■.■■■■■■■...' 111 l« :;v^,',:-;;-''.:,?. ■ H CORNELL UNIVERSITY LIBRARY BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND GIVEN IN 189I BY /ILLIAMS SAGE r MT 55.P97 rn i890 IVW,,,y "*"* Smm ™Ri i nt: s,rict and free 3 1924 021 789 650 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924021789650 AUGENER'S EDITION, No. 918S. COUNTERPOINT: STRICT AND FREE. BY EBENEZER PROUT, B.A. Lond. (Professor of Harmony and Composition at the Royal Academy of Music), Author of "Harmony : Its Theory and Practice," etc. THIRD EDITION. PIANO ft MUSIC DEPfirJ. W. BRUNT & SONS, DRAWBRIDGE, BRISTOL.. LONDON : ATJGENER & CO. {entered at stationers' hall.] Copyright for all Countries.] [Rights of Translation Reserved. PREFACE. The present volume is the partial fulfilment of the promise made in the preface to Harmony : Its Theory and Practice, to follow that work by a treatise on practical composition. The author's first intention was to write a book on this subject, as a companion to his Harmony ; but as soon as he began to think the matter seriously over, it became apparent that it was quite impossible, within the limits of a single volume, to treat so extensive a subject except in the most superficial manner. Holding firmly to the opinion that whatever is worth doing at all is worth doing thoroughly, he thereupon modified and enlarged his original plan, and resolved (should life and health be spared) to prepare a complete series of treatises on composition, which should embrace all the different branches of that art. Naturally, the first volume to follow Harmony was " Counterpoint." Before referring to the plan and special features of the present work, it will not be out of place to set forth some considerations showing why the study of Strict Counterpoint should form an essential part of the training of every one who aspires to be a thorough musician. This is the moire necessary, as there is a certain school of theorists at the present day who disparage it, ignore it entirely, and even oppose it vigorously. Their chief argument is that the study of Strict Counterpoint is a mere waste of time, because the restrictions imposed by it are never enforced in practical composition. The fallacy underlying this argument is, that it confounds the means with the end. If Strict Counter- point were studied for its own sake, the objection would have force ; but this is not the case. This branch .of study is the preliminary technical work for actual composition, just as Herz's or Plaidy's are the preliminary technical exercises for pianoforte playing; and to commence at once with "Free Part- Writing " before learning to write in the strict style is as absurd and un- profitable as it would be for a pianist to begin to study Mozart's or Beethoven's sonatas before he had practised any scales or five- finger exercises; we may add that the result would, in most iv Preface. cases, be equally unsatisfactory. A revolt against all technical exercises whatever would be just as reasonable as the outcry against Strict Counterpoint. The special advantages to be derived from this study are twofold. In the first place, the student learns how to make his parts flow smoothly and melodiously ; and, secondly, he acquires the instinct for correct harmonic progression. The fact that he has but a limited number of notes at his disposal (chromatic notes being excluded) really facilitates his task, by familiarising him in the first instance with the use of the most important notes and chords of a key ; while the prohibition of second inversions, and of all essential discords, further simplifies his work, because he is allowed only to use those harmonies in a key which have no fixed progression; and these are the very chords which he does not know how to treat. Any book on Harmony will teach him how to follow a second inversion, or a discord ; nothing but Strict Counterpoint will enable him to acquire the instinct for the best progressions of triads and their first inversions. Besides this, the value of the strict mental discipline involved in working with limited resources cannot be over-estimated. One of the strongest arguments in favour of this sjudy is the fact that no composer has ever attained the highest eminence without first submitting himself to its restraints. It should nevertheless be added that, in the author's opinion, the study of Strict Counterpoint, like that of Harmony, needs a certain amount of modification, to bring it more into conformity with the musical thought of the present day. At the time when the science was developed, tonality, as we now understand the term, can hardly be said to have existed. The old ecclesiastical modes had an importance in the music of that day which they no longer possess ; and many of the finest of the old Church melodies, and even of the chorals of the Reformation, are con- structed on scales now obsolete. Many of the subjects treated in the works of Fux and Marpurg, nay even in those of Cherubini and