This book is due at the on the last date stamped under "Date Due." If not on hold, it may be renewed by bringing it to the librai ^%rrT<»Tp t tdp A"RY ^J| RETURNED P^l RETURNED , fMi5 r ~" _ i! i 7 • i > «?Sr^ -~< ■ _^, -*£-*&n?y £&M Jl S i ^ ■■ '- ~>* \ i YM - — m ■ » *» ENDOWED BY THE DIALECTIC AND PHILANTHROPIC MT59 .P8T 00005810982 2_ /i?/ 56 L THE LIBRARY OF THE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL MUSIC LIBRARY Gift of WILLIAM S. NEWMAN H N Digitized by the Internet Archive in 2013 http://archive.org/details/fugueprout AUGENER'S EDITION, No. 9185. MUSIC LIBRARY UNC--CHAPEL HILL .hi FUGUE BY EBENEZER PROUT, B.A., Lond. Hon. Mus.Doc. Trinity Coll., Dublin and Edinburgh, and Professor of Music in. the University of Dublin. NINTH IMPKESSION LONDON: AUGENER Ltd. Printed in England by AUGENER Ltd., 287 Acton Lane, London, W. 4. 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 Andre, 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 Andre saying thai 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. iv Preface. 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 Gesell- schaft, 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, Beet- hoven, 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 Preface, v 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 con- fesses 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 Counter- subject, Exposition, Episode, and Stretto, contain not only numerous illustrations from the great masters, but specimens ot 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 vi Preface. 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 ;*re already in great part collected, which will contain a selection of the finest fugues of the great masters in various styles and for ms. These will be all printed in open score (like the tw r o 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 I The requisite preliminary knowledge, I — Definition of the term Fugue, 1 — 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 Counter subject, 10 — The Exposition, 11 — Episode, 12 — The Counter-exposition, 13 — The middle section of the fugue, 14 — The final section : Pedal points, 15 — The Srretto, 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 viii Contents. 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 sub- dominant, no— Answer in two keys, in — A real answer always possible when there is no modulation to the dominant, 112 — Warning to students, US- CHAPTER IV.— The Answer {continued) page 49 Subjects that modulate to the dominant, 1 14 — 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 super- tonic, 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 Counter subject defined, 159— Must be in double counterpoint with subject, 160 — Need of contrast, 161 — Examples, 162, 163 — Key of countersubject, 164 — The inganiiOf 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. Contents. ix 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 counter subject, 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 intro- duces 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 epi- sode 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 im- portance 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 — Ex- amples 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. x Contents. 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 " Wohltem- perirtes 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 ; Cherubim'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 Ijl 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 XL— 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. Contents. xi 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 — Ex- ample 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 — Modula- tions, 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. Fugue. chapter I. INTRODUCTION. i It is absolutely necessary that any one who begins to study fugue should have a thorough knowledge not only of Harmony and Counterpoint, but of Double Counterpoint and Canon. Without such knowledge any attempt to master fugal composition is a mere waste of time. A previous acquaintance on the part of the pupil will therefore be presupposed throughout this work, either with the preceding volumes of the present series, or with other books treating of the same subjects. 2. A Fugue is a composition founded upon one subject, announced at first in one part alone, and subsequently imitated by all the other parts in turn, according to certain general principles to be hereafter explained. The name is derived from the Latin word fuga, a flight, from the idea that one part starts on its course alone, and that those which enter later are pursuing it. 3. Though the definition of Fugue just given may be accepted as generally correct, it should be mentioned here, to prevent misapprehension, that fugues may be written on more than one subject. If there are two subjects, the fugue is said to be a double fugue ; if there are three, it is a triple fugue, and so on. In such cases the composition will not begin with one part alone ; the subjects will appear together, although in all probability they will not all commence exactly at the same time. It must also be said that we often meet, especially in modern music, with vocal fugues having an independent instrumental accompaniment. In such cases what has been said as to the entry of the subject with one part alone does not apply ; a fugue of this kind has some analogy to an accompanied canon. 4. From the description just given of fugue, it would seem at first sight to have a considerable resemblance to Canon. The latter, indeed, was formerly called fuga canonica, and it will greatly assist the beginner to understand the real nature of a fugue if we point out the chief differences between it and the canons which, it may be assumed, he has already studied. One most important difference is that, whereas in a canon the leading voice is imitated throughout by all the parts that follow, this I Fugue. ichap. i is never the case in a fugue. The opening theme, known as the " subject," is always imitated ; frequently also one or more of the accompanying counterpoints to . the various imitations of the subject are themselves imitated, as will be seen later in this chapter ; but continuous imitation of one part by another throughout the whole piece is scarcely ever met with in a fugue.* This is one of the most important distinctions between the two forms. 5. Another respect in which fugue differs from canon is that in the latter the imitation by the second voice must always be exact as to the name of the interval, though in many cases (as for instance in a canon in the ninth) the quality of the interval is changed {Double Counterpoiiit and Canon, §§ 339, 340 1). In a very large number of fugues, on the other hand, the first imitation is not an exact copy of the subject, but requires more or less important modification, as will be explained later. 6. A third distinction between the forms which we are now comparing is that, while in a canon the first imitation may be at any interval, it must in a fugue be always at the distance of a fourth cr fifth above or below the subject. This, it must be added, refers only to the commencement of a fugue ; in its later develop- ments the entries may be at other intervals. 7. Before proceeding to treat separately of the various parts of a fugue, it will be advisable to give a general description of its form, and an explanation of the names applied to the different parts. Fugues differ so much in their structural details that it is impossible to give more than a general outline here ; the numerous variations will be noticed when in later chapters we treat of the various parts one by one. 8. The Subject of a Fugue is the theme announced in the first instance by any one part or voice without harmony (except in the cases mentioned in § 3), on which the whole composition is founded. By this it is not meant that the subject is to be heard continuously throughout the fugue ; this would probably cause great monotony, although instances are to be met with {e.g., in the first fugue of Bach's ' Wohltemperirtes Clavier ') in which the subject is rarely absent. What is intended is that the subject is to make its appearance, at more or less frequent intervals, throughout the whole of the fugue. 9. The Answer is the transposition of the subject into the key of the perfect fourth or fifth above or below the key of the subject. Iu an enormously large majority of cases the keys for the subject and answer will be the tonic and dominant ; occasionally we find the answer in the subdominant instead * As an exceptional instance of a fugue in which two parts are in canon throughout should be mentioned the ' Fuga canonica in Epidiapente' (i.e., in the fifth above) in Bach's ' Musikalisches Opfer.' f The references to " Harmony," " Counterpoint," and " Double Counterpoint and Canon " throughout this work refer to the preceding volumes of this series. Chap. /.) Introduction. J of the dominant. (See § 71.) The answer will in the first instance be given by whatever voice has the second entry, and the choice of this voice, as will be seen later, will largely depend on what voice first announces the subject. The answer is frequently an exact transposition of the subject; in this case it . is called a real answer ; and a fugue which contains a real answer is said to be a " real fugue." At other times the answer is a modified transposition of the subject, alterations being necessitated by the form of the subject itself. Such an answer is called a tonal answer ; and a fugue in which there is a tonal answer is called a "tonal fugue." The rules which enable us to decide whether an answer should be real or tonal will be fully discussed in Chapters III., IV. 10. The first voice, which announced the subject, should never be silent while the second voice is giving the answer. It always accompanies with a counterpoint, which may or may not be intended for subsequent use. If it be, it must be written in double counterpoint, so as to be able to accompany the subject or answer either above or below. A counterpoint which accompanies subject or answer systematically (though not of necessity invariably) is called a Countersubject. We sometimes meet with fugues which have more than one countersubject. 11. A fugue may be in any number of parts, but, whatever the number, they should all (with very rare exceptions) enter in turn at the commencement of the fugue with either the subject or the answer. That portion of the fugue which extends as far as the conclusion of the subject or answer (as the case may be) by the voice that last enters is called the Exposition of the Fugue 12. The exposition is usually followed by the first Episode. An episode is that part of the fugue in which for a while neither subject nor answer is heard. It is usually founded upon some material taken either from the subject or from one of the accompanying counterpoints, in order to give unity to the composition as a whole. The episode is also employed for the purposes of modulation, as will be seen when we come to treat of it later. 13. The close of the first episode is sometimes, though not always, followed by what is called a Counter-Exposition. This is a second exposition in the same two keys as the first, but with this difference, that the voices which before had the subject now usually have the answer, and vice versa. Sometimes the counter- exposition precedes the first episode, and follows the exposition immediately. Very frequently also it is only partial; that is to say, only some of the voices, and not all, take part in it. 14. The counter-exposition, if there be one, will generally be followed by a second episode, different from the first one. To this second episode (or to the first, if there be no counter- exposition) succeeds the Middle Section of the fugue. Here a 4 Fugue. [Chap. 1 much greater amount of freedom is allowed to the composer ; in fact there are hardly two fugues the middle sections of which are identical in their construction.- There are no restrictions in this section as to order, interval, or key of entry, though in the best models we mostly find that here the two principal keys (tonic and dominant) of the fugue, which have been almost exclusively employed during the exposition, are in general avoided, or only incidentally touched on. The entries of the subject in other than the chief keys of the movement are here also mostly divided by episodes 15. The Final Section of a fugue is that in which a return is made to the original key. Here the subject appears once at least ; very frequently the answer is also repeated. It is not uncommon, especially in vocal fugues, to find a Pedal point (Harmony, Chapter XX.) introduced toward the close of this final section. Sometimes there will be two pedal points ; in this case a dominant pedal will come first, and a tonic pedal at the conclusion of the piece. Pedal points are also occasionally, though much more rarely, to be met with in the middle section of a fugue. A good example will be seen in the fugue in F major, No. 1 1 of the second book of Bach's ' Wohltemperirtes Clavier.' 1 6. An important feature of many, though by no means of all, fugues, is what is known as a Stretto. This is an Italian word meaning " close," and is applied to that part of a fugue in which the entries of the subject and answer succeed one another more closely, that is, at a shorter distance of time, than in the first exposition. For instance, if the subject be four bars in length, the answer will, in all probability, enter at the fifth bar. If, now, in the subsequent developments of the fugue the subject is followed by the answer (or by the subject itself) in another voice at the fourth, third, or second bar instead of the fifth, so that the first entry, so to speak, overlaps the second, we have a stretto. A stretto may be merely for two voices, or all the voices of the fugue may take part in it in turn. Very frequently we find more than one stretto in the same fugue. In that case the interest of the music is not only maintained, but heightened by making each successive stretto closer than the preceding. 17. We sometimes find fugues in which a stretto is seen in the first exposition, that is to say, in which the answer enters before the completion of the subject, not infrequently immediately after its commencement. A fugue of this kind is called a Close Fugue. 18. The old theorists used to draw a distinction between strict and free fugues. A Strict Fugue was one which either contained no episodes at all, or in which the material of the episodes was entirely drawn from the subject or countersubject. Most of the fugues in Bach's * Wohltemperirtes Clavier ' belong chap i.j Introduction* 5 to this class. If the episodes were chiefly constructed on matter unconnected with the subject or countersubject, the fugue was said to be a Free Fugue. The fugue in Handel's overture to 1 Samson ' is an excellent example of a free fugue. 19. A strict fugue in which the various scientific devices, such as canonic imitation, augmentation, diminution, &c, were largely employed, was formerly known as a Ricercare, or Ricercata, that is a fugue with research. Two elaborate fugues, one for three and the other for six voices, in Bach's { Musikalisches Opfer ' are entitled "Ricercare." The name was also sometimes given to fugues without episodes. 20. We occasionally find fugues in which the answer, instead of being, as usual, a transposition of the subject (§ 9), is given by inversion, or by augmentation or diminution. We shall see examples of these as we proceed. Such fugues are called fugues by inversion, augmentation or diminution, as the case may be. 21. A fugue of only small dimensions, and not developed at any great length, is called a Fughetta — an Italian diminutive, meaning a little fugue. Many specimens of this kind are to be found in Bach's organ arrangements of chorals. A good example will also be seen in Beethoven's ' Thirty-three Variations on a waltz by Diabelli,' op. 120, at the twenty-fourth variation. 22. We very frequently meet with passages written in the fugal style, that is, in which a subject is announced in one part and imitated by the others, but in which the imitation is not at the regular intervals of reply of subject and answer. Such passages are called Fugato passages. A whole movement is sometimes written in this way; but more often fugato passages are introduced incidentally. The chorus " Their sound is gone out " in the ' Messiah ' is an example of fugato. 23. It must be clearly understood by the student that what has been said in this chapter is to be regarded only as a very general description. There is, probably, hardly any other form of composition in which there is so much room for variation of detail as the fugue. Beyond the fact that all fugues contain an exposition, a middle section, and a final section, there is little or nothing that they necessarily have in common. The one point to realize is, that a fugue should be, so to speak, an organic growth, the materials of which are to be developed mainly from the subject and its accompanying counterpoints. How this is to be effected we shall endeavour *to show in the following chapters, in which we shall deal in succession with the various portions of a fugue. Fugue. ichap. n. CHAPTER II. THE SUBJECT. 24. One of the most important points to be considered in the composition of a fugue is the choice of a good subject. It would be possible to write a fugue of some kind — or, to speak more correctly, a piece in fugal form, on almost any subject that might be selected ; but it is by no means every melody that is adapted for fugal treatment ; and it is no more possible to make a really good fugue on a bad subject than it would be to make a really good coat out of rotten cloth. In this chapter we shall endeavour to show what are the essentials of a good subject. 25. A Subject has been already denned (§ 8) as " the theme announced in the first instance by any one part or voice without harmony, on which the whole composition is founded." In the overwhelmingly large majority of cases this definition is correct : it is only in fugues with more than one subject, or in fugues with accompaniment, that the subject on its first announcement has any harmony. Many theorists speak of the countersubject (§ 10) as a second subject, and call a fugue with a regular counter- subject " a fugue with two subjects," or " a double fugue." In this volume we shall restrict the meaning of the word " subject " to that theme which is announced at the very commencement of the fugue, and speak of a " second " or " third " subject only when such accompanies the first subject before it has been answered in another voice. It is possible also for a second subject to appear later in the fugue, provided it has a separate "exposition" (§ 11) of its own, and is subsequently heard in combination with the first subject. 26. The first point to be considered in writing a fugue subject is clear tonality. This is a matter of the utmost importance, because if we are in any doubt as to our key, it may be very difficult, if not impossible, to give a correct answer, as will be seen in our next chapter. It is_ quite true that in many of the older fugues the tonality sounds vague and undecided ; but this is because they were written in the old church modes, about which, except as a matter of antiquarian curiosity, the student need not trouble himself. It is not necessary that a subject remain throughout in the same key ; but if a modulation is made it should be unmistakable, and there should in general be no difficulty in determining where it takes place. 27. It will greatly facilitate the student's labours in this respect if he accustoms himself, when inventing a subject, to think Chap. 11. The Subject. of the implied accompanying harmony. Every musical phrase that has any meaning at all must be capable of being harmonized, probably in several different ways ; and if from the first we think what harmonic progressions go best with the subject we have chosen, there will be little fear of our losing the distinct feeling of a key. 28. To illustrate our meaning we will give a few examples of simple subjects which remain in one key throughout — Handel. ' Messiah. (*) 111 1 egg j JTJj ! r r c LL^ Handel. 'Judas Maccabaeus. m If the student will examine these subjects, he will see that in both of them there can be no possible doubt about the key. Both begin with the notes of the tonic chord (the semiquaver C in (p) is only an ornamentation of the D) ; and both end with the descent from supertonic to tonic. The following example J. S. Bach. Wohltemperirtes Clavier, Fugue is somewhat different. Here the progression is by step from tonic to dominant, and if we look at the first bar alone, the tonality is a little less decided than in the examples from Handel But the prominence given to the dominant in the second bar fixes the key clearly, and the impression is strengthened by the subject ending on the mediant (E). 29. Our next example J. S. Bach. Wohltemperirtes Clavier, Fugue 31. g rpr f §H is perfectly clear. The key is fixed at once by the leap from tonic to dominant at the commencement ; for although the first note, E, might be the dominant of Aflat, it would be most unlikely to leap to the supertonic of that key; and if it were the subdominant in the key of B flat, it would be quite unprecedented for it to leap to the tonic. Besides this, we must always mentally supply the most natural harmonies to a subject. In this case, the first chord must of course be E flat ; the second will be either another position of E flat, or the chord of B flat — in either case strongly suggesting the key of Eflat; and the suggestion is changed into a certainty by the A flat immediately following. In general, if a fugue subject begins with an upward leap of a perfect fifth, or a downward one of a perfect fourth, the first note will be the tonic of the key, and the second the dominant ; if, on the 8 Fugue. [Chap, n other hand, it begins with an upward leap of a fourth, or a downward of a fifth, the first note will be the dominant and the second the tonic. There are occasional exceptions to this rule, as in the following example — Mozart. Mass in C, No. 12. Such exceptions are, however, extremely rare, and in these cases, the close of the subject, or the beginning of the answer, will always determine the key. In our example, if the subject began in A minor, it could not end with an implied modulation (§ 118) to G. This fugue, also, being on three subjects, the key is denned as C by the other subjects, which accompany the theme here quoted (see § 406). 30. Similar reasoning will apply to our next example — J. S. Bach. Wohltemperirtes Clavier, Fugue ax. If we try to think of the simplest and most natural harmonies to accompany this melody, we shall obtain something like this — mm S^FSt m ^ 8 7 8 7 Here the A natural and E flat in the second bar prove the key to be B flat ; for there is no other major key in which both these notes are found, unless one be a chromatic note ; and there is no suggestion of chromatic harmony in the subject, which is diatonic throughout. Our last example in a major key Beethoven. Mass in C requires little explanation. Though the leading note is not used, the feeling of the whole subject is decidedly that of the key of C, and not F. Compare the end of the subject with that of example (c) of § 28. 31. In a minor key we find the tonality equally clear, as will be seen from the following examples — J. S. Bach. Wohltemperirtes Clavier, Fugue 2. Chap. II.] The Subject. J. S Bach. Organ Fugue in C minor. At (a) the juxtaposition of the minor sixth and major seventh of the scale fixes the key at once. The same result is obtained at (I?) by following the arpeggio of the dominant seventh by that of the tonic chord (Harmony, § 241). At (c) we are in doubt till the third bar, though we feel that the key is C, whether the mode will be major or minor ; the A flat settles the question in favour of the latter. 32. In our next example Handel. ' Muzio Scevola. the key is fixed by the arpeggio of the tonic chord (compare example (b), § 30). (*) ^te r r r ggg Mozart. Requiem. i» t -r- m- Here the interval of the diminished fifth followed by B flat shows the key to be G minor. In our last example Mendelssohn. 'Elijah. gr-^ s r\ rJJ m q-^ the first three quavers of the second bar fix the key 33. Sometimes the subject, instead of being in the key of the tonic, is in that of the dominant throughout, as in the following instances — J. S. Bach. Cantata, " Ein ungefarbt Gemtithe." yi b(c) Handel. ' Samson. I 1 ^ =f— 1 f TT1 -1+41 — ^ — 1 — lA-j f 1 ^ • j ^J That we have here the key of the dominant is shown, not only by the signature of the movement, but also (as will be seen in the next chapter) by the interval at which the answer replies. Fugue. [Chap. II 34. A fugue subject often ends in a different key from that in which it begins. The case most frequently met with is that in which it begins in the tonic and ends in the dominant — ■ (a) Key : C. J. S. Bach. Cantata, " Ich hatte viel Bekiimmerniss." Key : G. @-'-.(* J " 1 J|*j*"' , |*- 1 y -\ — Though the leading note of the new key is not introduced here, the construction of the melody in the last two bars clearly indicates the key of G. This is further proved by the answer Bach gives to the subject. In the following examples T. S. Bach. Cantata, "Singet dem Herrn.' {b) Key : D. Key : A. fTTg CT*^ , U! (c) Key: F. -/m 1 g f* ' 1*- Kev • C Handel. ' Hercules. 1 1 » l U ' w a ££&— ' _j — . (rf) Key: El Schumann. Mass, Op. 147. Kev:Bb. m ^ p ^=& the leading note of the dominant key appears in the subject. 35. If the subject be in a minor key, it is very important to remember that the modulation must be to the dominant minor, and not to the dominant major key. J. S. Bach. ' Matthaus Passion.' {a) Key : A. minor. .^. — Key : E_mirior. Here, though the dominant chord of A minor is, of course, E major, the modulation is not made into that key, but into E minor. Our next example shows a chromatic note in a subject — Schumann. Fugue, Op. 72, No. 1. (b) Key : D minor. ^_^ |^ Key : A minor. In the second bar of this subject the G sharp, though the leading note of A minor, does not cause a modulation into that key, because it is preceded by B flat, and immediately afterwards contradicted by G natural. The modulation does not take place till the latter half of the fourth bar. Our last example Rubinstein. 'Paradise Lost.' Key : C minor. shows a chromatic note (F sharp) as an auxiliary note, and is therefore similar to the preceding. Chap. TT.| The Subject. i i 36. Less commonly we meet with subjects that begin in the key of the dominant and end in that of the tonic. Two examples will suffice — ir... .a J- S. Bach. Mass in B minor. Key - A - Key:D. .*_, ^- _-»- (»- „ (*) Key : C. fe -H-J4 ~Ch Key: F. (■ ^ r f Handel. * Rinaldo.' gr ( ' "i * ^ u> L — i =....Lj!- 1 — H ' r C£Ti > rl Lb ffL In the second of these subjects, the close looks at first as if it were in the key of C. That it is not so, is proved by the auxiliary note in the last bar being B flat, and not B natural. 37. It is also possible, though somewhat rare, for a subject to begin in the tonic, modulate to the dominant and return to the tonic, as in the following example- Key : E minor. J. S. Bach. Cantata, "Sehet, welch' eine Liebe. Key: B minor. ± X=£z Key : E minor. £nrr_rr j=eirr r t 0^ 38. Occasionally, instead of tonic and dominant, the two keys employed for the subject are tonic and subdominant. The following passages Handel. ' Alexander's Feast.' Key : G rnjnor. Key : D minor. (8) Key:G. &m Key : D. J. S. Bach. Mass in B minor. SW l^g » begin in the subdominant and end in the tonic. In our next examples Key : G. J - ^- Bach. Fugue in E minor. (c) Key : E minor. Key : A minor. ((f) Key : A minor. 5* Mendelssohn. 3rd Organ Sonata. Key : E minor. Key : D minor. the subject begins in the tonic and ends in the subdominant. In example (d) we also find an intermediate modulation to the dominant ; and in (c) to the relative major. Fugue. [Chap. II. 39. Quite exceptionally an entire subject is to be found in the Key of the subdominant — Handel. Jephtha. The key of the piece is D minor; but this subject is decidedly in G minor, the B natural being, as its subsequent treatment shows, the chromatic major third of the minor key. 40. In addition to the modulations already spoken of, we frequently meet with incidental modulations in the course of a subject which ends, as it began, in the key of the tonic. Of these the most usual are to the subdominant key for a major subject, and to the relative major for a minor subject — J. S. Bach. Cantata, " Wer Dank opfert." i% g ga 17^ m Mendelssohn. ' St. Paul. $*= *o=t In all these examples will be seen a short modulation to the key of the subdominant. 41. The same modulation is sometimes found with a subject in a minor key — Handel. ' Messiah. More frequently, however, the incidental modulation for a minor key is, as said above, into the key of the relative major — Bach. Organ Fugue in G minor. a M Handel. Anthem, " In the Lord put I my trust.' Chap. Il.l The Subject. »3 42. A good fugue subject should always (or at least with extremely rare exceptions) contain a complete musical ph?-ase. By the word " phrase " is here meant a passage containing some distinct idea, and terminating with a cadence of some kind (Counterpoint, Chapter XV.). It is not intended by this that there is actually to be a cadence introduced at the end of the subject, but only that the final notes of the subject shall be capable of being harmonized as a cadence — not necessarily a full cadence, though in a large majority of instances this is the case. If the student will examine all the subjects already quoted in this chapter, he will find this condition invariably fulfilled. In almost every instance the subject ends with either the root or third of tonic or dominant. In the rare cases where the subject ends in the subdominant (see § 38, (c), (d), the close will be made on the root or third of the tonic of that key. 43. In order to obtain a proper cadential effect, it is necessary in common lime that the subject should end on an accented note — either at the first or third beat of the bar (see for instance the examples in § 28). In this case, if the cadence is felt as occurring on the strong beat in the bar, a continuation of the harmony is sometimes added, as in § 31 (c). 44. The only exception to this rule in common time is, that the subject may end on an unaccented note, provided that the preceding accented note has the character of a suspension or an appoggiatura — J. S. Bach. Wohltemperirtes Clavier, Fugue 37. Here the end of the third bar suggests the chord of the dominant seventh ; it is resolved at the beginning of the fourth bar, where the B is clearly an appoggiatura. See also examples § 32 (b) and § 35 (b). 45. In triple time this rule does not apply, because here it is possible for the final chord of the cadence to come on the second beat (Counterpoint, § 484). As an example of this see § 34 (d). 46. It is impossible to give any definite rules as to the length of a fugue subject. In the works of the great masters we sometimes find them quite short, consisting in fact of only a few notes — J. S. Bach. Wohltemperirtes Clavier, Fugue 5. I J. S. Bach. Wohltemperirtes Clavier, Fugue 22. S$3f r-gf Mozart. Quartett in G, No. 14. I (c) ffzz: i4 Fugue [Chap. :i. At othei times they are of very considerable extent — / 7\ J. S. Bach. Toccata in C minor. , L n (■/) . ^ — » . — Beethoven. Quartett in C, Op. 59, No. 3. llll In long subjects such as these, we very often find sequential passages introduced. As a general rule, the slower the time, the fewer should be the bars in a fugue subject. It is important that the hearer should readily recognize the subject when it reappears, and this is much more easily done if it be concise than if it be long and straggling. Many of the finest fugues existing are those written on short subjects. It should be added that the length of the subject in vocal fugues will partly depend on the words, as the cadence should always come where the sense of the text allows it. Think, for example, how absurd it would be if the fugue subject at § 28 (a) ended with the words, " and he shall reign for ever and " — ! 