Ex Libris C. K. OGDEN THE STUDENT'S HARMONY. NO W READ Y. Demy Svo, doth, 2/6. KEY to the STUDENT'S HARMONY, CONTAINING WORKINGS OF THE FIGURED BASSES, HARMONIZATIONS OF THE MELODIES, AND ANSWERS TO THE MORE IMPORTANT QUESTIONS. [THIRD AND REVISED EDITION.] THE STUDENTS HARMONY BY ORLANDO A. MANSFIELD. PRICE FOUR SHILLINGS AND SIXPENCE. LONDON: WEEKES & Co., 14, HANOVER STREET, REGENT STREET, W. Philadelphia, U.S.A. : THEODORE PRESSER. PREFACE. HAVING no wish whatever to add to the defects of this little work by the insertion of the orthodox apologetical preface, the Author proposes to confine himself, in the limited space allowed him, to a short explanation of the purpose, style, and theory of THE STUDENT'S HARMONY. As implied by its title, the book is essentially designed for students ; but, while primarily intended to ensure success in examination work, it claims to be equally adapted to give the student a knowledge of chord construction and progression sufficient to enable him to analyze the harmonic structure of the classics, and to solve the problems contained in some of the finer progressions of the great masters. In style, while endeavouring to avoid the Scylla of pendantry, every effort has been made not to fall into the Charybdis of superficiality, remembering that a student's harmony should be instructive first and readable afterwards. The divisions into sections and the fiequent use of cross references will, it is hoped, be of immense service in refreshing the memory as to the meaning of the terms employed in the text, and removing the difficulties which may occur in the working of the exercises. In the latter there has been no attempt at originality ; only an honest effort to acquaint the student with ordinary harmonic progressions. Nor should the exercises be regarded as models of musical composition, the idea of the writer being to introduce therein as many examples as possible of the particular chord or chords to which the chapters preceding the various exercises are devoted. The original examples occurring in the text apply almost exclusively to vocal harmony, it being believed that after the acquisition of this art the student will find no great difficulty in writing under the freer conditions of instrumental music. A series of selected illustrations, numbering over 400, has also been inserted, in the compilation of which every effort has been made in the direction of eclecticism, the examples being cited less as authorities than as proofs that the rules laid down in this work are based upon the practice of all good classical and modern composers. For quotations from his own humble 1057524 ii PREFACE. contributions to musical literature the Author makes no apology. These examples are simply inserted to show the student how a fellow student has endeavoured to carry out the rules he suggests for the guidance of others. In all cases preference has been given to examples illustrating as simply and concisely as practicable the chord or progression under discussion, and containing as few chords as possible which, at that particular stage of his progress, must be unfamiliar to the student. The connection should in all cases be consulted, and efforts made to discover similar illustrations to those given in the text. Those assigned to the appendix are considered of secondary importance, or contain instances of exceptional treatment or progression. The hints upon the harmonization of melody form another special feature of the work, and one which has been lamentably neglected in several larger and more pretentious text books. Finally, the questions at the end of each chapter are designed to assist both teacher and student in preparing for examinations in the theory and practice of harmony. The theory adopted in this work is one which subject to the modifications dictated by increased knowledge and observation the Author adopted many years ago, at a time when the student had not access to so many excellent manuals as are now to be obtained. This theory, despite its want of originality, he has been using with more or less success ever since, and it is satisfactory to find that it is in general agreement with the works of Macfarren, Prout, and others. Ignoring any scientific basis, it leaves the student perfectly free to accept any other system upon which his private judgment may ultimately decide, and its adoption in the present work is entirely due to the fact that it is convenient, and can be made to satisfactorily explain the harmonic progressions of the great composers. Beyond this no system of harmony should be required to go. ORLANDO A. MANSFIELD. TORQUAY, February, 1896. PREFACE TO SECOND EDITION. THE Second Edition of the Student's Harmony, which has been rendered necessary by the exhaustion of the first edition in little more than twelve months, will be found to contain some important additions, also corrections of slight errors almost unavoidable in