Albrechtsberger, being written in these old modes, are in no "key," in the modern sense of that word. But the study of the old modes, however interesting to the musical historian or antiquarian, is of little or no practical value to the student of composition. It therefore becomes expedient, not to say neces- sary, if counterpoint is to be of real use to the student, to make it conform strictly to the requirements of modern tonality. To Preface. v the late Sir George Macfarren is due the credit of being the first to recognise this important fact ; unfortunately his treatise on Counterpoint, excellent as it is in this respect, contains so many of its writer's peculiar ideas, and prohibits so much that other theorists allow, that the beginner who studies the subject under its guidance is hampered and harassed by needless restrictions, until really musical writing becomes all but impossible, and his exercises sink to the level of mere mathematical problems. All honour, nevertheless, to Macfarren for first enforcing the principle that modern tonality should be the basis of Strict Counterpoint ! In the present volume the author insists first and foremost on a clearly defined tonality ; but, so long as this be preserved, he would allow far more liberty in the matter of melodic pro- gression than was permitted by the older theorists. Will any one maintain at the present day that any valid reason can be given for the prohibition, for example, of the major sixth, or even of the diminished seventh, in melody, if properly treated ? Surely the real benefit of the study of Counterpoint may be obtained without hampering ourselves by restrictions' imposed when music was, so to speak, in its infancy ! We have here, apparently, used the very argument employed by the opponents of Strict Counterpoint, who will doubtless endeavour to turn it against us by saying, " Very good — we heartily endorse your view ; then why confine the student for his harmonies to triads and first inversions ? " The answer is that the cases are not parallel ; because no possible good is obtained by excluding - such intervals as we have named, while the restriction of the harmony to triads and first inversions is of the utmost benefit. We said above that the progressions of second inversions and discords were fixed by rules ; what the student wants to learn is, how to use those chords of which the progression is not fixed ; and this he will best learn if he have no other chords to use. With a view of assisting him in this most important matter, the author has given, at the end of Chapter II. of the present volume, a complete table of all possible progressions of diatonic triads and their first inversions, both in a major and minor key, classifying them as "Good," "Possible," and "Bad." Without claiming perfection for this table, it may at least be said that it is the result of much thought, and of a careful examination of the practice of the great masters ; and the author hopes that it will be found of material assistance to the student in the earlier stages of his work, vi Preface. when he feels in doubt as to what chord or chords can best follow any one that he has just written. As every two-part interval, even in the strictest counterpoint, should be considered as an outline chord, the study of two-part counterpoint is preceded by exercises on four-part harmony in the strict style, i.e., using only triads and. their first inversions. The five species of counterpoint are then treated as usual, first in two, and subsequently in three'and four parts. Chapters on combined counterpoint, and on counterpoint in five, six, seven, and eight parts, complete the first section of the volume. The subject of Free Counterpoint has mostly been either altogether ignored, or but slightly touched upon in existing treatises. Many teachers even seem to consider that the student's ' labours in a contrapuntal direction are finished as soon as he can write strict counterpoint of all kinds. There can hardly be a greater mistake. The strict style is simply preliminary to the free — that is, to the counterpoint of Bach, Beethoven, or Schumann. An attempt has been made in this volume — how far successful it is for others to say — to systematize the teaching of this branch of the subject. The ground to be here trodden had been so little explored,. that the author must ask the indulgence of musicians for the- shortcomings which he doubts nof will be found in this portion of his work. Closely connected with Free Counterpoint is the harmonization of melodies, which is obviously impossible without a previous study of cadences. These subjects are there- fore treated in some detail, and the volume concludes with a chapter on the application of counterpoint in practical composi- tion. In the author's opinion, it is very desirable that Harmony and Counterpoint should be studied side by side. As soon as the student has mastered triads and their inversions, he should begin elementary