47. Another important matter to be considered is the compass of the subject. In vocal fugues this should rarely exceed an octave, because if it does, it will be very likely when it appears in other keys to go beyond the comfortable range of the voices. Exceptions are occasionally to be met with, as, for instance, in our example (a) of § 40, which has the compass of a tenth \ but Lhese are rare. In instrumental fugues a larger compass is possible ; but even then it is seldom expedient, because of the probability of its causing much crossing of the parts, and so impairing the clearness of the fugue. Many of the best fugue subjects lie within a small compass. In two of the finest fugues of Bach's " Forty-Eight " (Nos. 4 and 33) the compass of the subject does not exceed a fourth. In the examples given above at § 32 (b) and § 34 (b) the compass is only a fifth ; while at § 28 (c\ § 30 (b) t and § 34 (c) it is only a sixth. Chap. 11.] The Subject. »S 48. Though there are limitations (§ 42) as to the note of the scale on which a fugue subject should end, there are none as to that on which it should begin. In an enormous majority of cases, the subject begins on either the tonic or dominant ; but numerous examples are to be met with of the employment of the other degrees of the scale for the initial note. We give a few instances of each — J. S. Bach. Cantata, " Der Himinel lacht." -* — ■ m * Mendelssohn. " Surrexit pastor," Op. 39, No. 3. 4- Subjects beginning on the supertonic are rather rare. Another example will be seen in Bach's fugue in B flat, No. 45 of the ' Wohltemperirtes Clavier.' Subjects beginning on the mediant are also not very often met with — ,<0 Beethoven. Mass in D. m u W) Cherubini. 4th Mass. m *=x J m r r r i g 49. The following subjects begin on the subdominant- Handel. Dettingen Anthem. 1 \ ^ ^ riANUKL. uemngen Anmem. ffi*« r 1 m m 1 r J J ■ * 1 r Schumann. Fugue, Op. 72, No. 3. j^jiJj-'^P^ 1 Id the two next examples the subject begins on the submediant- Bach. Organ Fugue in E flat (" St. Ann's "). T" m T' — m m m m- A commencement on the leading note is very rare. We have given one instance in § 44 ; we add another — Hummel. 1st Mass. This subject is further interesting from its containing an incidental modulation to the key of the relative minor, which »s somewhat unusual for a subject in a major key. it Fugue. [Chap. II 50. There are still two points of importance to be considered in the selection of a fugue subject. First, it must be contrapuntal in character, or at least adapted for contrapuntal treatment. There are many beautiful melodies which would be utterly unsuitable for fugue ; it is difficult to imagine fugues written, for example, on such subjects as the following — *t («) Beethoven. Symphony in D. >=a=? Beethoven. Sonata, Op. 2, No. 1. It is impossible to give any precise rules as to what constitutes a contrapuntal subject ; but the student who has properly studied counterpoint will feel it instinctively. One probable reason why the melodies just given are unsuitable is that they are too much cut up by "middle cadences" (Counterpoint, §§ 480, 505). Sometimes a cadence is met with in the middle of a subject, as in example (c) of § 41 ; but in general the subject should flow continuously, as is the case in the large majority of examples already quoted. 51. Though not indispensable, it is often advisable that the subject itself should be adapted for stretto ; that is, for imitation at less than the original distance (§ 16). This question will be fully dealt with later (Chapter VI II.). 52. The last point of importance to be mentioned is the necessity of distinct character in a fugue subject. A mere meaningless collection of notes, resembling a clumsy counter- point exercise, will never make a good fugue. The chief essentials in this respect are a clearly defined melody, and a well- marked rhythm. Such examples as those we have given in § 28 (a) (b\ § 34 (a), § 46 (a) (b) (c), illustrate the former; while in § 36 (a), § 41 (b), and § 46 (d) the melody and rhythm are of equal importance. As the invention of melody is impossible to teach, we must content ourselves with pointing out what is required, leaving it to the student's own imagination and skill to carry the principles here laid down into actual practice. 53. In analyzing a fugue, it is important to be able to deter- mine exactly where the subject ends. In exceptional cases there may be a doubt about this ; for instance, three different text- books give three different lengths for the subject of the C sharp major fugue in the second part of Bach's ' Wohltemperirtes Clavier.' In general, however, there is no difficulty. It has been already said (§ 42) that the subject should end with a cadence. If the subject begins with an accented note, the last note of the subject will usually (though not invariably) be that on which the answer enters In other cases, the subject Chap, it J The Subject. i 7 will generally end on a cadential figure either just before or just after the entrance of the answer. If in doubt we cap generally decide the question by seeing how much of the subject is imitated in the answer; this will be more clearly seen in the next chapter. In the case of a close fugue, where the answer enters before the subject is ended, the length of the subject will be generally decided by observing how much is imitated in the subsequently entering voices. 54. The student should now practise the invention of fugue subjects on the lines indicated in this chapter, bearing in mind the chief requirements which may be thus summarized: — (1) clearness of tonality; (2) distinctness of form; (3) moderate length and compass ; (4) good striking melody ; (5) contrapuntal character. He need not trouble himself much about originality ; all the best melodic and harmonic combinations for fugue subjects have been so frequently employed that novelty in the subject itself is now hardly possible. In modern fugues, originality (if it exists at all) is to be looked for in the treatment of the mater*als rather than in the materials themselves. (8 Fugue. [Chap. 111. CHAPTER III. THE ANSWER. 55. In our first chapter (§ 9) we defined the answer as " the transposition of the subject into the key of the perfect fourth or fifth above or below the key of the subject." It is most necessary that the student should know how to find the correct answer to any given subject ; unfortunately there is hardly any point on which the rules given in the older text-books differ so widely from the practice of the greatest composers. The rules to be given in the present chapter will therefore not be taken from existing treatises, but deduced from the works of the great masters themselves. 56. In by far the largest number of cases, the keys in which the subject and answer are found are the tonic and dominant. If the subject be in the tonic, the answer will be in the dominant ; if the subject be in the dominant, the answer will be in the tonic. If the subject begin in the tonic and modulate to the dominant, the answer will begin in the dominant and modulate to the tonic, and vice versa. Occasionally, however, as will be seen presently, the place of the dominant is taken by the subdominant. 57. The answer of a subject may be either real or tonal. It is said to be real when it is an exact transposition (with one possible exception, to be noticed in its proper place — see § 69) of the subject ; it is called tonal when certain alterations, the nature of which we shall explain later, have to be made in transposing it. («) mgm & g J. S. Bach. Wohltemperirtes Clavier, Fugue 33. ss. ,» — f± -Si . erf ■ S Mozart. Quartett in G, No. 14. In the above examples the subject is marked S and the answer A. At (a) the answer is real ; at (b) it is tonal, the interval of a third from G to B being answered by a second fiom D to E. Let the student also notice that at (a) the last note of the answer is longer than the last note of the subject. We shall meet witb Chap. III.) The Answer. '9 other instances of this common procedure as we advance ; it is always allowed either to lengthen or shorten the first or last note of the answer. 58. As being the easier, we shall first speak of real answers. The rule for knowing when a subject can have a real answer is very simple, and may be thus stated : — Every subject in which there is no modulation to the dominant, either expressed or implied,* may have a real answer, excepting, first, when it begins on the tonic and leaps to the dominant either direct or with the third of the scale as an intermediate note ; and secondly, when it begins on the dominant. But even in these two cases a real answer is always possible (§§ 101, 105-107). 59. We shall first give examples of real answers in the dominant key to subjects which are in the tonic throughout. We shall in each case give the counterpoint to the answer, which is, as will be seen, the continuation of the music by the voice which has just had the subject; we shall also extend our quotations beyond the end of the answer, as this will help the student in determining the limits of the subject. Our first example illustrates what was said in § 53 — that when the subject commences with an accented note, the answer usually enters on the last note of the subject — J. S. Bach. Wohltemperirtes Clavier, Fugue 15. zfcS — r-q*-^ — ^ **"l #m * - j--f <+F m ' h»j^ r *r r rrfTfri SB -» ** M «* W: p^p«_^ 1 r=rrr--i i ' i 1 U I'S' JJJJv-i^ -J~i -■HsM — **— — *-|--^ "^ ~f*~ g F g p ' T ' i T g r ~ ? m T * » r F — f~ ^ &c That the subject here ends on the F sharp of the fifth bar (the third of the dominant chord — § 42) is proved by the fact that the next note, G, is not imitated in the answer. In this example the answer is below the subject. * What is meant by an implied modulation will be seen when we come to speak of tonal answers (§ 118). 20 Fugue. 60. In our next examples (Chap. 111. / ga i&&t> 1 r -T-^- 3=» , g 1* — vi— -Till LaT r-r- §^— ■ , ■ A 5 / » \ *) the subject ends (as will be seen by comparing the answer) on the first note of the third bar, and the answer does not enter till the fourth. Such cases are of frequent occurrence. Here it would have been quite possible for Handel to have commenced his answer in the third bar ; thus — p I &c. but if the student will remember what was said in the last chapter about the implied harmony of a fugue subject, he will see that at the end of the second bar of this subject there is clearly a chord of the dominant seventh implied ; and the continuation we have suggested would have been far less satisfactory from a har- monic point of view. The passage introduced between the end of the subject and the beginning of the answer, which we have marked with a | ~| , is called a codetta. In many cases some such connecting portion is absolutely necessary. 63. The following example A Haydn. 4th Mass. # fff « a tad I U &c. shows a more chromatic subject than those already given. Here Fugue. [Chap, m the answer enters on the last note of the subject, because it begins on an accented beat. Our last example was an exception from this rule. 64. In our next example 1 Hummel. 1st Mass. A te=£ fcg *fz ggg 1 r m 1 r-^E-flvr i c^ 7 ^ £= we see a somewhat rare case. The first voice ceases for some time to accompany the answer. The quotation is the commence- ment of a fugue with independent orchestral accompaniment ; and the tenor, therefore, though the bass is silent, is not left entirely alone.* Such treatment is, however, exceptional ; and the student is not recommended to imitate it. 65. Our last example in a major key Mendelssohn. 2nd Organ Sonata. i fjM=a= w Wm Ji'-u'j j> j - j| i^r^ PFg shows the leading-note of the dominant treated as the third of the supertonic chromatic chord, and therefore inducing no modu- lation. It is consequently answered by C sharp, the third of the supertonic chromatic chord in the key of G. The last note of the subject, also, is here slightly altered in the answer, being delayed by a suspension. 66. We now give some answers to subjects in minor keys. These will always be in the minor of the dominant — never in the major. We have seen already (§ 35) that if a minor subject See § 441, where the complete exposition of this fugue is quoted. Chap. III.] The Answer. 23 modulates to the dominant, it is always to the dominant minor ; and the same rule holds good when the first modulation that is made is on the entrance of the answer. This will be seen from the two following examples — >) J. S. Bach. Wohltemperirtes Clavier, Fugue 4. A gggS S : F= 5 Bffiw rj [gJ EEp zm = r r ' * s ^ ^=tt g g* r r J ^ ^zt J. S. Bach. Wohltemperirtes Clavier, Fugue 20. 67. If the student will examine the various counterpoints accompanying the answers we have given, he will see that (like the answers themselves) they are in the key of the dominant. Were it otherwise, the feeling of tonality would be obscured, for the music would be in two keys at once. Occasionally, however, the harmony of the dominant key is not clearly defined till toward the end of the answer, as in the following example — J. S. Bach. Wohltemperirtes Clavier, Fugue 42. 24 Fugue. [Chap. III. :£:£=££: -r ■ t • i7~~T-g :x^c 'n C'lf pj.tr I p h-j ^5 &c. fej , / J 1 1^ 1 j i J jj Here the key of D sharp minor, the dominant of G sharp minor, is not reached till the third bar of the answer. 68. Our next example illustrates a point of considerable importance — J. S. Bach. Wohltemperirtes Clavier, Fugue 46. ta isa m *r- *^=£ Igj^JJ-". Jl^^ J k j i h -^ s [ ^■qj- Jjjir-j ,^j i-jj,^ 'I ffiUEP gj JZS+fr r -rJi& m^ Here the last note of the subject is D flat, the minor third of the tonic ; but the last note of the answer is not A flat, the minor third of the dominant, but A natural, the major third. 69. That this is by no means an isolated case will be seen by the following examples, taken from a much larger number that might be given — Mozart. Requiem. Chap. Ill j The Answer. 25 (pip ^~ ^m Ci.ementi. ' Gradus ad Parnassum, No. ?t t=t ■ •F= -^ < £-PC» « S Codetta. mm .Further illustrations of this point will be met with when we come to tonal fugues. The following rule is fully justified by the practice of the great masters : — Whenever a subject in a minor key ends on the third of the tonic, the answer may end on either the major or minor third of the dominant, as may be preferred. 70. If the subject be throughout in the key of the dominant, the answer will be in the key of the tonic- (*)s, J. S. Bach. Ouverture (Suite) in F. fH -1 1 rf m ]* a=xfc£zg I p g p ig— (rr) 1 - — ' ' ! 'mwiii ■■' J '. 1 1. 1. 1 1,, 1 *i &C. .S^SK^^^S^ <*> A — r~f- Handel. ' Samson. -r — r — m — r — i -f" — i- "M 1 ^ - =3= — r 1 , =j p m m J J^-Jr^r il 11 ^ j -1 — «- -f— - -*-r- =4= « • 1 1 1 1 1 It is important to notice that the answer is now a fourth above, or a fifth below, instead of being (as in previous cases) a fifth above, or a fourth below, the subject. 26 'UGUE. (Chan. III. 71. By an extension of this relation of subject and answer, we sometimes find that when the subject is in the tonic, the answer is in the subdominant, instead of the dominant — J. S. Bach. Cantata, " Der Himmel lacht. " (a)S Here the subject is in C, and the answer is no less clearly in F. The commencement of the answer illustrates what was said in § 57, the initial notes being lengthened — /i\ g J. S. Bach. Organ Fugue in C. efc^pgpgWg^r -pL-^jp Pg& rfr*r • wSL ~ ^ryj% jFff: n A — - iM 1 , LU m i.„i 1 „^, ±±^yj tss -rfam &c. r ^r 1* ^s y — ■g.-g* 1 i ad- -- — p^ — J — Here again the answer is in the subdominant. The alteration of the semitone near the end (B natural answering F natural) is frequently to be met with (§ 144) — if) Mendelssohn. " Surrexit pastorv m 9 *-*— - r^J JUj j jj7^^ » ^=^ &c. i m Here the answer is in the fourth above, instead of the fifth below. This fugue has an independent organ accompaniment (not quoted), which still more clearly proves the key of the answer to be C. 72. If we examine the three subjects last given, we shall see that in all of them prominence is given to the dominant or to Chap. III.] The Answer. 27 notes of the dominant harmony. The same thing will be found in our examples in a minor key, in which an answer in the subdominant is much more common than in a major key — „ J. S. Bach. Partita in B minor A Here the subject commences with the arpeggio of the dominant seventh ; then comes tonic harmony, and then dominant harmony again. The answer is now in the subdominant, in order to carry out the important principle that dominant harmony should be answered by tonic. 73. As the possibility of a fugal answer being in the key of the subdominant has not, so far as we know, been touched upon in any existing treatise, it will be needful to give a considerable number of examples by the greatest masters — not only to establish the fact, but to enable us to deduce the necessary rules for the student's guidance in deciding when such an answer is advisable. Our next example deserves close examination — J. S. Bach. Cantata, " Herr, Deine Augen. A Here the subject does not, like those previously given, begin with a note of the dominant chord ; but the diminished fifth immedi- ately following clearly indicates the chord of the dominant seventh. In the next bar is a modulation to the dominant key, the return to the tonic being made in the third bar 28 Fugue. [Chap. III. 74. Now let us examine the answer. The first note is C This cannot be regarded as a subdominant, because the tonic at the commencement of a subject cannot be answered by a subdominant. We have already seen that it is almost invariably answered by dominant — that is to say, by the tonic of the key in which the answer appears. The C here must therefore be considered not as the subdominant of G minor, but as the tonic of C minor. This choice of a key for the answer enables Bach to carry out the important general principle already mentioned, and of which we shall have more to say when we come to speak of tonal answers, that dominant harmony in the subject should be replied to by tonic harmony in the answer. Here we have the do?ninant seventh chord in G at the first bar of the subject, answered by the notes of the tonic seventh of G in the first bar of the answer. It would have been quite possible to give a real answer for this bar, beginning on the dominant ; but then the dominant harmony of the subject would have been answered by the supertonic harmony, instead of the tonic. 75. It will also be seen that at the second bar of the subject there is a modulation to the dominant key. Such a modulation is almost invariably answered by a return to the tonic key. Here, however, the tonic harmony in the answer is really the harmony of the dominant of C minor. Had the answer not been in the key of the subdominant, a tonal answer would have been necessary. 76. Our next illustrations, containing no modulation, J. S. Bach. Organ Fugue in D minor. > * , — P» — y , -u u |j ii* — 1* — m — r — ff m M , ,r>r »r-r 1 (' h 1 r 1 r — 1 .1 l — ' ' ■- L. Chap. Ill .1 The Answer. ** further show the answering of dominant harmony at the commencement of the subject by tonic harmony at the beginning of the answer. The two subjects are somewhat similar in character. 77. The same point is exemplified in the following — J. S. Bach. Art of Fugue, No. 10. f fgg u g r =g iw^ pt& st ■ m& r (g The subject here begins on the leading note. We shall see when we come to tonal answers that the leading note, excepting when it is merely an auxiliary note of the tonic, is almost invariably considered as the third of the dominant, and answered accordingly by the major third of the tonic (§ 131). This is the case here, and any other answer than that which Bach has given in the subdominant key, will either sacrifice this reply of tonic to dominant, or (if a tonal answer) distort the subject almost beyond recognition. It should be specially noticed that the ' Art of Fugue ' from which this example is taken, was expressly written by Bach for the purpose of showing the possibilities of fugal composition ; his giving an example of an answer in the sub- dominant key may therefore be fairly taken as proving, apart from all the other examples we have given, that he considered such an answer correct. 78. The last example we shall give from Bach J. S. Bach. Suite for Orchestra, in D. is similar in character, and even more pronounced. The subject, except the last note, is formed entirely of dominant harmony, 3° Fugue. [Chap. 111. which is therefore answered by corresponding tonic harmony. The counterpoint accompanying the answer conclusively proves the key of the answer to be G. 79. We now add a few examples, by other composers, of rea) answers in the subdominant key — Handel. ' Solomon. Beethoven. Quartett, Op. 131 P Sfr r jJ*J p ^ J^g g g 1 — ^ — n — 1 ^-] =££& ■' — 1 ' &c. r 9 (c) -^Hp i-*v- Schumann. -1 - T ughetta, Op. 126, No. 2. A , | ^\) P w M- : u V ' Codetta. s 1 J_ 1 1 1 1 n■ • z In this case the relationship of the two keys is evidently the same as that of tonic and dominant. 82. If the subject begin in the key of the subdominant and modulate to the tonic, the answer will begin m the key of the tonic and modulate to the dominant — Handel. 'Alexander's Feast.' The subject here ends on the first crotchet of the third bar. It begins in G minor and modulates in the second bar to D minor. The answer begins in D minor and modulates to A minor. The proof that the subject commences in G minor is found in the first note of the answer. If Handel had regarded A as the dominant of D minor, instead of the supertonic of G minor, he would have answered it, according to the laws of tonal fugue, by D and not E. S3. Intermediate modulations (except to the key of the dominant) should be imitated exactly in the answer — (M^f Iandel. ' Semele.' fl5!- / i$ — 1 : ~z~. | — : z s r "l*~ 1* ^m ■ St (& : L>.(k 1 1 1 r T -£- 3E —0 *- -r- — l f— 1 i V 1 1 — ' — 1 r— ! 4=1= -1 — 1 r-e> \ W=t t=± m -0—r- g t=3 =f r r?0r 3* Fugue [Cha P . in J. S. Bach. Organ Fugue, in A minor. (pi In the second bar of the major subject at (a) is seen a modulation to the subdominant, imitated at the same point of the answer; and in the third bar of the minor subject at (b) a modulation to the relative major, replied to by a similar modula- tion to the relative major (G major) of the dominant. 84. In order to understand what is meant by a tonal answer, we must remember that each of the old Ecclesiastical scales, out of which our modern scales were developed, had two " modes," one of which was a fourth below the other, but contained the same notes. If the scale was from final to final (or, as we should now say, from tonic to tonic), and the dominant was in the middle, the mode was said to be authentic, if, on the other hand, the scale was from dominant to dominant, with the final in the middle, the mode was called plagal. Each scale was divided into two unequal halves by the dominant or the final. Let us take, for example, the old Dorian mode — Authentic. $ Plagal. ■&- •=>" The dominant in the authentic mode and the final in the plagal are marked in this example. It will be seen that the lower half of the authentic scale has the compass of a fifth, and the upper half the compass of a fourth ; while the plagal scale has a fourth for the lower half, and a fifth for the upper. 85. The old rule for fugal answer was that a subject made in Chap III.] The Answer. 33 either half of the authentic scale should be answered in the corresponding half of the plagal scale, and vice versd. For instance, if the subject began with the leap between tonic and dominant, in the lower half of the authentic scale, i w the answer would begin with the leap between dominant and tonic, i these being the corresponding lowest and highest notes of the lower half of the plagal scale ; and conversely, if the subject began in the lower half of the plagal scale, with the leap up from dominant to tonic, or down from tonic to dominant, the answer would begin in the lower half of the authentic scale with the leap up from tonic to dominant, or down from dominant to tonic. 86. The rule to be found in nearly every work on fugue respecting tonal answer is, that if a subject leaps from tonic to dominant, either direct or through the third of the tonic, the answer must be tonal — that is to say, the tonic must be answered by the dominant, and the dominant by the tonic. This is a good rule enough, if it were only observed ; but, as we shall proceed to show, the great masters, from Bach and Handel downwards, " drive a coach and four through it " continually. If we wish to conform to their practice, we shall have to modify this rule very considerably. 87. Evidently the first thing to be done is, to find out what the practice of the great masters really was in this respect. For this purpose a large number of quotations will be necessary. It may be at once admitted that in the majority of instances they conformed to the old rule ; but quite enough examples will be found in which it is broken to show that they did not regard it as one of the laws of the Medes and Persians. In the examples now to be given, we shall no longer add the counterpoint that accompanies the subject, because the student will by this time have learnt how to find out where the subject ends ; instead of this, we shall put the answer under the subject, in order that the two may be more easily compared. 88. We first give examples in which the old rule is strictly followed. Of these there are plenty. a J. S. Bach. Wohltemperirtes Clavier, Fugue 31 ■m- This specimen of a simple tonal answer illustrates more than one point of some importance. The subject is here in the tonic ; the 34 Fugue [Chap. III. answer will therefore be in the key of the ck minant ; and, except the first note of the second bar, every note of the subject be- longing to the key of E flat must be answered by the corres- ponding note of the key of B flat. It must be especially noticed that though the note B flat (the dominant of E flat) is used four times in the course of the subject, it is answered every time except the first by F, and not by the tonic, E flat. The rule of answering tonic by dominant, and dominant by tonic, applies only to the beginning of a subject and to passages where a modulation to the dominant occurs. In the present case the claims of the law are satisfied as soon as E-B at the beginning of a subject has been answered by B-E ; after this, the rest of the subject is transposed,, as if the answer were real, into the key of the dominant. The following notes of the subject are respectively the subdominant, mediant, submediant, and dominant of E flat ; and they are answered by the subdominant, mediant, submediant, and dominant of B flat — and so on, to the end of the answer. There is no mistake which students are more apt to make in beginning to write tonal answers than to answer dominant by tonic every time these notes occur. This is almost invariably wrong. 89. If we look at the second bar of the above example, we shall find that an interval of a second in the subject has become a unison in the answer. Whenever a subject begins with the leap from tonic to dominant, it always, if answered tonally, causes a change in the following interval. Here the first and third notes of the subject are the tonic and subdominant of the tonic key ; the first and third notes of the answer are the tonic and sub- dominant of the dominant key : but the difference in the size of the first leap of the subject (a fifth), as compared with the leap of a fourth in the answer, makes a difference also in the interval between the second and third notes. We give two more illus- trations of the same point — J. S. Bach. Wohltemperirtes Clavier, Fugue 17. ,(*)S At (a) a third in the subject becomes a second in the answer ; at (b) a second in the subject becomes a third in the answer. Note. Chap. III.) The Answer. 3.5 in passing, the shortening of the last note of the answer at (*)-(§ 57). 90. That the answering of tonic by dominant, and dominant by tonic, applies only to the beginning of the subject is clearly shown by the examples of real answers quoted in § 59 and § 83 (&), both of which contain the leap from tonic to dominant in the second bar, not answered by the leap from dominant to tonic. 91. Though the general practice of the great masters is, as has been already said, to answer the leap between tonic and dominant tonally, a real answer under such circumstances is not infrequent, especially when the leap is downwards— (*)S J. S. Bach. Organ Fugue in G mi Handel. ' Susanna m $ ^^ J ri i r j r*rrr 1EE (P^V r^ [— f 51 - pi Handel. * SauL \— w^= & . pp= -f*~ 1 r r r 1*' P" jEJ f=*= IFh-Sj V -1 1 — 1 1 ■ 1 r -*-J Handel. Violin Sonata in A. 1*- | P- j^^ a=* / h W s Schumann. Mass in C minor. /( \y , >| ^ ^, If b A 1 &c. (v l>: ^ — sH — — S Hummel. 3rd Mass. These are parallel cases to those given in §§ 94-99. In all of them the subject begins with tonic harmony and the answer replies with dominant harmony. Notice in example (/) an incidental modulation to the key of the supertonic minor. The imitation is here exact (§ 83). 44 Fugue. [Chap TTI. 106. We next give instances in which the leap from dominant to tonic is not followed by another note of the tonic chord — Handel. Utrecht Te Deum. .(«) S f)flt ws Handel. Anthem, " O come let us ULl IS 1 r : * 32: A m m 3^ (c)S Beethoven. Mass in D. ,ff r-l!"T C J m *=& (d)3 SE m Beethoven. ' Mount of Olives.' g dtp rrTr i r S ll a i ps £ ^ The answer at (*) looks irregular ; but there is here an implied modulation (§ 118). The subject after the second note is regarded as being in the dominant key, and therefore answered by the corresponding notes of the tonic key. 107. Lastly we give examples in which the dominant is followed by some other note than the tonic — g J. S. Bach. Cantata, "Gottes Zeit ist die allerbeste Zeit." Chap III.] ,(3)S The Answer. J. S. Bach. Fugue for Clavier, in A. 45 Handel. Anthem, " Have merc y upon me, God. tfti W J J- 3 J.j I J a &c. J ffi ^ J j-^J .Jl ^^ (/)S ho... Mendelssohn. 95th Psalm. teflKJ i r r p r r Up- - r 1 f ^ I A I I p fe^FFg -r p ^ S x=t » • P ■ Q F^H ^bn 1 F ■ — P |P r - f p^e= * • * 1 jg _pr _ 1 1- — \— f r nl 9 1 F — ' 1 — \ 1 j We have only to note with regard to these examples that in the first bar of (b) is a not uncommon case, G sharp being answered not by D sharp but by D natural. Such disregard of the exact quality of intervals is not infrequent; we shall meet with more instances later. At the end of (/) the subject modulates to the dominant \ the answer here is exceptional, and will be discussed in our next chapter. 4<> Fugue. [ChaD. Ill 1 08. We have given quite enough examples to prove that the rule as to answering dominant by tonic at the commencement of a subject is by no means so " absolute " as it is declared to be by many theorists. For this there are two reasons. First there is the general principle already referred to in § 100, that tonic harmony in the subject should be replied to by dominant harmony in the answer. This is illustrated by the examples in §§ 105, 106. Besides this, the melodic form of the subject should be kept unchanged as far as possible; and it is quite evident that in many cases the great composers felt this to be of much more importance than the keeping of an old rule which was made before modern tonality was established. 109. A further proof that but little weight was attached to the necessity for a tonal answer is found in the fact that sometimes in the first exposition of a fugue the first answer will be tonal and the second real, as in the following case — ' M BM. 3=3= e J. S. Bach. Organ Fugue in A. &c. I A A 1. *=4=* 3^ £ &c. m A 2. f & r- m ■&c Here the first answer is tonal, the first note being shortened (§57)> but the second answer (still forming part of the ex- position, in which strictness is expected) is real. In the later entries of a subject, we continually meet with real answers where tonal have been given at first. no. We saw in § 104 a subject which, except the first note, was in the key of the dominant, the answer being in the key of the tonic. We have also seen, in discussing real answers, how an extension of the same relation of subject and answer rendered an answer sometimes possible in the subdominant key (§ 71). A similar answer is also possible where the first note of the subject is answered tonally, as in the following examples — J. S. Bach. Cantata, " Es ist euch gut dass ich hingche." Chap. III.] The Answer. 47 Buxtehude. Organ Fugue in G minor. /-fM, W£ V ■/ b^-p > m p m m — 1 J3TJ J;- p j^-J-J- Jjr^i ■'* " A ^P-L- hJJJJ 1 J J * J * jJ* J'J J-^J,jJ ' J- In example (a) we have quoted the counterpoint accompanying the answer, to prove more clearly that the latter is in the sub- dominant key. The two examples by Buxtehude are very similar in the character of their subjects. In all these subjects the prominence given to dominant harmony, which we have already mentioned as a feature of all subjects which are answered in the subdominant, will again be noticed. in. Sometimes in the exposition of a fugue the first answer is in the key of the dominant, and the second in that of the subdominant, as in the following passages — (a) J. S. Bach. Cantata, " Es wartet Alles auf Dich. <*) s Schumann. 