 7th. How does it resolve? 2. Write a phrase of four or eight bars, introducing the supertonic 7th, either in its root-position or in its inversions. 3. How is a supertonic fundamental discord of the 9th formed ? State which are the chromatic notes in this chord in a major and in a minor key. 236 PART II. — CHAPTER XIV. 4. Give examples of the supertonic 9th and its inversions in a major and in a minor key. Add resolutions, and figure the bass. 5. Give an example of the chord of the tonic 7th, either in a major or in a minor key. Resolve it in various ways. 6. Write a phrase of four or eight bars, introducing the tonic 7 th and one or more of its inversions. Figure the bass. 7. What are the intervals of a " tonic 9th " ? Say which are the chromatic notes of this chord in a major and in a minor key. 8. Give examples of the tonic 9th and 13th, with resolutions, in the key of D flat. Mark the chromatic notes with x. 9. Write a phrase of eight bars in a major key, introducing the chords of the dominant minor 9th and 13th. 10. Describe some of the most ordinary chromatic resolutions of the dominant 7th, and give examples in a major and a minor key. 11. Write a phrase of eight; bars, introducing chromatic resolutions of the dominant 9th and 13th. 12. Take a chord of the diminished 7th on A, and by enharmonic changes resolve it into each of the twenty-four keys, re- garding it (i) as an inversion of the dominant minor 9th ; (2) as an inversion of a supertonic minor 9th ; and (3) as an inversion of a tonic minor 9th. 13. Complete the following exercises : — Supertonic 7th. H-: 5 t)6 6 3 2 Supertonic 7th. 9 8 6 6 5 4 7 6 5 4 3 2 6 # 7 - q7 5 — 4 it 6 7 5 -0— i — i-tS i 6 4 5 4 3 — 77 5 i_i — 06 5 i A* — ^ : t= 6 6 6 5 4 ^\-M-um^d- 5 4 6 —7 S 2 t3 b7 6 5 6 7 4 S EXAMINATION QUESTIONS. Tonic 7th. 6 5 '54 4 a 2 ne %7 ^ 6 b5 5 5 33 D3 133 4 Q Tonic 7th. n7 56 S6 S6 4 54 0.5 4 2 56 - 56 5 4 135 3—3 Minor 9th and 13th on the tonic. 6 p9 6 56 6 6 7 — 4 7 4 4 4 6 5 53 5 - Minor 9th and 13th on the tonic. Major key. 1 1 — ^ -^b a ! \ 5 6 b7 — 6 3 4 6 5 q4 3 — b J 6 6 ce — 4 b 5 — -l^-i Hr- 06 5 6 — 4 3 b5 — b 7 6 6 7 . G 6 5 4 2 . • ^ ^ 1 J — ^ k- 4 8 9 6 6—3 5 be 5 3 4 :=±: 1 ^ 4 6—6 2 5 4 4 3—3 ' J J J 6 5 6 6 6 4 3 4 b b 6 6—43 4 4 — 2 — 238 PART II. — CHAPTER XIV. Chromatic resolutions. 1 — * — • — * w — 1 4 6 4 3 3 _J 1 V — b7 6 - CO C4 — D5 3 2 b £ 6 b7 D6 — 77 4 5 P5 — 5 52 3b — 1 ^ 1 — 4 Q6 D7 Be P6 (7 7 4 6 4 b6 — 6 b6 2 05 b5 4 b5 5 2 3 4 — 4 1?5 4 2—2 2 136 — D6 7— 6545 05 — 45 — 4 3 23 2 3 Minor 9th on the supertonic. CHAPTER XV. Chromatic Chords of the Augmented 6th and the Augmented 5th. I. The chord of the augmented 6th may be taken upon the minor 2nd and the minor 6th of both major and minor keys. The chord on the minor 6th of the key, which is far more generally employed than that on the minor 2nd, consists of the minor 9th of the dominant, and the major 3rd and minor 7th of the supertonic. Thus it has two roots— the dominant and the supertonic of the key. The chord is here shown on the minor 6th in the key of G, Et? being the minor 9th of the dominant, and C$ and G the major 3rd and minor 7th respectively of the supertonic of the key :— In a major key, as above, both the notes which form the interval of the augmented 6th are chromatic ; in a minor key the upper note (the major 3rd of the supertonic) is chromatic. 2. This is the simplest form of the chord, containing only the augmented 6th and the major 3rd from the bass note. When so written, it is called " the Italian 6th." When the 4th from the bass note (the supertonic root) is added, the chord is called " the French 6th " ; and when the 5th (the minor 9th of the supertonic) is added, it is called " the German 6th." Example (see Note^) : — ^ It is stated by Dr. Crotch, amongst others, that the Italian, French, German, and Neapolitan 6ths were so named after the nations who first used them. Italian 6th. French 6th. German 6th. 240 PART II.