counterpoint. His study of the two subjects can then be pursued simultaneously, and each will be found to throw light upon the other. But, inasmuch as all possible harmonies are available in Free Counterpoint, this subject should not be com- menced until the student has completed his course of Harmony. As Counterpoint chiefly consists of technical exercises, it has not been possible here, as in the author's Harmony, to select most of the illustrations from the works of the great masters, because these are very rarely written in Strict Counterpoint. It has been necessary to prepare most of the examples expressly for this work, Preface. vii and the whole of them have been written on three or four short subjects, in preference to taking a larger number, in order to show the student the almost infinite capabilities of even the simplest themes. No modulations have been introduced in the examples of Strict Counterpoint, because, though not forbidden, they are un- advisable, as it is far more useful to the student to practise himself in varying the resources of one key. In Free Counterpoint, modulation has been frequently employed ; the examples in this part of the volume have been, as far as possible, taken from standard works. If the explanations in some of the earlier chapters be thought needlessly minute, the author would urge that what is very plain to a practised musician is often very confusing to a beginner ; and it is only by the reiteration of simple elementary principles that these can be firmly impressed on the student's mind. While, however, the author has endeavoured to afford all possible assist- ance to the learner, he has not the slightest toleration for the indolence which will not take the trouble to master the C clefs. Every one who aspires to be a musician ought to be able to read and write the C clefs just as easily as those in G and F. For this reason the alto and tenor parts of the examples (excepting when in short score) are written in their proper clefs throughout the volume. Those who do not choose to undergo the slight labour involved in learning these clefs must study Counterpoint from some other book than this. It will be seen that the important subject of Double Counter- point is not dealt with at all in the present volume. The omission is intentional ; its proper place is in the next volume of this series, when it will be treated together with Canon and Fugue: London, February, 1890. TABLE OF CONTENTS. [N.Ii. — The numbers refer in every instance to the sections, not to thepages.~\ PART I.— STRICT COUNTERPOINT. CHAPTER I.— Introduction page 15 Meaning of the word Counterpoint, 1 — How it differs from Harmony, 2-5 — Simple and Double Counterpoint, 6, 7 — Triple and Quadruple Counter- point, 8— Strict Counterpoint, 9 — Free Counterpoint, 10 — The use of the study of Counterpoint, II — Open score, 12 — The C clefs, 13 — The com- pass of the voices, 14. CHAPTER II.— Melodic and Harmonic Progression ... page 20 Conjunct and disjunct motion, 16— The best leaps, 17^-The leap of an augmented interval, 18 — The leap of a diminished interval, 19 — The leap of a seventh, 20 — Leap of a seventh or ninth, with one intermediate note, 21 — Approaching and quitting large leaps, 22— ^The leap to an accented note, 23 — Repeating the same note, 24 — Similar motion : forbidden con- secutives, 25 — Hidden octaves and fifths, 26-28— Discords with the bass, 29— The diminished fifth and augmented fourth, when allowed, 30 — Over- lapping and crossing of parts, 31 — Selection of harmonies, 32 — Forbidden positions of chords, 33 — The harmonies available for Strict Counterpoint, 34 — Progression of the mediant chord in the major key, 35, 36 — Root Progressions, 37 — Root rising a fourth, 38 — Root falling a fourth, 39 — Root rising a third, 40 — Root falling a third, 41-43 — Root rising a second, 44 — Root falling a second, 45 — Importance of considering root pro- gressions, 46. APPENDIX TO CHAPTER II.— Table of Root Progres- sions ., page 30 CHAPTER III.— The Harmonizing of a given Melody in the Strict Style page 34 Necessity of well-defined tonality, 47— The Subject, or Canto Fermo, 48 — Transposition of the Subject, 49-53— Position of the chords, 54— The cadence, 55, 56 — Modulation, when to be used, 57-59 — How to begin an exercise, 61 — What to consider in choosing chords, 62-64— Repetition of a note of melody, 65 — Anticipating the harmony of an accented beat, 66 — A melody harmonized, 67— The melody in the bass, with faulty Contents. harmony, 68-71— The same, harmonized correctly, 72— The melody in the treble, badly harmonized, 73-75— The same, correctly harmonized, 76-78— The student's difficulties illustrated, 79-81— The melody in a middle voice, 82— The melody worked in the alto, 83-94— Melody in the tenor, 95, 96 — Harmonizing a melody in a minor key, 97— -Danger of in- correct melodic progression, 98 — Chord progressions in a minor key, 99 — A melody in a minor key harmonized, 100 — Melody in the bass, 101, 102 —Melody in the treble, 103— Melody in the alto, 104, 105— Melody in the tenor, 106— How to acquire the instinct for good root progressions, 107 — Exceptions to the principles here laid down, 108. CHAPTER IV.