the first issue of so detailed a work. The Author gladly avails himself of this opportunity to express his great indebtedness to Dr. Cyril Bowdler for numerous invaluable suggestions, as well as for much kind assistance in revising the proof sheets. TORQUAY, October, 1897. PREFACE TO THIRD EDITION. THE continued popularity of the Student's Harmony has necessitated the publication of a Third Edition some- what earlier than was anticipated. Advantage has been taken of this demand to make a few corrections in the text and to add a great deal of valuable matter in the shape of foot-notes in the body of the work and some extra pages in the Appendix. A Key, containing answers to the more important questions and workings of all the figured basses and melodies, is now published, and this, it is hoped, will render the work increasingly useful. ORLANDO A. MANSFIELD. TORQUAY, August, 1899. CONTENTS. PAGE CHAPTER I. INTRODUCTORY i II. TRIADS ; THEIR CONSTRUCTION AND CLASSIFICATION 3 ,, III. TRIADS (continued) : THEIR TONALITY AND COM- PARATIVE IMPORTANCE 5 IV. ELEMENTARY RULES OF FIGURED BASS AND PART- WRITING 8 V. CONSECUTIVES AND FURTHER RULES OF PART- WRITING II VI. ADDING THREE PARTS TO A FIGURED BASS 21 ,, VII. HARMONIZING MELODIES ; CADENCES AND MODU- LATION 24 VIII.- INVERSIONS OF THE DIATONIC TRIADS 34 IX. THE USE OF INVERTED TRIADS IN HARMONIZING A MELODY ... 48 X. CHORD OF THE DOMINANT 7TH 57 M XI. CHROMATIC TRIADS AND CHORDS OF THE 7TH ON THE TONIC AND SUPERTONIC 79 XII. BYE TONES ; PASSING AND AUXILIARY NOTES ; CHANGING NOTES AND ANTICIPATIONS ... ... 101 ,, XIII. SUSPENSIONS 114 XIV. CHORDS OF THE QTH 142 XV. CHORDS OF THE IITH 173 XVI. CHORDS OF THE I3TH 194 XVII. DOUBLE ROOT CHORDS 221 XVIII. SECONDARY 7THS AND PEDALS 251 APPENDIX 26 _ 294 THE STUDENT'S HARMONY. CHAPTER I. Introductory. I. Harmony may be defined as that branch of musical study which relates to the construction, classification, and progression of chords. 2. A complete chord consists of not less than three notes* which must be selected from a given scale and sounded simultaneously, or, in the case of an arpeggio, successively. One of the three notes is sometimes omitted (28). 3. The key of a chord (60) is that of the scale from which the notes employed in its construction are derived. If the notes of a chord be common to several scales (19) the key of such a chord is identical with that of the context, and may be determined by a reference to the latter. 4. The name of a chord is derived from the compass and quality of its intervals, as the chord of the diminished 7th (185), the chord of the augmented 6th (248), etc. 5. Hence, because chords belong to definite keys and contain various intervals, a knowledge of scales, intervals, and the rudiments of music generally, is an essential preliminary to the study of harmony, and the possession of this knowledge on the part of the student is presumed throughout this work. 6. With reference to the impression they produce upon the ear, chords are divided into two classes, concords and discords. These differ from each other in construction, in progression, and in mental effect, 7. A concord is a chord consisting of consonant intervals only, as : Here the intervals C to E (a major 3rd), C to G (a perfect 5th), and E to G (a minor 3rd), are all consonant. 8. A discord is a chord containing one or more dissonant intervals, as : 5 or -w Here the first chord *- ' &- ' - contains but one dissonant interval, C to B (a major yth), while the second chord contains two dissonant intervals, G to F (a minor yth), and B to F (a diminished 5th). But as experiment will prove the first * i.e. three different notes. 2 THE STUDENT'S HARMONY. {Chap. I. discord to be the more pungent of the two, we infer that the character of a discord is determined by the nature rather than by. the number of the dissonant intervals it contains. 9. In progression, concords differ from discords because, subject to the rules of correct part-writing (Chaps. IV. & V.), concords may succeed each other in almost any order, while discords have fixed progressions, frequently require preparation (74), and, in all cases, resolution (87). 10. Finally, concords can be distinguished from discords in that, like the consonant intervals of which they are composed, they leave a satisfactory and finished effect upon the ear. Hence, every piece of music must terminate with a concord. But a discord does not produce an unpleasant effect unless improperly approached or quitted ; it merely lacks finality, and fails to impart a feeling of repose. QUESTIONS ON CHAPTER I. i. Define Harmony. 2. How many notes are required to form a chord ? 3. Distinguish between a chord and an arpeggio. 4. How is the key of a chord determined ? 5. State the sources from which the name of a chord is derived. 6. What knowledge is necessary to a correct understanding of Harmony, and for what reason ? 