— CHAPTER XV. 3. The chord of the augmented 6th on the minor 2nd of the key is not so much used as that on the minor 6th. It consists of the same intervals as the latter chord ; but they are derived from the tonic and the dominant, instead of from the dominant and super- tonic. Example :— Italian 6th. French 6th. German 6th. ^ 1 1 4 — k-r^ =¥ v-> H Minor gth of tonic. Major 3rd and yth of dominant. Dominant root added. ^p- Minor 9th of domi- nant added. I Resolutions. 4. The augmented 6th on the minor 6th of the key may resolve (i) upon the tonic comm_on chord; (2) upon the dominant common chord or. its first inversion; (3) upon a supertonic discord; or (4) upon a dominant discord. The resolutions upon tonic and dominant harmony are the most usual. The two notes composing the interval of the augmented 6th must never move in similar motion. Contrary and oblique m.otion are equally employed, though the former generally has the best effect. The other notes of the chord will have the same progressions that they would naturally take as portions of a fundamental discord. Example : — Italian 6th. . Resolved upon , x Upon the , . Upon a super- ^ ^ tonic harmony. ^ dominant. tonic discord. , V Upon a domi- nant discord. CHROMATIC CHORDS — AUGMENTED 6tH AND AUGMENTED 5TH. 24 1 German 6th In the foregoing resolutions it will be noticed that the notes composing the augmented 6th chiefly move in contrary motion, and that the other notes move as they do in the chord from which they are derived. For example, the 7 th of the supertonic being in its second inversion, i.e.^ being the 3rd to the bass note, may be doubled (see a) ; and then one may rise while the other falls, or remains to be a note of the next chord. When it is not doubled it should fall or remain (b). The root, being either the supertonic, tonic, or dominant, is free. Consecutive 5ths arise when the German 6th is resolved upon a common chord on the note below. To avoid them, the 5th must resolve first, as at {a). A more usual resolution of this chord is to a I on the note below, as at {b). Resolutions of the Chord on the Minor 2Nd of the Key. 5. In a major key this chord may be resolved on the tonic common chord ; but this resolution is not available in a minor key. Otherwise, the notes proceed in the same way as those of the chord on the minor 6th : — Major key 56 - 5 — 06 - 4 — 3 — 136 6 5 4 3 |6 — b7 7 4 - tj a .3 — PART II. — CHAPTER XV. Inversions. 6. The chords of the augmented 6th are comparatively seldom used in their inversions. Generally speaking, such inversions are available as do not necessitate the inverting of the interval of the augmented 6th, which inversion would produce a diminished 3rd. The last inversion of the German 6th, however, is sometimes seen, and examples of its use will be given. The Italian and French 6ths are very rarely, if ever, taken in the last inversion. In the resolution of the inversions the notes which constitute the interval of the augmented 6th should move in contrary or oblique motion ; the other notes of the chord are free. The inversions resolve like the original chord, mostly upon some form of tonic or dominant harmony : — I Italian 6th. | French 6th. | German 6th. | „ I 1st inv. 1st inv. 2nd inv, 1st in v. 2nd inv. 3rd inv. The Augmented Triad. 7. This chord consists of a major 3rd and an augmented 5th, and it is chiefly found upon the key-note and the dominant of major keys. The chromatically-raised 5 th ascends to its resolution ; and thus, having a fixed progression, it must not be doubled. The chord, with its two inversions, is given below. Sometimes the 7th is added, as at (a). The resolution of the augmented triad is to a chord whose root is a 4th above that of the discord : — 1st inversion of tonic On the tonic. On the dominant. With the 7th. augmented triad. CHROMATIC CHORDS — AUGMENTED 6TH AND AUGMENTED 5TH. 243 2nd inv. of tonic augmented triad. 