— Two-Part Counterpoint : First Species page 58 Two-Part Counterpoint, 109— The five Species of Strict Counterpoint, no— The first Species, III— No discords allowed, 112 — Implied harmony, 113 —Outline chords, 114— Ambiguous intervals, 115-117— The forms of cadence, 119-122 — The first chord, 123 — Contrary and similar motion, 124 — Consecutive thirds and sixths, 125 — Oblique motion forbidden, 126 — The "false relation of the tritone," 127 — Its real nature explained, 128 — How to avoid it, 129, 130— Clear tonality essential, 131 — The minor seventh of the minor scale, when used, 132 — An exercise worked, 133 — Subject in the treble, 134-136— Subject in the alto, 137-139— Subject in the tenor, 140-142 — Subject in the bass, 143-145 — Counterpoint in a minor key, 147 — Subject in the treble, 148-150 — Subject in the alto, 151- 153 — Subject in the tenor, 154-156— Subject in the bass, 157-159 — The proper way of working, 160 CHAPTER V. — Two-Part Counterpoint : Second Species page 73 The second species of Counterpoint, 161 — The first bar, 162— Accented and unaccented beats, 163 — Outline chords, -164 — Treatment of passing and auxiliary notes, 165-169 — When these are impossible, 170 — Auxiliary notes, 171 — One and two chords in a bar, 172 — Faulty progressions, 173) '74 — Fifths and octaves between unaccented notes, when possible, 175-177 — How to save hidden, fifths and octaves, 178 — Unisons, and crossing parts, 179 — Implied second inversions, 180, 181 — The first chord, 182 — The cadence, 183-185 — The major sixth, and minor seventh in the minor key, how used, 186, 187— Monotonous counterpoint, 188 — Examples worked in a. major key, 189-193 — Ditto in a minor key, 194-198 CHAPTER VI.— Two-Part Counterpoint : Third Species page 86 The third species of Counterpoint, 200 — One and two chords to one note of the subject with counterpoint of four notes to one, 201, 202 — The first note a concord, 203 — The second, third, and fourth notes ; Arpeggio of a chord, 204 — Two consecutive passing notes, 205, 206 — Changing notes, 207-209 — Their position, 210 — Their order, 211-216 — When unavailable, 2 1 8— Passing notes in the minor key, 219 — Consecutive ditto, 220 — The minor seventh as a harmony note, 221 — Consecutives between Contents. xi harmony notes, 222 — The fifth of a chord, when available in the bass, 223, 224 — A doubled leading note, 225 — Harmony notes treated as passing notes, 226 — Progression from a second to a unison ; crossing of parts, 227 — The best position for a leap in the counterpoint, 228 — The first chord, 229 — The cadence, 230 — Examples worked, 231-235 — Counterpoint of three notes against one, 236 — Passing and changing notes, 237 — The cadence, 238 — Examples worked, 239-242 — Counterpoint ot six or eight notes to one, 243 — Compound duple and simple triple time in six-note counterpoint, 244 — Examples, 245-247 — Directions for work- ing the third species, 248. CHAPTER VII. — Two-Part Counterpoint : Fourth Species page 102 The fourth species of counterpoint, 249 — Syncopation ; its nature explained, 250-252 — Suspension, 253, 254 — What suspensions are allowed in strict counterpoint, 255-257 — Position of harmony notes in fourth species, 258 — This species oftener a variation of the second than of the third, 260 — Fourth species with two notes against one, 261 — Syncopation sometimes impossible, 262 — Breaking the syncopation, 263 — Consecutive thirds or sixths, 264 — The cadence, 265 — The commencement, 266, 267 — Examples, 268-271 — Double counterpoint illustrated, 272 — The fourth species in a minor key ; difficulty of avoiding monotony, 273 — Examples, 274-278 — Transposing the subject, 278 — Syncopation with three notes against one, 279 — "Ornamental resolutions," 280, 281 — Two chords against one note of the subject, 282 — The cadence, 283 — Examples, 284-287 — Counterpoint of the fourth species with four notes against one, 2S8 — The practical use w of the fourth species, 289. CHAPTER VIII. — Two-P art Counterpoint : Fifth Species page 115 Florid Counterpoint defined, 290— Employment of preceding species, 292- 296 — Ornamental resolutions, 297-300 — The employment of quavers, 301-305 — One chord in each bar, 307 — The commencement, 308 — The cadence, 309 — Need of variety in this species, 310, 311 — Examples in a major key, 312-314 — Ditto in a minor key, 315, 316 — The fifth species in triple time, 317, 318. CHAPTER IX. — Three-Part Counterpoint .