'Neujahrslied. gyr-r-g-r-ry L r I : L a* Lfi * rff^ Al. a rr^r m i» %»■ i — r ftt i r ^ 5E?E ft* a-*£g- ^^^^^^ r^JT^ H5 ^g=ES ii2. The proper method of answering subjects that modulate into the key of the dominant will be treated in the next chapter. We now sum up our conclusions with regard to the subjects we have already dealt with. From a careful investigation of the practice of the greatest composers, we deduce the following principle : — Though frequently expedient, and even preferable, a tonal answer is never absolutely necessary for any subject which does not modulate between the keys of the tonic and dominant* * A merely incidental modulation to the dominant (as in the example to § 73) does not necessitate a tonal answer. 48 Fugue. [Chap. in. 113. In concluding this chapter it is needful to give the student a most urgent warning with regard to the use of this book. It is not written as a " cram " for examinations ; and although all the rules given in the present chapter are founded upon the practice of the great masters and enforced by their example, yet in the present condition of musical examinations, any student who attempts to carry into practice the principles here given will almost inevitably be "ploughed." The old theorists mostly follow one another blindly, like a flock of sheep through a hedge; and examiners in general adhere to the musty rules of two hundred years ago, taking little or no account of the progress made by music since that time. The old rules have therefore been in all cases given in this chapter, and those who are going up for examination had better adhere to them until examiners become more enlightened and liberal. Our object in this, as in the other volumes of this series, has been to found our teaching on the practice of the great composers who have brought our art to its present state of advancement ; but Bach himself breaks far too many of the antiquated rules to have had much chance of passing, had he gone up for a Doctor's degree at one of our universities. on»p. iv. ) The Answer. 49 CHAPTER IV. 1HE ANSWER — CONTINUED. 114. In our last chapter we showed that a tonal answer, though often advisable, was never absolutely necessary for any subject which did not modulate to the key of the dominant. We have now to deal with the treatment of the answer to subjects in which such a modulation occurs. 115. In order to render intelligible the principles on which we shall have to proceed, it is needful here to anticipate some- what, and to say that in the exposition (§ 11) of a fugue, only two principal keys are employed— mostly tonic and dominant, occasionally tonic and subdominant. In an enormous majority of cases the keys will be tonic and dominant. We saw in the last chapter that if the subject were in the key of the tonic, and remained in it, the answer would be and remain in the key ot the dominant. The third voice will almost invariably enter with the subject, and the fourth, if there be four, with the answer. In such cases the answer will generally be real, or if there be any tonal alteration, it will only affect the first two or three notes of the subject. 116. But now suppose that instead of ending, as it begins, in the tonic key, the subject modulates to and finishes in the dominant, as in the case given at § 57 (b). It is quite clear that if we give a real answer in this case, the answer will end in the dominant of the dominant, that is, in the key of the supertonic — p S Here we have not only introduced a third principal key, where, as was said in the last paragraph, there ought only to be two ; but (what is still more objectionable) we have modulated to an unrelated key (Harmony > § 273). To get back to the tonic key for the entry of the third voice, we shall have to introduce an awkward and probably clumsy join by means of a codetta. In order not to wander away into an unrelated key, and to confine ourselves to the two chief keys already mentioned, which will always be at a distance of a fifth apart, we require a tonal answer here, and adhere to the old rule. This is : — If the subject begin in the tonic, and modulate to the dominant, the answer must begin in the dominant and modulate to the tonic. 5° Fugue. fChap. »v. 117. This important rule needs to be supplemented by another: — The modulation in the answer from dominant back to tonic must be made at the same point at which the modulation was made in the subject from tonic to dominant. This rule will be fully illustrated as we proceed. 118. The modulation in a fugue subject may be either expressed or implied. It is expressed when the leading note of the dominant key appears as a note of the subject, as in example, §57 (&)• It i s implied when, although the leading note of the new key is not actually present, the whole form of the melody, and especially its last notes, show more or less distinctly that they are looked at as belonging to the key of the dominant, and when they produce the mental effect of being in that key. 119. The examples now to be given will show what is meant by implied modulation — J. S. Bach. Cantata, " Ich hatte viel Bektlminerniss." <*) wT r ' g m g p^- g m . V) J. S. Bach. Cantata, " Gotl ist mein I 1 | I — ^—\ — K.onig." IUI ic) J. S. Bt — V, __ iCH. Cantata, ' Ein' feste Burg. " Handel. ' Saul. It will be seen that in all these passages the mental impression of the last notes is unmistakably that of a modulation to the dominant ; and it may be stated as a general rule that, whenever a subject ends with the descent from the submediant to the dominant of the tonic key, a modulation is implied, and these two notes are considered to be the supertonic and tonic of the dominant key. 120. Sometimes the great composers choose to consider a modulation as implied when there is no absolute necessity for it — J. S. Bach. Organ Fugue in C. Here we see from the answer given by Bach that he implies a modulation in the second bar, though a real answer would have been perfectly correct. Had he regarded E as the third of C t he Chap. IV.] The Answer. 5» would have answered it by B, the third of G ; but he regards it as the sixth of G, and therefore answers it by A, the sixth of C. When a subject modulates to the key of the dominant, all that part which is in the tonic key is transposed in the answer a fifth higher, or a fourth lower ; and that part which is in the key of the dominant is transposed a fourth higher, or a fifth lower. 1.2 1. The next question is, when there is a modulation, at what point are we to consider it as taking place ? The general practice of the great composers is to regard the modulation as being made at the earliest possible pointy and from that point to consider every note in its relation to the new key. 122. That the student may quite clearly understand what is meant by this, we will take all the notes in the scale of C major, and show how each can be correctly answered in two ways, according to the point of view from which it is looked at. Sup- posing our fugue to be in the key of C, and that a modulation to the dominant occurs in the subject, the answer to each note will depend on whether that note comes before or after the modulation : — C, if regarded as tonic of C, will be answered by G ; but if regarded as the subdominant of G, it will be answered by F, the subdominant of C. D, as the supertonic of C, will be answered by A, the supertonic of G ; but D, as the dominant of G, will be answered by G, the dominant of C. Similarly E, as the third of C is answered by B, the third of G ; but if considered as the sixth of G (as in the example in § 120), it will be answered by A, the sixth of C. F, the subdominant of C, is answered by C ; but, as the minor seventh of G, it will be answered by B flat. G is answered by D when it appears as a dominant, and by C when it is treated as a tonic. A as a submediant is answered by E, and as a supertonic by D. B, the leading note of C, is answered by F sharp ; but if the context shows it to be the major third of G, it will be answered by E, the major third of C. 123. If the student clearly understands this possible double relation of every note it will save him an infinity of trouble in making a correct tonal answer. We will now analyze a few short examples illustrating the principle just laid down that the modu- lation should be considered as taking place as early as possible. 124. As an extremely simple example, we will first take the short passage by Mozart, already quoted in § 57 — Mozart. Quartett in G, No. 14. i ti=§E £ 52 Fugue, [Chap. IV. Here there is in the subject a distinct modulation to D ; the answer therefore modulates back to G. B, the second note of the subject, could have been answered either by F sharp or E ; but had Mozart answered it by F sharp, the resemblance of answer to subject would have been spoilt — There would, besides, have been another fault of almost more importance. The subject has a distinct modulation to the dominant; the last three notes unquestionably suggest the key of D. The answer therefore should as clearly suggest G ; but in its altered form it does not do so at all, as the first four notes all belong to the tonic chord of D. Neither shall we improve matters by putting B for the third note of the answer instead of A ; for then the answer will not distinctly suggest any key at all, the first four notes now being notes of the tonic chord of B minor. There is, therefore, no other correct answer than that which Mozart gives, and, having reached the dominant key at the second note, he regards all the rest of the subject as being in that key, and accordingly treats E as supertonic of D — not as submediant of G — and answers it by A, and not by B. The last two notes of the subject, of course, admit of only one answer. 125. After our full analysis of this example, few words will be needed in explanation of the following, which illustrate the same point — . \ a Handel. ' Israel in Egypt.' i p r r 1 r nr r I r r m IS s 1 r * r 1 r r r 1 r r «f 32: w J S. Bach. Matthaus Passion. . -r * * — „ At (a) the C in the subject is regarded as sixth of E minor, and answered by F; and at (h) G sharp is considered not as the leading note of A minor, but as the chromatic major third of the dominant, and it is accordingly answered by the major third of the tonic. 126. The reason why the tonal change Ts made as early as oossible is because in this way a closer general resemblance of the Chap. I V.J The Answer. 53 answer to the subject is obtained than \i the modulation be regarded as taking place later. Sometimes, however, the form of the subject does not admit of an early change — J. S. Bach. Toccata and Fugue for Organ, In C. ( S" 1 .J J J J J*3 • ■- - p, , |V f ' tf"| j j 1 ^- 1 — f* 1*1 J (a) _J*JJ s-^-J- i*f rr i* 1 ! *i»- 1 ni n #'•.„.« m l*» , ¥ 'LeLI UJ ' The first notes of this subject were spoken of in § 93. It is impossible here to regard the modulation as taking place till after the subdominant harmony at (a). The length and variety of this subject render it a very suitable illustration of the rules we gave in § T22. The student will here see nearly every note of the scale of C in both its relations ; we have even at (b) the rare case of the subdominant considered as the minor seventh of the dominant. 127. It is very important to be able to tell when answering a subject that modulates, in which of its two possible aspects any note is to be regarded. The only notes with which any difficulty is likely to be found are the third and the seventh of the tonic, which are also the sixth and third of the dominant. An examina- tion of the fugues of the great masters will guide us in laying down definite rules for the treatment of both these notes. 128. As we have to regard every note in its relation to the new key as early as possible, the third should be considered as the sixth of the dominant, and answered by the sixth of the tonic, as in our examples to §§ 120, 124, and 125 (a), excepting, 1st, when it comes between other notes of the tonic chord, or is followed immediately by the tonic; and 2nd, when the subsequent appearance of the subdominant in the subject shows that the modulation cannot yet have taken place. The following passage shows the third in both aspects — J. S. Bach. Cantata, " Lobe den Herren, den machtigen Konig. flttd s 4» - r m0~P~mP- r* m *.0 m \ mm m ^ fm [•", i -j ;! '1 >5LT ' fa pr 1 A -*- (*; m m * m* JBj f. s— fc H i— ^— V The F's in the second bar of the subject prevent our regarding it as in the key of G ; but at (a) the change is made at the earliest 54 Fugue. Chap. rv. opportunity. The first E, being the resolution of the F in the preceding bar (the chord being the dominant seventh), must of course be the third of the tonic, and must be answered by B ; the second E is treated as the submediant of G, and answered by the submediant of C — viz., A. 129. We give a few more illustrations of the same point. («) s J. S. Bach. Cantata, " Gott ist mein Konig. ' Here the second note of the subject is regarded as the sixth of the dominant, and all the rest is plain sailing. V) S Mozart. Mass in F, No. 6. Here the presence of the subdominant prevents our regarding the subject as being in the dominant key till we reach (a), where the third of the scale is treated as sixth of dominant, and answered accordingly. There is an i?nplied modulation (§ 118) in the subject, for it is very rare to find a subject ending on the leading note. It is almost invariably regarded (as here) as the third of the dominant key. 130. In our next example Handel. Concerto Grosso in C tr the change is not made at the earliest possible moment (in the first bar), for this would have disfigured the subject too much. The mental effect of the music is distinctly that of the key of C, till we come to (a) where the double significance of the third of the scale is very clearly shown. The 6rst E, being followed by Chap. IV.] The Answer. 55 C, is the third of the tonic, and is answered by the third of the dominant ; the second E is not followed by a note of the tonic chord, and is therefore regarded as sixth of the dominant. Our next example (fi\ S J* ^" Bach. Cantata, " Singet dem Herrn ein neues Lied. **=^ Sao illustrates a different point. The first F in the third bar cannot be regarded as belonging to the dominant key, because of the G natural that follows, neither can the second which resolves the preceding G ; but the F preceding the G sharp is treated as the submediant of A. 131. The same principles will guide us in dealing with the leading note. Let the fundamental principle be thoroughly grasped that the tonal change must be made as soon as possible, and the whole thing is easy. If a subject modulates, the leading note must be always treated as the third of the dominant, and answered by third of tonic, except \* T hen it is merely an auxiliary note of the tonic to which it at once returns, e.g. — J. S. Bach. Wohltemperirtes Clavier Fugue 2. (tNFt — F^ j g| g S^-aa" L* La ^ , »fo 9-f&£ ^ V S ■ -g s^j u = This subject does not modulate, but it shows the use of the leading note as an auxiliary note. 132. The following examples («)S J. S. Bach. Organ Fugue in C. J. S. Bach. Wohltemperirtes Clavier, Fugue 18. / (3) s -r» f l» 1 *i» r OjtL _ A , Jg3 Jl J fJ^J^^ -• -m ] - J- J- *-*- -md- 5<5 Fugue. (c)S m^rnr m l Chap. IV. Naumann. ist Mass. rrTTir ts T=t show the leading note very early in the subject treated as the third of the dominant, and answered by third of tonic. The following notes of the subject are all answered as belonging to the dominant key. 133. So strongly is the leading note felt as the third of the dominant that it is not seldom answered by the third of the tonic, even when there is no modulation — J. S. Bach. Wohltemperirtes Clavier, Fugue 19. Here Bach treats the second and third notes of his subject as the third and sixth of E, and answers them by third and sixth of A, though the subject ends in the key of the tonic. In our next example Macfarren. ' The Resurrection.' (*) S_ _ .«. a» wm i m m g the second bar is treated as containing a modulation to the key of E, the leading note being answered by the third of the tonic. 134. If the subject begin in the dominant, and modulate to the tonic, the process will be reversed. We shall now, as soon as possible, consider the sixth of the dominant as the third of the tonic, and the third of the dominant as the seventh of the tonic, g BUXTEHUDE. The first half of this subject is in A; in the second bar it modulates to D ; and F, the sixth of A, is therefore at once regarded as the third of the tonic. 135. Our next example shows the third of the dominant in both its aspects. Cha D . I V.J S 1S^ ^_h^2_ The Answer 57 KlRNBERGER. ?=^fc= («) i^5* g rjTJl^ 7 " Let it be noticed that this subject might have been considered as in the key of B flat throughout ; it would then have taken a real answer. Kirnberger has preferred to regard it as in F until the last two bars. The tonal change might have been made after the B flat in the fifth bar ; but this would have altered the form of the subject needlessly. The point, to illustrate which this passage is quoted, is the treatment of the A in the penultimate bar. It is first regarded as third of dominant, and answered by D, and then looked at as leading note of B flat, and answered by E natural. We saw in § 88 how two notes in the subject were answered by the same note; here is the converse — the same note in the subject has two different notes in the answer. 136. The answering of one note by two is sometimes to be met with in the case of the dominant and supertonic, as in the following passage — o J. S. Bach. Fugue for Clavier, in A. Here the supertonic at (a) is first answered by the supertonic of E, and then treated as dominant of E, and answered by dominant of A. Evidently had it been so regarded the first time, it would have utterly spoilt the answer. 137. Sometimes the dominant is answered first by tonic and then by supertonic, even when there is no modulation. ^ f \ g Handel. Anthem, " I will magnify thee. 58 Fugue. TChap iv t 58. If a subject begins in the tonic, modulates to dominant, and returns to tonic, the answer makes the converse modula- tions — from dominant to tonic, and back to dominant. No new principles are involved here ; two examples will be sufficient. i \ g J. S. Bach. Cantata, " Sehet, welch eine Liebe. <« s jll j J 1 j h is 1 r E. Prout. 2nd Organ Concerto. l^^i^H \ 1 1 1 j ^ ^n^^ 139. In general, any leaps of a dissonant interval, such as a seventh, especially of an augmented or diminished interval, should be reproduced exactly in a tonal answer. The student will find illustrations of this in several of the examples already given. At § 93 (c) and § 126 will be seen a diminished fifth; at § 125 (b) a diminished fourth; and at § 132 {b) an augmented fourth, all of which are retained in the answers. We add one example of a diminished seventh — J. S. Bach. Wohltemperirtes Clavier, Fugue 44. f This subject also contains a diminished fifth which is retained in the answer. Chan. IV.] The Answer. 59 140. There is, however, one important exception to the rule just given. When one of the two notes forming the dissonant interval is the tonic or dominant, and the modulation is made at that point (sometimes even when no modulation is made), a leap of a dissonant interval in the subject will often become a leap of a consonance in the answer, and vice versa. We give some examples — (a) KlRNBERGER. SLdfe m &c. m ^m ±m ^ 321 Here both the B and A of the subject are answered by E, on the principle explained in § 88. Our next example shows the converse case — an octave in the subject becoming a seventh in the answer — / fljflg s d ~ 1* — P i> J - g ! r** — r~F~f — -CUTS BE {GER. ) n\ & A («)_ i^fe=g gJ Here there is an implied modulation, and the change to the dominant key is assumed as early as possible (§ 121). Obviously it cannot be before the third bar at (a). The first G is treated as third of tonic, and the second as sixth of dominant (§ 128). 141. In our example (a) of § no, we see a seventh in the subject becoming a sixth in the answer. The following interest- ing passage illustrates both the rule and the exception that we art now discussing — , s . »- f r . — L , * *f -f t* f bF KlRNBERGER. rV b r r- 1 ^ A • — (• — • — r~bi . r *r if-ij^-PTp- Mh£*3 r 1 — 1 — 1 — 1 J H [ 1 'i i y ^^ The tonal change at the beginning of the answer alters the seventh into a sixth, but the claims of the tonal answer having been satisfied in the first bar, the augmented and diminished intervals in the second and third bars are exactly imitated. 6o Fugue. [Cbap. IV 142. In the following passages we see an augmented fourth in the subject becoming a major third in the answer. j. S. Bach. Cantata, " Ihr werdet weinen und heulen. MR J^j^T- ■ r ' 1 — m — , g \u* A -»■ ~V g-gf » m m , pfca-^ — \ " " Notice that here the augmented second and the minor seventh in the second bar are retained in the answer, and the change of interval comes where the modulation takes place. Albrechtsberger. This is a similar instance to the last. The form of the melody renders it impossible to introduce the modulation earlier. (c)S Mozart. Mass in C, No. 4. This is a curious example, because Mozart by the way he answers the subject implies three modulations — to the dominant and back in bar 2, and again to the dominant at the end. It would have been simpler to treat the first F sharp, which is almost imme- diately contradicted, as a chromatic note, and to have given the answer the following form — which would have been equally correct here (compare § 65). 143. Our next example shows the converse case, a major third in the subject becoming an augmented fourth in the answer. Albrechtsberger. m _#_, m — *— m~ Chap. IV. The Answer. 61 This passage illustrates the partiality of fugue writers for treating the third of the tonic as the sixth of the dominant, and the leading note as the third of the dominant. There is no necessity for a tonal change till (a), and the answer might have been j^TTT^Z g ^ I Jfl JS]S J7J^ Here we have another example of what we have already seen more than once, that it is sometimes possible for a subject to have two different answers, both correct. The student will learn by experience, in such cases, which is the better. 144. Though, as a general rule, the transposition of the subject a perfect fourth or fifth should be strictly carried out, we often find the position of the semitones disregarded, a semi- tone being answered by a tone, and a tone by a semitone. This is especially the case with the subdominant and leading note, as will be seen by the following passages, selected from a much larger number we had marked for quotation — J. S. Bach. Fughetta on " Allein Gott in der Hoh sei Ehr . <*> s (*)S J. S. Bach. Mass in B minor. i — A !=#= p .-!■ — 1 — 1 f— i 1 r 1 r if =s= l \ -I £=t= _J — l_J 1 — 1 148. Our last illustration of this point is instructive. J. S. Bach. Wohltemperirtes Clavier, Fugue 10. Notice, in passing, the minor third at the end of the subject answered by a major third (§ 69). We see here the only example in all Bach's works of a real answer given to a subject that closes in the key of the dominant ; but here it can be not only explained but justified. We have already spoken (§ 139) of the importance of retaining augmented and diminished intervals as far as possible in the answer. Had Bach given a tonal answer here, he would have had to sacrifice the diminished fifth in the second bar, and the harmonic framework of the bar would have been entirely changed. But there is a further reason here. We said, in § 116, that a tonal answer was required when the subject modulated to the dominant, in order to get back to the tonic for the entry of the third voice. But the fugue we are now discussing is for two parts only ; and after the first entry of the answer, the exposition (§ 11) is complete, and we reach the first episode, where, as we shall see later, modulation usually begins. There is, therefore, here no occasion to return to the tonic key. The same reason may probably explain the putting the second answer into the key of the subdominant, noticed in § in. Students should always keep to the regular rule, and answer a subject modulating to the dominant by a return to the tonic. 64 Fugue. [Chap. IV 149. Chromatic subjects usually take real answers, unless there be a modulation expressed or implied. J. S. Bach. Toccata in F sharp minor. %* tH gjj*g t_ r i»«n? J m^T^ /m a J» S. Bach. Fugue for Clavier, in E flat. WS # H- b- , ^-^_ m A - ff *- ^m- m^ *=t ws Mozart. Mass in C minor. i 1 g j j b jLj-j a j jj 1 j. g ^ j g^jjj,; W x=± =6* J 1 J I 1 J At (£) the leap of a fifth is answered tonally, but the chromatic passage itself is exactly repeated. The answer is in the sub- dominant (§ 71.) At (c) other notes occur between the chromatic notes. 150. Sometimes a composer has chosen to consider a modula- tion implied where there is no real necessity for it. Mozart. Quartett in D minor, No. 13. Here a real answer, as at § 149 (a), would have been much more usual, and (with all respect to Mozart, be it said) much better. The threefold repetition of D spoils the form of the answer. 151. If there be a modulation before the chromatic notes are introduced, such notes must be considered as belonging to the new key, and answered accordingly — Handel. 'Jephtha,' Chap. IV.] I^he Answer. 65 KlRNBERGER. j| J I J I 1 J flTJ-iphn>TJ~l=a 152. Fugue subjects are sometimes answered by inversion. In this case the answer is not generally in the key of the dominant; but that species of inversion is used in which dominant is answered by tonic, and tonic by dominant (Doubk Counterpoint^ §§ 281, 282). Sometimes the answer by inversion ifc given in the first exposition, as in Bach's ' Art of Fugue,' No. 5 — J. S. Bach. Art of Fugue, No. 5. 4- More frequently, however, this device is reserved for the .ater developments of the fugue, in order to heighten the interest, as in Nos. 15, 20, and 46, of the ' Wohltemperirtes Clavier.' An answer by inversion is much more common with a minor subject than with a major. 153. We also sometimes find answers by augmentation and diminution. In these again there is no need that the answer should be in the dominant key. The object of putting the answer in the dominant is to prevent its being a mere monotonous repetition of the subject ; and this end is sufficiently attained either by inversion or by altering the lengths of the notes. In Nos. 6 and 7 of the ' Art of Fugue ' will be seen examples, too long to quote here, of answers by augmentation and diminution. 154. Sometimes, especially in vocal fugues, in order to keep the answer in a more convenient compass, the change of an octave in pitch is made in the course of the answer, as in the following passage — Schumann. Requiem. A similar example, which is familiar to everybody, will be found in the "Amen" chorus of the 'Messiah' 6f Fugue. [Chap. IV. 155. It is often said that there are no rules without excep tions; and in the works of all the great masters we occasionally find fugue answers which cannot be explained on any of the principles laid down in this chapter. As our last illustrations, we give one specimen by each of the greatest composers, of an irregular fugue answer. If the student has mastered the contents of this chapter, no notes will be needed ; he will see at once wherein the irregularity consists. («>s J. S. Bach. Fugue for Clavier, in A minor. <*) S Handel. ' Choice of Hercules.' Key : C minor. ws Beethoven. Mass in C H J r r 1 r • r i r \ \ tr i^= ffzrzr=3: f A/)S Weber. Mass in E flat. The Answer. t>7 Mendelssohn. Fugue in E minor. j( U /I* p M "iT* Schumann. Fugue, Op. 72, No. 2. A V " /fib dt z — i ^ ** £ .f J_J — J C — J J^J -— j p =5— 1 — F f» - IS ^L-* — 1 ' 1 ^dnijj The only remarks required by these examples are that (£) has an independent orchestral accompaniment, the harmony clearly proving — what does not appear from the quotation itself — that the subject ends in C minor, and the answer in F major ; and that (ti) may possibly be considered an extreme instance of the disregard of semitones spoken of in §§ 144, 145. 156. We have now arrived at the end of a very long and difficult task — that of explaining the principles of fugal answer. The rules here given differ widely in some respects from those generally laid down ; but not one new rule has been advanced which we have not justified by the example of the greatest composers. We shall now, by way of summary, endeavour to put the general principles into the fewest possible words. I. The answer to a subject which is in the key of the tonic should be as a rule in the key of the dominant ; but if dominant harmony is prominent in the subject, the answer may occasionally be in the subdominant. II. A real answer is possible for any subject which begins and ends in the key of the tonic without modulating to the dominant ; but if the subject begins with a leap between tonic and dominant or commences on the dominant, a tonal answer is mostly preferable. III. If the subject modulate between the keys of the tonic and dominant, the answer should make the converse modulations between dominant and tonic. IV. A modulation should always be made as early as possible. In a modulation from tonic to dominant consider the 68 Fugue. [Chap, nr third and seventh of the tonic as sixth and third of dominant as soon as the modulation can be considered as having taken place, and answer them accordingly. 157. These few sentences embody all the fundamental principles of a fugal answer ; the less important details have been dealt with in this and the preceding chapter. The student who has thoroughly understood the rules here given will have but little difficulty in answering any fugue subject that may be set him, unless (as is sometimes the case in examinations) a bad and unsuitable subject is given as a " catch." In such cases, he must trust to his luck ; we have seen subjects in examination papers to which a good answer was absolutely impossible. 158. We conclude this chapter with giving a number of fugue subjects, original and selected, for the student to answer. We also, as a useful exercise, give a few answers to which he is to find the subjects. This will of course be the converse process. If the answer ends in the key of the tonic, the subject must have ended in the key of the dominant, and vice versa ; if the answer begins with the dominant, the subject most probably began with the tonic. First ascertain in what key the answer ends, and if there has been a modulation, make that modulation as early as possible in the subject. The rules for the treatment of the third and seventh of the tonic (§§ 128-133) will be of considerable assistance in this matter. Exercises. (1.) Find the answers to the following subjects — .(in.) f^m sm m m mf \ mlfJ ^H m (IV.) i (VI.) £9 iHH w=^ (VII.) I> — B r »r W=m warn -m£-m- ES *a=F (X.) (XI.) It (f^JMeH-g^ f^t tiL qr[\ Jm (XII.) (XIII.) 'fr-j- J -F-Rj J g r iT^Mf i J J r*r^ g (XIV.) * 4 b r s E ffr+r-g ■J-l ^J -T JEiJE (XVII.) * m ^^ i i (XIX.) ^-^f-r-rf- g r i r r r fif c r~r~nr 4— [ -i — i — r (XX.) w&mm (XXI.) (XXII.) * Subjects marked with an asterisk can have more than one correct answer. 7« FlTGUH. [(.■hap. IV. (XXIV.) (XXVI.) i m& m,r* \ .rr L^l^-j JJ l[j' l r i i£r (XXVII.) "- J I J i j J JTjI j i j ' ttJ j (XXVIII.) * 4 (XIX.) * (2.) Find the subjects of which the following are the answers — (I -prr II.) 1 — H j — t k- /r (I v -> p v * r— trg : ± ■ * ff r — ]•■ *^ (V.) (VI.) (VII.) '-3 s^ bJ — sJ — ' The Answer. »"-JJJ a JJNJ a J^B (XI.) (XII.) Note. — The greater part of these answers are taken from fugues by Bach. All the more elaborate and difficult ones are from his works ; and the trouble involved in finding the proper subjects will be well repaid. 7 2 Fugue. [Chap, v CHAPTER V. THE COUNTERSUBJECT. 159. In our first chapter (§ 10), we defined a Countersubject as " a counterpoint which accompanies answer or subject systematically, though not of necessity invariably." We have now to consider the essentials of a good countersubject, and to endeavour to show when its introduction into a fugue is advisable. 160. The first and most important requisite for a counter- subject is, that as it has to accompany either the subject or the answer in whatever part these may appear, it must be written in double counterpoint with the answer, as an accompaniment to which it is first heard. The double counterpoint is, in by far the largest number of cases, in the octave, but it is also sometimes in the tenth or twelfth. Sometimes a countersubject which has been used in the octave at first is subsequently employed in one of the other intervals. In Double Counterpoint will be seen in § 163 an example of a countersubject used both in the octave and in the tenth j and at § 175 of the same book a similar instance of the octave and the twelfth. 