7. Distinguish between concords and discords as regards (a) construction, (b) progression, and (c) effect. 8. Why cannot a piece of music terminate with a discord ? 9- Upon what does the harshness of a discord depend ? CHAPTER II. Triads : their Construction and Classification. II. If, upon any given note in any key, we endeavour to form a chord, our first impulse will be to add to the note given (in contormity with the key signature) a note a 3rd above, that being the nearest and most satisfactory consonant interval. In fact, all chords (with the exception of those described in Chap. XVII.) are originally formed by ascending by 3rds from given notes called roots, radical or funda- mental basses. But as two sounds a 3rd apart are too fragmentary in construction and too indefinite in tonality to constitute a chord, we add (in the same key as the note and its 3rd already obtained) another 3rd, a 5th from our root. This gives us the number of notes sufficient to form a chord (2), and termed a triad, because consisting of three sounds, of which the second shall be a 3rd above the first, and the ihird a 3rd above the second. 12. Like other chords, triads derive their names from the quality of their intervals (4). TABLE OF TRIADS. NAME. CHARACTER. COMPOSITION. -j2_ Major. Concord (7). \ (or a minor 3rd above a major). ^=g= Minor. do. \ (or a major 3rd above a minor). l= j Imperfect. J Discord (8). \ (or two minor 3rds). ^iP IJ do. / Major 3rd and augmented 5th* Ym fe-5 Extreme. J \ (or two major 3rds). tMg- 13. The major and minor triads derive their names from the quality of their respective 3rds, the augmented and diminished triads from that of their respective 5ths. Hence, to determine the name of any given triad we must ascertain the quality of both its 3rd and its 5th. 14. On account of their frequent occurrence in music, the major and minor triads are often called common chords f A common chord must have a perfect 5th, and can be changed from major into minor (or vice versa) by lowering (or raising) the 3rd a chromatic semitone. The dissonant triads (which are really fragments of discords to be explained * i.e. from the bass or lowest note. 1- and, because their 5ths are perfect, perfect triads. 4 THE STUDENT'S HARMONY. \Chap. II. elsewhere) (91, 187, 224) are not common chords, because their 5ths are not perfect. Hence, while all common chords are triads, only major and minor triads are common chords. 15. Common chords are the only concords (7) possible in harmony, every other combination of sounds involving the introduction of an interval dissonant either with the root or with some other note of the chord.* QUESTIONS ON CHAPTER II. i. How are chords formed ? 2. What is the root of a chord, and by what othei name or names is it known ? 3. Why is a triad so called ? 4. Which triads are concords, and whicn discoras t 5. By what other names are diminished and augmented triads known ? 6. What are major and minor triads sometimes called ? 7. Why are the dissonant triads not termed common chords ? 8. What intervals respectively prove the diminished and aug- mented triads to be discords ? 9. Why cannot the character of a triad be determined by reference to one of its intervals only ? 10. In two different ways express the difference between a major and a minor triad. ii. Write out major, minor, diminished and augmented triads on each of the following notes : G, B, A, and F$. 12. Account for the name given, and the important position assigned, to the common chord in harmony. * It should, however, be observed that certain other chords, to be explained hereafter, are treated as concords, e.g., the first inversions of common chords (64), the first inversions of the diminished triads (see note to p. 35) the chord of the Neapolitan 6th (267), &c. CHAPTER III. Triads (continued): Their Tonality and Comparative Importance. 16. Every degree of a major scale will bear a triad (11) in accordance with the signature, e.g., in C major, Degree of scale. Tonic. Supertonic. Mediant. Subdominant.Dominant.Subraediant. Leading Note. Triad. Quality. Major. Minor. Minor. Major. Major. Minor. Diminished. Hence, in every major key we have three major triads, on the tonic, subdominant, and dominant ; three minor triads, on the supertonic, mediant, and submediant*; and a diminished triad on the leading note. 17. Similarly every degree of a minor scale will bear a triad in accordance with the signature (it being understood that the harmonic form of the minor scale is the one used in chord construction!), e.g. in C minor, Degree of scale. Tonic. Supertonic. Mediant. Subdominant.Dominant. Submediant. Leading Note. Quality. Minor.Diminished. Augmented. Minor. Major. Major. Diminished Hence, in every minor key we have two major triads, on the dominant and submediant ; two minor triads, on the tonic and subdominant ; cwo diminished triads, on the supertonic and leading note ; and an augmented triad on the mediant. 