„ ... page 124 Two of the three parts in the first Species, 320 — The fundamental difference between two-part and three-part counterpoint, 321 — Combinations of the voices, 322 — Position of the parts, 323 — Complete chords, 324 — The fourth, when a consonance, 325 — Hidden fifths and octaves, 326 — The false relation of the tritone, 327 — Consecutive thirds and sixths, 328 — Employment of the unison ; repetition of a note, 329 — Root-progressions, 330 — The commencement, 331, 332 — The penultimate chord in the xii Contents. cadence, 333— Cadence of the first species, 334— Examples of the first species, 335-341 — Cadence of the second species, 342 — Examples of the second species, 343-348— Cadence of the third species, 349 — Examples of the third species with four notes against one, 350-355 — Ditto with three notes against one, 356— Cadence of the fourth species, 357— Ex- amples of the fourth species, 358-363 -Cadence of the fifth species, 364— Examples of the fifth species, 365-370— The fourth and fifth species in triple time, 371 — Variation of counterpoints; choice of keys, 372 — Additional subjects, 373. CHAPTER X.— Four-Part Counterpoint ... page 143 The general principles of four-part counterpoint, 374 — Overlapping of parts, 376— The use of the unison ; repetition of the same note, 377, 378 — Repetition of a chord in different positions, 379— Combination of voices, 380 — The cadences, 381 — Difference between harmony and counterpoint illustrated, 382 — Four-part counterpoint of the first species, 383-386 — The cadence in the second species, 387 — Examples of the second species, 388— Ditto of the third species, 389, 390 — Ditto of the fourth species, 391 — Ditto of the fifth species, 392. CHAPTER XI. — Combined Counterpoint ... ._ ... page 153 Combined Counterpoint defined, 394 — Its two kinds, 395 — Its special diffi- culty, 397 — Illustrations, 398, 399 — The employment of dissonances, 400, 401 — Combined counterpoint in three parts, 402 — Two parts of second species, 403 — Two parts of third- species, 404 — Two parts of fourth species, 405, 406 — Two parts of fifth species, 407 — Combination of second and third species, 408 — Second and fourth species, 409 — Second and fifth species, 410 — Third and fourth species, 411 — Third and fifth species, 412 — Fourth and fifth species, 413 — Combined counterpoint in four parts, 414, 415 — Examples, 416-421 — The use of combined counterpoint, 422. CHAPTER XII.— Counterpoint in Five, Six, Seven, and Eight Parts page 165 Counterpoint in more than four parts, 423 — Its increased difficulty, 424 — Relaxation of strictness of rules for five parts, 425, 426 — The additional voice, 427 — First species in five farts, 428 — Second species in five parts, 429— Third species, 430— Fourth species, 431— Fifth species, 432 — Com- bined counterpoint in five parts, 433-435 — Counterpoint of six, seven, and eight parts ; further relaxation of the rules, 436— The best method of working counterpoint in many parts, 437 — First species in six parts, 438 —Ditto in seven parts, 439— Ditto in eight parts, 440— Second species in six parts, 441 — Third species in seven parts, 442 — Fourth species in six parts, 443 — Fifth species in eight parts, 444 — Combined species in six parts, 445 — Ditto in seven parts, 446 — Ditto in eight parts, 447 — Con- clusion, 448. Contents. xiii PART II.— FREE COUNTERPOINT. CHAPTER XIII. — Free Counterpoint in General ... page 182 The object of counterpoint, 449 — The harmonies possible in free counterpoint, 450 — The laws of root-progression in free counterpoint, 451 — Approach- ing a discord, 452 — The treatment of auxiliary notes, 453 — Chromatic auxiliary notes, 454 — Anticipations, 455 — Suspensions, 456 — Needful warnings, 457 — A bad example of free counterpoint analysed, 458. CHAPTER XIV. — Free Counterpoint upon a Canto Fermo. Imitative Counterpoint page 187 Free Counterpoint on a Canto Fermo, 459"— To be written in four parts, 460^ The cadences, 461-463 — Examples of first species, 464, 465 — Ditto of second species, 466, 467 — Ditto of third species, 468, 469 — Ditto of fifth species, 470, 471 — Combined free counterpoint of the fifth species, 472 — Imitative Counterpoint, 473 — Direct imitation ; Example, 474 — How to write it, 475 — Imitation by inversion, augmentation, and diminution, 476 — Example explained, 477 — The use of imitative counterpoint, 478. CHAPTER XV.— Cadences ... page 198 Various forms of cadence, 479; — Compared to stops in punctuation, 480 — The use of cadences, 481 — Authentic and Plagal Cadences, 482 — Position of the accents in the authentic cadence, 483-^485 — Varieties of the authentic cadence, 486, 487 — Leading up to a cadence, 488-495 — Repetition of tonic and dominant chords in a final cadence, 496 — The Plagal Cadence, 497 — Mostly used at the close of a movement, 498 — Preceded by an interrupted or inverted cadence ; employment of the " Tierce de Picardie," 499, 500 — Use of the minor seventh of the key, 501 — A different form of plagal cadence, 502 — Exceptional forms of full cadence, 503, 504 — The Inverted Cadence, 505 — The Half Cadence, 506 — The Interrupted Cadence, 507 — Cadences only used at the end of a phrase, 508. NOTE TO CHAPTER XV. — The Harmonic Nature of the Cadence page 211 CHAPTER XVI. — The