161. A most important point in writing a countersubject is individuality of melodic character, and contrast of rhythm as compared with the subject (Double Counterpoint, § 129). This will be best illustrated by examples, which we shall mostly take from Bach's ' Wohltemperirtes Clavier,' as being a work accessible to everybody. 162. In our first examples && yw r J. S. Bach. Wohltemperirtes Clavier, Fugue 2. ' J/'jb - — ?*f-f p fe g Mgj , m $0 fJ Q.b cs — -4- J — F= ->. H — ' — 1 ^ H •'•fj^, ■"- *J ■ tt* 1 w * L ^-h« Chap. V.] ffcft^ The Counters ubject. 73 J. S. Bach. Wohltemperirtes Clavier, Fugue 37. $Szp= gfT r f fT^ gyyur the countersubject (CS.) is mostly in longer notes than the subject, though at the beginning of (a) contrast is secured by accompanying the quavers of the subject by semiquavers. Let the student play the countersubjects by themselves, and notice how different they are from the subjects, and at the same time how thoroughly suited to them in character. 163. Our next illustration shows the opposite case — J. S. Bach. Wohltemperirtes Clavier, Fugue 44. A $ **■ e f f r r r»r r r r r m ■'Mii—>niiiLi-m '— ■ U. jCOtCT Here the countersubject does not enter with the first note of the answer ; but between it and the subject are a few notes of codetta (§ 62). This often happens ; sometimes, as will be seen presently, only a part of the subject or answer is accompanied by the countersubject. In the above passage we see a subject in long notes accompanied by a countersubject of very short notes. 164. On its first appearance, in company with the answer, the countersubject should be in the same key as the answer. In the example last given the answer is in E minor, and the counter- subject is no less distinctly in the same key. Sometimes, however, as in our example to § 67, the key of the answer is not clearly defined by the counterpoint until nearly the close. 74 Fugue. [Chap. v. 165. It was said in the last chapter (§ 115) that the third voice in a fugue almost invariably entered with the subject. In the very common case in which the subject is in the key of the tonic throughout, the answer will be in the key of the dominant. In order to return speedily to the tonic key, and to allow the third voice to enter at once, we often find in such cases that at the end of the countersubject the leading note of the dominant key is flattened, becoming the subdominant of the tonic key. J. S. Bach. Wohltemperirtes Clavier, Fugue 33. Here the subject ends in E ; the answer and countersubject are in B. To enable the third voice to enter immediately, a return is made to the key of E at the end of the third bar, by contradicting the A sharp. Where this is not done, it is mostly necessary (as will be seen in the next chapter) to introduce a codetta before the entry of the third voice. The evasion of a full cadence in the dominant key by the device just explained is frequently called by its Italian name, inganno, i.e., "deception" — a deceptive cadence. 166. Sometimes the countersubject is constructed of material suggested by the subject itself, as in the following passage. J. S. Bach. Wohltemperirtes Clavier, Fugue 18. A (y J * j * _j _j j j Here the figure of the subject W^f^ 1 furnishes the chief idea for the countersubject. More frequently, howevei, the counter- Chap V. The Countersubject. 75 subject contains an entirely fresh idea, as in the examples previously quoted. 167. It is in general desirable that the countersubject should contain some distinct melodic or rhythmic idea, which may be used later for codetta or episode. A particularly fine example of this will be seen in the twelfth fugue of the 'Wohltemperirtes Clavier.' J. S. Bach. Wohltemperirtes Clavier, Fugue 12. Notice here the strongly marked contrast between the subject and the countersubject. This fugue contains altogether six episodes (bars 16-19, 22-27, 3°"34, 37-4°, 43"47> and 5°~53)» a11 of which are founded on the first six notes of the countersubject — 1 68. Not infrequently the countersubject accompanies only a part, and not the whole of the subject or answer. J. S. Bach. Wohltemperirtes Clavier, Fugue 34. ^EE 7 6 Fugue. [Chap, v That the countersubject has only the limited extent nere marked for it, is proved by the fact that the rest of the counterpoint does not systematically reappear later in the fugue as an accompaniment to the subject or answer (see § 298, where the whole fugue is given in score and analyzed). 169. In tonal fugues that modulate to the dominant, the entry of the countersubject is often deferred till after the modulation has taken place. This allows the countersubject to appear without alteration against either subject or answer. Wohltemperirtes Clavier, Fugue 24. ttf&F — =r-^ — 1 *=* 9-*- ZSZ -m 1 — (S> P "t* r fg TJJb ! fj* 1 -1 @*F ■fLf^ * -f J This subject is quoted in some text-books as a particularly difficult one to answer. There is, however, no real difficulty here, if we remember our rule (§ 121), that the modulation must be regarded as taking place as soon as possible. Here it cannot be till after the fourth quaver, because G natural does not belong to the scale of F sharp minor \ but from the fifth note of the subject all is regarded in its relation to F sharp minor, and answered exactly by the corresponding notes in relation to B minor, and the whole countersubject is distinctly in the latter key. Notice the curious, and doubtless accidental, resemblance of this countersubject to that of the fugue in E minor, quoted in § 168. Chap. V. The Countersubject. 11 170. If, on the other hand, the countersubject begins before the modulation has taken place, it will often need modification similar to that of a tonal answer, according to whether it is accompanying the subject or the answer. J. S. Bach. Wohltemperirtes Clavier, Fugue 7. CS ~v ^ -<•- ^ ■ 1 / _J T' i* -i»- «• / 1 D — ft 9 m _,, g m r — 1 f f r j i r j L | A- 1 — p55=i 1 g—fl V t 1 J .«[ * *7j. ' At (#) the countersubject accompanies the answer; at (b) it accompanies the subject itself, and the third from C to E becomes a second from A to G. This is because the third in the answer, between F and D, was only a second (between B and A natural) in the subject. The change in the countersubject must be made, like that in the answer, at the point of modulation. Sometimes, also the countersubject is somewhat altered, even with a real answer, as in the fugue in E, referred to in § 165 (see the extract given later in § 269). 171. It may be as well to remind students that, as the countersubject is first heard against the answer only, it must not make with the answer any intervals which would not be allowed in free two-part counterpoint. The laws regulating the employ- ment of these intervals will be found in Double Counterpoint, Chapter V. 172. Though, as a general rule, the countersubject makes its first appearance as an accompaniment to the answer in the exposition, we not infrequently meet with fugues in which its first appearance is deferred. The great fugue in C sharp minor (No. 4 of the ' Wohltemperirtes Clavier ') is an example of this kind. We have already quoted the subject and answer in § 66. The counterpoint against the answer seen in that example accompanies also the entry of the third voice, but not those of the 7« Fugue. [Chap. v. fourth and fifth, nor is it subsequently used at all. We cannot therefore consider it a countersubject. But at the 35th bar a genuine countersubject makes its appearance ia) cs J. S. Bach. Wohltemperirtes Clavier, Fugue 4. This countersubject accompanies every subsequent entry of the subject till the coda of the fugue. At the 49th bar a second countersubject is introduced — i fcS (*)S m :*?=£ 3=£§ P CS2. ' i j j 1 j ,^ Both countersubjects are worked together with the subject in triple counterpoint. Another fine example of two countersubjects introduced late in the fugue will be found in the 38th fugue (in F sharp minor) of the same work. 173. A remarkable example of a fugue with two regular countersubjects, both of which appear in the first exposition, is seen in No. 21 of the 'Wohltemperirtes Clavier.' We quote the commencement of the fugue, writing it in open score, that the separate parts may be more clearly followed — J. S. Bach. Wohltemperirtes Clavier, Fugue 21 ffiS Kt m ^ r^ ^pff |" | Codetta. cs 1. T«rjr-k A ■ Bt«* f ^» — T- \ fcBrb — 5 r r r Lrl^^^ s^-b 1 1 Chap. V.l The Countersubject. 70 -< r> i cs2.- p gp r r r r I gp r r g r 1 \ \ * gpl CSl. Here the first countersubject accompanies the answer ; when the third voice enters with the subject, the alto, which has just completed the answer, takes up the first countersubject, while the treble continues with a second countersubject. Every subsequent entry of the subject or answer down to the end of the fugue is accompanied by both the countersubjects. 174. A different method of employing two countersubjects will be seen in the 47th fugue (in B major) of the same work. The first appearance of the answer is accompanied by a counter- subject. J. S. Bach. Wohltemperirtes Clavier, Fugue 47. (#**F ^ 1 1 -fp 1 — 1 P ft 8 B- =* ^ L gg sgi a — p =f= -r-p- Bpf= ^-fTi p^ \iy..j.jii -&- ■^ 1 U This is regularly introduced against subject and answer throughout the whole of the exposition, after which it is heard no more. Its place is taken on the next entry of the subject by an entirely new countersubject, written in double counterpoint in the twelfth, and invariably inverted in that interval. We gave it as an illustration of this species of counterpoint in § 171 of Double Counterpoint, to which the student is referred. It is very rare to find two different countersubjects used, not simultaneously, but as here, successively. 8o Fugue. tchap. v 175. Some theorists speak of a fugue with a regular counter- subject as u a fugue with two subjects," or "a double fugue." It is best, however, not to apply this name to fugues such as those we have been speaking of, unless the countersubject, as is sometimes the case, does not appear in the first exposition, but has later an independent exposition of its own, and is not at first used as an accompaniment to the subject, with which it is not combined till its own separate exposition is completed. We shall treat of fugues of this kind, as well as of the other variety of double fugue, in which the second subject first appears not against the answer (as in the examples here given), but against the first subject, later in this volume (Chapter XL). 176. It is by no means necessary that every fugue should have a regular countersubject. Of the forty-eight fugues in the ' Wohltemperirtes Clavier ' there are seventeen which have none ; and the question naturally arises, When it is desirable to write a countersubject to a fugue, and when can it be suitably dispensed with ? It is impossible to lay down a hard and fast rule on the matter ; but a careful examination of those fugues which have no countersubject shows that, in a large majority of cases, it is unnecessary, if the subject is intended to be elaborately combined with itself. The exact meaning of this will be better understood when we come to speak of the middle section of a fugue, and of stretto ; but one or two illustrations will help to make the matter clearer. In fugues Nos. 1, 22, 26, 29, and 31, we find no countersubject, because the subject itself is so largely treated in stretto (§ 16) that a countersubject would only have been in the way. In fugues 8 and 20, the subject is treated by inversion and in canon, and in No. 27 extensive use is made of inversion and diminution. On the whole it may be said that, when there is no countersubject, we mostly find the more scientific devices of fugue writing applied to the subject itself. This, however, must rot be taken for more than an attempt at generalization. There is no form of composition in which there is so much liberty of treatment and variety of detail as that of fugue. 177. The student should now compose countersubjects to all the fugue subjects given at the end of Chapter IV. He should try to write at least two or three, differing in character, to each subject. For this purpose he should write the subject on one staff, following it on a second by the answer, above or below which, according to its position, he should write his countersubject as the continuation of the subject. He may always introduce a short codetta, if necessary, between the end of the subject and the beginning of the countersubject, but it is best not to leave a rest between the two. The first voice should go on continuously to the end of the countersubject.* * We occasionally find exceptions to this sound general principle, e.g. , in Nos. 16 and 30 of the ' Forty-Eight ' in both of which the entry of the countersubject is preceded by a rest, probably to cali attention to it more strongly. We shall see later that a rest is generally advisable before the re-entry of the subject. Chap, vi] The Exposition. 8, CHAPTER VI. THE EXPOSITION AND COUNTER-EXPOSITION. 178. If the student clearly understands how to answer a fugue subject, and how to write a good countersubject against the answer, he will be ready to commence the next stage of his work — the composition of a complete exposition of a fugue. By the exposition, as mentioned in Chapter I. (§ 11), is meant that part of the fugue during which the voices make their first entries in succession, and which extends as far as the conclusion of the subject or answer (as the case may be) by the voice that enters last. If the student has mastered the preceding chapters of this volume, and has had sufficient practice in counterpoint to be able to add free parts to two parts that are in double counterpoint with one another (Double Counterpoint, Chapter VII.), he will find that the tasks now before him will offer him but little difficulty. 179. The first question to be considered is the order in which the different voices should enter in the exposition. The subject may in the first instance be announced by any voice, but the order of the subsequent entries will largely depend upon what voice has led. 180. In order to understand this clearly, it is needful to bear in mind the fact that the answer should always be at a distance of a fourth or fifth above or below the subject. It is also necessary to remember that the compass of the alto voice is about a fourth below that of the treble; that the tenor is an octave below the treble, and the bass an octave below the alto. We are speaking here of vocal music ; but the parts in an instrumental fugue are mostly treated pretty much as if they were voice parts. For the purposes of fugal answer, we group the voices in pairs, the higher pair being the treble and tenor, and the lower the alto and bass. If the student remembers the directions for transposing a given subject which are given in Counterpoint, § 53, he will be aware that a subject given in the treble must be transposed a fourth or fifth low/er for the alto, an octave lower for the tenor, and an eleventh or twelfth lower for the bass. 181. If we apply this principle to the matter now undei consideration, we shall see that a subject announced by one of the higher pair of voices should be answered by one of the lower pair, and vice versa. This is the usual practice of fugue 82 Fugue. iChap. n writers, though occasional exceptions, with which we need not now concern ourselves, are to be met with. 182. Our next question is, By which voice of the other pair (supposing the fugue to be for four voices) should the answer be given ? If, for instance, the treble leads with the subject, should the alto or the bass have the answer ? It is seldom difficult to decide this point, if we remember that it is generally best, for the last entry in the exposition to be in an outer, rather than in a middle voice. The reason for this is that it is easier to distinguish the subject or answer when it is in an outer part, especially in fugues with four or five voices. In three-part fugues, owing to the thinner harmony, an entry in a middle part can be more clearly heard. In the forty-eight fugues of Bach's ' Wohltemperif tes Clavier,' the last entry is in an outer part in no fewer than forty- two — seven out of every eight. 183. In a two-part fugue, the exposition will be a very simple matter. One of the voices (it is indifferent which) leads with the subject; the other follows with the answer, which the leading voice accompanies with the counterpoint or countersubject, as the case may be, and the exposition is complete. 184. In a three-part fugue, the operation is somewhat longer. If one of the outer parts has the subject, the middle part usually has the answer, and the remaining outer part has the subject again. If the middle part commences, the answer may be equally well in either of the outer parts — it is quite immaterial which. Occasionally we find one outer part leading, and the other outer part following, the middle voice being the last to enter. This, however, is rare ; out of twenty-six three-part fugues in the ' Wohltemperirtes Clavier' there are only two (Nos. 27 and 28) in which this method is adopted. 185. While the second entering voice gives the answer, the first continues with the countersubject, supposing there to be one ; on the entry of the third voice with the subject, the second voice, which has just concluded the answer, continues with the countersubject, as the first voice did before. The counter- subject, which previously accompanied the answer, must now be transposed a fourth or a fifth to serve as a counterpoint to the subject. It may also, in the case of a tonal fugue require some modification (§ 170). Meanwhile, the leading voice, having now completed the countersubject, adds a fresh counterpoint, which may also be a second countersubject in this case the subject and the two countersubjects must be written in triple counterpoint. If the third part be a free part (as is mostly the case), triple counterpoint is not necessary. 186. Here the exposition of a three-part fugue may end; but, for a reason now to be shown, it is often continued a little further. It was said in the last chapter (§ 160) that a counter- subject should be written in double counterpoint to the subject, so as to be able to be used both above and below it. But Chap. VI.] The Exposition. «3 whenever a subject is announced by an outer part, and the other voices enter in regular ascending or descending order, a moment's thought will show the student that the countersubject, if given (as is best) to the voice which has just completed the subject or answer, will always occupy the same relative position to the subject or answer. If the treble leads, the countersubject will always be above \ and if the bass leads, it will always be below. In such cases, in order to show the countersubject during the exposition in both its aspects, as an upper and lower counterpoint, we frequently find one additional entry of subject or answer by the voice that flist led, while the last entering voice has the countersubject. If the middle voice leads, it is evident that we shall have the countersubject in both positions without this additional entry, as it will be below the upper part and above the lower one. In such a case, as also when there is no regular countersubject, the additional entry is not needed. What has been said in this paragraph applies equally, under the same circumstances, to fugues with more than three voices. 187. To illustrate the matter now under notice, look at the example given in § 173. Here is an exposition of a three-part fugue, which, as it stands, might be considered quite complete. Before proceeding, however, to the first episode (see Chapter VII.) Bach introduces the answer in the treble (the voice which first led) in order to. let the first countersubject (which has hitherto only been heard above the subject) appear below it in the bass — the voice which has just finished the subject. 188. Very frequently in the exposition of a fugue we meet with a codetta (§62) either before the first entry of the answer, or between the answer and the second entry of the subject. We must now show when such a codetta is expedient, and when it is necessary. 189. Before the first entry of the answer a codetta will be necessary in the following cases. First, if the subject begin on the tonic with an accented note (e.g., on the first beat of a bar), and also end on the tonic, and the answer be below, it is clear that, as the answer will begin on the dominant, this note being a fourth below the tonic, cannot be sounded as a harmony note against it in two-part counterpoint. (*)S- Here it would be very bad to introduce the answer against the last note of the subject; it will be necessary to add a short codetta, (6) S ; — ; 1 Codetta. thus deferring the entry of the answer till the following b? 8 4 Fugue. [Chap. VI 190. Another case in which a codetta is needed before the answer enters, is when the subject begins on an unaccented note near the end of a bar, and ends on an accented note at the begin- ning of a bar. J. S. Bach. Wohltemperirtes Clavier, Fugue 36. "1 Codetta. 191. A codetta is also sometimes introduced before the answer to avoid the collision of tonic and dominant harmony. J. S. Bach. Wohltemperirtes Clavier, Fugue 7. Z2 Here the implied harmony of the first half of the second bar is clearly that of a full cadence in the dominant. If we introduce the answer on the last note of the subject j'"^i - r ' n \^ &c. the effect, as everyone will feel, is simply atrocious. 192. We much more frequently find a codetta between the answer and the second entry of the subject. The reason in many cases is the same as that spoken of in our last paragraph — to avoid the collision of tonic and dominant harmony. If the subject begins and ends with a note of the tonic chord, such a codetta will mostly be desirable. J. S. Bach. Wohltemperirtes Clavier, Fugue 8. The student will see at once that if the third voice enters here on the last note of the answer, there will be the same unpleasant effect as in example (b) of our last paragraph. Bach therefore inserts two bars of codetta before the entry of the next voice. 193. If the subject begins with the tonic and ends on the third or fifth of the tonic, a codetta is generally necessary, as the Chap. VI.) The Exposition. 85 last note of the answer will be the third or fifth of the dominant, against both of which the tonic is a dissonance. J. S. Each. Wohltemperirtes Clavier, Fugue 22. J. S. Bach. Wohltemperirtes Clavier, Fugue 17. 1 In both these examples the answer ends with the tonic chord of the dominant key ; and of this chord the original tonic forms no part. 194. We will now write an exposition of a fugue in three parts, taking a very simple and straightforward subject, and adding a regular countersubject. m r r ->JlLrr ^^ at tar Here the bass treats the last part of the subject sequentially, while the figure of counterpoint propounded by the alto is Chap. VII.] Episode. 95 freely imitated by the treble in contrary motion. It must be noticed that, though the fugue is for four voices, both the episodes are in three parts. This is very common in four-part fugues ; it would be bad for all the voices to be continually at work throughout. Three-part, and even two-part, harmony is often met with, especially in the episodes, furnishing relief and contrast. In the four-part fugue in F minor (No. 12 of the same work), five out of the six episodes are for three voices only. 220. In our next example the episodes are formed from the countersubject. The subject and countersubject of the fugue are the following — J. S. Bach. Wohltemperirtes Clavier, Fugue 14. We have quoted the. codetta preceding the entry of the third voice, because (as we shall see directly) it is used at the beginning of the first episode, though it does not appear in the others. 221. This fugue contains three short episodes. (*) ag ^^TO^ ^^ 9 6 Fugue. [Chap. VII. The first bar of (a) consists of the codetta, with the addition of a middle part ; the rest of it, as will be seen, is made out of the first notes of the countersubject. At {b) the same theme is seen in the bass, with free upper parts ; while at (c) it is treated sequentially, the outer parts which move in tenths imitating the inner parts moving in thirds. Here again, though the fugue is for four voices, two out of the three episodes are in only three parts. 222. In § 191 we gave the subject of the seventh fugue in the ' Wohltemperirtes Clavier.' In the second bar was seen a codetta before the entry of the answer, the reason for which we showed. From this codetta the episodes of the fugue are chiefly developed. J. S. Bach. Wohltemperirtes Clavier, Fugue 7 In this episode the codetta is treated by sequential imitation between the outer parts with a middle part, made from the augmentation of the semiquaver figure of the bass. The first part of the next episode 1 *i 1-3 — r— 1 r—n *m isl ■JTfi ffT\ is an inversion of the preceding, the augmentation being now in the bass. By the substitution in the third bar of B natural for the B flat of our preceding quotation, a modulation is effected to the key of the relative minor. The figure of the codetta is maintained in the upper part till the end of the episode, the last two bars of which are in two-part harmony only. 223. In another episode in the same fugue, of which we give only the beginning, the codetta has only a subordinate part ; it evidently suggested the arpeggio figure which is seen in the bass in the second half of each bar. The chief figure here is the sequence, the theme of the upper voice being a modification of the subject of the fugue. In our last example from this fugue, the same material is used as in our quotations {a) and (b). In its general character this episode much resembles (a) ; but the 9 8 Fugue. iCliap. VII. figute taken from the codetta is now allotted to the two lowei voices, and is seen in the alto by free inversion, and in the treble by augmentation. 224. As all our examples hitherto have been from Bach, we will now give one by Handel. The second of his ' Six Fugues for Organ or Harpsichord ' is particularly rich in interesting episodes. We first give the subject and countersubject. gg Handel. Six Fugues, No. 2. Codetta In the first episode that we shall quote, —p-$ J J> J 1 —-j a>m> ^ m J — J «! — 3 tr — 22. -ts- \ , j* j. J? :J J. J3 j ®* ■* mJm -* " * .-- —__-_-__..-.. _ . ; v> w j |" r r i " c r " ' 1 r r r ' r r r r "^ the first notes of the subject in the bass are imitated at half a bar's distance by the treble, and also accompanied by the countersubject in the middle voice in double counterpoint in the tenth ; the passage is twice sequentially repeated, after which an inverted cadence brings back the subject. chap, vi /.j Episode. 225. The following episode 99 ml jJZjj: ^ a jrj i tj j j^ ^ fPE£ * *c £ ^ i P"^ u Lijg a SE ^ imm : e^3 t w r r j I ^ fea begins with repetitions of the first four notes of the subject (or answer), after which the same material is employed as in episode {&); but the notes of the countersubject are now used against a different part of the subject. The episode from which we shall next quote is too long to be given entire. I w Sri: ±^4 1 j rT E jir \ r § ^ pm ^3 t»t-£- ^3C ^=ft ^^ g^-^TC £fe , f,~ 1= g ffc ±=t ^^ Bi Ji J J ■ J5i J -.H-N - ^fa R S? ir r r ra r i * S J- ; *5 &c Mm*d nr » r j J X- PfM Here the last notes of the subject and countersubject (instead of the first, as hitherto) are developed. The first four bars of our extract show a sequential treatment of a one-bar theme ; at the fifth bar, the subject is in the bass, and is accompanied by the countersubject in inverse movement. At the ninth bar, the close of the subject is in the middle voice, and is accompanied by the countersubject, in direct movement above, and in inverse movement below. too Fugue. (Chap. VII. 226. Two more short passages will conclude our examples from this fugue. Here we see two inversions of the subjects of episode (b). Though the second one, in which the original countersubject is in the bass, is not developed at any length, enough is given to show that the passage is written in triple counterpoint. i t J < I J , J J J =at 52 ?=P f^ 4 ^4- i s JLT_H1 In the first bars of this passage we see the second and third bars of (b) treated by inverse contrary movement (Double Counter- point, § 454). In the fourth bar we see the inverted subject in sixths accompanied by the inverted countersubject in thirds. 227. Occasionally the episodes of a fugue are formed from entirely fresh material. In this case care must be taken that the new matter is in keeping with what has preceded. An example of episodes of this kind will be found in Bach's Organ Fugue in D minor, arranged from one of his violin fugues — Chap. VII.] Episode. toi We give extracts from two of the episodes. J. S. Bach. Organ Fugue in D minor. {a) -1 "' | » P^rrn* ^B g h ^T p m ^zM i^ffS.u^r^ ^^e ^ i $=* ^=X ^=4 S 3t &C. - 1 * '«J i w &C. Another good example of the same kind will be seen in Bach's great Organ Fugue in E minor, 228. In both the cases just referred to, the episode is of a more florid character than the subject of the fugue. In the great fugue which forms the finale of Beethoven's Sonata, Op. 106, the theme of which commences thus — we find an example of a different kind. Here is an episode in the key of D major, which itself begins like the exposition of a fugue — rs Beethoven. Sonata, Op. 106. Dolce e cantabile. §§ rirrnrrrigg ^FT After this episode has been developed for 29 bars, Beethoven ro2 Fugue, [Chap. VII. combines it with the first part of the subject of the fugue in the following manner — i ±± -I v ^^W* ^ffjf w =^ P S£=F si J|& A i^ ftfNp r -r — r r J 1 "r i i — -* ^ &c Ur to ?=£fcv^ h£= It looks at first sight as if there were here a double fugue (§ 175), with an independent exposition of its second subject. That this is not really so, is shown by the fact that the episodical theme does not subsequently appear regularly as a counterpoint to the subject. 229. Sometimes in the same fugue some of the episodes will be made from material already used, while others will be constructed of entirely new matter. An excellent example of this will be met with in the 37 th fugue of the ' Wohltemperirtes Clavier. We have already quoted the subject and countersubject of this fugue at § 162 (b). There are altogether four episodes. Of these the first and third were quoted in § 256 of Double Counterpoint, as an example of triple counterpoint in all its possible positions. The second episode is made from a sequential treatment of the countersubject, and the fourth is a transposition of the second, with inversion of the upper parts. This is often met with : for instance, in the two-part fugue in E minor (No. 10 of the 'Wohltemperirtes Clavier') there are four episodes, of which the third is an inversion of the first, and the fourth of the second. 230. We could multiply examples to any extent, and have, in fact, noted far more for quotation than we have room to insert ; but we have already given enough to allow us to deduce general principles from them as to the construction of episodes. The first, and one of the most important inferences to be drawn from our illustrations, is the essential part played by sequence in nearly all the episodes. If we were forced to restrict ourselves to giving the student only one rule in this matter, we should select, as the most valuable we could give him, "Construct your episodes sequentially." Sequences not only furnish a very easy and simple means of modulation, but they combine variety of detail with unity of design in a degree which perhaps no other artistic device can attain. It is not necessary that the sequential chap, vin Episode. 103 imitations be at any regular distance. Sometimes they are so, as in our examples to §§ 222, 223 ; at other times, as in the second part of our quotation in § 225 (dj, the distances of imitation are irregular. 231. Sequential treatment, important as it unquestionably is, is by no means the only point to consider with regard to episodes. A no less necessary requisite is variety. Each episode must have some feature which has not been seen in any of the preceding episodes. A mere transposition of one episode into a different key will be invariably weak and bad if no modification be made. On the other hand, some of the best episodes are made by repetition of an earlier episode with inversion of parts. This gives the requisite variety, and at the same time preserves the artistic unity. 