Fugue (Prout)

AUGENER'S EDITION, No. 9185.

FUGUE.

BY

Professor of Harmony and Composition at the Royal Academy of Music;
Author of "Harmony: its Theory and Practice," "Counterpoint:
Strict and Free," "Double Counterpoint and Canon," &c.

NEW YORK:

G. SCHIRMER, 35, Union Square.

PREFACE.

There is probably no branch of musical composition in which theory is more widely, one might almost say hopelessly, at variance with practice than in that which forms the subject of the present volume. In Harmony, we are frequently meeting with cases in which the rules of the old text-books need much modification; but with regard to Fugue there are few indeed of the old precepts which are not continually, not to say systematically violated by the greatest masters. The reason for this is no doubt that the standard authorities on the subject, Fux and Marpurg, treated it from the point of view of the seventeenth century, and that most of their successors, such as Cherubini and Albrechtsberger (to name two of the most illustrious), have in the main adopted their rules, taking little or no account of the reformation, amounting almost to a reconstruction, of the fugue at the hands of J. S. Bach. Somewhat more liberality of tone will be found in the treatises of André, Richter, and Lobe; but not one of these, excepting Lobe, has taken Bach's work as the starting point for his investigations. Lobe, on the other hand, is too revolutionary; he even abolishes the names "subject" and "answer," using instead the terms "first imitation," "second imitation," &c.

When we find a distinguished theorist like André saying that Bach is not a good model because he allows himself too many exceptions, and are informed that one of the principal German teachers of counterpoint is in the habit of telling his pupils that there is not a single correctly written fugue among Bach's "Forty-Eight," surely it is high time that an earnest protest were entered against a system of teaching which places in a kind of "Index Expurgatorius" the works of the greatest fugue writer that the world has ever seen.

In writing the present treatise, the author has consulted all the standard authorities, but (as may be inferred from what has just been said) has followed none. He has proceeded on the same principles which have guided him in all the preceding volumes of this series, and has gone to the works of the great composers themselves, has carefully analyzed and examined them, and from their practice has deduced his rules, without paying the least regard to what might be said on the subject by Marpurg or Cherubini. He has started with the axiom, which few will be bold enough to dispute, that Bach's fugues are the finest in existence, and that whatever Bach does systematically, and not merely exceptionally, is the correct thing for the student to do. He therefore first put into open score and carefully analyzed the whole of the forty-eight fugues in the "Wohltemperirtes Clavier." He next examined every fugue, vocal and instrumental, to be found in the forty volumes of Bach's works published by the Bach Gesellschaft, making notes of all points of importance. But he did not confine his attention to Bach. He examined probably at least a thousand fugues, including all those by Handel, Mozart, Beethoven, Mendelssohn, and Schumann, besides a large number by other writers of more or less eminence, to find out what had been actually done by the greatest masters of our art. The farther his researches extended, the deeper became his conviction of the necessity of placing the laws of fugal construction on an altogether different basis from that hitherto adopted. The result of his investigations will be found in the following pages. In the words of the Psalmist, he may say, "I believed, therefore have I spoken." A great deal to be found in this book will probably horrify old-fashioned musical conservatives; but not a single new rule is propounded for which warrant is not given from the works of the great composers; and if he shrank from the logical consequences of the examination of these works, the author would be untrue to his own convictions.

The general plan of this volume is to some extent the same as that adopted by Mr. James Higgs in his admirable Primer on "Fugue," by far the best treatise on the subject in our language. It would be dishonest of the author not to acknowledge the assistance he has derived from this little work, which indeed it would be impossible for any later writer on the same subject to ignore. To Mr. Higgs we owe the clearest exposition yet written of the important matter of fugal answer; and, though it will be seen that the rules given in this volume differ in several material respects from those in the "Primer," the author frankly confesses that it was Mr. Higgs who first put him on the right track.

It is on this very subject—fugal answer—that the great composers depart most widely from the old rules. The new and, it is hoped, very simple rules given in Chapters III. and IV. are enforced by nearly 150 examples, of which more than sixty are by Bach. Other composers are also freely drawn upon; but throughout the volume, in all cases of doubt, Bach is treated as the final authority.

In order to assist the student, it has been thought best to take the different portions of a fugue separately, that he may learn how to construct each part before he proceeds to the composition of an entire fugue. The chapters on Countersubject, Exposition, Episode, and Stretto, contain not only numerous illustrations from the great masters, but specimens of each, written expressly for the guidance of the student. While an endeavour has been made to make them musically interesting, it must be remembered that they are merely intended as exercises, and have no claim to be judged as compositions.