Harmonizing of Chorals, and other Melodies - page 213 The use of counterpoint in harmonizing melodies, 509 — The position of the cadences, 510 — Rhythm defined, 511 — Finding the place of the cadences, 512-514 — The cadential possibilities of melodic progressions, 515 — Phrase ending on the tonic, 516, 517— Phrase ending on the supertonic, $1% Phrase ending on the mediant, 519— Phrase ending on the sub- dominant, 520 — Phrase ending on the dominant, 521 — Phrase ending on xiv Contents. the submediant, 522 — Phrase ending on the leading note, 523 — Modu- lation, 525 — Variety of cadence, 526 — Length of harmony notes in chorals, 527 — Repetition of the same chord, melody note, or bass note, 528 — Harmony to be changed in approaching an accented beat, 529 — The use of the . chord, 531 — Auxiliary notes, 531 — A choral harmonized, 532-535 — The same choral harmonized by Bach, 536-539 — Simple harmony recommended, 540 — The choral in a middle voice, 541-543 — The harmonizing of more florid melodies, 544— Use of auxiliary notes, 545-547 — Notes of small value, 548 — Passing notes in the accompani- ment, 549 — A melody harmonized, 550 — A weak harmony, 55 ' — A stronger harmony, 552 — The melody in a middle Voice, 553 — The harmonizing Of pianoforte music, 554 — Broken chords and arpeggios, 555 — Rule for their treatment, 556 — Examples, 557 — Freedom of writing by the great masters, 558 — Strict observance of rule recommended, 559 — Exercises, 560. CHAPTER XVII. — The Application of Counterpoint to Practical Composition ... _ page 240 Free Counterpoint used in actual composition, 561 — The practical -use of counterpoint, 563 — Counterpoint on " Plain Song" by Bach, 564, 565 — The same subject treated by Cherubini, 566 — Counterpoint on a choral, by Bach, 567— Ditto by Handel, 568 — The choral in instrumental music, 569 — The choral in opera, 570 — Counterpoint as an added part to a known theme, 571, 572 — Combinations of different subjects ; example by Handel, 574— Ditto by Bach, 575, 576^Ditto by Mozart, 577— Example by Wagner ; conclusion, 578. COUNTERPOINT: STRICT AND FREE. PART I.— STRICT COUNTERPOINT. CHAPTER I. INTRODUCTION. i. By the word Counterpoint is meant the art of adding to a given melody one or more other melodies, above or below, in such a manner that all the parts when sounded together shall produce correct harmony. The word is derived from the Latin " contrapunctum." In old music the notes were written as dots (Latin, punctum — a point, or dot), and if, when one melody was given, another was to be added to it, this was described as "punctum contrapunctum " — dot against dot, or (as we now say), "note against note." This, as will be seen presently, is the simplest kind of counterpoint. In its wider sense, counterpoint may be defined as the art of combining two or more parts or voices, each of which possesses independent melodic interest and importance. 2. The essential difference between harmony and counter- point is that in the former the construction of chords and their relation to one another are the principal subjects of study; and although the rules for melodic progression (see Harmony, Chapter IV.*) need to be regarded, the melody of each part separately considered is a subordinate matter in comparison with the correctness of the harmony, and the connection of the different chords. In counterpoint, on the other hand, while the need for harmonic purity is strictly insisted on, this in itself is not sufficient Each part should move independently of the others, and possess some special features of its own. It should be added that in the earlier stages of contrapuntal writing this is only possible to a limited extent. 3. An example will best illustrate what has just been said. * The references to " Harmony " throughout this volume are in all cases to the author's " Harmony : Its Theory and Practice." (Augener & Co.). 16 Counterpoint . [Chap. i. Supposing that we wish to add three upper parts to a simple bass such as the following — This bass suggests as the most natural harmony a triad in i root position on each note. The simplest way of arranging the chords will be Here every rule of harmony is observed, and the passage is perfectly correct. But if the different voices be examined singly, it will be seen that there is very little melody, and almost no individuality about them. The soprano and tenor parts each lie within the compass of a minor third, while the alto consists entirely of two notes. Such a passage, however correct as harmony, can scarcely be called counterpoint. 4. Now let us adopt a different plan. We take the same bass as before, and use the same chord progressions above it ; but we how introduce the voices in succession, and give each of them a different melody — If the student will play each of the upper parts of this example separately, he will see that there are here three distinct melodies above the bass, making correct harmony when played together, but each being different from the other, though we have inten- tionally made : them all begin with the same ascending passage. Here is : seen an example of florid counterpoint. 