232. Beyond these general principles, it is impossible to teach the student how to write episodes for his fugues, excepting by showing him how the great masters have written them. It is here (just as with the " free fantasia " of a sonata or symphony) that the composer's imagination has the fullest scope. So long as he keeps within the bounds of the artistic and beautiful, he may in this part of the fugue do whatever seems good in his own eyes ; and it will be in this part of the work, more than in any other, that his originality (if he have any) will be likely to assert itself. 233. Besides its use for the purposes of modulation, the episode serves, as already said, to separate the different groups of entries, or isolated entries, of the subject. We shall see, when we come to treat of the middle section of a fugue (Chap. IX.), that there is no restriction as to the number of these middle entries. Sometimes they are very few, at other times they are numerous. Consequently we find great differences as to the number of episodes in different fugues. For example, in the 1 Wohltemperirtes Clavier' the 31st fugue has only one episode, and the 16th only two; but the 3rd, 12th, and 15th have six each. The number will depend entirely on the number ot middle entries. 234. The length of the episodes is as variable as their number. In the majority of fugues they are comparatively short — often only two or three bars each ; and in many cases it is better not to have too long an interval between the different entries of the subject. But they are occasionally found ot considerable length. For instance, of the six episodes in the fugue in C sharp major (No. 3 of the ' Wohltemperirtes Clavier '), the first four and the last do not exceed four bars in length, but the fifth extends to fourteen bars. In the F major fugue (No. 35 of the same work) is seen a very unusually long episode of 28 bars. This, however, is quite an exceptional case. The composer's feeling of proportion and balance must be his guide in deciding both on the number and length of his episodes io4 Fugue. [Chap. VII. 235. Occasionally, though very rarely in modern music, we find fugues without episodes. Such fugues were more frequently written, and more highly esteemed, by the old contrapuntists than they are at the present day. There is always danger of monotony if there are no episodes ; even the first fugue of the 1 Wohltemperirtes Claviei ' — perhaps the finest fugue without episodes ever written — is from a purely musical point of view somewhat inferior in interest and charm to many others in the same collection. 236. As it is only by actual working, and not by any amount of mere verbal instruction that fugal composition can be learned, we shall now practically illustrate the directions given in this chapter by writing a series of episodes suitable to follow the expositions given in the last chapter — in three parts in § 194, and in four parts in § 204. They are both in the key of D major; and we will assume that the next appearance of the subject is to be in B minor, which is one of the most probable keys for the next entry. Our exposition ended in A. major, from which key a modulation to B minor is perfectly easy, either direct or touching on D major first. In each of the episodes we give, we shall make use of material found in the exposition. We shall write all our examples in open score, that the student may be able to follow more easily the progression of the different voices ; and we strongly advise him to follow the same plan in all his fugal exercises. 237. We first write some episodes to follow the three-part exposition in § 194, and in each case begin by completing the unfinished bar at the end. In this passage, the last half of the subject is treated sequentially in the treble, and accompanied by imitative counterpoint in the other two voices. Chap, vii.] Episode. . 238. For our next episode 105 Mr 9 ^^ — (■ "1 F ^-1 - >f rf-- &h~r*M ! P- ! £bd?!Z_ ^-fl— sa — L U- H*"M — BS — '£±sfcH«*- J P=&c we take the codetta in the second bar, which precedes the entrance of the answer, treat it sequentially, with imitation in the fifth above between the two upper parts, and accompany it in the bass with a semiquaver figure, developed from the figure EE ^zdf~P = m tne second crotchet of the first bar of the alto part. 239. In both the above episodes we have returned from A to D, before going into B minor. In our last example in three parts we will make the modulation direct. This episode is made from the first part of the countersubject, which is accompanied by a new semiquaver figure in the alto freely imitated in the tenth below by the bass. iob Fugue. [Chap. VII. 240. We now give some episodes suitable for our four-part exposition. Although in actual practice, it is neither necessary nor expedient that all the episodes of a four-part fugue should be in four-part harmony, yet, as the episodes we are now writing are simply meant as illustrations of the method of composition, and as our previous examples have been in three parts, we will write these in four. As before, we begin by com- pleting the last bar of the exposition. imp ^^ip i ^ m r etc ^^TT: This episode is founded on the first three notes of the subject, treated sequentially in the bass, imitated by inverse movement in the tenor, and accompanied by a semiquaver figure in the upper voices, which is an imitation, partly inverted and partly direct, of the tenor part in the first half bar of the passage. 241. We not infrequently find in fugues that an episode is founded, not on subject or countersubject, but on one of the incidental counterpoints. To illustrate this, we construct our next episode in this way. Chap. VII. Episode. 107 The sequence here seen in the treble is founded on the figure employed in the tenor in the second half of the seventh bar of the exposition in § 204. It is accompanied by a sequence in the tenor, formed from the beginning of the countersubject, and imitated in the second above, and at one crotchet's distance by the alto. 242. Our last episode is more elaborate, and is given to illustrate the incidental employment of canon in fugal writing. In the second bar of this passage the first bar of the counter- subject is introduced in the alto, and treated sequentially in the following bar. It is also accompanied by a sequential counterpoint. Both these parts are imitated by the tenor and bass, making a "4 in 2" canon ; but the inversion of the voices, instead of being, as usual, in the octave, is in the tenth. r 08 Fugue. [Chap. vn. thus giving a somewhat rare combination of canon and double counterpoint in the tenth. In the last bar of the episode, the canon is abandoned, and we have merely ordinary imitation, direct and inverted, of a fragment of the countersubject. 243. These examples will show the student how much variety of episode is possible, even with such commonplace subjects as we have been treating here. He will now see clearly what we meant when in Double Counterpoint (§ 307) we spoke of Imitation as "a most important ingredient " in fugues. In fact, imitation and sequence are the chief essentials of good episodes. Let the student now turn back to the expositions he has written as exercises on the last chapter, and utilize his material (subjects, countersubjects, codettas, and incidental counterpoints) for the construction of many different episodes, after the manner which we have shown him in this chapter. He should write five or six episodes for each fugue, varying the keys to which he modulates. For the present he should not go beyond the nearly related keys Own VIII.j STRETTO. I09 CHAPTER VIII. STRETTO. 244. The word " Stretto " is the past participle of the Italian verb, " stringere," — to draw close. It is occasionally used in music other than fugues as equivalent to the present participle of the same verb, " stringendo," in the sense of pressing on, or hurrying up the time ; but when employed, as it mostly is, in connection with fugue, it is the name for that part of a fugue in which the entries of the subject or answer follow one another at a shorter distance of time than in the first exposition. 245. Most theorists name the stretto as a necessary part of every good fugue. Cherubini speaks of it as an " indispensable condition " and an " essential requisite " ; and he adds that "a good fugal subject should always give scope for an easy and harmonious stretto." But this rule, like most others given in the old text-books, will not stand the test of applying it to Bach's practice. Out of the forty-eight fugues in the ' Wohl- temperirtes Clavier,' about half have no stretto at all; and of the remainder some have only a fragmentary, or partial one. If a stretto is really an essential part of a fugue, then it is evident that more than half Bach's fugues must be badly written. The simple truth is, that it is not Bach's workmanship, but the rule that requires to be altered. Any rules regarding fugue, which will not fit the works of the greatest fugue-writer that the world has ever seen, carry their own condemnation on their face. 246. Instead, therefore, of laying down a law that every good fugue must contain a stretto, we maintain that, though often a most valuable ingredient of fugue writing, it is never absolutely indispensable. In the ' Wohltemperirtes Clavier ' some of the fugues which have no stretto {e.g., Nos. 2, 12, 21, and 40) are among the finest and most perfect works of art of the whole collection. 247. It is by no means every fugue subject that adapts itself easily and naturally to the purposes of stretto. A subject intended for this should be expressly designed for it in the first instance ; otherwise there will most likely be a certain stiffness or harshness about some of the imitations. For example, in writing the fugue subject of which we gave expositions in I IO FUGUF [Chap. VIII §§ 191, 204, it did not happen to occur to us to make one which would be suitable for stretto afterwards. Consequently, though it is quite possible to introduce later entries at a shorter distance than two bars, these will not be so effective, nor flow so naturally as if the subject had been written with this object in view. We give a few stretti as illustrations. P M 3==^ te (6) ^m t=fr r ^ l uf r - §H s &c &c. WmM W ^^5 F=t id) &^ ^¥ fsig^ i=5t *S! JJ^JJ Si 248. These examples, which must not be regarded as models of a good stretto, but are written to show that a stretto of some kind is mostly possible even for a subject not at first designed for it, illustrate several points relating to its construction. We see at (a) a case of common occurrence. Here the imitation is not in the fourth or fifth, but in the octave. As a matter of fact, the imitation in a stretto may be at any interval, though in general those in the fourth, fifth, and octave will be found the best. At (b), as at (a), the imitation is at one bar's distance ; but it is here in the fifth below ; the answer leads, and the subject replies. The imitation of the answer by the subject often gives a different set of combinations. 249. At (*■ m p-t r r r r Cj" r V l tilrr cr'r As there is here in the subject an implied modulation to the dominant, the answer will be tonal. In accordance with the rule given in § 121, we regard the modulation as being made as early as possible — here, after the first note of the subject. The answer enters at the beginning of the fifth bar. 2 55- We will first try to bring in the answer as near the end of the subject as we can. Clearly if we keep the tonal answer, we cannot introduce it in the fourth bar of the subject. This is manifestly impossible, though the addition of thirds below the answer would render it practicable. But we said • n § 2 53 tnat ^ was allowed to use either form of the subject Tit Fugue. [Chap. VIII. in the stretto of a tonal fugue. It would therefore be quite feasible to introduce the answer against the last bar of the subject thus — p i i i ji^ i ^' ^ j j^ g &c. As this passage is written in double counterpoint in the octave, the answer could also be introduced above the subject. &c. 256. We will now reduce the distance of entry by half a bar, bringing in the answer, per arsin et f/iesm, on the second half of the third bar. ^ _J j|j J_J J3 | J J ^Mjij &c. r f } r' r crr r The student will see that at this distance of entry, it is impossible to complete the subject. Note also that in consequence of the bare fifth at the end of the third bar this stretto cannot well be inverted (at least in two-part harmony) as the last one could. 257. If we next try to make a stretto with the answer at two bars' distance, we shall have either to discontinue or to modify the subject on the entry of the answer. == &c It would, however, be possible here to continue the subject unchanged to the end, if we make the imitation in the octave instead of the fourth. We shall have to shorten the first note of the imitation (§ 57). • r r cr f i 1 This stretto, like that in § 255, will also invert in the octave cr P ^^ rz'irrr^ &c Chap. VIII.] Stretto. "3 258. At one bar's distance we can get a stretto in the fifth below. i (a) I 1- Jllj J J JJlJj^ r rcr'r efr gg j -w-* 1 »* ^^£ FfPPr? r * l = ^ We might here also have preserved the tonal form of the answer by treating the A in the second bar as an accented passing note. &c. In the fourth bar we have varied the rhythm of the imitating voice, to retain the subject in the leading voice for half a bar longer. Obviously we could not write Such slight modifications, either of rhythm or melody, are very common, and always permissible in a stretto. We now give the inversion of the above. 259. Lastly, we can make a stretto with this subject at only half a bar's distance. Like most of the preceding, this stretto can be inverted in the octave. ft) J J3 j j >. OJJT? 260. If now we begin with the answer instead of the subject, we shall obtain a different series of stretti, though resembling those already given in their general character. ii4 Fugue. [Chap Vlll. Here the subject enters three bars after the answer. We give the inversion, (*) y_J. JJ3-t.LJ-JJ3.JI 261. We next show the answer followed by the subject at two bars' distance. («) I U J J . j-J *Ld- Ul J AA S-J-Z&i- s* &c £ 1 — r It will be seen that the leading voice cannot here continue the subject to the end. This imitation inverts as follows — 1 V) 1 1 1 j J rrri f^g &c 1 1 r J k r r crir r r Cr i r 51 5H 262. At one bar's distance the answer cannot be comfortably imitated by the subject. Here, therefore, we make the imitation in the octave; and even at this interval we cannot continue it long. j j J «D =F r r r a* 263. At half a bar's distance, it is possible to reply with the subject, and the imitation can be continued somewhat farther than in the last example. 1 («) ^ J-J I J JJJ-J jJ ^/^ &c. ^=5^ T-f 1 ■ ■ - The above will also invert — &c. 264. Hitherto we have only given stretti in two parts ; but the subject we have chosen will also work in stretto in Chap. VIII.) Stretto. "5 three or tour parts in many different ways. We give two specimens in three, and two in four parts. i * ■— ' — i- zsz: &c. £=£ t=^ Here is a simple example, in which each part follows at a distance of one bar. The intervals of entry are irregular ; the alto being a fifth below the treble, and the bass a seventh below the alto. 265. In our next example, p ^ Ty F^-Cnrr ry i r crrr ,r r t=n P ^U^* 3=F &c. *t i ^ e-uz the intervals of entry are the same as in the last ; but a quite different effect is produced, because now the answer leads and the subject replies ; and, besides this, the distance of time in the entries is irregular, the second voice being two bars later than the first, and the third voice only one bar later than the second. 266. In our first four-part example, P &m^ m £3E 1 1- SE &c ^ r=r=rmt -*—r- m J j u J '-^ the entries are regular as regards distance of time (one bar), but irregular as to interval. In this stretto it is not possible in any of the voices (except, of course, the bass which is the last to enter, and in which it should be complete— § 252) to continue the subject to any great length. Fugue. [Chap. VIII 267. We lastly give the closest possible stretto in four parts. 4 Here the entries are regular both as regards time and interval, each succeeding voice being introduced half a bar later, and a fourth below the preceding one. It will be noticed that in each voice the subject is carried down to the same point. 268. We have now given more than twenty stretti on the same subject, of which we have by no means exhausted the possibilities. It is probable that, by using all the combinations in three and four parts at the various distances of time and entry, we might make at least forty or fifty stretti on this subject. The student may not unnaturally be inclined to ask, What is the difference in character between this subject and the one worked in § 247 ; and how is it that so few good stretti could be obtained from the one, and so many from the other? The explanation is very simple. We said in § 247 that a subject intended for stretto should be expressly .designed for that purpose. The best and easiest way of so designing it is, to write it in the first instance as a canon in the fourth or fifth at the shortest distance at which it is intended ultimately to be introduced. In the present instance we began by composing the little canon seen at § 259 (a), as far as the first note of the fourth bar. We then completed the subject by the addition of the notes — $ The entries at longer distances were then found by experiment — trying to fit the answer against the subject, or the subject against itself, at all possible intervals and distances of entry. It will nearly always be found that subjects which, like this one, work in close stretto, can also be employed at longer distances. 269. The stretto is mostly met with in the middle and final sections of a fugue, of which we shall speak in the next chapter ; but when the fugue has a counter-exposition, the first stretto (as already mentioned in § 209) is frequently intro- duced at that point. A good illustration of this is seen in fche 33rd fugue of the * Wohltemperirtes Clavier.' We quote the exposition and the counter-exposition. Chap. VIII.] Stretto. i 1 7 J. S. Bach. Wohltemperirtes Clavier, Fugue 33 tA Sfe « Hi CS- sa fa ea g r -^ J y =g: 3*3:^ -m — (si ±=ft *fe *=* *=t I *& S9E cs- I *£ g ;= ft g -r ^-p- rf-f^-tf te W g r w 1 C! r r e ml ' ' ' ^^» rj ^ 3 s «=t P ^A f rrr r ^ r> r rrr . ^ i r r t=t * p— jjjj m j j ^^ g -25«- HV»r^r r - pr i f r rr-f-u ^g cs- i j 1 § si -^z. ^9=?z 3^ =*z=at s** m B g s=? 32: ! JJ^ I a=ss Him j r-f 1 r r ii J I e n i i r CS- Sc. £*EEE }=T ^^g \ I ^=^ ^= J * *, fll# -g — ^- * J 3tJ* =£££ as r-» cJ » 10 11 12 The bars are numbered for convenience of reference. Note the altered forms of the countersubject spoken of in § 17a Fugue. [Chap. VIII. The exposition ends at the beginning of the seventh bar. The two bars that follow have hardly enough distinct character to constitute an episode ; ,they are rather a kind of codetta — a prolongation of the exposition, leading up to a half close, to introduce the counter-exposition. Here we see (§ 207) that the voices which before had the subject (the bass and alto) now have the answer, while the tenor and treble have the subject ; we also see the entries in a rather close stretto. It looks at first as if the introduction of a close stretto so early in the fugue were premature ; but Bach has other devices in reserve for the later part of this fugue, as we shall see presently. 270. In the 31st fugue of the same work, the counter- exposition contains a canonic imitation in stretto, first between tenor and bass, and then between alto and treble. We quote the passage ; the subject and answer of the fugue were given in § 88. J. S. Bach. Wohltemperirtes Clavier, Fugue 31. Slap. VIII.] Stretto. 119 Here, as in our last example, the answer leads and the subject replies ; but a deviation is made from the usual practice, inasmuch as the tenor, which had the answer in the first exposition, has it again here, and the bass (as before) has the subject ; but with the other pair of voices, the usual plan is followed, the alto now giving the answer instead of the subject, and the treble giving the subject instead of the answer. The irregularity is probably due to the fact that Bach intended to invert the canon on its repetition by the upper pair of voices. Canonic imitation in stretto is not uncommon in a fugue ; the student will see other instances of it in Nos. 20 and 46 of the ' Wohltemperirtes Clavier ' ; but it is seldom met with so early as in the counter-exposition ; more frequently we find it in the middle or final section of the fugue. 271. Though, as has been already said, the imitations in a stretto may be at any interval, it is generally advisable to observe some kind of order in the entry of the different voices. Our next example will illustrate this point, as also that mentioned in § 252, that one voice in a stretto may discontinue the subjecl as soon as another voice enters with it, but that the last voice that enters should complete the subject. The student will find the subject, answer, and countersubject of this fugue in § 169. J. S. Bach. Wohltemperirtes Clavier, Fugue 24. — incomplete. fe T20 Fugue. [Chap. VIII Here the entries are at a regular distance of one bar after each other ; the alto is a fifth below the treble, the bass a fifth (twelfth) below the alto, and the tenor the fourth above the bass, which is the inversion of the fifth below. Each voice, except the tenor, which is the last to enter, discontinues the subject when the next voice enters with it. In the fifth bar of the extract is seen a fragment of the countersubject in the alto, which, in the following bar, is continued by the treble. It is not uncommon in the middle section of a fugue to find a countersubject begun by one voice and completed by another. It should be noticed that the counterpoint of semiquavers, seen first in the bass and then in the treble, is developed from the codetta in the fourth bar of the example in § 169, before the entry of the countersubject. 272. Sometimes not only the subject, but the countersubject of a fugue is used in a stretto. A remarkably fine example of this is seen in the great five-part fugue in C sharp minor of the ' Wohltemperirtes Clavier.' It will be remembered that this fugue has two countersubjects, both of which we quoted in § 172. Only the second one, shown at (b) is employed with the subject in the stretto. Though the passage is rather long, it is so interesting, and deserves such careful examination that no apology is needed for quoting it in full. cs 2 § m 1 mi n e CSl- Chap. VIII.] Strrtto. XI l^^^p — L s r f p_ ^— ir ~ -i ■ f *d - „ fl ^-^ C S2 -f ^ = ^= 1 te | L^ p 1 i c s ° C S ° Ih'i a it ', r j j i j,n ,' | — [— 1 J * — t- i H* 1 * V -I & rVtt J 1 j J p r ^ — ^ — *-f — j a J ' - — S (invd. & dimd.) n. f j 1 ! v- m-=- — - j * m -j— -j — i 1 1 — 1 s fl*. -g — 1 ■: 4 « • -£ g- ^ ^ rv e ^-_ rf P- p 1 n-^-r r 1 ' S (inv d . & di zd C" f*^ * m Till 1 [.■ t flhff P V r p- tA) , ■ f— h»-r-f inlfl* \ 1 — !— f- j(l..S—zx= r - • ' i^=* J * - 1 11 1 e*A f * r r- 1 ^ S(dimd.) ^ p r ^f 2 1 1 = -J 1 -J - 1 , S (invd. 1..J r . q ^ g-g-i — 1 — i— 1 1 1 s! *" 1 w 1 * ' ' P 126 Fugue. [Cbap. VilZ. & dinA)- S (invd. & dimd. ) &/s r J r V g • jg InFf 1 *) :*£: rs2T. The first half of this passage shows us the subject treated by diminution, and imitated mostly at half a bar's distance. In the second half, the subject is both diminished and inverted, the first note being varied, and in this form it is used as a counterpoint against the subject in its original shape. 277. We said above (§ 252) that one voice was allowed to discontinue the subject in a stretto when the next voice entered with it. It is, however, sometimes possible for each voice to continue the subject to the end, so that the stretto is a canon at short distances of time for all the voices. A close stretto of this kind was called by the old theorists a stretto maestrale — that is, a " masterly stretto." The following is a fine example — J. S. Each. Wohltemperirtes Clavier, Fugue i. S — Chao. VI11.] Stretto. 127 Here, though the interval of entry is irregular, there is a certain symmetry observable ; the alto is a fourth below the treble, and the tenor a fifth above (the inversion of a fourth below) the bass. Such slight modifications of the subject as are seen in the tenor here are always permissible in a close stretto. The first notes of the bass are the conclusion of an entry of the subject in that voice. 278. Another interesting example of the stretto maesirale is seen in the following — J. S. Bach. Wohltemperirtes Clavier, Fugue 29. Here the distances of entry are regular, both as regards time and interval, each voice entering a third (or tenth) below, and a crotchet after the preceding. The entries of alto and bass are consequently per arsin et thesin. Even a finer example may be seen in the fugue which forms the finale of Mozart's "Jupiter" symphony. The passage was quoted in Double Counterpoint, § 305, as an illustration of close imitation. 279. There is still one variety of stretto to be mentioned. Sometimes, though comparatively seldom, the first exposition of the fugue is in stretto, the answer entering before the completion of the subject, and very often immediately after its commence- ment. In such cases the second pair of voices will mostly follow the first pair with subject and answer at the same distance of interval and time. («) J. S. Bach. Motett, "Der Geist hilft uns're Schwachheit auf. fA'V - ' JUL ' ' IB ' JB m y \< ■aii> vi» ■ ' 1 -= — r^—^ — rr r r r r r r r h nl 4|2 -, — f- ' ' ^ — 1 — 1 — V — I — [- — 1 — 1 — 1 W-.b/i* = — 'fr- r r r 1 r r r r i r r * r i r r—^^ M? % — f— _J ! ! 1 1 1 j_ — | — {_ — | 1 ! L : 28 Fugue. iChap. VIII. 3V - -\ A -= = F — r f r r r f r F-r-f- r — = — J g -[- 1 L_L_4~|_M— T-f— F— U- BB-b ~ j= i r r fi r r r r i r-rr^^r-^ .}|E-= 1 _J 1 , -L_...|.. |. | ,| . | . ,_ -| ... . .!__ | _1_ _| m? r-4Z r t^ r — n — f-5- -j-r ' " iftr — — \~ — ! J h^U p f p__ff — d_| &*j r *rr r- -^ p — = — f- — ^ — f g r F- ^_j — *j_j — p_ f_ f= 1 1 1 — L — ! A fugue of this kind is generallv called a " close fugue." We give two specimens of the beginning of a close fugue by other composers. y V K— -— — A Handel. ' Israel in Egypt.' --J ! I--J cj to* — - 1 t= ■zj ^ gJ J^j (S* =-( j £ 1 ■ Ui,u - M ■ — » — h~ — ■ . — \— -i =- - -fs< B — &- -p* — m—m KR^p — 1 | \^-f\T- i r\\ \ H -J 1U1 , | F r" 3 &c. — ^ 1 h — tFrhP^ — — — Vr - ra ^~ — n — i_j — i — i — i — i — (c):/|> ^~ ^j t^-4 r=j • >— ^ — (— ~ 1 1 f»-i r^- (c) 3=^1 -1 — 3= -r— J Mendelssohn. • St. Paul. 1 •■ ■■ - |- A J^ fiP— i 'j <=> \ jjji-P-fj _ — z=s (S> « p - -f w 1 ^ ™ -r — p — ^H — - 1— 4 Mm A IN lLjI— m m Fli *j — fS*- — isa_ — p_ T~^r g r s- J 1 1 , G* — f^ 1 — — fs> p-s o4 -T3 - Sbj-p _4— r -1 1 i — \ Chap. VIIL] Stretto. 129 I 22= =P P *Z= Ukr g g in I &c. E =f=PF 280. The second pair of entries in a close fugue is sometimes at a different distance of time from the first. Handel. 'Jubilate. I !ESE m rrr g 4SL d=t ^^ tafc £ 4==t t=sp I rJ fet s 22: £ r J k- r i f Bi ^ g ?z n j r r r i r rir r- 1 r" rir; &c. 3=£ S - — U- -1 — p . p ... i &c. ■ini s 1 P r^ I ^FS — 1 — m —\ — h- ■p- ■ f p — -r-f- -^— 1 -i — p=p= 1 1 ^ 1 sS> i . J 1 — r #> -i — i — \ * \ 1 J- 1 - -1 — I ' is the last and closest stretto, and is founded only on the first part of the subject. In this all the voices take part. 284. The fugue in Mozart's quartett in D minor (No. 13), of which we gave the subject in § 150, is particularly rich in good stretti. We give some of the closest. Violino imo. VlOLINO 2do. Viola. Violoncello. Mozart. Quartett in D minor, No. 13. is * m c» fc -1 r j^ gr cp gp frc i=t $ee -*p-fr ^S Sffi 'V? I 1 1 r -j — 1- |g=te ^^f^ 1 " 1 jg I g br If ttr »p tir ^» (*) i r~ i*~ *y E ^:-~p-^ &c. 1 1 -f- wb p 1 — -1 — L*- L ■ « 1 ' ' 1 -^L. j 34 Fugue. [Chap. VIII. P 1 = -i 1 1 1 F ' ^?*=h?c I I I I I K I ir>av "r I b ^JbJ rg*rr i 1 * La ! -J ^=^Mi^ IZ+^Fr ^■i.^fflijj - 1 j imi JU I 1 1 UiiJ a J IqJ-J J, «l | ^Qj » r Cr»p' S g Jt i J jqj bJ J & g J j •' I J 3 I ( g )^- ftg- I?- |^U i — r r- r- u* feg 4^- (* » r #-i *- 1=t II — I i*r ^r *r jjg i r r i -"VH^^-a ffr br g* be :£=£ £=p= 1 E 4= h»- br b § i I I fp£=- fr r r nr j r i ; W) i r r J * I J"^3^^ ^=t Chap. VIII.] Stretto. 135 |A ■■ — # — 1 — 1 — i— W ^ 1— =t — i— 4- — H — 1 & ^-^t- *■ — U 1— 1 I Btfifc: r/o — sL "5» ! 1— — \ — 1 . -#- W= -1 "I 1^— sr 1^ L^-^— 1— kit -^ -1 After the full explanations given of previous examples, but few words are needed with regard to these. Observe that at (b) both subject and answer are employed by inversion, as well as in their direct form ; and that at (d) all the imitations are in the unison and octave. 285. It is not uncommon in a stretto to find the. last notes of the subject slightly altered. In the fugue occurring in the course of the second chorus of Mendelssohn's 95th Psalm, we find a stretto so continuous that if the original subject g ^-^l-r-r , ^ r-h~ =^ had been retained unaltered, we should have had a stretto masstrale. It will be seen that the modification is in the melody, not in the rhythm. Mendelssohn. 95th Psalm. #*#= f-J . 1 — , s- — p — r H |-*r== — ~f~f~ g-ft - 1 s • m O 1 =P=P=* -f-r~ o- 1 •or* J J -^ «j_, r r r r 4-i- ...r Oq =4=1= S 1 ' l — Hr^— 1 — U-l — 1 — fr» s r ' i r 1 • err b * 1 1 1 «* 1 — r~ £*6 JL-*!. — Ff5?— J 1 -i — u- S— 1 i f - — rir.o _£ — CJ 1 -0- p 1 W *l * * \ — 1 — 1 — 1_ "1 1 ■ u i .1 -I — y -r* — r 1 r ■ f ffi» • — m- 1 -O-l ^ • — (& — -0- "I 3 " - f— — 1 J 1 * 1 ' > 1 1 s— 1= — r _ ->^ —J j L_ 4sU — 1 — H ^*- -OI -^a — — 1 ri T # Jfg ' -*o- _| — 1 — ! .ALL* m-^ — 1 — -J — -1 — m 5 Ff= — f=^ • B* ■**- P^ ' WK** '**— ««- V~ l ^r_i - gryf- ... f- — p. -- . jSS. ffF&J »- -42- fj^gjfo»flg, f£ ^m§£:m r *> 37 38 39 -0 8 • ^ .- p. [ 1 rJ3 Jft-^eqq s m3 rr i inj^. 1 ^J ' •* * j-^gfle tfjf rrVi-Vfi^ — fc?— , 1 1 q Ihi H fea ; i=^= 'l asa — 1 | ^" "j g i . — . — ?-rf — i — -I K 43 1 44 -f — h— r 45 l~* *-^-J i 4 4 Fugue. iChap. IX J>% 1 1U1 % m S S- K3 ' S , r Lgi f^gg^zzd r ^.^ * 'Vlf — p^ff f*rTi if r =5 =t : IW-Wsr -uU U-L1L_ .,*• r ^Y" r ,*ff ^N 49 50 51 cs- R:tt g § * r 52 53 54 chap i x.j Middle and Final Sections. "45 i'-i- 1 ^ ,f f- T 1 1 ■— l"*"1j 1 f s» U G^gJfr* - 1 ^H — f= ^CTUU- ^mftff ^fTf p . i^gpij- BtocHi — « 61 62 63 J 1 Iff* ^ J* I I ■ r i i i i f-^rT 'err- Tcr r ^c n r r r r «rf i f r f =^ c-r-f 299. The first section of this fugue contains only the exposi- tion. Though the subject is announced in an outer part, we do not find here the additional entry spoken of in § 186 ; perhaps because of the extent of the subject, which is the longest of any in the 'Forty-Eight.' The exposition ends in the 18th bar, and is immediately followed by the first episode (bars 18 to 23). As this episode does not introduce a new entry in either tonic or dominant key, but modulates to the relative major, we see chap, i x.j Middle and Final Sections. 147 that it belongs to the middle section of the fugue, and not to the first (§ 293). This first episode is formed from the last bar of the subject, continued sequentially in the bass as far as bar 20, and accompanied by a figure, evidently founded, as regards its rhythm, on the third and fourth bars of the subject, and treated by free imitation between treble and alto. The second half of the episode contains a new sequence in the bass — a modified form of the treble of bar 7 — accompanied by the last notes of the subject, given alternately by inverse motion in the treble and direct motion in the alto. 300. The first episode, ending, as we have seen, in G major, leads to an entry of the subject in that key (bar 23). It is accompanied by the countersubject, which enters in the alto at bar 26, and which here for the first time appears below the subject. At bar 29 the answer enters in the alto. That it is to be looked at as an answer here, is shown by the fact that it is a fourth below the preceding entry in the treble. The countersubject is given, as usual, to the voice which last had the subject. The bass accompanies with a free part, the material of which is taken partly from the treble of bars 7 and 8, and partly from the last notes of the subject. These two appearances of subject and answer form the first group of middle entries, which extends from bar 23 to bar 35. 301. The second episode (bars 35 to 41) is made of the same material as the first — mainly the last notes of the subject, but with different combinations from the previous ones, and modu- lates to B minor. In this key, the next middle entry is made by the bass (bar 41), the countersubject now being in the alto, and the treble supplying a counterpoint mostly made from the last notes of the subject, direct and inverted. It must be noticed that all the middle entries after the first are isolated entries — that is, each one is divided from the following by an episode. 