1st inv. of dom, 2nd inv. of dom. augmented triad, augmented triad. -J w — - — ^ If the augmented 5th be enharmonically changed to a minor 6th, the chord is identical with the fundamental discord of the minor 13th, with the root and 3rd ; or with the 3rd and 7th (refer to " Chroma.tic Chords of the 13th on the Supertonic and Tonic," Chapter XIV., 5). The notes in the following examples are precisely similar to the previous ones, the change of notation being the only differejice : — Minor 13TH. On the tonic. On the dominant. i i)6 be With the 7th. ^eJ r Examples of the Augmented 6th. Italian 6th (x). Beethoven. op. 53. i it ^- 7*- 244 PART II. — CHAPTER XV. French 6th (x) ; Italian 6th (^). j^^^dn. - The Creation." i -J- German 6th (x) ; French 6th (0). Schubert. Sonata. Xo. i. , , , \ L CHROMATIC CHORDS — AUGMENTED 6tH AND AUGMENTED 5TH. 245 j Beethoven. Sonata, Op. 10, No. 3. German 6th (x) ; French 6th (^). m T Sterndale Bennett. " Woman of Samaria." French 6th (x ) ; Ita lian 6th (0). r ' . — ^=5- m i Mi- £E5 r I ^1 German 6th (x). Spohr. " Last Judgment." ^— N ^-r— 5 German 6th (x) Beethoven. Op. 31, No. 3. 1^ -<^- The following chromatic passage shows a succession of German 6ths upon a bass rising in 4ths and falling in 5ths (x). A German 6th upon the minor 6th of the key is seen at ^, and the second chord in the last bar will be recognised as a Neapolitan 6th : — XXX Cherubini. Mass in D minor. ^- g-^ 1=— =3? 1L. \^ 246 PART II. CHAPTER XV. 2nd inversion of German 6th (x). GoUNOD, " The Redemption." 1 ! J J -1'r -4 1- -4= 1 — 8ve lowe -J — 1 \' ^ — ■ — ' 1 — I ■ _H [_ t— ' ' — r — r—r^ Last inversion of German 6th (x). Mendelssohn. " Hear my prayer." — \ — -H — 1 ^ -H— 1 — ^ — 1 \ -H ^ =1 Meyerbeer. 91st Psahn. Last inversion of German 6th. CHROMATIC CHORDS — AUGMENTED 6tH AND AUGMENTED 5TH. 247 1 Last inversion (x). Gounod. "The Redemption." X i' J j. — 1 1 N — (S> * ■a — r Last inversion (x). GouNOD. " The Redemption. X — & ^ — J- -J^ Examples of the Augmented Triad. Root position (x). Mendelssohn. " Elijah." \ Spohr. *' Last Judgment. 1 ( U we- =1 — «— ^ — m — B« _? — « — — « - :X - \- — 1st inversion. Mendelssohn. " Hymn of Praise.' X X 2nd inversion. DussEK. Sonata in Ej?- In instrumental music the augmented 5th is sometimes doubled, as below:— Gade. Novelletten. RECAPITULATION. Chapter XV. 1. Augmented 6th. — A chord containing the interval of an aug- mented 6th, taken upon the minor 6th or minor 2nd of the key. 2. Technical na?nes. — Italian 6th: when it consists of an augmented 6th and a major 3rd. French 6th : when it consists of an augmented 6th, a major 3rd, and a perfect 4th. German 6th : when it consists of an augmented 6th, a major 3rd, and a perfect 5th. 3. Resolutions. — To tonic or dominant concords, or to dominant or supertonic discords. Except — -the augmented 6th on the minor 2nd of the key may not resolve upon the tonic common chord. 4. Rule for resolving the German 6th. — AVhen the resolution is to a tonic chord on the note below, the 5th must resolve first, to avoid proceeding in consecutive 5ths. 5. Inversions. — Such inversions may be used as do not necessitate the inversion of the interval of the augmented 6th. 6. .Progression of the two notes forming the aug7nented 6th. — They must move either by contrary or oblique motion. 7. Augmented triad. — A chord with a major 3rd and augmented 5th, chiefly found upon the tonic and dominant of major keys. 8. Inversions. — Two, as in ordinary triads. 9. Resolution. — To a chord whose root is a 4th above that of the augmented triad. 10. Progression of the chromatic ^th. — It ascends to its resolution, and therefore cannot be doubled. 250 PART II. CHAPTER XV. EXAMINATION QUESTIONS. Chapter XV. 1. Describe the chord of the augmented 6th. Upon which degrees of the scale does it occur ? 2. What are the roots of a chord of the augmented 6th taken (i) upon the minor 6th and (2) upon the minor 2nd of a key ? 3. In the keys of AI? major and its relative minor give examples of the chord of the augmented 6th in three forms, both on the minor 6th and on the minor 2nd of the scale. Add the technical names and the roots of the chords. 4. Take Et? as the-lower note of a " German 6th" and resolve it in four different keys. Give roots and key-signatures. 5. Take BJ as the upper note of a " French 6th " and resolve it in four different keys. Give roots and key -signatures. 6. Enharmonically change the note mentioned in Question 4, and resolve the chord into one major and one minor key. Give roots and key-signatures. 