18. Comparing 16 and 17, we notice that the triads on the dominant and leading note of any major scale and its tonic minor are identical ; also that the dominant triad in a minor key is always a major triad ; and that while every degree of a major scale, except the leading note, bears a common chord, the minor scale only furnishes us with four common chords : on the tonic, subdominant, dominant, and submediant. 19. The key of a triad cannot be determined without reference to the context, for it is evident that as major triads are found on the conic, dominant, and subdominant of a major scale, and upon the dominant and submediant of a minor scale, a major triad is common to foe keys, three major and two minor, e.g., f Tonic in C major. Subdominant in G major, may be on the \ Dominant in F major. I Dominant in F minor. I Submediant in E minor. Also termed superdominant. f See Appendix, p. 207. 6 THE STUDENT'S HARMONY. \Chap. 111. Similarly, as there are three minor triads in a major key, and two in a minor key, it follows that a minor triad is also common to five keys, three major and two minor, e.g., f Supertonic in BjT major. Mediant in A? major. \ may be on the \ Submediant in E? major. I Tonic in C minor. LSubdominant in G minor. Also, as there are two diminished triads in a minor key and one in a major, a diminished triad is common to three keys, one major and two minor, e.g., ( Leading note of D? major. may be on the -! Leading note of D7 minor. ^ __ ^ Supertonic of B? minor. The augmented triad, however, as far as our present know- ledge extends (vide 224), can only belong to one key, e.g., C, E, GJ, can only be on the mediant of A minor. 20. Of the triads upon the various degrees of a major or a minor scale, the principal are those upon the tonic, the subdominant, and the dominant. These, which between them contain all the notes of the scale, are termed fundamental, principal, or primary triads, the other triads being called secondary. The triad upon the tonic of any scale is said to be the common chord of that key, the key chord, or the tonic common chord Hence the expression " chord of C " would mean C, E, and G. QUESTIONS AND EXERCISES ON CHAPTER III. 1. Which degrees of a major scale bear minor triads? 2. Upon what degrees of a minor scale do major triads occur? 3. State where the dissonant triads occur in major and minor keys. 4. Name the triads which are identical in a major key and that of its tonic minor. 5. In a minor key, how many triads include the leading note ? 6. Why cannot the key of a triad be determined apart from the context ? 7. To how many major and minor keys can (a) a major, (ft) a minor, (c) a diminished, and (d) an augmented triad respectively belong ? 8. Distinguish between primary and secondary triads. 9. By what other names are primary triads known ? " 10. Write out the names of the notes forming the triads upon the various degrees of the scales of G? major and G# minor, B major and B? minor, and state the quality of these triads. Chap. 11 7. j TRIADS. ? ii. Write an augmented triad on Ap and one on A El, and say to what key each triad belongs. 12. Describe the following triads, and state the keys to which they may belong : 13. Write out, and state the quality of the following : (a) Supertonic triad in EJ? minor. (/>) Subdominant triad in F minor. (f) Supertonic triad in Fit major. (d) Mediant triad in A? minor, (t') Tonic triad in G? minor. (/) Dominant triad in I> minor. () Submediant triad in G minor. (A] Mediant triad in Qjt major, (z) Subdominant triad in DJ7 major. (/) Dominant triad in B major. (k) Submediant triad in F$ major. 14. Say which of the above triads are identical. 15. What is meant by the expression " chord of G minor," and by what other names could such a chord be called ? ! 6. Write down a major triad on D#, then change it enhar- monically into another major triad, and state the keys to which the triads may respectively belong. 17. Can more than one common cnord be found upon the same root? CHAPTER IV. Some Elementary Rules of Figured Bass and Part-writing, 21. A chord is said to be in its original or root position when its root (n) is in the bass (i.e., the lowest part, irrespective of pitch), whatever may be the arrangement or doubling of the upper notes. Hence all the following chords of C major are in their root position : O -&>- 22. A figured bass, or " thorough "* bass, consists of a bass with figures underneath denoting certain intervals. In figuring basses the highest number is placed uppermost, doublings are not regarded, nor is the particular octave in which an interval occurs specified, compound intervals (i.e. intervals exceeding the compass of an octave), with the exception of the pth (vide Chaps. XIII. & XIV.), being regarded as simple. Hence all the chords in 21 would be figured 3, because they contain a 5th and a 3rd from the bass note. 23. But, as common chords are of such frequent occur- rence, they are not figured when in their root position unless (a) they are preceded by another chord on the same bass note, or (b) contain accidentals. The same applies to dissonant triads. 