302. The third episode is the shortest of any (bars 47 to 49). It is a transposition a fourth lower (with a slight modification at the end) of bars 18 to 20 of the first episode, and leads to an entry of the subject (alto) in the original key (bars 49 to 55). In a large number of fugues a return to the tonic key is not found till we reach the final section of the fugue ; but we sometimes, as here, meet with a middle entry in the tonic. We see another instance in the third fugue (C sharp major) of this work. When an entry of the subject in the tonic is not followed by any entry in another key (except possibly the dominant), this tonic entry indicates the beginning of the finai section of the fugue ; if, as here, another subsequent modulation is made, the tonic entry forms part of the middle section. In the entry now under notice, the countersubject appears for the first and only time in the bass. Though this entry and the preceding (in bar 41) bear to one another the relation of tonic 1 48 Fugue. tcbap. ix. and dominant, we have not described the B minor entry as an answer, because it is separated from the next by a short episode. 303. The fourth episode (bars 55 to 59) presents us with the old material — the last notes of the subject sequentially treated in the treble — with new counterpoints for alto and bass. It modu- lates to A minor, in which key the last middle entry is made by the treble (bars 59 to 65), the alto having the countersubject. 304. The fifth, and last episode (bars 65 to 70), like all the others, shows the last part of the subject in fresh combinations. It leads back to E minor, to introduce the final section of the fugue, which will always be in the key of the tonic. The pause after the half cadence in bar 70 is rather rare in an instrumental fugue, but somewhat more common in a vocal one. 305. One introductory bar after the pause leads to the final entry of the subject (bass) in the tonic key (bars 71 to 77). In some fugues all the voices enter with either subject or answer in the final section. This is especially the case in fugues which have a stretto, a feature which, it will be seen, is wanting in the one now under notice. But in many of the fugues of Bach, the final section contains, as here, only one entry. This is followed by the coda (bars 77 to 86). A coda {Italian = tail) is a passage added at the end of a piece of music to bring it to a satisfactory conclusion. Sometimes, as here, it will consist of only a few bars ; sometimes, as in many symphonies and sonatas, it will be of considerable length and importance. The chief feature of the present coda is the ornamented dominant pedal (bars 78 to 81); we also, quite exceptionally, find a second pause (bar 83), here on the last inversion of a dominant minor ninth. 306. Another point of importance is illustrated in this coda. In the 83rd and last bars will be seen the introduction of an additional voice. This is often met with at the conclusion of a fugue. Out of the 48 fugues in the ' Wohltemperirtes Clavier' we find such additional parts in sixteen, mostly in approaching the final cadence, but occasionally (e.g., in fugues 35 and 39) earlier in the coda. Let the student examine, as striking examples of this procedure, the last bars of the fugues in A minor (No. 20) and C sharp major (No. 27). 307. We will now tabulate, for future use, the entries of the subject in the fugue just analyzed, noting the succession of keys, and the voice to which each entry is given. I. Exposition. 1. Subject (treble) — bar 1. E minor. 2. Answer (alto) — bar 6. B minor. 3. Subject (bass) — bar 12. E minor. II. Middle Section. 4. Subject (treble) — bar 23. G major. 5. Answer (alto) — bar 29. D major. Chap. 1X0 Middle and Final Sections. 149 6. Subject (bass) — bar 42. B minor 7. Subject (alto) — bar 49. E minor. 8. Subject (treble) — bar 59. A minor. III. Final Section. 9. Subject (bass) — bar 71. E minor. It will be seen that no two consecutive entries are for the same voice, or in the same key. 308. Before proceeding to lay down any general principles, we will analyze another fugue from the same work, constructed on a different plan, and illustrating several points not shown in the fugue in E minor. J. S. Bach. Wohltemperirtes Clavier, Fugue 29. 1 Episode 1. ■*—m-> £=m #1 r g g W r g -i J r< ^=^ ^ =*=* w ^r* Middle Section. -*-* — r Mh 1 5 iif 3 ^ «* usee: ^^ 3==T a?~*w 10 ** s :» 11 13 [Chap. IX. 15 16 13 ^^eDJijrr-EUrp 17 -p* — *" ** -^^p-^ ^ - IB;- 1 i r # 5 ^ *'^ v — . =^-%F Jfc ^ ^ <•«" -v ^ 1 i- raj — 3 # ^it* ~~= A — d — i j i i — 1 — 1 — i R'l gpf-l Jjnri g g-g^ — K 24 25 ^2« Chap, ix.] Middle and Final Sections. A— 1 I.5I I 5ffi I II F « r» g J J*'J ! J r * >* U J . Jl ^J^ TT ^ 35~ * l g a . j ' l *wj* , f Episode 5. i5 2 Fugue. Chap IX. Coda. i cCn err n c^ | J ■ ^GTcT ' g r I « i* 48 49 47 50 This splendid fugue — one of the most perfect of the * Forty- Eight' — is a remarkable example of Bach's power of letting art conceal art. There is not one which flows more naturally and unconstrainedly, and yet there is not one which is fuller of scientific device. This will appear from our analysis. 309. Let us first look at the subject. We see here an exception to the general rule given in § 29, that with a downward leap of a fifth the first note will be dominant, and the second tonic. The subject begins with a leap from tonic to sub- dominant, and consequently takes a real answer. Had D been a dominant, the key of the fugue would have been G, and the answer 3 As C sharp is not used in the subject, the key is doubtful at first , in such cases the answer always decides the point. 310. As Bach intends the fugue to contain a large amount of close imitation and stretto, there is no regular countersubject (§ 176); but instead of this, the last half of the subject is ingeniously made to serve as a counterpoint to the first half. chap ix.] Middle and Final Sections. 153 against which it is mostly employed in double counterpoint in the tenth (compare bar 3 with bars 6, 10, 21, etc.). The figure ^=P^h4 cannot be called a countersubject because it is not contrasted with, but derived from the subject. We shall see that it forms the germ of all the episodes. In the fourth bar it is already used in imitation to make a codetta. 311. The exposition foreshadows the treatment by stretto which Bach intends ; for the entry of the bass in bar 6 is half a bar sooner than its regular place. The exposition ends at the 7th bar, and the first episode is made from the figure just quoted, by close imitation, in all the voices at one crotchet's distance. 312. As the following entry of the subject (bar 10) is in E minor, we should expect the episode to modulate to that key. Bach, however, does not do this, but makes his modulation on the first notes of the subject itself. As the original keys ot tonic and dominant are not quitted till after the episode, we include this in the first section of the fugue, and consider the middle section to begin in bar 10. 313. The first group of middle entries, bars 10 to 13 — subject (alto), answer (treble) — is followed by the second episode, only one bar in length. We count this as an episode because it effects a modulation from B minor to A. At bar 14 the first stretto is introduced. It is for two voices only, in the fourth above, and at a distance of half a bar. It is seldom that so early a return is made to the tonic key ; but it may be said here, that in fugues containing much stretto, we often find a much greater prevalence of the original keys, and less modulation, than in fugues in which there is no close imitation. Nos. 1 and 4 of the 1 Wohltemperirtes Clavier ' are illustrations of this. 314. In the third episode (bars 16-21) we see the figure of the second, a sequential prolongation of the first, treated by close imitation in all the voices. It leads to the second stretto (bars 21 to 23). We said in § 251 that when there were several stretti, their interest should gradually increase. We see this illustrated here. Three voices now take part in it ; the treble enters one bar after the tenor, and the alto half a bar after the treble. The intervals of entry (fifth and octave) are again regular. 315. Bar 24, though not containing subject or answer, cannot be considered as episode, because it does not modulate to a fresh key, but introduces an entry which clearly belongs to the preceding group, being the regular answer to the last preceding entry — the subject in bar 22. We therefore regard bar 24 as a codetta, similar to that so often seen in an exposition. 154 Fugue. [Chap, ix 316. At bar 27 the third stretto is introduced. The interest is here heightened by bringing in the imitations at a closer distance — one crotchet instead of half a bar. Variety is also obtained by introducing all the voices in the octave. We have marked the entries with ' A ' instead of ' S,' because the G natural of the tenor in the 28th bar proves the key of the music to be D. The ' A — ? ' in the alto of the same bar indicates an incomplete entry. Another, similarly marked, will be seen in bar 44. 317. Another series of close imitations will be found in the fourth episode (bars 29 to 33). This leads to the fourth middle entry — another stretto for three voices, each a sixth above the preceding, and at a crotchet's distance. This stretto is an advance upon the preceding, inasmuch as now all the three voices complete the subject. 318. The fifth and last episode leads to the final section of the fugue, in which the subject is once more introduced in the tonic key (bar 40). It is now accompanied with simul- taneous double counterpoint in the tenth and octave (compare bar 40 with bar 3). The entry of the answer at bar 43, with chromatic alterations, leads to the last and closest stretto. This is the stretto maestrale, already quoted and described in § 278, and it is followed by a short coda, in which the figure of imitation, so often referred to, is maintained to the very last note. 319. It will be seen that this fugue differs in many important respects from the fugue in E minor, and nearly every leading feature of a fugue which is not shown in the one is illustrated by the other. One point of difference is that in the former there are scarcely any rests ; all the voices are almost continuously occupied. In the fugue in D, on the other hand, we find not only one, but in bar 16 two voices resting at once. It is generally better to give occasional rests to some of the voices. After such a rest, the voice that has been silent should enter with the subject, or with some decided feature of the counterpoint (see the entries in bars 17 and 18), and not drop in, as it were, inci- dentally, and without anything particular to say. 320. Another point to notice in this fugue is that nearly all the entries of the subject are preceded by a rest. That this is not absolutely necessary was seen from the fugue in E minor, in which very few of the entries are so approached ; but it is nevertheless preferable as marking the entrance of the subject more clearly. Where this cannot well be managed, the next best thing is to approach the entry by a leap, as in the fugue in D, bars 27, 33, and 43. 321. In bars 16, 20, and 27 of the fugue in D will be seen full cadences, and at bars 10, 33, and 44, inverted cadences. The latter are very common, the former are rarer. It must be remembered that when a full cadence is employed in a fugue, the music must never come to a standstill ; the last note of the cadence must always be a starting point for a new entry, chap, ix.] Middle and Final Sections. 155 either of the subject (as at bar 27) or of some important figure 01 .counterpoint (as at bars 16 and 20). Occasionally in old fugues, we meet with a full close in some related key just before the final stretto ; but this is not to be recommended. 322. To what keys, and in what order, is it advisable to modulate in the middle section of a fugue ? To this important question it is not possible to give more than a general answer. The rule given by the old theorists was that the modulations in a fugue should be confined to the nearly related keys. We quote Cherubini's remarks on this subject : — " When a fugue is in a major key, the key into which we should modulate first is that of the dominant with its major third', then into the sixth -the relative minor key of the principal key ; after that into the major key of the subdominant, to the minor key of the second, and to the mediant, also minor ; and then return to the key of the dominant, in order to proceed to the conclusion, which should be in the principal key. "It is permitted in the course of a fugue in a major key to change the principal key into the minor ; but this permutation should be employed only for a few moments, and merely to bring in a suspension on the dominant, in order afterwards to attack the principal major key. ' ' When a fugue is in a minor key, the first modulation is into the mediant tnajor key, which is the relative major of the principal key ; then we modulate in turn into the dominant ntinor key, into the sixth major key, into the subdominant minor key, and into the seventh major key ; and lastly from one of these keys return to the principal key." 323. We have quoted Cherubini somewhat fully, because it is well that students who are working for an examination should know what the old rules are ; but when we come to apply to them the test of Bach's practice, we find that they will not hold water for a moment. In the whole of the ' Forty-Eight,' there is not one single fugue in which the order of modulation prescribed by Cherubini is observed. What is even more to the point — in the ' Art of Fugue,' a work written by Bach, to show the proper method of fugal construction, we also find no fugue written on Cherubini's plan. 324. Besides this, we find that Bach, though he generally keeps within the circle of nearly-related keys, has no hesitation about going into unrelated keys when he has a mind to. No. 4 of the ' Art of Fugue,' the key of which is D minor, contains a modulation to B minor. In the fugue in E minor (No. 10 of the ' Forty-Eight ') there is at bar 30 an entry of the subject in D minor ; and in the fugue in A flat (No. 41 of the same work), we see at bar 32 an entry in E flat minor. The great organ fugue in D contains entries in C sharp minor and E major, and the organ fugue in B minor has an entry in C sharp minor. It is quite clear, either that Bach did not know how to write fugues properly, or that the old rules need altering. Of course we choose the latter alternative. 325. The rules as to the course of modulation and the middle entries in fugues which we deduce from Bach's works, are as follows : — I. It is best in general to keep within the circle of nearly- i5° Fugue. [Chap. ix. -elated keys, but an entry in an unrelated key is occasionally possible, if such key be naturally introduced, and not (to use Mozart's immortal phrase) " pulled in by the hair of its head." II. A middle entry may either be isolated — that is a single appearance of subject or answer in one voice ; or there may be a group of entries, two or more voices in succession giving subject or answer. In the latter case it is best, except in a close stretto (see bars 44, 45, of the fugue in § 308), that the entries should be at the distance of a fourth, fifth, or octave. III. No two successive groups of entries should have the same order of voices. IV. No two groups of middle entries should be in the same key, nor should the same voice have subject or answer twice in succession. 326. This last rule is not always strictly observed. A remarkable exception will be seen in the 19th fugue of the 1 Wohltemperirtes Clavier,' where the bass gives the subject in bar 4, and the answer immediately after in bar 6. Another example will be seen in the fourth fugue of the same work, where at bars 19 and 22 there are two consecutive entries of the subject in the tenor. The rule is, nevertheless, a good one, and the student will do well to adhere to it carefully. 327. It is not necessary that all the voices should take part in a group of middle entries. In a two-part fugue it will of course be needful, but in one with more than two voices, one at least may rest, if desired. This, in fact, is often expedient, for the sake of obtaining the contrast of thinner and fuller harmony. For an example, see No. 15 of the ' Forty-Eight,' bars 34 to 46, and 51 to 55. In the final section of a fugue, which always begins with the last return of the original key, it is imperative that all the voices be engaged, though it is not necessary that all should have subject or answer. If, however, the fugue contains stretti, it is best that all the voices take part in the final stretto, which should also be the closest. 328. We have already seen that there is no fixed number of groups of middle entries, which may vary from one or two to five or six, or even more. Neither is there any rule as to the order of voices for these middle entries, except in so far as concerns the point referred to in Rule III., § 325. It must not be forgotten that if stretti are used, their interest should always be cumulative. 329. When a pedal point (either dominant or tonic) is met with in a fugue, it is almost always in the final section. Occasionally we find a pedal earlier in a fugue, as, for instance, in No. 35 of the 'Wohltemperirtes Clavier,' and in the choral fugue, " For holy blood must be " in Schumann's ' Paradise and the Peri.' Such cases are, however, exceptional, and the student, if he wishes to use a pedal point, had better reserve it for the final section, as it is seen in the fugue in E minor in § 298. In a fugue containing stretti, the last is often made upon a pedal Chap. IX.] Middle and Final Sections. '57 which sometimes in this case is an additional voice, as in fugue 20 Of the ' Forty- Eight,' bars 83 to 87. 330. A few general principles will conclude this part of our subject. We have already (§ 321) spoken of the necessity of continuity in fugal writing. This necessity will be best shown by quoting a passage from Mozart's ' Musical Joke,' written as a burlesque of unskilful composers. This work is full of the most ludicrous mistakes in composition, intentionally introduced. Consecutives, passing notes quitted by leap, and similar atrocities, abound in it, but treated so skilfully that the joke is always perceptible. In the finale, Mozart introduces a little bit of fugue, thus — Violino imo. Violino 2do. Viola. fe — 1 — 1 1 f r r r r f^Z (W: L 2 fg 1 p f rr p ~1 m F~ ~s — H — -1 — LLLf pr *r 1 1 1 1 1 — r ^z: *~ T S J=t 22: E=* — m^^- rr ff=== |-n — pp- -^e- -•r- T *>- '"X -1 ^ — t= ■ 1 r — =P- — ^ ~ 1 1 — _Lj — 1 -1 — l ■ ■ t f -J 1 1 49- =3= f- Hi* r -1 — ' — ^^ 1 — 1 -p-* — -i 1 — 1 — — r= — The student will see that there is here a subject, a counter subject, and a regular exposition; and yet how ludicrous the <5* Fugue. LChap. IX. effect of the whole is ! This is because of the want of continuity ; the piece is chopped up by the full cadences into lengths of four bars each. A full cadence in a fugue (which should in all cases be sparingly used) must always be a point of departure for some new entry, if not of the subject, at all events for some important feature of counterpoint. We have referred to this above, but we repeat it as a point of vital importance in fugal writing, which will be enforced by the example just given. 331. We saw in the fugue in D (§ 308) the expediency of occasional rests in the voices (§ 319). After a rest, the voice which has been silent may enter on any part of the bar ; but it should always end before a rest, on an accented beat. 332. One final point remains to be noticed. It has several times been incidentally said that a fugue is essentially a. polyphonic composition. It is therefore of great importance that each voice should preserve its individuality. Passages for two parts in thirds or sixths, though not absolutely prohibited, should be sparingly used, and, in any case, not for long together. Passages in which a subject is accompanied by plain chords are also seldom advisable, though they are occasionally to be used, even with good effect, as in the following example — J. S. Bach. Wohltemperirtes Clavier, Fugue 18. ml — 1 L & =1 — ha — k* — =1— ha — 3- u ' 1 C 1 1 p l» 1 1 U I ■&=*- 1 U y i r ft r y L g Eg - i?JE£Eg 3zzr The student will do well in his attempts at fugue to keep to the strictly contrapuntal style. 333. The student may now begin the composition of a complete fugue. To show him how to set to work, we shall write three fugues for him, one in two parts, one in three, and one in four. We will take the subject we wrote in § 254 to illustrate stretto, as this will give us the opportunity of intro- ducing several stretti at different intervals and distances. The student had better begin by writing a few two-part fugues, as these are easier than those with three or four voices. He must remember not to introduce any progressions between the voices which would not be allowed in free two-part counterpoint. He should also always bear in mind the harmonic progressions indicated by the outline harmony. Chap. IX. Middle and Final Sections. *59 334. The first thing to do is to lay out clearly in the mind the general plan of the fugue. We know that the first and the final sections will be in the keys of the tonic and dominant ; but we ought also to decide on the keys and order of the middle entries, and not start on our journey like Abraham, not knowing whither we go, and trusting to luck to come out somewhere. As we do not intend any of our specimen fugues to be very long, we will content ourselves for the one in two parts with two groups of middle entries — one in A minor and the other in F major. The outline of the fugue will therefore take the following form : — (1) Exposition, to which, as there are only two voices, we shall add a counter-exposition. (2) First episode, modulating to A minor. (3) First middle group of entries in A minor, with first stretto. (4) Second episode, modulating to F. (5) Second middle group of entries in F, with closer stretto. (6) Third episode, modulating back to C. (7) Final section of fugue; entries in C, with closest stretto. 335. Some such outline as this ought to be clearly in the student's mind before he begins to write. We now give the complete fugue. Allegro. m CS; *—TT B r g rr h e rrr? :*==£ ( if — ' ^*f ■a* r & — H*- -*— =(£= =Pffi f r -M- -4^ n 1 »ri r -m- -| — =F= cs- _| 1 1 =s_ — J 4KL i — r ■J£m qt -m — 1 rff-r -m- -] — m — 1 V <4 lil in n - — 12 (cjb=c£cm 1 CS j j 1 rrn , q=\ m-i l i 1 g-r «igj J _ * «B j J= ^ * * ^ — j — g* 1 f 1 1 r r r 1 r r r Cr m -0- ■*- T~-*- 1 i \ u = t5 1 _| ! 1 — j_j ! 13 14 15 16 too Fugue. [Chap. IX "I Middle Section. ( J "-<*m- -* « — pju »*»,, ^=T^ c f r r i _j_ 1 1"]*"] — | 1 1 1 ! r ' 1 . $w— 1 Episode 2. iHSJb P V 25 26 ^flj rf- J - — 1. 27 28 '■ ^.ff F i S3=e H^ J J J j l j r -e-J-^J-^3 ^^ ; Episode V 33 ' 34 ' 35 ^ 36 ' « 1 1 1 pa Final Section. H — . 1 r c r ~ — r — J=h £*— (■ 1— I J J J-« *-* — J—t-* — — J— i h •*- A 1 Pr -J 1 1 r-V -4— p— t* SP f ^~ 37 38 -• Jd\ ft j — j jjys- p i 1 39 40 l-f 1— J 3 -? i i ft— -j :=3— -~— I IP 1 «J if r r -*sf- r e ' s rail. — 1 (W-:— » — = — p — |* — -* — i*<» » -m — ft ftfqw *ip- mPmm • 1 J 5w_, 1? — p — 1 M j ' ' -1 ^— 42 -\ — J *»LJ s«J_ 13 i 1 i i K— ir -= — \ 45 Chap, ix.] Middle and Final Sections. 161 The rule given in § 325 that two successive entries should not be in the same voice does not apply to two-part fugues ; for if it did, the same voice would have either subject or answer mostly all through a fugue. We shall therefore modify the rule in this case, and say that in two-part fugue " the same voice should not have subject or answer twice in succession, unless separated by an episode." 336. We have written a countersubject against the answer (bars 5 to 9), but shall be unable to make much use of it in the middle and final entries, because of the stretti , for the countersubject must evidently be discontinued when the voice that is giving it has to take up the subject or answer. But fragments of it will be seen in bars 26 and 34. 337. In the counter-exposition (bais 10 to 18) the treble which first had the subject leads with the answer, and the bass replies with the subject. The first episode (bars 18 to 21) is made from the inversion of the last three notes of the subject, treated sequentially by the treble, and imitated in the fourth below by the bass. 338. The first group of middle entries (bars 22 to 28) is led by the answer, and imitated in the octave, also by the answer, at two bars' distance. The leading voice is here able to complete the answer. The second episode is founded on the fourth bar of the subject, imitated in the fourth above ; it will be remembered that the imitation in the first episode was in the fourth below. This second episode is only two bars in length. 339. In the next group of middle entries (bars 30 to 35), the subject in the bass is followed in the regular interval by the answer at one bar's distance. The third episode is a sequential treatment by the treble of an ornamented form of the counter- subject in bar 8, imitated in the fifth below by the bass. The final section of the fugue contains the closest stretto (bars 40 to 45) at half a bar's distance, the answer being lengthened by the repetition in bar 43 of half a bar, to bring the piece to a satisfactory close. 340. We will now write a three-part fugue, and for the sake of variety will take the answer of the last fugue as our subject. As this answer was in the key of the tonic, it follows that the present answer will be in the key of the dominant, and will consequently be identical with the subject of the last fugue. We will write an entirely new countersubject — this time, for a change, in double counterpoint in the twelfth, and will begin the fugue with the middle voice, so as to show the countersubject in both positions in the exposition. Our plan of modulation shall be the same as in the last fugue, with middle entries in A minor and F, and each group of entries after the exposition shall contain a stretto. l62 Fugue. ICliap. IX. A llegr* s A 1 l |- 4- =+-p- PgH g — ■ p ^— ~f~^"~W~f_ j Jj ^ CS- 101 — 1 — P =S^=h^ — ' J1| 1 — i — r 1 1 r — p 1- 1 | J ri? r w=\ P- *-* — * — • L -^ 1- u* - — -uJLL 1 ' 1 1 m — — 5 — — =_ ^ 5 6 7 8 cs- cs ^ 17 18 U->^ 19 45 r-^2- 20 fe— r cr ir r ^ ^ ^-pe * , » * * ,. r S * r ^^^ ^ ~f'^ m 1 — fa t ^ ^=t 21 23 24 ^-r ^n~rj \ j j J J i ^5 =e Episode 2. B ^rn^r -•-*- L / I r r r r L£^ ^ i i i -> 25 a* 2^ m i r r r 27 ' 26 yj j p i r c a "r c r i J H ^ =221 e 28 ^ 29 ^~ir r r a- 30 31 CS- i -1 — t 1=E fe 1»-f- ^-H*i r^ ^ g -y— r §ee* * p r rr *■ j rt : J=£ q I K i ^ r r if r r crir r r Crir_fjLT Cr i Episode 3. S^ 1 I 164 Fugue [Chap. IX a Final Section. pfl (2 ...... -r . . f _ r 4^—*-^ gi 1 1 -1 1 1 ==— 1 ! ^— -1 — — — g r - «» rtti — ■p 1 1 if r r r " ,f^f — -m- ^--m- m ,M- J — t ^ J j — r— 1 — ' — J *!??_J ! |J =_J j 'iii g: P p g -p— • i } „ F ztPhp- h» r r^H ^ 40 41 42 « 341. After the explanations given of the last fugue, this will need but few remarks. Note that in all the stretti the last voice to enter always has the subject or answer complete (§ 252). Observe also, as showing how much variety is possible in a subject well adapted for the purpose, that none of the stretti here given are identical with those in three parts made from the same subject in §§ 264, 265. The incomplete entries are, as before, indicated by S ? Where the entries are at irregular distances, they are marked with S, whether they resemble subject or answer. 342. Now let us look at the episodes. The first is made from the sequential inversion in the bass (bars 13 to 16) of the last notes of the subject, accompanied by sequential imitations in treble and alto of a variation of bar 4 of the subject, by direct motion. The second (bars 25 to 30) is a canon in the fourth below between treble and bass, founded on the first part of the countersubject, and accompanied by a florid counterpoint in quavers for the alto. The third (bars 36 to 40) is another piece of canonic imitation between treble and bass, now at half a bar's distance, made from the beginning of the answer in a varied form, while the alto has partial imitation (mostly rhythmic) of the first notes of the subject. Note in bar 43 the transient modulation to the subdominant, to avoid the awkward progression of a tritone in the alto and bass. 343. For our last illustration we write a four-part fugue. We take the first half only of our subject, so as to make the piece Chap. IX.] Middle and Final Sections. t6 5 more concise. A short subject is frequently advisable with a larger number of parts ; with a longer subject there is often danger of the fugue becoming straggling and tedious. As we intend to combine the theme with itself in stretto as much as we can, we will write no countersubject (§ 176). We will also i-ntroduce some points not illustrated in the preceding fugues. We will make a larger number of modulations, giving middle entries in G, A minor, D minor, F, and E minor (all the nearly related keys) before we reach the final section of the fugue. Allegro. -< S i 1 , • — JL *fr p 9 J ~J *' !* g r ~^ — J •* p r~ ' *" ■* r p 5 p ■ w Vm - = — 1 * •Ml 1 1 1 ==—*^ ^ 1 1 i, M P r 5 1 f — r — f- . r *-i 81 4 — ^4 - 1 = — ! E p 1 E 1 r 1 — W- iPli-4 ftM-4 !w_ 4 S 1 2 3 4 ff ;: -. H -: -<■==*= rrfJi 1 jryi ^ =a ^— r M-p 1 — «J *^ Codetta. ,. — ^ «* * * r In! 1 1 1 1 j H - 1 - 1 s _p p — -1 m 1 1 i - 1 ^5 6 7 8 Middle Section. i66 Fugue. [Chap. IX. gj/H crcccr l - 1 & r CEfaW =ft=P= -C££r^-^ -r— t § i rT r r- t^H^^ ^ 1 * 7T aPff *i*l* H — p — = A P" U g — i — i rt^-^r-^ S ha e **-p— -S Pffl^ =^^= -J — T— »— &— Ini ! ! =t= WH" — ffrr -1 1 1 != w n ~F — Wf Jg -t- 1 k L_ : J£l — | 1 j ~ u-i-T r 1 r- Hjj; dg J =ta= it S (inverted.) ^ 17 18 19 20 J 4 J B r f — H ^— !• — r- ^p-J — i — J «H j r r- frb * J * | 1 =-* f— r- j— ll-H-jjp - ^ — p y^ g r — p^, m Lj - — J * **fl J UT ■ Episode 2. to p j^,- p a — f. 1 = - i — r Liiu t L— 1 j i*i * - ft ffp rt|i«i » , "i ^ f r r r — J J J j *3-j- ^ ' ' 22 23 1 " ^ L r i* ^H r » r i r r r^=i Chap. IX.] Middle and Final Sections. 167 ffT-r-^T- r I f "Cr>r i^^ ^^ fflt te Episode 3. Ul-tf FB=F «=» r p = feLJ^^Ij- rrf- S S£ 30 31 32 £ pi 1 * 5 ^=ac te^^TXi y """ - m m ■* p» — ; s 1 — r — *-~i h— p — ui ' r — l ft - m P — F 1 — —J — F r .#-4? jS=j ^ 33 34 - - £j— :— 1 35 I q*=ff; ^ 4=t b» f- r - g j g * ,i g =3 b*- l* 1 g r is r 1 I L ^^ ft=^= ±ac=ff=^p:Spr P g m S3: S~ ^^ • gr-g act Sac g=^=^ S t=t Episode 4. liJ a I r i& ^ ^ £==*: rfiS Fugue. [Chap. IX. Final Section. flrrrrivrr j r cjm-|r 1 Coda. fe rTrr r fr r ^ -r r m 4=±= B Qa=L *=•£ 56 57 ^ I [ 58 59 Chap. IX.) Middle and Final Sections. 169 \ 1 L m m — g-g-j-jj—g — r f--r 344. In bars 5 to 7 we have introduced a codetta. There was no necessity for this, as the tenor could perfectly well enter with the subject in bar 5 ; but, as Bach frequently has such a codetta in his fugues, we have written this to show how to manage it, if it is desired. The first episode (bars 12 to 16) is made by inverting the codetta in the tenor and bass, and adding a sequential counterpoint in quavers for the treble. The first group of middle entries (bars 17 to 22) shows the first (partial) stretto, the bass entering half a bar before the regular time with the inverted subject. Here a modulation from G to A minor is made during the entries, instead of (as is more usual) during the episode. 345. The second and shortest episode is made from the beginning of the inverted subject in the treble, with a continuation freely imitated by direct and inverse motion in the alto and bass. Both first and second episodes are for three voices only. 346. The second group of middle entries, in the keys of A minor and D minor, gives a stretto at one bar's distance in all the parts — the alto entry being incomplete. It leads to the third episode, the most elaborate of the three (bars 30 to 35). It is a short canon 4 in 2, at one bar's distance, by contrary motion, and with inversion of the voices, founded on the first notes of the subject with a counterpoint of quavers. The third group of middle entries (bars 35 to 43) is again a stretto at one bar's distance ; but it differs from the last, inasmuch as now all the voices have the subject complete. At bar 41 is a modulation to E minor, in which key a partial stretto, for alto and tenor only, at half a bar's distance is seen. The last short episode (bars 43 to 46) founded on a sequential continuation of the last notes of the subject, leads to the final section of the fugue. 