The chapter on "The Middle and Final Sections of a Fugue" will, it is believed, be found new by English readers. The author cannot, however, claim the credit of the first discovery that a fugue is written in ternary form. That honour is due to Dr. H. Riemann, in his analysis of Bach's "Wohltemperirtes Clavier." It is nevertheless so obvious when once pointed out, that the author of course availed himself of it, and herewith acknowledges his obligations to Dr. Riemann for the idea, though he has developed it in a somewhat different way from that of the original discoverer.

Of the later chapters of the volume not much need be said here. The concluding chapter, on "Accompanied Fugue," deals with a branch of the subject not touched on in any book we have met with; but its importance in modern music rendered it desirable to say a few words about it.

As belonging to practical composition rather than to mere theoretical study, fugue is a subject which is best taught by examples. In the present volume it was impossible to give more than a very few complete fugues; but this will be followed as soon as possible by a companion volume on "Fugal Analysis," the materials of which are already in great part collected, which will contain a selection of the finest fugues of the great masters in various styles and forms. These will be all printed in open score (like the two fugues by Bach in sections 298, 308), and fully annotated. It is hoped that they will be found a most valuable aid to the student.

With the subject of fugue, the strictly theoretical part of this series is completed. The remaining volumes will deal with actual composition, and the next to follow (after "Fugal Analysis") will be on "Form."

London, December, 1891.

TABLE OF CONTENTS.

[N.B.—The numbers refer in every instance to the sections, not to the pages.]

CHAPTER I.—Introduction

page 1

The requisite preliminary knowledge, 1—Definition of the term Fugue, 2—Double, triple, and accompanied fugues, 3—The difference between Fugue and canon, 4–6—General description of a fugue, 7—The Subject, 8—The Answer: real and tonal answers, 9—The Countersubject, 10—The Exposition, 11—Episode, 12—The Counter-exposition, 13—The middle section of the fugue, 14—The final section: Pedal points, 15—The Stretto, 16—Close fugue, 17—Strict and free fugues, 18—The Ricercare or Ricercata, 19—Fugues by inversion, augmentation, or diminution, 20—The Fughetta, 21—Fugato, 22—The essential nature of fugue, 23.

CHAPTER II.—The Subject

page 6

The essentials of a good subject, 24—A Subject defined; fugues with two or more subjects, 25—The necessity of clear tonality, 26—Implied harmony, 27—Subjects that remain in one key: major, 28–30—Ditto, minor, 31, 32—Subjects in the dominant, 33—Subjects that modulate from tonic to dominant, 34—Ditto, in a minor key modulate to the dominant minor, 35—Modulation from dominant to tonic, 36—Ditto, from tonic to dominant and back, 37—Modulation between tonic and subdominant, 38—A subject in the subdominant, 39—Incidental modulations, 40, 41—The cadence of a fugue subject, 42–45—Length, 46—Compass, 47—A subject may begin on any degree of the scale, 48–49—The subject must be contrapuntal in character, 50—Adaptability for stretto, 51—Melody and rhythm, 52—How to determine the limits of a subject, 53—Directions for work, 54.

CHAPTER III.—The Answer

page 18

The Answer defined, 55—Key relation of subject and answer, 56—Real and tonal answers, 57—When a real answer is possible, 58—Examples of real answers: in a major key, 59–65—The answer of a minor subject must be in the dominant minor, 66—Examples, 67, 68—The last note of a minor subject, 69—Subject in dominant, answer in tonic, 70—The answer in the subdominant, 71—Ditto, in a minor key, 72—Example by Bach analyzed, 73–75—Ditto, 76—Ditto, from the "Art of Fugue," 77—Further examples, 78, 79—When an answer in the subdominant is possible, 80—Subject in the key of the subdominant, answer in the tonic, 81—Modulation between subdominant and tonic, 82—Treatment of intermediate modulations, 83—Tonal answer: its origin, 84—The old rule, 85—Its usual application; modification required, 86—The practice of the great masters, 87—The leap from tonic to dominant answered tonally, 88, 89—The rule applies only to the beginning of an answer, 90—Examples of a real answer in such cases, 91—The dominant approached through the third of the scale, 92—Subjects beginning with the notes of the tonic chord: tonal answers, 93—Ditto, with real answers, 94–99—The principle involved, 100—Rule for our guidance, 101—Subjects that commence on the dominant, with tonal answers, 102–104—Ditto, with real answers, 105–107—The reason for real answers here, 108—Fugues with both tonal and real answers, 109—Tonal answers in the subdominant, 110—Answer in two keys, 111—A real answer always possible when there is no modulation to the dominant, 112—Warning to students, 113.