24. When an accidental is placed on the left hand side of a figure, as tf5, it indicates that the particular interval denoted by that figure is to be accidentally raised or lowered a semitone ; but an accidental underneath a bass, without a figure attached, refers to the -\rd of the chord. Hence -fe=$g [T_fy n would be fi S ured #5 and i>5 re . ^F " spectively, it being understood that the #5 implies a 3, and that the unngured j? of the second chord refers to the 3rd from the bass note. tff i tK K ?" g ! C0f * fmuo) > and so ed because placed on a separate a MS U f ? C SC r T C ' n ? h l thr U ? h the com Psition. There is in existence a MS score of an anthem, Lord, let me know my end," by Dr. M. Greene, entitled t Eve U r n wa a 5 Made" '" 4 V iCeS l a ""**' Th r U S h Base - ^ Finest Anthym Chap. IV.\ RULES OF FIGURED BASS. 25. In vocal music the usual number of parts \sfour, viz : r o n Soprano (or treble), sung by high voices of women and boys. Al'.o, sung by low voices of women and boys, or high voices of men. Tenor, sung by high voices of men. Bass, sung by low voices of men. In short score the treble and alto parts are written in the treble clef upon the upper staff, the bass and tenor being placed upon the lower staff and written in the bass clef, e.g., ro :toz^ :to: :to: J Treble. g Alto. Tenor. ~ Bass. 26. As a triad consists of only three notes, one of these must be doubled, either in the octave or the unison, in order to form a four-part chord. In the common chord the root is always the best note to double, or, failing this, the 5th or even the minor 3rd ; the major 3rd should rarely be doubled (42), and the doubled leading note should be most carefully avoided (37).* IZ2I Doubled Root. Doubled 5th. Doubled Doubled Doubled minor 3rd. major 3rd. leading note. Good. Fair. Fair. Allowed. Bad. 27. It is interesting to notice that if we double the 3rds in the minor triads belonging to a major key, the doubled note must be either the subdominant, the dominant, or the tonic, these notes being the 3rds of the supertonic, mediant, and submediant triads respectively. * Rules for doublings in dissonant triads will be given later on, when the derivation of these chords is explained. For the present the student may double the bass note. B 10 THE STUDENT'S HARMONY. [Chap. IV. 28. In order to avoid consecutives (31), to secure conjunct movement (30), or to allow the leading note to ascend (36), // is sometimes necessary to omit the $th from the root of a common chord. In this case the root will be sung by three voices. The yd of a common chord can never be omitted.* Good. Bad. 29. In order to prevent thinness, the parts should be kept as equi- distant as possible, none of the upper parts beirig, as a rule, more than an octave apart. When a wide gap is unavoidable, it should occur between the bass and tenor, (a) e.g., (a) J - ~ ^ "" .*-. " ~ ~^ ^^ ^^ H r> -f*- -H- : 1| " ^ ^>- >- Q ~^~ rj nro ft): p "- 53 " -W- D H Good. Bad. QUESTIONS AND EXERCISES ON CHAPTER IV. i. What is meant by the " root position " of a chord ? 2. What is a figured bass, and by what other names is it known ? 3. Give rules for the placing of the figures and the treatment of compound intervals when figuring basses. 4. How and when is a common chord figured ? $. Explain 5, and the meaning of an accidental without a figure. 6. According to example in 24, correctly fill up the following, and say what intervals are implied in the -6*^ >-, || U [I b^> H figuring of each chord. II H 7. State the number, names, and ordinary compass of the parts usually employed in vocal music. 8. What do you understand by the term " short score " ? 9- Why is it necessary to double one of the notes of a triad when writing in four parts ? 10. Give rules for doubling, and say what doublings are (a) merely tolerable, and (/) generally forbidden. i 1 What have you to remark upon the doubling of the 3rds of the minor triads of a major key ? 12. Which interval may, and which may not, be omitted in a common chord ? 13. Give a rule for the best position of the notes of a common chord, and say between which parts a wide interval is forbidden or permitted. 14. According to the model given in 29, write, in as many good positions as possible, the common chords of E? minor, B^ major, and G minor. 'Unless to produce a special effect, as in the last chord of the Chris te Eleison of Mozart's " Requiem," where the voices end upon described by one critic as " a Gothic combination, to which the ear is with difficulty reconciled." CHAPTER V. On Consecutives and further Rules of Part-writing. 30. When two or more parts move in the same direction, they are said to be in similar motion ; when in opposite directions, in contrary motion ; and when one or more parts move and one remains stationary, the movement is termed oblique.