347. This final section (bars 46 to 63) is far more extended than in the other two fugues. It begins with a stretto maestrale (§ 277), led by the treble, each succeeding voice entering at half a bar's distance, and a fourth below the preceding. At bars 51 to 57 a pedal point is introduced, with four voices above it (§ 329). Here there is a second stretto maestrale, the order of r7o Fugue. [Chap. ix. entry of the voices being now reversed, and the bass leading. The pedal is continued over a passage of free imitation founded on the treble of bar 35 ; and at bar 58 is a coda, with a final entry of the subject in tenths for treble and tenor, imitated by alto and bass in tenths in the following bar. 348. From the full analysis of the way in which we have written these three fugues, the student will probably learn as much as is possible to teach in a book as to fugal construction. More can be learned by analysis than in any other way. For this reason we shall follow this book by a companion volume on Fugal Analysis, which will contain a collection of some of the finest fugues ever written put into score and fully annotated. There is not room in this volume for a sufficient number of examples to illustrate the matter thoroughly. But mere analysis will not of itself suffice : the student must practise for himself, writing each separate part of a fugue (exposition, episode, stretto, &c.) till he has xcquired fluency. Nothing but natural aptitude, aided by a great deal of study and hard work, will ever make a good fugue writer. Chap X.J FUGHETTA AND FUGATO. 171 CHAPTER X. FUGHETTA AND FUGATO 349. In the preceding chapters of this, volume we have explained the construction of the most common kind of fugue — that with only one subject. Before proceeding to treat of fugues with more than one subject, fugues on a choral, or fugues with free accompaniment, there are two other varieties of fugal writing with which this is the most suitable place to deal. These are the Fughetta and the Fugato. 350. The word " P'ughetta " is the Italian diminutive of " Fuga," and merely means " a little fugue." It is a term of somewhat vague application ; and it is impossible to lay down a hard and fast. line of distinction between fughetta and fugue. For example, among Bach's works for the Clavier, we find a so-called 1 Fughetta ' in E minor, beginning which is a regularly developed fugue, extending to 105 bars, with a long middle section. In its number of bars it exceeds 46 of the 48 fugues in the ' Wohltemperirtes Clavier.' This is an exceptional case ; but we refer to it to show the vagueness with which the term is sometimes applied. 351. In the form most frequently met with, a fughetta is an abridged fugue, and is almost always a complete movement in itself. It contains a regular exposition ; but the middle section will have at most not more than one group of middle entries, and in many instances it is omitted altogether. In such cases the exposition is followed either by an episode leading to the final entry of the subject in the tonic key, or this final entry may follow the exposition immediately, without any episode whatever. 352. These variations in fughetta form will be most clearly shown by examples. We first give an illustration by Bach of the longer fughetta, containing the regular three sections of a fugue, though all are on a small scale. J. S. Bach. Fughetta in D minor. § ¥W m 5* 1 » >f ^^ s 172 Fugue -j>? jm tf J?5S3 S 5 1213. JJJJJjJ. *• | " " -** -£f B^-j J J $5%^" %£i£^~l 34 35 36 37 38 Cbap. X.] FUGHETTA AND FUGATO. Final Section. '7.3 As the fugue is for only three voices, and contains no crossing of parts which might render it difficult to follow, we give it, to save space, on two staves. The student will by this time be sufficiently accustomed to analysis of fugues to render it superfluous for us to mark, as hitherto, the entries of the subject. 353. An unusual point in the exposition of this fughetta is, that the third voice enters with the answer instead of the subject. The group of middle entries appears to commence with the subject in the tonic key; but the following reply at bar 25 shows that the entry in bar 20 is really the answer to the subject in the key of G minor. Further entries in the same key, now at the octave, are seen at bars 33 and 37, after which, without a second episode, the final section, containing two entries of the subject succeeded by a coda, follows immediately. This fughetta is really a complete fugue, much condensed — a sort of " Liebig's extract " of fugue. •74 Fugue. [Chap. X. 354. An interesting fughetta of a different kind, also by Bach, is that in F. It will be seen that the subject is identical with that of the fugue in A flat, No. 41 of the ' Forty-Eight ' ; and if the two pieces are compared, it will be found that, except as regards key, they are exactly the same down to the 24th bar, where the fughetta ends. The latter is the earlier version, and it contains a complete exposition, an episode of four bars — no middle section at all — but a large final section with entries for all the voices, which, when Bach rewrote the fugue for the ' Wohltemperirtes Clavier,' was made to do duty as a counter-exposition. If the student will read the first half of the A flat fugue, he will see the fughetta complete ; there is therefore no occasion to quote it. 355. Our next example, by Handel, is different in form. Handel. U'recht Te Deum. th»- m i=t l S3 T=2 M* g ?=*=% T-P- a*=Sfc 1 -w~r 1*3=^ ]^_^_L t=q£=t t=X=± 1 1 ±R ifc t=t &=F :ff=p: r m I m-f B t=t 1^ r r ^rM ^g gg^H ppe^ Jht 10 11 Cljap. X.i FUG H ETTA AND FUGATO. '75 This fughetta is for five voices. It begins like a close fugue (§ 279); and it will be seen that at the entry of the fifth voice (tenor), in bar 5, the subject is varied. Handel's fugues are usually freer than Bach's. There is no episode at all, but there is a fragmentary group of middle entries (bars 7 to 10). This embryo middle section, if we may so term it, is followed by a final entry of the subject in the tonic key (bar 12), and a short coda completes the movement. 356. Another variety of the fughetta form is that which consists merely of a complete exposition, followed by one final entry of the subject by the voice that first led. A very neat specimen of this variety is the following, taken from one of Mozart's Masses. Mozart. Mass in F, No. 6. m 1Z=W r m m i ±s E fee ijb Fugue. [Chap. x. l ^aA^ ±=t ^33g ■■ ki!.. g - & 5 ^ P^: s «= sr^ iir~ ^p It will be seen that here the final entry is in stretto at close distance of time for all the voices ; but in this form it is not necessary to observe the rule (§ 252) that the last voice that enters must complete the subject. Here the tenor in bars 10 and 1 1 gives the subject in an abridged and slightly varied form. 357. Sometimes, after a complete exposition, the final entry will only be fragmentary, and will be followed by a coda. fcfct 1 I p g Beethoven. Mass in C. m^^^mz-^z i *- TTF-J =3 S^ :£S5=t K* j£-^g£. JtW- B P fei sS FUG H ETTA AND FUGATO ^-8-S ♦ «a- 1 p -«>- -mh m m- ■ jg -P- f MK ^ m 1 f- (•■- « ■ f . P |. r Inl fl 8 £*** -0L 1 .. » | 1 n ] g ^ 13 14 _£_r — L — 15 JL-J ' 16 It is somewhat unusual for the first voice to leave off on the entry of the third, as here at bar 5 ; generally (and preferably) it continues, as in our other examples, with a free counterpoint. The final entry (bar 10) is only partial, not more than the first half of the subject being given by the treble ; from the eleventh bar, the polyphonic style is abandoned, and in the coda all the voices move together in plain chords. 358. The word Fugato simply means " fugued," and is applied to passages written in the fugal style — that is to say, in which the same subject is introduced successively in the different voices — but in which the entries are not at the regular i 7 8 Fugue. [Chap. X. interval of subject and answer, or, if they are, their employment is only incidental. Passages of imitation, provided that all the voices take part in them, will very often be also fugato passages ; but in general in such cases the voices will enter in succession, the first voice being either unaccompanied by any harmony at all, or only accompanied by instruments, and not by any other voices. Such passages are often found in pieces not otherwise in fugal form. 359. In consequence of the freedom allowed in fugato, it is quite impossible to give any fixed rules for its construction. Its nature will be best understood by the examination of specimens by different composers, and in various styles. Our first example will be by Bach. Bach. ' Matthaus Passion.' m j jut ^ i iJ J j j J 1 iiJTTJ J J UJ j j j j J In this passage we omit the semiquaver accompaniment in the Coap. X.] FUG H ETTA AND FUGATO. I 79 bass, which is to some extent independent of the voices ; the bare fourths in the sixth and seventh bars are filled up by the instrumental part. We see here that, though the interval of entry of the voices is quite regular, it is not that of fugue subject and answer as regards the third and fourth voices ; we have here therefore a passage of fugato. 360. The following well-known extract from the ' Creation ' is given in short score to save space, and the independent orchestral accompaniment is omitted. Haydn. ' Creation. P s m F=fi n Jl*_ * ~*J I WJ i^ m 1 M? j j t^ This example is somewhat similar to our last ; but while the first three entries are at regular distances — each a fifth above the preceding — the treble is only a fourth above the alto. 361. Similar passages to these are of frequent occurrence. As fine examples may be mentioned, the passage in the Offertorium of Mozart's ' Requiem ' to the words " ne absorbent eas tariarus, ne cadant i?i obscurum" and the beginning of the allegro of the chorus, " Praise ye Jehovah's goodness " in Beethoven's ' Mount of Olives.' We merely refer to these, and prefer to quote for our next illustration a fugato of a totally different style — the opening bars of the slow movement of Beethoven's first symphony. We condense the orchestral score on two staves. Beethoven. 1st Symphony. 1 m o* -jL±JTLrc P pp* is CfiJ i8o Fugue. iChap. x. i >JSB Jji B i s p m rm *~st$ Although the commencement of this passage looks at first like the subject and answer of a fugue, a moment's examination of the counterpoint accompanying the answer will show that we have here only fugato. The rhythm of subject and counterpoint are identical, and the style of the whole passage is distinctly homo- phonic rather than polyphonic. After the end of our extract, every attempt at imitation is abandoned. 362. We conclude this chapter with two more modern examples. Mendelssohn. ' Elijah. DH :ff_ — Lf- f— P— -L. 1 T - j J 1 r ' ' In this passage the small notes on the bass staff indicate the real bass of the harmony, which is given to the orchestra. It will be seen that here no two consecutive entries are at the same distance of interval. 363. In our last illustration, , Mackenzie. ' The Rose of Sharon. fegg Chorus Basses of orchestra. ^ -r-w r | J - JOT Chan. X. FUGHETTA AND FtTGATO. the basses of the orchestra have so independent a part that it is needful to write it on a separate staff. Here we have an example of the modern free treatment of the contrapuntal style. Not only the interval of entry, but the form of the subject itself varies on nearly every repetition. 364. It is hoped that these examples will sufficiently show the nature of the fugato. It is, of course, far easier to write than a strict fugue, or even a fughetta, and is not of sufficient importance to require a lengthy notice ; but as this volume might perhaps have been considered incomplete without it, we have devoted a few pages to its consideration. » 82 Fugue. ichap xi CHAPTER XI. THE FUGUE ON MORE THAN ONE SUBJECT. 365. Having in the preceding chapters of this book fully explained the construction of those fugues which, being founded on only one subject, are sometimes termed " simple " fugues, we have in this chapter to speak of the important class which contains two, three, and occasionally even more subjects. We shall first deal with the Double Fugue, in which, as its name indicates, there are two subjects. 366. In speaking of the countersubject, we incidentally men- tioned (§ 175) that some theorists speak of a fugue in which the subject is regularly accompanied by the same countersubject as a " double fugue." If, however, we adopt this nomenclature, we have no means of distinguishing between fugues with one subject and fugues with two or more. It is very much better and clearer to restrict the name of double fugue to two classes of fugue now to be described : — First, those in which the two subjects are announced simultaneously ; and, secondly, those in which each subject has a separate and complete exposition before the two are heard in combination. Of these, the first kind is by far the more common and the more important ; we therefore deal with it first. 367. A fundamental distinction between the kind of double fugue we are now noticing, and the fugue with a regular counter- subject (with which the student is already familiar) is, that in the latter the countersubject never appears before the first entry of the answer, and, as we have seen (§ 172), not always then. But in a double fugue the second subject, which is really a counter- subject of the first, accompanies the leading subject on its first entry. This, as we shall see presently, makes a difference (some- times a very considerable difference) in the form of the ex- position. 368. It ought to be hardly necessary to remind students that the two subjects of a doable fugue must be written in some kind of double counterpoint with one another. In the enormous majority of cases, this will be double counterpoint in the octave. In the ' Kyrie ' of Mozart's ' Requiem,' the two subjects (which we quoted in § 175 of Double Counterpoint) are so written as to be capable of inversion both in the octave chap, xi i Fugues on More than One Subject. 183 and in the twelfth. It is also necessary that there should be contrast, both melodic and rhythmic, between the two subjects, so that each may be easily recognized whenever it appears. 369. It is best that a double fugue should be written for at least four voices, and in vocal music this is almost invariably the case. It is nevertheless possible, though less advisable, to write a double fugue with only three parts. In any case, the student will do well to attend to Albrechtsberger's recommendation that a fugue should always have at least one more voice than it has subjects. Thus, a double fugue ought to be in at least three parts, and a triple fugue (with three subjects) in at least four. But in fugues with more than three subjects (which are very rare), *his rule is not always observed, probably because in a fugue with four subjects it is seldom that all four are present at once. The object of the extra voice is, to be able to add a free part when all the subjects are going on at the same time. 370. The exposition of a double fugue can be managed in more than one way. In a four-part fugue, the best arrangement is to let two of the voices announce the two subjects, which the other two follow with the two answers by inversion — that is to say, the upper of the two subjects will appear as the lower of the two answers, and vice versa. A few examples will make this quite clear. I J. S. Bach. Cantata, " Aus der Tiefe rufe ich." gge=JEE Al. i* -1 r S2. Wr^f 1 ^ g^ Wi 5t as t=±t The small notes on the bass staff here show the instrumental bass ; the bass voices have only the second subject, which is r84 Fugue. [Chap. XI. printed in large notes. Here the two subjects are announced by the outer voices ; when the middle parts bring in the answers, the two themes are inverted in the octave. Notice that the two subjects do not begin simultaneously. It is extremely rare foi this to happen. Frequently the second commences only a crotchet, or even a quaver, after the first ; but it is undesirable that they should start together, as it would make it more difficult to distinguish them. The counterpoint in the treble of the last two bars is, as will be seen, a free part. 371. In our next example, Handel. Six Fugues for Harpischord, Nc. 1. j 1 ' "" i 1 ' " i„:'j^,L^ n rrf r rr w& S2. gffi the order of entry of the preceding is reversed. Here the two middle voices have the subjects and the outer ones the answers. Note in the answer in the treble the change of an octave in pitch (§ 154) to keep the music within the reach of the hands. The alteration at the end of both the answers is an illustration of what has been more than once mentioned — that Handel's fugue writing is usually much more free than Bach's. 372. It is not always necessary that the two voices which enter with the answers should be in the opposite relative positions to those which announce the subjects. Sometimes the part which was the higher at first is still the higher, as in the following example. Cnap. XL] FUGURS ON MORR THAN ONE SUBJECT. I 8? --m SI. Haydn. 1st Mass. Al. -&=&- t=t S2. A 2 ^SL §333, S2. i* m m 1 r~j » ^ ^ §g^^ :2^i We have here a subject taking a tonal answer ; the second subject (which corresponds to the countersubject of a simple i86 Fugue, [Chap. XI. fugue) also needs modification (§ 170). We have quoted the whole exposition, as it shows a very frequent manner of com- mencing a double fugue. 373. After the first entries of the two subjects and answers, we see other entries in the same keys as before, but differently distributed between the voices. At bar 5, the tenor has the first subject, and the alto the second ; in the seventh bar the bass has the first answer, and the alto a modified form of part of the second. Lastly, at bar 10, the first subject is seen again in the treble, while bass and tenor both have the second subject, the tenor being written in double counterpoint in the tenth. When an exposition contains only one entry each of the subjects and answers, it will be very brief. This is the case with the example in § 371, where our extract is immediately followed by the first episode ; more frequently, as here, additional entries precede the introduction of any episodical matter. 374. Occasionally after two voices have announced the subjects, the other pair, instead of giving the answers, repeat the subjects, but inverted in their relative positions. P Handel. ' Judas Maccabaeus.' SI. w^vrr j if 3tF m ^^ iSE £ Chap. X!. Fugues on More than One Subject. i*7 ^ m &=* ^m SSt x=st &c. « I m^E ±iE 10 11 12 It looks at first sight as if the first subject extended to the sixth bar. That this is not the case is proved by the second subject. If bars 4 and 10 are compared, it will be seen that they are quite different. Now it is an important rule in writing a double fugue that, though the two subjects had better begin one after the other, they must always finish together. Bar 10 proves that the second subject ends on the first note of bar 4 ; consequently the first subject must end at the same point, and bars 5 and 6 must be regarded as codetta. 375. The exposition of a double fugue is sometimes arranged in quite a different manner, which will be best understood by an example. Hummel. 2nd Mass. i PSI=E pgi 82 Al. I m A 2. 4e si. M m Fugue. (Chap. Xi -^8 2. ^ -^ A1 - ^fe~F"^=j J =?= J I g -^= g f f Eg z^z=g=rr=H r M ft b J — J — J — f 1 = " " «fc-b Mm, 10 11 12 13 As in the preceding examples, the two subjects are announced together, here by the tenor and bass voices ; but instead of the two answers being given by the other two voices, the tenor, which has just completed the second subject, continues with the first answer, the alto entering with the second answer. The bass continues as far as bar 7 with a free counterpoint, and is then silent till it re-enters with the second answer in bar 14. 376. The alto, having completed the second answer, continues with the first subject, while the treble enters with the second subject, going on in its turn with the first answer. This gives the bass the opportunity of bringing in the second answer below the first (as in the additional entry of a simple fugue), and the exposition is completed when both the subjects (or answers) have been heard in each voice. 377. In the above example, each new voice entered first with the second subject. In the following we see the reverse case, all the fresh entries being with the first subject. chap, xi.] Fugues on More than One Subject. 189 Cherubini. 2nd Mass. * * =sz ti*» r-y g s Al. ^T?E 4^P HP- ^=y s 10 11 12 13 14 /» p fS" h»— n 1 1 feN= ^ 1 1 1J>= g -J.-j-j- - g g T 1 "" ~i Ff llfli" I mfff h S2. i -, r >** — f.f 1 -f y— 1 ifiig 1 — A^Ht -j — 1 — — ! I — 1 — p-j — SI. ~p p H K 15 16 17 18 1 f- 19 20 — i : st* r p -r»rr ir v -~ — r y^r — — Fj — ! — : — 'CP '' — L -^~ i ' — 01 ** ct. f r*r — f — f — *~^~ ^ * ,y ^* ,r r f * — ' — ^ — A 2. to-HfS? r= = .?+ %• * * -7= -= — = «i fry- 21 22 23 24 25 26 :t jt 9° Fugue. [Chap. XI After the explanations of the preceding exposition, few words are needful concerning this one. If the student will examine it, he will see that a codetta is introduced before each new pair of entries. The treble, which led with the second subject, makes its final appearance at bar 27 with the first, showing the inversion of the two subjects, just as they were shown at bar 14 of the example by Hummel. 378. Another important point is illustrated by the two ex- positions just quoted. It will be seen that though both are for four voices, only three are present at any one time, while a considerable part of the exposition in § 375 is for two voices only. We often find this in the exposition of a double fugue ; the reason is that it is absolutely necessary that both the subjects shall be clearly and easily distinguished, and this end is attained by leaving them either without any other counterpoint, or with only one added part. Clearness is, if possible, of even more importance in a double fugue than in a fugue with only one subject. 379. The general form of such double fugues as those we are now describing mostly follows the plan shown in Chapter IX. But there are some differences of detail often to be met with that must be mentioned. In the first place we sometimes find less episode in a double than in a simple fugue. For instance, the ' Kyrie ' of Mozart's ' Requiem,' one of the finest double fugues ever written, contains only one episode, and that is but a bar and a half in length. When there is so little episode, its place is usually taken by developments of one of the two subjects without the other. 380. In general, both subjects should be heard together in each group of middle entries. Occasionally, we find such an entry for one subject alone ; but this is far more exceptional than the entry of a subject in a simple fugue without its counter- subject. 381. It is seldom practicable in a double fugue to write a stretto in which both the subjects shall take part. We have already seen with simple fugues that if there is much stretto, there is generally either no countersubject, or, if there be one, it is omitted in the stretti. The obvious reason for this is. that chap, xi.] Fugues on More than One Subject. 191 that part of the countersubject which is written against the latter part of the subject can seldom be also made to fit the first part which, in a stretto, will be appearing in another voice ; while, if all the voices are joining in the stretto, there will evidently be none left to give the countersubject. As the second subject in a double fugue is virtually a countersubject to the first, it is clear that the same reasoning will apply to it. Consequently the stretti, when there are any, in a double fugue are mostly made from one subject alone, and very often take the place of the episodes. 382. The general rules as to the order of entries, etc., given in § 325, apply also to double fugues, excepting that in the latter there should be no isolated entry for one of the subjects un- accompanied by the other. One entry of the two subjects together may, however, be divided by episodes from the preceding and following. 383. Our space will not allow us to give complete examples here of double fugues, as we did of simple fugues in Chapter IX. In the volume on Fugal Analysis, which will follow the present one we shall insert some fine specimens of this kind. Meanwhile it is hoped that the explanations given in this chapter will enable the student to understand the construction of a double fugue, and, if necessary, to write one for himself. 384. We have now to speak of the second variety of double fugue — that in which each of the two subjects has its own separate exposition, and it is only in the latter part of the fugue that they appear together. Though some very fine examples of such fugues are to be found, they are far rarer than the kind of which we have been hitherto speaking, and they are constructed after a different plan. 385. It is, of course, just as necessary in this kind of fugue as in the other that the two subjects must be composed together in the first instance, and that they must be in double counterpoint with one another ; otherwise it is in the highest degree improbable that it will be possible to combine them. The essential difference between this and the other class of double fugues is, that here the combination, instead of being shown at first, is reserved for the climax, whereby its effect is frequently much increased. 386. There is considerable difference in various fugues of this class as to the amount of separate treatment which each subject receives before they are brought together. Sometimes the first subject will have a regular exposition, and the second only a partial one, as in the following passage, which, to save space, we give in short score. Handel. Dettingen Anthem. J ,,, j.-.u^ y gi "22 — ■ — m ' f mm (Chap. Xt OS l l J 1 J J -J J*~^ /U tf ■ J . -= J =r^3 *d =* « s P"P m F" (rr^^- — «J a* «i J — J- i,q»j i j J-. j j J j » i | r i ■ i h r'-r — -J-J-T-J J -J J ■ J * J J • r r r r , V 1 ff 'r 1 '^— -if' 'rr J J^Til J J *m & * j. r j ■ Bi rrfrirVrF/rr'n/ 5 ^gb i SLMr'.^r ' r.M ' . ^^ fel fc: ^g r g Chap. XL] Fugues o-n More than One Subject. 193 fe^r 3TD ^^ * jLfcir^J j -1 — r-=T=f-' ^z=3=z2=\ ~&~^ 3PC S =«<=±rifcfc*=g=, ^^ ei r/ff ff j j ^=F =*=d— m> -J J-j, 1— • — ^ J ^ ij. j 1 i =P^E r * f r 1 — fs ^rT-^ ^23 V _J j I SSgi ■J 1- pSfe f777 1 1 T 1 1 r- J Hi ^-y s £a i=t -&J _ — _ A J J- ! "^J ■ , -J ■ !-n 1 1 B*t «> — ■ ra *M^- — \~& • ii v — 1 J Here the first exposition is separated from the second by a short symphony for the orchestra. In the second exposition, the subject in the alto is answered by the treble ; but the bass and tenor have only free imitations of its first notes, and there is no complete exposition of the second subject. After the cadence in G major, the two subjects are combined ; but the freer style is soon resumed, as will be seen from the last bars of our quotation. 387. Our next illustration is somewhat more regular in treatment. J. S. Each. Cantata, " Lobe den Herrn, meine Seele." i^fP S ^ *94 Fugue. [Chap, xt The subject here (as will be seen later when the two are combined) extends to the D at the beginning of the fifth bar. We have here therefore a "close fugue" (§ 279), though the answer does not enter so immediately after the commencement of the subject as in the examples of this kind of fugue previously given. The small notes on the bass staff show, as in other cases, the real (instrumental) bass of the harmony. We have here a quite regular exposition, of which (to save space) we have omitted the last two bars of the bass entry. In the continuation of the passage there are two instrumental entries — subject (2nd violins), answer (1st violins), making in all an exposition of a six-part fugue. 388. After three bars of interlude for the orchestra, there is a counter-exposition of the first subject. Here the bass leads with the answer and the tenor replies with the subject, all the entries being in the reverse order of that of the first exposition. We exceptionally find here that it is only the order of entry that is reversed ; usually a voice that had the answer in the exposition will have the subject in the counter-exposition, and vice versa. 389. The counter-exposition is followed at once by the exposition of the second subject. ^-f Chap. xi. j Fugues on More than One Subject. '95 This subject, like the other, is four bars in length ; it is also treated in six parts by the addition of entries for two violins ; but the irregularity of the intervals of reply show that this exposition belongs to the fugato (§ 358) rather than to strict fugue. 390. To the counter-exposition succeeds immediately the combination of the two subjects, of which we quote the first bars. For the sake of clearness, we here give them in open score. m m vf &c 9 6 Fugue. LChap. XI It will be seen that modifications are made in the second pair of entries ; in bar 7 of our extract the close of the first subject is transferred from the bass to the treble. We have already seen the same thing (§ 271) in the case of a countersubject. A little later we find the two subjects combined in a different manner. -a g 1 — u — p^— | — j-| — ««, _ — r 1 — I 1 — -L- -1 — — 1 — | — 1 , mi ff^ - - j 1 — » • *]% \fe» rwf*r *rrr *PTrpi — %m ? ^\ Here the first half of the first subject serves as a counterpoint to the second half of the second subject — a combination which we just now remarked (§ 381) was very seldom possible. But almost anything seems to have been possible to Bach. The whole fugue which we have been describing is a marvel of scientific contrivance, though we do not recommend students to imitate the consecutive seconds seen in the last bar but one of our last example. 391. One of the most perfect examples, as regards its form, of this kind of double fugue is an organ fugue by Bach in C minor. The piece is too long to quote here ; it will be found in the Peter's Edition of Bach's Organ Works, Vol. IV., p. 36, to which we refer the student, confining ourselves here to a short analysis of the piece. It will be seen to differ considerably from the examples already described. 392. The first subject of the fugue, which is in four parts, is Organ Fugue in C minor. tr This subject receives a regular exposition (bars 1-14) followed by an episode of four bars. To this succeed four isolated entries in the keys of G minor (bar 18), E flat major (bar 23), and C minor (bars 29 and 34). After a full close in G minor, with the " Tierce de Picardie," the second subject is announced (bar 37) : This subject, like the first, has a complete exposition, the second and third entries of which are divided by a codetta (bars 42, 43). This second exposition ends in bar 49, and is followed by entries of subject or answer in G minor (bar 49), C minor (bar 52), F minor (bar 55), C minor (bar 57); then, after an episode chao. xi.] Fugues on More than One Subject. *97 (bars 60 to 63), C minor again (bar 63), and an altered entry (bars 66 to 69), partly in F minor, and partly in C minor. 393. At bar 70 the two subjects appear together tor the first time. We quote the first two entries. j J. S. Bach. Organ Fugue, in C minor. TF~ry m ^[gasr Cr Manual. ^m ^m Pedal. Bi BE The modifications in the tonal answers will be easily understood if Chapter IV. of this volume has been thoroughly mastered. It will be seen that the figures of semiquavers have been simplified for the pedals. This is probably less because of their technical difficulty than because of the very practical reason that the lower notes of the pedal organ cannot be depended on to speak with sufficient rapidity. When the second subject (the more florid of the two) is given to the pedals, as at bars 77 and 88, it is even more simplified than the first subject. 394. The fugue we are now examining contains five entries subsequent to those last quoted. All of them are either in the tonic or dominant key, and in all both the subjects appear in their complete shape. A coda of six bars (bars 99 to 104) concludes the movement. 395. By comparing this fugue with those we have previously spoken of, we see what may be approximately described as the 198 Fugue. [Chap. xi. limits of variation in the form now under notice. In both our earlier examples, the second exposition followed immediately on the first, — in the case of the fugue in " Lobe den Herrn, meine Seele," after the counter-exposition. In the C mir or fugue, on the contrary, each subject has a considerable amount of working out before the next is introduced. In the fugues in §§ 386, 387, the combination of the two subjects followed close after the second exposition ; here it is not so. In fact, it is left entirely to the judgment of the composer in a fugue of this kind, how much development he will give to each of his subjects separately before he proceeds to treat them in combination. 