7. Transpose the note mentioned in Question 4 a minor 3rd higher, and that in Question 5 a minor 3rd lower, and make them, as before, the lower and upper notes of chords of the augmented 6th. Resolve each into two different keys. Give roots and key-signatures. 8. Write the inversions of a chord of the augmented 6th on the minor 6th of the kev of F. Give the roots. 9. Name the roots of the following chord : Write two phrases of four or eight bars each, introducing it (i) on the minor 6th and (2) on the minor 2nd of the key. Give key-signatures. 10. Describe the augmented or extreme triad. With what funda- mental discord is it often identified ? 11. Write examples of the augmented triad and its inversions in the key of E major, both on the tonic and on the dominant. Give resolutions. 12. By enharmonic change and additional notes present the aug- mented triad as a fundamental discord, and resolve it in various ways. EXAMINATION QUESTIONS, 1 3. Complete the following exercises : — The Augmented 6th. 11 6 6 4 6 Jf4 2 Q 7 86 S5 - J6 4 6 4 2 7 7 4 3 3 2 1 1 t= * _ ' — ^ — « — « — * — «5 6 86 8 5 6 56 4 84 2 — +— ^ 1 * • 6 *56 5 — % l\ — 4 2 S6 t)6 6 86 — 8 3 6 1 — r 4 6 6 86 — 6 5 2 Q5 — 4 3 Jf2 - ^ — n — 1 — (5» 56 6 a 7 6 5 4 3 7 6 fl5 - D - 56 5 4 4 3 2 86 6 7 4 5 4 3 0- \& 1 6 86 6 6 4 H5 9 8 86 8 - 5 «6 4 3 6 5 6 4 8 fl5 6 5 4 8 252 PART II. — CHAPTER XV. The Augmented Triad, -.=^ ^ — --r — i t4 — Jt5 7 6 CHAPTER XVI. Modulation. 1. Modulation, or transition, is the passing from one key to another. It is either (i) Natural or Simple; (2) Extraneous; ox (3) Enharmonic. 2. Natural or simple modulation consists in passing from any given key to one of its five attendant or related keys.* These are, in the case of a major key, (i) the relative minor ; (2) the dominant ; (3) its relative minor ; (4) the subdominant ; (5) its relative minor. In a minor key, (i) the relative major; (2) the dominant minor; (3) its relative major; (4) the subdominant minor; (5) 'its relative major. Thus the attendants of D major are: (i) B minor; (2) A major; (3) FJ minor; (4) G major; (5) E minor. And of D minor : (i) F major; (2) A minor ; (3) C major; (4) G minor; (5) BP major. Therefore the attendants of any key are those keys which have (i) the same number of inflected notes ; (2) one more ; and (3) one less. 3. Modulation to a related key is generally made by some form of the dominant chord of the key— as the dominant triad, the domi- nant 7th, the dominant 9th, or their inversions. The dominant 7th and its inversions are perhaps the most commonly used. The chromatic chords of the 7th and 9th are also frequently employed. 4. Modulation may be either gradual or sudden. Gradual modulation implies the preparation of the modulating chord by some doubtful or ambiguous cliord, i.e., one that may belong to the key we are leaving, or to that to which we are going. Sudden modulation is when the modulating chord appears without prepara- tion, being preceded by a chord which only belongs to the key which is being quitted. Except for special effect, gradual modulation is generally pre- ferred. Care should be taken to introduce the modulating chord agreeably, and to avoid harshness. * Also called Auxiliary Keys. 254 PART II. — CHAPTER XVI. The following are examples of gradual and sudden modulation by means of the dominant 7th : — D to A— gradual. D to A— sudden. D to G— gradual. D to G— sudden. i ■cL J. l l„ 1 As no single chord can define a key, in passages where modu- lations are introduced, a few chords should follow the modulating chord, in order to confirm the new key ; and the modulation should generally be completed by a full close. The following is an example of modulation to the attendants of the key of F : — D minor. 1 — \ — h -J— i — r — ^ — 1 1 ' 1 H K ' |g- ' 1 1 1 23 -G>- 1 1 ^ 6 6 — 6 5 C major. r A minor. , 1 „ — 1^ =]=1= - '=t=: 1 ' r 1 ' . 