* Conjunct movement is that produced by a part proceeding by steps of a second ; disjunct move- ment being produced when a part proceeds by skips or leaps. Similar. Contrary. Oblique. Conjunct. Disjunct. As a rule not more than three parts should move together in similar motion, which is considered to be much feebler than contrary and more likely to involve consecutives (31). Every effort should be made to cause each part to move as conjunctly as possible, hence, at any rate in the student's earlier exercises, notes common to two chords should be kept in the same part (a), and when quitting a note a part should move to the note in the next chord nearest to the one about to be quitted (), e.g., (a) (*) 1-^^. fl -& -e 31. In harmony it is strictly forbidden to have any parts moving in similar motion at the distance of an 8ve or a 5th. Such progressions are termed consecutive or parallel 8ves and 5ths. Apart from the ugliness of most consecutive 5ths, consecutive 8ves, 5ths, and unisons are forbidden because the individuality of one of the I arts causing the consecutives is, for the time being, lost. The avoidance of consecutive 5ths and Sves is one of the greatest difficulties to be overcome in the early study of harmony. ( rr g 11 " ** 11 c^i-o H =-41 7 g ~|]~^ ^~ {"* ^^-" ^ ig. -" 8^ "" H Consecutive Sves. 5' ns - 8v< __o js & 5ths. Unisons. * The term parallel movement is applied writers (e.g., Albrechtsberger) to cases in whic more notes are repeated between the same par In a stationary part the notes may be sustained or by some n \ | fi two or yfo "J ^ <^3=^ s. In a t/ (^ j > - repeated. I2 THE STUDENT'S HARMONY. [Chap. V. 32. The following instances of consecutives are not considered move in Sves or unisons (d) When a particular part is doubled throughout an entire phrase in the Sw above or below, or both. , SMART "Andante in F." (Organ). Ex. 2. i_ij. JLE j +H-4S-*-* . i. tr At a we have consecutive 8ves by contrary motion between the outside parts, and at b and c consecutive 5ths by contrary motion between the lower parts. Although classed as allowable, consecutive 5ths and 8ves by contrary motion are not recommended for the student's imitation. Chap. V.} CONSECUTIVES AND PART-WRITING. (d) When a perfect yh is followed by a diminished $th as at b in Ex. 5. This is allowed between any parts, but a diminished 5th followed by a perfect 5th, as at a, is forbidden between the outside or extreme parts. These rules also apply to the juxtaposition of perfect and augmented (a) 77:- HANDKL "Judas." tfc=5 ' -^ - H=rf ' (e) When Sves and $ths are repeated, as indicated by the dotted ties in Ex. 6. MENDELSSOHN " Lieder ohne Worte." No. 3, in A. Ex. 6. (/) When the 8ves, 5ths, or unisons, do not occur between the same parts, e.g., Here the dotted lines show the 8ves, and the angles show the sths, but the 8ve in the first chord is between the bass and the tenor, while in the second chord it is between the bass and alto. Similarly, the 5th in the first chord is between the tenor and the treble, but in the second chord it is between the tenor and the bass. (See Appendix^ p. 268.) 33. No two parts should be allowed to overlap* (a), except occasionally in proceeding in the bass from dominant to tonic (b) ; nor except as a last resource, should the parts be allowed to cross (c). 34. Augmented intervals, especially 2nds and 4ths,** shoui-j be carefully avoided,! at least in preliminary exercises (174), as should also the unvocal interval of a major yth. 35. When a part skips a diminished interval, ^- ^ 'p* it should return to a note within that interval : -fe-- f^~ The same applies to all wide skips. * i.e. when the upper note of any two parts skips lower than the note previously sung by the voice beneath, or vice -versa. ** called tritones because including three whole tones. t i.e. in the progression of any part, unless in sequences or between repeated chorus. THE STUDENT'S HARMONY. [Chap. V. U 35 The leading note should generally ascend to the tonic* and should not descend to the dominant except in an arpeggio (as at a in Ex. 7), or when the dominant chord is repeated (b, Ex. 8), or in a sequence (a, Ex, 9), or when the dominant returns at once to the tonic (f, Ex. 9). HAYDN" Seasons." CHKRUBINI " 4th Mass." Ex.7- Ex.8. P At a, A, the leading note in Bb major, descends to the dominant, the bass moving in arpeggio (2). At b, E, the leading note in the key of F major, descends to the dominant, the dominant chord being repeated. 37. At a in Ex. 7 we have an allowed doubling of the leading note in arpeggio. This is also occasionally permitted when the leading note is the 5th of the triad on the mediant of a major key,** or in a sequence, i.e. the repetition of a passage of melody or harmony (or both) at a higher or lower pitch. (See Appendix, p. 292.) BACH "Organ Fugne in G." Vol. IV t 11. l"!