5. There is another important distinction between harmony and counterpoint, from the student's point of view. In harmony exercises it is always the bass part that is given, and the chords to be employed are indicated either by figures placed over or under the bass, or (in the case of the root' position of a triad), by' the absence of figures. In counterpoint, on the other hand, the given melody may be in any of the voices, and even when it is in the bass, the student is left absolutely without any direction as to what harmony he shall put above it. Very often, more thaD Chap. I.] Strict ano Free. *7 one harmony is possible, and the choice will depend on what has preceded, or on what follows. 6. If a counterpoint be added to a given subject, and can only be used in its original position, either above or below, as the case may be, it is called a Simple Counterpoint. But if it be so con- structed as to be capable of inversion with the subject, or if two parts of the counterpoint can be inverted with regard to one another, we have Double Counterpoint. The word " double " in this connection simply means " invertible." The inversion may be at any interval, but in actual practice the only intervals usually employed are the octave, or fifteenth (the double octave), the J tenth, and the twelfths "" Of these, double~~cbunterpoint at the "» octave is the mostttequent and the most useful. 7. As an illustration of what has just been said, let the student examine the alto and tenor parts of the example given in § 4. If these be played together, omitting the treble and bass parts, they will be found to make correct harmony by themselves. If now the tenor part be written above the alto, either by placing the tenor an octave higher, or the alto an octave lower, the harmony will still be correct, though somewhat free — The alto and tenor parts are therefore written in double counter- point in the octave. 8. If three parts are so written as to be capable of inversion between themselves, so that each part can be either the upper, middle, or lowest part of the harmony, we get Triple Counterpoint ; and with four parts similarly treated, we have Quadruple Counter- point. Triple and quadruple counterpoint are much rarer than double, and it is very seldom that all the possible inversions will be available in such cases. 9. In the development of music, counterpoint was in use long before harmony. A great number of the compositions of the fifteenth and sixteenth centuries consisted of the addition of parts to some given well-known melody — either a popular air, or some old ecclesiastical theme. The given part was usually called the Canto Fermo, or " fixed song ; " and, as the science of harmony was still in its infancy, very strict rules as to the accompanying parts were enforced. Only triads and their first inversions were allowed to be employed; no unprepared discords, excepting 1 8 Counterpoint : [Chap. i. passing notes taken by step, were allowed to be used ; the interval of the perfect fourth was considered as a discord between the bass and any upper part ; and no chromatic chords in a key were available under any circumstances. As a matter of fact, the use of such chords had not then been discovered. Counterpoint written under these restrictions is now known as Strict Counter- point. io. In the music of the present day, composers, when they write in the contrapuntal style, allow themselves much greater liberty. In modern counterpoint, any combination may be used which does not violate the laws of harmony. Second inversions are allowed; essential discords may be freely employed, either with or without preparation ; chromatic chords in a key may be used, as may also auxiliary notes, whether diatonic or chromatic ; and these may be taken by leap, as well as by step. The im- portant point to be^ regarded is the individuality of the separate voices. The counterpoint we are now describing is called Free Counterpoint. ii. Some modern theorists argue, with a certain show of reason, that as the restrictions of Strict Counterpoint are never enforced in actual composition, the study of the subject is useless, and a mere waste of time to the student, because he finds himself forbidden to do things which all composers of eminence are constantly doing. In other words, the rules of the old contra- puntists are broken on every page of the works of the great masters. This may be at once admitted; and there would be force in the argument, if strict counterpoint were studied for Us own sake. But this is far from being the fact. No sensible teacher will ever tell a pupil that it is wrong- to use a second inversion, or a fundamental discord. Strict counterpoint is only a means to an end. Just as a student of the pianoforte practises technical exercises for the hand, frequently in peculiar and cramped positions such as he will seldom, if ever, meet with in the pieces he will play later, in order to acquire freedom in the muscles of the fingers, so the student of composition learns to work in the first instance under apparently arbitrary restrictions, in order that he may be able to use his freedom judiciously when the restrictions are removed. There is no instance of any com- poser having attained the highest eminence without previously submitting himself to this course of discipline. 