1 1 1 1 1 I — — " 1 1— us Bl? major. J- -01- hs*- -e*- -J- 4 s MODULATION. G minor. — 1 1 — -g- r S , _| 1 h 5. A chord may be approached as belonging to one root, and quitted as belonging to another. For instance, a chord may be taken as a dominant chord of one key, and quitted as a supertonic chord of another. All fundamental discords may be considered as derived from any one of the three roots, i.e., from the dominant, the supertonic, or the tonic. This will be made clear by the following explanation of the appended examples : — A chord may be approached as dominant, quitted as supertonic (a). „ supertonic, „ dominant (^). tonic, tonic, supertonic, dominant. dominant (c). supertonic (d). tonic (e). tonic (/). (a) Approached as dominant of D ; quitted as supertonic of G. Approached as supertonic of D quitted as dominant of A. H 1 ^- I 1 1 I I I 1 T I I 6 7 B7 7 — ii , . Approached as tonic of D ; Approached as tonic of D ' quitted as dominant of G. ^ ' quitted as supertonic of C. m 37 PART II. CHAPTER XVI, Approached as supertonic of D ; , Approached as dominant of D ; quitted as tonic of E. ' quitted as tonic of A. — 1 1 — i jm . ^ " — ' 1 ! 1 1 1 -0- -G. i ^ 1 ^ r — r-^ 1 II i 'II 6 S6 7 86 6 6 5G 4 J 4 5 5 4 3 3 3 6. The chromatic concords on the supertonic and the minor 2nd of the key may also be considered as characteristic chords of a new- key, or as the major chords on the minor 6th of other keys. For example, (i) the chromatic chord of the supertonic may be quitted as a major chromatic chord on the minor 6th of a new key {a) ; (2) that on the minor 2nd may be quitted as a dominant chord {b) ; (3) or, as the major chromatic chord on the minor 6th of another key {c). {a) Approached as supertonic chro- {b) Approached as major chromatic con- matic concord of D ; quitted as cord on minor 2nd of D ; quitted as major chord on minor 6th of G J . dominant of A |7 . 1 — ir%=T^ '1 ' X L|^_U j 1 85 [55 _ t)6 6 b4 1 a {c) Approached as chromatic concord on minor 2nd of D ; quitted as major chord on minor 6th of G. 1 r G> P • 1 J 1 — 1 — ^-i — b5 5 b 1 — — a 1 Extraneous Modulation. • 7. Modulation to any other than the five attendants of a key is termed extraneous. It may be effected either gradually or suddenly, MODULATION. and by means of either diatonic or chromatic concords, fundamental discords, or by the chromatic chords of the augmented 6th and the augmented 5th. Some of the most frequent of extraneous modu- lations are — - 1. In the case of a major key : — To its tonic minor and to the five attendants of it ; to the major keys of the minor 2nd and of the major 2nd of the scale. 2. In the case of a minor key : — To its tonic major and to the five attendants of it ; to the major key of the minor 2nd of the scale. The major key of the minor 2nd of the scale is very easy of access, for the tonic of the first key is the leading note of the second key, and the latter can be immediately reached by means of the dominant 7th. For example, in passing from G major or G minor to A I? major, G is the leading note of At>, and the modulation can at once be effected as follows : — l-n — tJ7 8. Modulation is rendered easier if the tonic triad of the first key contain some note in common with the tonic triad of the nev; key. This is the case in some of the following examples, as from b1? to Bb minor, or to F minor, or to G1? major : — Modulations from Bi? major to its tonic minor and the five attendants of it. To t^ie tonic minor. Dominant minor. — ^ 1^- m J- U-i A -1 — i — ' — ^ Subdominant minor. 1 — V Relative major of dominant — 1^-^ h- 1 1 1 — I m 1 3 & I -■ H — I- 1 258 PART II. CHAPTER XVI. P Relative major of subdominant minor. I J I I , A I 1 ' Modulations from D minor to its tonic major and the five attendants of it. i A I t I -J- J. I J ^1 ■J — 1 — \ 1 1 ! 1 J 1 'i i — ^r-^i — V i 1 1 ! r Ml,— ^ 'J — ^=^r — t— 9. It is very common, in modulating to a remote key, to pass first through one or more keys, related in some degree to either the first or the last key, or to both. This is called " Compound Modulation." Examples are appended; an enharmonic change being introduced in passing from F minor to GJ minor: — From G through Compound Modulation. B minor to D |: minor. From A th rough C to E r>. MODULATION. ■59 From F minor through G |l minor to B. Examples of Extraneous Modulation. CtoF#. ^ ^ Dp^toA. G to E. J- 1 • 1 .