^ 1 ""? I a I-* J -* '* Observe the doubled leading note at a. 38. Sequences are of two kinds, real and tonal. A real sequence is one in which the key changes at every repetition of the model, or one in which every interval of the subject is exactly re- produced, both cases necessitating perpetual modulation (i.e. change of key). An ascending real sequence is sometimes termed Rosalia. 1 A tonal sequence, as its name implies, confines itself to the limits of the key, in which case the intervals of the model cannot be exactly reproduced, but major intervals have to be substituted for minor, and vice versa. Ex. 9 shows an ascending tonal sequence. Ex. 10 gives us a descending real sequence. GOUNOD" Redemption." Kx. 10. ' See Appendix, p. 270. h * See Handel's " Dettingen Te Deum," No. 4, 'oar 5, and Mendelssohn's March in " Athalie," 4ist bar from the end. f Peters' Edition. * Provided it ascends a tone or semitone at each repetition. Chap. CONSECUTIVES AND PART-WRITING. J- Hl Sequences formed by the exclusive use of certain chords, such as supertonic, tonic and diminished yths, augmented 6ths and secondary 7ths, will be explained in the chapters dealing with those chords. 39. When a part taking the 3rd of a chord moves to some other interval in the same chord, the 3rd should be transferred to another part, e.g., Here the tenor takes up the 3rd, E, quitted by the treble, and while the former goes from the 5th to the 3rd, the latter proceeds from the 3rd to the 5th, a common progression, of which examples will be found in the exercises following this chapter. 40. Lines drawn under bass notes signify that the notes of the chord preceding the lines are to be repeated or sustained (in the same or a different position) through- out the duration of the lines : *4I. A false relation is the separation of the two notes forming a chromatic semitone by giving them to different parts in two successive chords instead of to the same part (a). A false relation is not con- sidered objectionable when the 3rd of the first chord is the root or 5th of the second, or, in other words, when the false relation occurs between two chords of which the root of the second is distant a major 3rd or 6th above the other (<). But the bad effect of a false relation is not always saved by the interpolation of a chord between the two chromatic notes (c). () (*>. -) II jt^-j H JLji 1 "IT tJ ^ //aV P m m %rj 2 II (W; ~ * < * * i* -f- : i T ^^ * 1 1 1 " Bad. Good. Allowed. Allowed. Bad. At a and b in Ex. 1 1 will be found an allowable false relation between two chords whose roots (E and Gf, and A and Cf) are a major 3rd apart, and at c and d, Ex. 12, one between two chords whose roots (B|? and G, and C and A) are a major 6th apart. S. S. WESi.KY-"The Wilderness." Ex. ii. VT ^ See Appendix, p. 270. THE STUDENT'S HARMONY. [Chap. V. SCHUBERT " Mass in F." Ex. 12. & Observe the sequences real in Ex. 12, and tonal in Ex. n. 42. When in a minor key the dominant chord is preceded or followed by that of the submediant, the yd in the submediant chord must be doubled 'in order to avoid consecutives or augmented intervals.! CHERUBINI "Quartett in C." I s Ex. 13. QUESTIONS AND EXERCISES ON CHAPTER V. i. Describe the various methods of part progression, and say which are to be preferred. 2. Give two rules for securing conjunct movement. 3. What are the advantages to be obtained from the employment of contrary motion ? 4. What is meant by consecutive 8ves or 5ths, and by what other name are they sometimes called ? 5. Why are consecutives considered objectionable ? 6. Distinguish between consecutives and doublings, also between consecutives and repetitions. 7. When are consecutive 8ves tolerated ? 8. Name two cases in which consecutive 5ths are allowed. 9. What do you understand by (a) the overlapping and (l>) the crossing of parts ? 10. What melodic intervals* should be avoided in part -writing ? * i.e. intervals occurring between any two notes in the same part, t Sometimes, in order to allow the leading note to ascend, the minor 3rd of the submediant triad is doubled in a major key. See (a) Ex. IV., p. 18. 'Jhap. V.} CONSECUTIVES AND PART-WRITING. ii. Is the following why, and re-write it, sub- incorrect ? If so, say stituting another note for the one requiring alteration. 12. State two exceptions to the rule that the leading note must not descend to the dominant ; also two exceptions to the rule that the leading note must not be doubled. 13. Is there any exception to the rule which forbids the over- lapping of parts ? 14. What is a sequence ? 15. How many kinds of sequences are there? 1 6. Name them and distinguish between them. 17. Continue the following sequence, and say whether real or tonal. fta G H i s g j &c - fj f^ i~"> 1 8. When, and in what mode, is a doubled major 3rd unavoid- able ? Give examples in the keys of G and E minors. 19. What is a false relation, and how may it be avoided ? 20. Explain the meaning of lines drawn underneath a bass. 21. What rule given in 28 determines the necessity for the statement made in 39 ? 