CHAPTER IV.—The Answer (continued)

page 49

Subjects that modulate to the dominant, 114—Only two chief keys used in exposition, 115—Rule for modulation, 116—Point of modulation, 117—Expressed and implied modulation, 118—Examples, 119, 120—Modulation to be made as early as possible, 121—Double significance of each degree of the scale, 122—Its importance, 123—Example of subject modulating, by Mozart, 124—Further examples, 125—Reason for making the tonal change early, 126—Treatment of third and seventh of scale, 127—Rule for third of scale, 128—Examples, 129, 130—Treatment of leading note, 131—Examples, 132, 133—Subjects that modulate from dominant to tonic, 134, 135—One note answered by two, 136, 137—Subjects modulating to dominant and back, 138—Dissonant intervals generally retained in answer, 139—An important exception, 140–143—Disregard of semitones, 144, 145—Dominant answered by supertonic, 146–148—Treatment of chromatic subjects, 149–151—Answers by inversion, 152—Ditto, by augmentation and diminution, 153—Change of an octave in pitch in course of the answer, 154—Irregular answers, 155 Summary of general principles, 156—Bad subjects, 157—Exercises for the student, 158.

CHAPTER V.—The Countersubject

page 72

Countersubject defined, 159—Must be in double counterpoint with subject, 160—Need of contrast, 161—Examples, 162, 163—Key of countersubject, 164—The inganno, 165—The material of the countersubject, 166—Often forms the basis of episodes, 167—Sometimes accompanies only a part of the subject, 168—Countersubject in tonal fugues, 169—Sometimes needs modification, 170—Must make correct two-part counterpoint with the answer, 171—Deferred appearance of countersubject, 172—A fugue with two countersubjects, 173—Two countersubjects used in succession, 174—A double fugue, 175—When a countersubject is unnecessary, 176—Directions for working, 177.

CHAPTER VI.—The Exposition and Counter-exposition

page 81

Exposition defined, 178—Order of entry, 179—Relative distance of voices, 180—How this affects choice of voice for answer, 181—The last entry best in an outer part, 182—Exposition of a two-part fugue, 183—Order of entry in a three-part fugue, 184—Place of countersubject, 185—Additional entry, when advisable, 186—Example, 187—Codetta, 188—When is a codetta needed before the entry of the answer, 189–191—Codetta between second and third entries, 192, 193—Example of an exposition in three parts, 194–197—Exercises, 198—Order of entry in a four-part fugue, 199—Alternation of subject and answer: exceptions, 200—How a four-part exposition differs from one in three parts, 201—When an exposition ends in the tonic key, and when in the dominant, 202—Cases in which all the voices do not appear in the exposition, 203—Example of a four-part exposition, 204, 205—Irregular expositions: an "octave fugue," 206—The Counter-exposition, 207—Often only partial, 208—Frequently introduces the first stretto, 209—Counter-exposition by inversion, 210—Counter-exposition quite optional, 211—Directions for work, 212.

CHAPTER VII.—Episode

page 92

Episode defined, 213—Its use for modulation, 214—Difference between episode and codetta, 215—The material for episode: sequence, 216—Use of imitation, 217—Example of episodes developed from subject of fugue, 218, 219—Ditto from countersubject, 220, 221—Ditto from codetta, 222, 223—Various devices used in episodes; example by Handel, 224–226—Episodes formed from entirely new material, 227, 228—One episode sometimes the inversion of another, 229—General principles; the importance of sequence, 230—Need of variety in each episode, 231—The freedom allowed to the composer, 232—The number of episodes variable, 233—Long and short episodes, 234—Fugues without episodes, 235—Examples to follow the expositions given in the last chapter, 236—Episodes for the three-part fugue, 237–239—Ditto, for the four-part fugue, 240–242—The chief essentials of good episodes; directions for work, 243.

CHAPTER VIII.—Stretto

page 109

Meaning of the word, 244—The old rule, 245—A stretto not indispensable, 246—Subjects should be designed for stretto originally, 247—Examples of stretto on a subject not so designed, 248–250—Interval of entry, and number of parts; closest stretti should come last, 251—Incomplete entries, 252—Varieties of stretto, 253—A subject and answer specially written for stretto, 254—The various stretti: in two parts, 255–263—Ditto for three voices, 264, 265—Ditto for four voices, 266, 267—How to invent a subject suitable for stretto, 268—Stretto in the counter-exposition of a fugue, 269—Canonic stretto, 270—Regularity desirable in the entries of a stretto, 271—Subject and countersubject used together in a stretto; stretto on a pedal, 272—Stretto made from modified subject, 273—Stretto by inversion, 274—Ditto by augmentation, 275—Ditto by diminution and inversion, 276—The stretto maestrale, 277, 278—Stretto in the exposition of a fugue; close fugue, 279, 280—In a close fugue the answer will be in the same key as the subject, 281—Examples of stretto by Mozart, 282–284—Example by Mendelssohn, 285—Ditto by Spohr, 286—Ditto by Brahms, 287—Necessity of analysis by the student, 288—Exercises to be worked, 289.