12. It is desirable that in commencing the study of counter- point the parts to be combined should be treated as voice parts, that is, that each part should be kept within the limits of the corresponding voice. The student is also strongly recommended to write all his exercises from the first in open score, with each part on a separate staff. This is more important in counterpoint than in harmony, as it allows the progression of each voice to be more clearly seen. The student should moreover accustom Chap. I.] Strict and Free. 19 himself to the use of the C clef for the alto and tenor voices, as this clef is used in all the principal theoretical treatises, as well as in the scores of the great masters. We shall therefore employ it throughout this book. 13. Though the C clef is usually looked upon as a bugbear by young students, there is no more real difficulty in mastering it than with the F or G clef; it is simply a matter of practice. All that it is needful to remember is that the line upon which the clef is placed, whether it be the soprano, t» = , the alto T~~ the tenor 3 as " middle C "—that is, the C which lies between the G and the F staves. In the following example — Treble. .fil . is the line on which is written the note known the same note is written in all the five clefs. In old music other clefs were used, viz. : the G clef on the first line, called the French violin clef (to be met with in some of Bach's scores) ; the C clef on the second line, called the mezzo-soprano clef; and the F clef on the third line, called the baritone clef. As these are now entirely obsolete, the student need not trouble himself about them. The soprano clef (the C clef on the first line) is still used occasionally, especially in France and Germany, where it is sometimes found in the vocal parts of full orchestral scores ; but it is much less generally employed than the alto and tenor clefs. We shall therefore write the treble parts of our examples, as usual, with the G clef. 14. The compass of the four voices is about as folllows — Treble, This compass should seldom be exceeded ; arid even the extreme notes should be sparingly used. b 2 io Counterpoint : [Chap, ii- CHAPTER II. MELODIC AND HARMONIC PROGRESSION. 15. Before the student begins to write Counterpoint, it is needful that he should clearly understand the laws regulating the progression both of his melodies and of his harmonies. With some of these he will be already familiar from his study of Harmony ; but inasmuch as the rules by which he must now be guided are not in all cases quite the same as those which apply to Harmony (in which many things are allowed which are pro- hibited in Strict Counterpoint), it will be advisable to give the laws which are enforced in the latter study, though some of these are repetitions of what is already known. 16. If a part proceed by step of a tone or semitone, either to the next degree of the scale, above or below,, or to the same degree chromatically altered — which latter in Strict Counterpoint will only take place when there is a modulation — the motion is called " conjunct." When a part proceeds by leap of any interval greater than a second, the motion is called ." disjunct." In a melody it is desirable that the parts should move as smoothly as they can; conjunct motion is therefore preferable to disjunct, when both are possible. 17. If a part move by leap, the leap of a consonance is pre- ferable to that of a dissonance, and the leap of a small interval, such as a third, fourth, or fifth, is better than that of a large one — a sixth or octave. A larger interval than an octave should not be used at all. 18. It is forbidden ' for any part to move by, leap of an augmented interval, excepting in one of the repetitions of a sequence {Harmony, § 137), when the interval of an augmented fourth (but no other augmented interval) may occasionally be employed. Bad. , Good. , 19. A leap of a diminished fourth, fifth, or seventh, is allowed in Strict Counterpoint, provided always that the second of the two notes forming the interval proceed to a note within, and not beyond, the interval, the best progression being to the note to Chap. II.] Strict and Free. 21 which it would have moved had the two notes forming the dissonance been sounded together, instead of in succession. Good. (g) Good. Possible. Bad. Good. Possible. Bad. At (a) are shown the correct and incorrect treatment of the diminished fourth, at (b) of the diminished fifth, and at (