22. Name a particular case in which a false relation is objec- tionable, and one in which it is not so. 23. What do you understand by the term Rosalia ? EXERCISES. TENOR AND ALTO TO BE ADDED.* II. Q 1 1 at -4- > -ri , (a) A major. . u f jiTr iU U r 24- 22: -f-*- r? B major. fJ r-_ ' * VII. (Double Chant.) S^n til^r rt-<^r 39- ti- (a) Doubled minor 3rd. (b) Doubled major 3rd. Chap. V.\ CONSECUTIVES AND PART-WRITING VIII. (C. M. " Farrant.") t-J rJ rJ f- m O ! & H*- w {& v ,\ *~^ *"*" r J 3 i (--) 1 1 f-^ i - .-H /w\. r2 ^-. II ii P~ -jS p> \\ - h^r & v \ ^ \ ^^ ^ ^ * ^ II r > ' r v 1 1 i ^ IX. 40. 24. 122. * - C major. A. -rlri ^ *- 3=t=d ' h H- 4 *--! ^) ^ ^ r ^ |J p 39-40. 33^- 36- 39- | ^ p r j | 42. > ~^ 2 ' ^ ( 1 J i 1 -i ^ ' 3- p D minor. C major. l^v d i i ! 1 1 J H 1^' 5 d , o r : 41- 39- \-& \ i & i 39- 2 rJ r J 33^ 15" H H p -pr-f: .,[_ 1 t r p i r * P 1 r. H (a) Doubled minor 3rd. (i>) Doubled major 3rd. XL \/ ' * m ~ i ' \ ,'\ L 1 , .-.-.. <^ 1 - .. * ' "fi\ 4 " " !-? 'f:. t+rJ^ __-f* _ , ^V g f*U F ' S ? =; .->. *>**) ~ i ' m * fZ. JOL /-+ ' ^n ~>- 5 i W-r- '^ rit| P g'r'.'-^ '" p r; lfr ^fcfe fzj awl BOU to p. CHAPTER VI. On adding Three Parts to a Figured Bass. 43. Bearing in mind the rules already given, the student should now endeavour to add three upper parts a tenor, an alto, and a treble to a given bass. Care must be taken (a) to end upon the tonic in the melody of the last bar whenever possible, (6) to make the melody move conjunctly rather than by wide skips (of which two in the same direction are generally of bad effect), (c) to employ contrary and oblique motion in preference to similar, (tf) to avoid hidden consecutives (44) unless occurring as stated in the following section, and (*), in the case of a repeated bass, to vary the position of the upper parts. A melody u.oving in arpeggio is always effective and may be freely employed. Not more than three repeated notes should be used in succession in the upper part 44. When two parts move to an 8ve or a 5th by similar motion from any interval other than an Sve or a 5th, such a progression is termed a hidden consecutive, and is forbidden between the outside or extreme parts, though allowed between any two inner or any out- side and inner part, and between different notes of the same chord, or between notes of different chords if one of the parts move conjunctly. But hidden consecutives between the extreme parts are allowed, in the case of the Sve, when occurring between different positions of the same chord (63) as at (a), and when the bass proceeds from dominant to tonic (i>) or from tonic to subdominant (c\ the melody moving con- junctly. Hidden 5ths are also allowed between the extreme parts when occurring between different positions of the same chord (^), between supertonic and dominant chords (f\ and. when the melody moves conjunctly, between tonic and dominant (/) or subdominant and tonic chords $), e^ sfe w w i -C7 1 5 *" * ri t*. Bad. Both hidden 5ths and Sves are pamitted between mlmosl any chords in sequential passages, provided the roodd of the sequence contains allowable consecutives, Hidden consecutives are also to be found in r rrw '~ w tv'E to a i as in Ex. i;d, or in the resolution of a fundamental discoid, in Exs. 70 and 304, or 222*. These rules are subject to occasional modification, hot their general vance will tend to parity of part-writing. THE STUDENT'S HARMONY. [Chap. VI. QUESTIONS ON CHAPTER VI. i. Give five general rules for adding three upper parts to a figured bass. 2. What do you understand by the expression " outside parts," and do you know of any other term possessing the same signification ? 3. What are hidden consecutives ? 4 . Where are they allowed, and where forbidden ? 5. Name five special cases in which hidden consecutives are allowed to appear between the outside parts, and give examples of these exceptions in the keys of D major and B? major. 6. Write at least four examples of the objectionable employment of hidden consecutives between the outside parts. EXERCISES ON CHAPTER VI. N.B. In the following exercises, in which only root positions of triads are to be employed, the particular interval from the bass upon which the melody is to commence is indicated by a figure which, how- ever, is purely conventional and not usual. I. II. s 3' III. IV. 38. &~%- P o P* rJ 1 - ^_ ^H II iMif n V. 1 | 5 43'- -O 1 1-| f ^ VI. 42. <$--$- c * ) I fj i ^ \ ^ \-&- H ? S-4_^ "-rJ-f 8 HH- J_ cA 1 .l_ VII. i f j II rc);. h b 4- 1 " ' rj ! ' 101 " 43- 32 TL 38. -^ ^ < ^ 11 ^? y 2 A \ ^9 ^ 1 T3-H T S' 39- VIII. (Double Chant" Per recte et retro."') m H 8 i.e. a Double Chant in which the melody and harmony of the third and fourth lines are those of the first and second reversed. Chap. VIJ\ FIGURED BASS. IX. 43*. -pa. s -ftq: i -P- X. (L. M.) 38. B|? major. 38. F minor. C minor. ^ 1 XI. P* 3 (6V note to 26 and 226.) :z XII. (3"