CHAPTER IX.—The Middle and Final Sections of a Fugue

page 138

Freedom of treatment of middle section, 290—Ternary, or Three-Part Form, 291, 292—Limits of the first section of a fugue, 293—Varied length of the middle section, 294, 295—Analysis of the 21st fugue of the "Wohltemperirtes Clavier," 296—How to distinguish subject and answer in the middle section, 297—Bach's fugue in E minor analyzed, 298—The first section, 299—First group of middle entries, 300—Isolated entries, 301—Return to the tonic key in the middle section, 302—The rest of the middle section, 303, 304—Final section: the coda; a dominant pedal, 305—Additional voices often introduced in a coda, 306—Summary of entries, 307—Fugue in D major, by Bach, 308—The subject, 309;—Absence of countersubject, 310—The exposition, 311—Commencement of middle section, 312—The first stretto, 313—Third episode and second stretto, 314—A codetta in the middle section, 315—The third stretto, 316—Fourth middle entry, 317—Final section, 318—Advisability of rests: method of re-entry of voices, 319, 320—The employment of cadences, 321—Order of modulation; Cherubini's rules, 322—These rules hardly ever observed by Bach, 323—Modulations beyond the nearly-related keys, 324—General rules for the treatment of middle entries, 325—Exceptions, 326—All voices need not take part in a middle entry, 327—Number of middle entries variable, 328—Treatment of the pedal point, 329—Need of continuity, 330—The last note before a rest, 331—Individuality of the voices necessary, 332—The composition of a complete fugue, 333—Should have a definite plan, 334—Specimen fugue for two voices, 335—Analysis of ditto, 336–339—A fugue for three voices, 340—The same analyzed, 341, 342—A four-part fugue, 343—Analysis of ditto, 344–347—Need of practice, 348.

CHAPTER X.—Fughetta and Fugato

page 171

Definition of Fughetta, 350—Its usual form, 351—Examples by Bach 352–354—A five-part fughetta by Handel, 355—Example by Mozart, 356—Ditto by Beethoven, 357—The nature of Fugato, 358—Example by Bach, 359—Ditto from the "Creation," 360—Ditto by Beethoven, 361—Ditto by Mendelssohn, 362—Ditto by Mackenzie, 363.

CHAPTER XI.—The Fugue on more than one Subject

page 182

Double Fugue, 365—The two kinds of double fugue, 366—How distinguished from fugues with a countersubject, 367—The two subjects must be written in double counterpoint, 368—Number of parts requisite, 369—The exposition of the first kind of double fugue; first method, 370–374—The second method, 375–377—Need for clearness, 378—The form of this kind of double fugue, 379—The middle entries, 380—The stretti, 381 Isolated entries, 382—The second kind of double fugue, 384—How it differs from the other kind, 385—The two expositions, 386–389—The combination of the two subjects, 390—Analysis of Organ Fugue in c minor, by Bach, 391–394—Limits ot variation in this form, 395—General form of this kind of fugue, 396—Small amount of modulation, 397—Triple Fugue, 398—An unusual form, 399—Fugue from the "Art of Fugue" analyzed, 400–403—The ordinary form; the exposition 404—Example by Albrechtsberger, 405—Triple fugue by Mozart analyzed, 406–409—Freedom of triple fugues, 410—Quadruple Fugue, 411—A spurious variety, 412—An exposition of a quadruple fugue by Cherubini 413—Its subsequent treatment, 414.

CHAPTER XII.—The Fugue on a Choral

page 216

The two methods of writing a fugue on a choral, 415—The subjects taken from the choral itself, 416—Example by Buxtehude analyzed, 417–421—Example by Bach, 422, 423—The form of such fugues, 424—The entries of the canto fermo, 425—Modern examples, 426—The second kind of fugue on a choral, 427—Example from Bach's Motetts analyzed, 428—Modulations, 429—The choral introduced during the episodes, 430—Example by Mendelssohn, 431—Why the freer style was adopted, 432—The first line of a choral taken as the fugue subject; example, 433—The freedom allowed in this kind of work, 434.

CHAPTER XIII.—Accompanied Fugues

page 229

Definition, 435—Accompanied exposition, 436, 437—Filling up thin harmony, 438—Variations of voice parts, 439, 440—Independent counterpoints, 441–444—General principles, 445–448—Importance of good models, 449—Our rules founded on the practice of the great masters, 450.

This work was published before January 1, 1927, and is in the public domain worldwide because the author died at least 100 years ago.

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