396. A double fugue of this class, like a simple fugue, is in ternary form ; but its three sections are different from those of a simple fugue which we showed in Chap. IX. A fugue of the kind now under notice will contain the three following sections : — (1) Treatment of first subject separately. (2) Treatment of second subject separately. (3) Treatment of both subjects combined. We have already said that it is optional how much each section contains. 397. There is one more point to be noticed with respect to thus variety of fugue. Owing to the fact that both the subjects will have their expositions in the original keys of tonic and dominant, we usually find very little modulation in a fugue of this sort. As a striking illustration of this, take the fugue in C minor which we have just analyzed. Not counting the expositions, it contains in all fifteen entries, either of the single subjects or of the two together. Of these, twelve are either in C minor or in G minor. Only three (one fifth of the whole) are in any other key. It is quite possible, as Bach conclusively proves in this masterly fugue, to obtain variety by other means than incessant modulation. 398. A lMple Fugue, that is, a fugue with three subjects, is very much rarer than a fugue with two, and when we find one, it is seldom strict. The first requisite for such a composition is, that the three subjects must be written in triple counterpoint, as each will in turn have to do duty as a bass. It is also needful that all the subjects be well contrasted in character, as we have already seen that they should be in the case of a double fugue. 399. It is possible to write a triple fugue after the second of the two methods above shown for a double fugue, that is to say, to give each of the three subjects a separate exposition before combining them. But this plan is seldom adopted, probably owing to the length to which it will cause the composition to extend. A striking illustration of this is seen in the final fugue in Bach's ' Art of Fugue,' of which we will sere give a short account before proceeding to speak of the moR common kind of triple fugue. Chap, xi.] Fugues on More than One Subject. 199 400. The fugue now to be noticed, one of Bach's latest compositions, was unfortunately never completed, being inter- rupted by the composer's blindness, which shortly preceded his death. Enough, however, exists to show the scope of the whole work. We first give the exposition of the first subject. f £SE I. S. Bach. ' Art of Fugue.' fo e " Al- ?=: m Sl- r ■ r \-& n -i r l j m ==P =t Jfu - 1 ■ 1 1 - 1 - 1 =q m 1 ■! 1 1 — l -j y- — ~ ^ — h= — r, i r ' r— a — h 2 : fip 1— — ! — M ' ! MU ^ s = — u — rv ^ * j p ifljj: _ e 1 1 1 1 — p_f " ■> 1 (j«X p* S 1 ^T f* jr J Jf * f « J h— 1 1 1 J 1 as — : V»- ^ r r ' * 1 »■ s r 1 r ^ j * j ^ — 1 — ^ — &- *"n 9 ' 10 11 ' 12 "^ • 14 13 [-^ Al |=| — & f ' r [Ml ^ ~ -^ J^ H-d P— — — — — — h 1 — 1 ' ' »■ ' P ~ — "T^ u ; £ ' Jl^h: 1 j 1 - r^ — ffrs 5 — p^ ~ " iw^ 1 , ^ 15 1 ! b£ 16 17 18 19 Fugue. [Chap. XI. After the entry of the answer in the treble (bar 16), we have in bar 21 the inverted subject in the bass, imitated in stretto and in direct motion by the tenor in bar 24. This subject is henceforth treated both by direct and inverse motion, and mostly in stretto at two or one bar's distance till bar 114, at which point a full close is made in the tonic key. We have thus far a fugue on one subject complete in itself, and the whole piece might end here. Bach, however, makes his cadence the starting point for a new departure. 401. We give the cadence closing the first part of the fugue, and the commencement of the second exposition, which is too long to quote in its entirety. Cfcap. xi.] Fugues on More than One Subject 20; -jh ' - =1 — — — g -' M" r rf r Trf f ir^frri r r«»r f -ffc F^rr-^^: ^= Iff Ecn !"=™~ fr — =^ ! '^j^ 1 ^^— ' l r i i ini Be • *r » ■f* — mw- 1 f 1 U I I ms j^7 1-^ A3 r-i 1 1 ! 1— 1 ~~p — d — a — d — » \~ W^ -< ■'i r r r 9 m J - to 7 r^T^F — — p* fi? — ^ T^^ ig" "^ — 1 1 F ■RH- — ' ' ' ' : : ' feP^ h-r—~- !•"! — f 55 — : ' E* d • — -F — r- g J r — r — a — — 1 — ' • 1 — ' -1 — 1 a as ^6 7 8 9 206 Fugue. [Chap. XI .-• tr 1 4 -j — i pa -j i qft — L—w 1 fg ' — r — -^ 3 1— P 1 - =fZ2= 1 r pq r. S3 — -r — sH a | " 1 1 L -1 1 — |_L S 2 -1— ■L_p] 1 r f-ff f • I * p p 1 r — : J ^ — -Ire-— U^ ^ — — 1 — ±T^" — * -_ ££ "-J • * 1 r =£= r r i ^s 10 ii 12 13 a 3= I s z Al- A2 It will be seen that each voice has all three subjects in turn, but that none has the same subject twice. 406. The form of this kind of triple fugue is the same ternary form as that of a simple fugue, and the construction of a complete piece of this character will be best shown by the analysis of a fine example from M>zart's Twelfth Mass, a work from which we have already had more than one occasion to quote Chap xi.] Fugues on More than One Subject, 207 Mozart. Mass in C, No. 12. =#= — ■■ si— --P f- -] j I j_ 1 — m m A3 41 • - r%<* g-p tii* ~1 H — A2- *_!i J u» LT __j 1 p ■ i» a 1 iiij — ■* r r " g i . p -_f r f 1 r~Tr* » * m 1 S2 ^ 4 5 *^f~ — F - 6 7f — m. m 'i» F ' "j ^ ■ » _ J | A 2 !*■ f — r- -1 ft r f jp — p — ((a) r -p [j * • « * rr * — * r =^==5 u r r == Al £ — | r, — r . r-^Fn -jSj — 1 ■■ r ! j \ 1 '.■ *•■ ■- j 1 — j S3 M — 1 r f r f if 8- — p-f — 1 m b- — - ■■■ — — pi — n 1 r I — : * — f-j ; I j ; fa p p pF F ^ ,* {> I A3 -j* p = 1 f i* m . ^7 8 _j j '—j-j J 9 2o8 Fugue. LChap. XI. $r*3= 1 Middle Section. , — 4^ Episode 2. -1 -m- E — ft 1 ^ r*p f i fil & 1 — ^ U, S2 j ii ii I * -g ""-^ — \ m 1 -IfS =F=x 1^— ' SI — ' — f— -T» — &#- —i^-p p r i ■^ 13 -J 14 ■ — -f — i— 15 1 a ! t= -j Al— ■ p . -» g £ fi i ==rfg g 1 r — ^- 1 1 ^Ui-^ i — — - ~A tHi -i tf r r r r ** * r _i - r s* fn= — — " i* P — ±J& — UJ — £_l k — i !__ A2- 1 - 1 — U -y- -m-f • * rf"- f +f * " ' * 9 m ■■ *->» 16 17 18 X r r s r f « rr qr r r^r~^~ 1 Tu * — m ft* - f » I* 1 i* N C\) i In 1. 1 — p 2Lp T ~ i J — *L_ Episode 2. q ^ — 1 m U 1 • *d si — *. _. i= 1 +-=- — n . p — f — c — i mi ^ l-^j g =fcb^ IfJ / "*n 19 20 21 — r ' cn.xp. XL] Fugues on More than One Subject. 209 Final Section. S 3 PUS m I *> A3 | r - -lie » m g -U-UrfL , — ? A2- ., rr r r y r c I r aa U> I UN ^ . ? A2 — , __ _ » m- Al -P — - — L_£l_u. j— C^ — s^ H— p — P — -t — *f- -jg^r r^-ry — F-r-P— S3 ? ' ! !- : 4_J >gd | 1 pn — q r r r ** 1 * — \~ -J P- (S)' m m * » \ A3 -(•-,. TTT^ 1 ^ 31 32 33 ^fcn— | Viol, i to SI- "^nhi r J i i * §* S* ?e£ -r~r -» i 1 g f 34 35 I » ^rjj^ £=g Fugue IChap. xv The small notes in the bass of bars 14, 21, 25, and 26, and in the treble of bars 34 to 36, are additional parts for the orchestra. We have omitted a few notes for the violins, which merely fill up the harmony, so as to show the fugal construction more clearly ; and we have not given the last nine bars of the movement, because these are merely a free coda, and not a part of the fugue itself. 407. The exposition of this fugue extends to the first note of bar 1 1 ; it will be seen that each subject has then been heard in all the voices. An additional entry of all the subjects leads to the key of A minor, the last note of the first subject being sharpened in the tenor, to induce the modulation. The middle section of the fugue therefore commences at bar 13, with an episode only one bar in length. At bar 14 is the first group of middle entries, the three subjects appearing in A minor. These are at once followed by incomplete entries of the three answers in E minor, shown, as in our preceding examples, by A — ? Fragments of the subjects are then treated sequentially in the second episode (bars 19 to 21), bringing the music to the key of F. In this key the second group of middle entries, incomplete in all the voices, is made at bar 21. The third and last episode (bars 23 to 26) leads back to the key of C, and to the final section of the fugue, which begins in bar 26. 408. This final section contains three groups of entries, all of which are in stretto. In the first and second, the answer enters at a bar and a half's distance after the subject, and all three subjects are present, though, as will be seen, some are incomplete. In the third and closest stretto (bar 34), a part of the first subject is treated by itself in imitation in the octave at one bar's distance in all four voices. It will be seen that at bars 34 to 36, a fragment of the second subject is given by the violins as a counterpoint to the first subject in the voices. 409. It will be noticed that as the subjects modulate to the dominant, they require tonal answers. The subdominant in the second subject prevents the modulation from taking place till Chap, xi.] Fugues on More than One Subject. 2 1 1 the third bar, and we see that all three subjects need modification in the answers. Of the six possible combinations of a triple counterpoint, Mozart has only employed three; but it must be noticed that each of the subjects appears in the bass {Double Counterpoint, § 253). One more point remains to be noticed about this fugue — the almost entire absence of free parts. For the sake, no doubt, of that clearness which is so essential in double and triple fugues, the three subjects always appear without any additions, which might prevent their being easily distinguished. It is not till bar 38 of our extract, and the coda which we have not quoted, that we find any continuous four-part harmony. 410. It is seldom that we find a triple fugue so strictly treated as that by Mozart which we have just been analyzing. Composers usually allow themselves considerable freedom in such cases. For example, the very interesting ' Fuga a 3 soggetti.' in Haydn's quartett in A, Op. 20, No. 6, the three subjects of which are quoted in Double Counterpoint, § 262, is, strictly speaking, not a triple fugue at all, but a double fugue, with one regular counter- subject; for the third subject appears for the first time as an accompaniment to the answer, and not to the other two subjects, and in some of the middle entries only two of the three subjects are employed together. 411. A Quadruple Fugue, or a fugue on four subjects, is so extremely rare that it will not be needful to say much about it. The four subjects will now evidently have to be written in quad- ruple counterpoint ; but it is very seldom that they will be all announced at once. In Haydn's ' Fuga a 4 soggetti,' in his 1 quartett in C, Op. 20, No. 2, only two of the . subjects are announced at first, the third and fourth subjects entering as countersubjects to accompany respectively the first and second appearances of the answers. The four subjects of this fugue, with their various inversions, were quoted as examples of quadruple counterpoint in Double Counterpoint, § 270. 412. In Handel's 'Alexander's Feast,' the final chorus, "Let old Timotheus yield the prize," is sometimes spoken of as a fugue on four subjects. So, in one sense, it is ; but it cannot be regarded as a specimen of a true quadruple fugue, because seldom more than two, and never more than three of the four subjects are employed simultaneously. The fugal writing, as is mostly the case with Handel, is far from strict throughout. 413 In Cherubini's 'Counterpoint and Fugue' will be seen a good example of a strict fugue on four subjects, the opening bars of which we gave in § 269 of Double Counterpoint ; but probably the finest specimen of a quadruple fugue ever written is the final movement of Cherubini's great ' Credo ' for a double choir, which has not only four subjects, but two countersubjects in addition, which make their first appearances against the answers. We have only space to quote the opening bars of this movement. 212 Fugue. (Chap. XI Chekubini. Credo k 8 voci. (J* t \*~ -- — i ■ ■ " f^ -p- p j J J J J 1 iffV — s a~ ■ 1 P (| ' 5 rf ff — s j- ■ 1 — I =~ Z ] J *£j^p V f ^^ — a P" „ 1 ; fciP § SOU 1 -= — r r r r r r* r n - • f" — § S2- § ^ pa_ C3 «g fli _ 1 — — 1 ! — 1 — 1 — P- 1 1 r m — — 1 — -i — 1 — f F p F i» i tu i*|fl(|*/- ' to&fr ! ' 1 V- 1 [— B H~ i r 1 ~ — J f r r rrrrcri V ^ 1 .^ b S3 A 2 i l i i i ^| 3 CS1 7 ;S J J r» r * * * *' & - f J hf flp — 5 — f" r r ! W J r r ftp Al — "H — r+-p 1 — H - 1 ir jg r r~i ihi y- 1 i - i r i i a " a IfllJ ^J "1 B" 1 \ r ?P '1' -« 1 „ jf^P =- 1 " a a Ifli ! feite l \ • » ? » m — f= h- -= &■ — ipjj*___-p- IHli r * * [ i i r ■ ^ _j — i — i — ^j 1 1 A2 — — 1 — -J — 1 i r P — | i V):fl T f^- i jg e r i r* r r p r ^=q ^ i— - - t _| --'--! ■ (= J 1 P- pS=? Chap, xi.] Fugues on More than One Subject. 213 A4 8=t g ; * g g ! # g i i i i ; i ' » g T- tf f- m m . g Si 1 CS2 re rrr^ Hi -r-w 3^ A4 !» r r g i i ! 1 * » * , * , vrrrrry i ii^ ^ / da p ^=3z^±=*£ -r * g CSl— i Sl- 3= n I S2 W1- ££ ,d * r -r-y- SE ! J •>-*- 10 ^ -*-*- S3 I i I 11 12 214 Fugue. CS2 f [Chap. Xi e r ^ -P— g — y S4 L7* g M^e- g=r tP~f~t--L- i ! ^q=3 f^Lr--^— J. 81 I 1 1 u "I S4- F=r ir- J ~^ i i Jr ^ i^^r * =^=f; T=£ IP S4 i T=T- i& 7^ — r~y — g — ^ ^tace ~W~i~9- AZZt I I » gz r^ r p =g =1E 5tat I I ! — ± glE^ -r p &—?=^ ^: ry - ^ t=t i=± 13 14 15 tP^-— s* —tS> m CS2 f= ! 1 1 =a $73 p — y= 1 Fl r— P f* * J-J-p — Sf Nj — £J — ! CS1 — r — i— i . .... -p - f -S* f-5- — 1« — -r-& w ~ r M'-r-F-fn ift|_t_^ z^rrEijzz ...| ! J* 4—1 ■---■ ' *■* i_i 1 — — pp-^- — _ — , — — — , ! — pf i — -\ p- f-r p fL #3=^— -j 1 j 1 1 -s — (*—- T-i • <$. , i . m j ^— ■ — —tr 3 -\ pgof 1 1 — i r r - r i i 1= d :fll ' J fe=^ ^r pr J J J i — i — | mm ffiU 1 £** 1 _^ — \— & tiSr* 17 18 chao. xi.] Fugues on More than One Subject. 215 p ^m 'Ztt- ? r r ll ■ I i 1 — r m A4 m & §* 19 20 As the last notes of this extract are the commencement of the first episode, we have here the complete exposition of the fugue. With the indications we have given of the entries of the subjects, &c, the student will easily understand it. In a fugue for so many voices and with so many subjects, it is not needful that each subject should be heard in every voice in the course of the exposition. Were it so, the fugue would be protracted to an inordinate length. Let it be also noted that, with so many subjects, the rule that all shall end together is relaxed. Here the second subject ends in the third bar, and the other three not till the fourth. Slight modifications will also be seen in the two countersubjects. 414. In the later developments of such a fugue as this, it is not necessary that all the four subjects should be invariably present together. It will give more variety if sometimes only two or three are treated and developed at once. We advise the student to obtain the score of this ' Credo,' by Cherubim, which is published for a mere trifle in the well-known ' Peters Edition,' and to analyze the whole piece carefully for himself, as we have done the opening bars for him. He will thus probably learn more about the construction of a quadruple fugue than we could tell him in twenty pages of this volume. 7 j6 Fugue [Chap. XII. CHAPTER XII. THE FUCUE ON A CHORAL. 415. In addition to the different varieties of fugues treated of in the preceding chapters, we not infrequently find fugues writien upon a choral. As with a canon on a choral {Double Counter- point, § 391), there are two ways in which this can be done. We can either take the melodies of the choral itself as the subjects of our fugue, or we can write a fugue on an entirely independent subject, introducing the choral in longer notes in one of the voices as a kind of canto fermo. Owing to the much greater freedom of its form, it is far easier to write a fugue on a choral than a canon. 416. We will first speak of that form in which the choral itself furnishes the subjects of the fugue. The plan most often followed is to write a separate fugal exposition for each line of the choral, the last entering voice, which, for the sake of clearness, is generally one of the outer parts, introducing the melody, in most cases, though not invariably, by augmentation. 417. As this method will be best taught by examples, we give two entire fugues of this kind, one very simple, the other rather more elaborate. The first is by one of Bach's great predecessors, the Danish organist Buxtehude. It is on the choral " Erhalt uns, Herr, bei deinem Wort." In the original there is only one flat in the signature, according to the custom of the time, though the key of the piece is G minor ; for the convenience of students, we adopt the modern key-signature. Buxtehude. 1 EE ^m ** Manual. Pedal. Chap. XII.] The Fugue on a Choral. 217 \W= ^ ! — J -+-H -f3-J J -0L -5 J ! * lJ U J d * ■» •>!, s , 1 My ^ uT 1 * \ fch fesiS^ ' ^4^ ^ 5 1 6 7 r v_L£'f" s*^ 1* P TPT- 57j S« B£ 5=t S 5^ 14 15 16 im 4=B- n =1 tn c ^j.. mjjjj s 1 rr ^y^:jt ip ss*g=g V^ji 1 ^TT"5 ' g5Tt SB r r~.Sf ^^ ■ rt — 1 >. — - L^ 1 — -^ ■ i±zd P^ J * 17 18 19 218 Fugue. CChap. XII. [l^. in-Bj - J; 1 5, fr 1 i ' # ^EJ & r ^S jTa*d! i U T I MEH, » 1 — - 3 )*2t> ^ 20 21 1 — 22 J (feH r* if~ ifea: y ■■ j j — 1 —mi I -1- - I - —I » mt m1 * ~i =fa 1 Al* -— *- P i Lx -'1 .p. * tF -3.. M» BBS — f*"** — r~ -d— p =- =g=£ --iSJ ^r* mt 1 J s-4 h ^n 29 (5 urn — J * —j — — 30 31 J I I I ±fz - r — tfrr wm 32 33 34 Cb*p. XI ( The Fugue on a Choral 2 ig £&—r AN* 1- 1 — i— — ; — -i f «i - — \ — ^— j- — i — -1 1 FrrH rr i ^^ • -rv n^ fiferb — r r » ■ - — ■> -i fe*— -^ 35 36 37 1 -A"-, .,ji — n i i i \ ptt *gg s fr^>- fa* r-^f r ci — » p§!§£* W J ^. e img ^^| 3 ^f-jfTrr — y~- -a»-| i i 1^" 1 ' g^ ' — m-rh 1 p- =4= j e= *s~4>: ] r K 38 39 40 — J d J 418. The first line of the choral is announced as a fugue subject in the tenor, and answered by the alto in bar 3. The treble gives the subject again in bar 6, and the bass (pedals) joins in with the subject at bar 8. The subject, and not the answer, is given to the bass, because, as we see from the rest of the fugue, this part has the character of a canto fermo, and gives nothing but the simple choral, line by line, throughout the piece. We there- fore find the subject here instead of the answer, as in an ordinary fugal exposition. It will be seen that the canto fermo is here only in notes of the same length as the other parts. More usually, as in our next example, the plain choral is given in longer notes. 419. At bar 10 begins the exposition of the second line of the choral. Here we see a little irregularity of treatment. The theme in an ornamented form appears in the tenor, and is imitated in stretto in the next bar by the treble. At bar 13, the answer is repeated, not by the alto (which had no' had it), Fugue. [Chap. XII. Dut by the tenor which gave the subject just before. The entry of the subject in the bass (bar 16) concludes the second section of the fugue. 420. The third section is longer. The subject is first heard in the alto (bars 18 to 20), the answer in the treble (bar 21), and again in the tenor (bar 23), followed by an additional entry of the subject in the alto (bar 26), and completed by the canto fermo on the pedals (bars 28 to 30). The treatment of the last line is on a similar plan, as the student will easily see for himself. 421. It will be noticed that this fugue really consists of four short expositions of different subjects, but that the first entries ir. all the lines of the choral, except the first, are accompanied by independent counterpoint. It is not necessary that all the inter- mediate expositions in a fugue on a choral should begin with one voice alone, though our next example will show that this may sometimes be done. 422. The above fugue is given not as a perfect model for imitation, but as showing one of the earlier and simpler ways of treating a choral in the fugued style. The following example by Bach is a much more finished and artistic piece of work. J. S. Bach. " Vom Himmel hoch da komm' ich her." !=Zi mm 1 1 V 1 f 1 1 i igg^I C'hap. XII The Fugue on a Choral. 221 i ^z se e r r J«L ri-tr i ^!j ^^ " r r I r r r r aS »L fcfcB 10 m <*~ ! ' U 11 12 5=t Fugue. [Chap. XI 1 WE&l m })g p^ CL7 1 S ^& 0^ S Sff=r£ rrf -l*_=,_p_ &£=£ t=t P 1 Ses?e I ? e r ! 19 20 21 -\ (S 1 — =r=^ dS* _*_ ... i — 1 ^^ /7\ -1 1 1 1 -r — r^ J 1 B T* "H* — ■J 1 -1 ^T^- HT S3 — "" — 1 -f- I'M J -1 r g — bad — 3= -1 <-H- 4-J-J -J — *- -hJ— *vr 1 23 29 chap, xi i. j The Fugue on a Choral. 223 423. Here the canto fer mo is in the treble, in minims against the crotchets and quavers of the other voices, and the fugue is a close fugue (§ 279). It will be seen that the second and third lines of the choral (bars 6 and 12) are treated in fugato style, the entries not being at the regular intervals, while the first and fourth (bars 1 and 20) are in the intervals of subject and answer. The close imitations, and the treatment of fragments of the subjects deserve careful examination. 424. If we observe the form of these two fugues, we shall find that they both differ considerably from the general fugal form described in Chapter IX. This will always be the case with a fugue on a choral ; and it is quite impossible to lay down any fixed rules for its form, because this will in all cases depend on the course of modulations of the choral itself. A certain amount of variety is always obtainable by varying the harmonies of the different lines of the choral, as Bach has done in the above example, by harmonizing the end of the second line of the choral (bars n and 12), not as a full cadence in E flat, but as a half cadence in C minor. B-ut in the case of short and simple chorals, such as the two given in our last examples, there will generally be comparatively little modulation, and only to nearly related keys. 425. Another point illustrated by these two fugues is, that the entries of the lines of the choral as a canto fermo need not be at any regular intervals of time. In Buxtehude's fugue, the first line enters at the eighth bar, there are five bars' rest between the first and second lines, nine between the second and third, and nine between the third and fourth. With Bach, there is a bar and a half before the entry of the first line, two bars between the first and second, three between the second and third, and three again between the third and fourth. The points at which the various entries should be made is a matter that is entirely within the composer's discretion ; he may introduce his canto fermo exactly where he finds it most convenient. 426. This form of fugue on a choral is less common in modern music than it was in the last century. Two effective examples maybe seen in the late Sir George Macfarren's oratorios. The chorus, "My soul, praise the Lord," in 'St. John the Baptist,' is founded on Dr. Croft's hymn-tune ' Hanover ' ; and the ' Old Hundredth ' is treated fugally in the final chorus of ' The Resurrection.' Both these fugues, however, differ from the models here given, inasmuch as, although the whole of the choral is heard as a canto fer?no y the actual subject of the fugue itself is in each case only the first line. These pieces, therefore, form a kind of connecting link between the variety already treated of and that now to be described. 427. The second method of writing a fugue upon a choral is to take an entirely independent subject — that is, one not suggested by any part of the choral itself — and against this to introduce the 224 Fugue. Chap. XII. lines of the choral as a canto fermo at such points as may be found most convenient. A fugue of this kind is very seldom strict as to the intervals of entry. Of the numerous specimens to be found in Bach's 190 Church Cantatas, there is not a single one which would not be more accurately described as a fugato with a choral. As these have nearly always an independent orchestral accom- paniment, we prefer to select as an illustration the first twenty bars of a fugue on a choral taken from one of the motetts. The movement is too long to be quoted in full. J. S. Bach. Motett, "Furchte dich nicht. I £* *=5£ * r w^ Am- B5 W£ S32 ?£te £te gPjg J ^— P E Chap. XII. J The Fugue on a Choral. 22 b t* Bp m i i g i ^p: p p^3 2 26 FUG LIE. [Chap. XII. 428. Here the key of the piece is A major; the subject, therefore, being throughout in the dominant, the answer is in the tonic (§ 70). The first answer is at the regular interval ; but the next entry of the subject (bar 4) is in the key of D instead of E ; and from this point the entries, though each is generally at a fourth or fifth above or below the preceding, are so irregular that it is impossible to say which are subjects, and which are answers. We have therefore marked them all with ' S.' 429. It must be remembered that it is not allowed to trans- pose any phrases of the ca?ito fermo into other keys ; consequently only such modulations are available as can be introduced without doing violence to the original form of the choral. The same rule, of course, applies to the variety of fugue noticed in the earlier part of this chapter. Any other modulations, if used at all, can only be employed in what may be termed the interludes between the different lines of the choral. For instance, in our last example is a transient modulation at bar 9 to the key of E minor, introduced between the first and second lines of the choral. 430. Though it is advisable, where practicable, to employ the theme of the fugue as a counterpoint against the choral, it is also allowed to introduce the latter during the episodes. This consider- ably lightens the composer's labours; for (as we have already seen in Chapter VII.), though the materials of the episodes should have some connection with the subject or countersubject of the fugue, considerable liberty of treatment is allowed ; and it will be much easier to introduce the choral than if we are bound to make it combine with a given theme. 431. A fine example of this method of treatment is seen in Mendelssohn's third Organ Sonata. There is here a double fugue, each subject having a separate exposition before they are combined. We quoted the first subject in § 38 (d). After a regular four-voice exposition, Mendelssohn at the 17th bar of the fugue introduces on the pedals the first line of the choral " Aus tiefer Noth schrei 'ich zu Dir," as a fifth part. The subject is only suggested above the choral, a new entry taking place on the last notes of the line. The entries of the second and third lines of the choral (bars 22 and 28) are similarly treated. At bar 35 the exposition of the second subject (a figure of semiquavers) begins. After it has been carried through all the voices there is an episode (bars 43 to 47) against the latter half of which (from bar 45) the next line of the choral is heard. At bar 57 the two subjects are combined, and the choral is introduced in the pedals from time to time ; but in no one place throughout the fugue is either of the subjects in its entirety ever combined with the choral. 432. Mendelssohn's organ sonatas are so well known and so accessible that we have contented ourselves with merely referring to this fugue instead of quoting from it, because no short extracts from it would have been of much assistance to the student. It Chap. XII. ] The Fugue on a Choral. -J? shows that it is not necessary actually to combine the fugue subjects with the choral. This fugue is a very fine specimen of its class, and it is no disparagement to Mendelssohn's genius that he has here preferred the freer style. It would have been very difficult (perhaps impossible for anyone except Bach, to whom nothing seems to have been impossible) to combine the choral with either of the themes he had selected for his fugue. He therefore wisely chose rather to write an effective composition than to attempt elaborate and difficult combinations, which, had he succeeded in effecting them, would probably have smelt strongly of the lamp. An over-display of technical cleverness is very likely to be dry. 433. Sometimes only the first line of a choral, instead of the whole, is selected for fugal treatment. A well-known example of this is Bach's organ fugue in E flat, known in England as the 'St. Ann's Fugue.' This is a double fugue of a somewhat unusual form, in three movements. The first is a simple fugue in five parts, the theme of which we quoted at § 102 (c), and which is the same as the first line of the hymn-tune, ' St. Ann's.' This movement ends with a full cadence in the tonic, introducing the second subject. (a) s 2. J. S. Bach. Organ Fugue in E flat, (' St. Ann's.') This second movement is in four parts only, without pedals. After a regular exposition, the new subject is treated by inversion, and then combined with the first subject, of which the rhythm is now altered, and which assumes the character of a canto fermo. si., , _r "_i i j. Subsequently the canto is also heard against the inversion of the second subject. A full close in C minor leads to the third move- ment, which, like the first, is in five parts. The theme will be seen at § 49 (c). We now have a third exposition, followed by combinations of the third subject with the canto fermo in various ways, of which one will serve as a sample. ^ m 1 -f- ^4i ■J c 3^ ^m S3- TmX. h VA ! — sP fgn— - Sl frs H E£!3?-_j_?Li <* j . r - v.? • 1 228 Fugue. iChap. XII S3 ' 1 ^ -m — =i — =i — i l 1 1 p — J J J - * — (^ ^ —m a#— -*- j i {±& — i — \>J m * F4= • — : -* • =1= i S3- & J * P P JTW-J^M $+=? -en-? m j^rojmga j Ac. s ^= g£3 * ^ It must be noticed that, though this fugue contains three subjects and three expositions, like the great fugue analyzed in Chapter XL, §§ 400-402, yet it is not really a triple fugue, as the three subjects are never all heard together. It more nearly resembles a fugue with two countersubjects heard in succession (§ 174). 434. The fugue on a choral affords an illustration of the general principle so often referred to in these volumes, that in proportion as the difficulty o f the task increases, greater freedom is allowed to the composer. This has been amply shown in our examples. By the time that the student is so far advanced as to be able to attempt a composition of this class, he ought also to have acquired sufficient experience not to permit his liberty to degenerate into license. Cbap. XIII.] Accompanied Fugues. 229 CHAPTER XIII. ACCOMPANIED FUGUES. 435. We not seldom find in fugues written for voices with instrumental accompaniment, that the instrumental parts are, to a greater or less extent, independent of the voice parts, by which latter the fugue is carried on. We are not now speaking of the doubling of voices in the octave above by violins, or other instruments, because mere doubling adds no new parts to the harmony, but of those cases in which either the harmony sug- gested by the voices is filled up by the instruments, or the latter have independent figures of counterpoint. Such fugues may be described as Accompanied Fugues. 436. In Bach's vocal works, especially in the great Church Cantatas, which deserve to be far better known than they are, we frequently find the first exposition of a fugue accompanied by the basses and organ, the latter filling up the harmony, as in the opening choruses of the cantatas, " Es ist dir gesagt," and " Sehet welch 'eine Liebe" (Nos. 45 and 64 of the Bach Society's edition). Sometimes, as in one or two of the motetts for a double choir, the exposition of a fugue by one choir is accompanied by full harmony for the other. J. S. Bach. Motett, " Singet dem Herrn.' ^ i j g3. m i j gkgg * 3 o Fugue. [Chap. XflL m pi £ s 4 iU ^ ad^.^^^ gja^B ff Ti rrr F Iff^W rE B s ^^: J— I-^UJ- J J JWJ Chap. XIII.) Accompanied Fugues. 23 Here the harmonic outline implied in the fugue subject is filled up by the chords of the second choir. 437. Our next illustration is part of the exposition of a fugue from one of Bach's cantatas. J. S. Bach. Cantata, " Wer sich selbst erhohet. m^ 1 ! m J— *- j sin -to ^sjj^^^j^^^^ ^ *6±flb Oboes. ■. Ob. ^ r W — * 3=z: 4* tT 7 instead of fi 7, according to the custom of his day. The passages in which there is nothing but a figured bass were accom- panied on the organ. The independent accompaniment of the orchestra, with the contrasted tones of the strings and oboes, is continued through the greater part of the fugue. 438. The following passages from Cherubim's first mass, which is for three voices only, show how thin harmony in the voice parts can be filled up. Cherubini. 1st Mass. 2.34 Fugue. fChap. XHl I m m Si F=f= : g 6^3 Pttp r J J: "J , * J3 I i—tr 4 ^^ £ « * S tlpS tsc The accompaniment here is for the full orchestra ; we give it in the condensed form in which it appears in the published vocal score. 439. A little further on, in the stretto of the same fugue, we find a different kind of independent orchestral accompaniment. As only a few instruments are employed, we quote the passage from the full score. Cherubini. 1st Mass. Violino imo. VlOLINO 2 i- 1 f i 1 1 B i i i i i j . — t i ^ l_r i i i ^— j 1 1 _L J— i ^ ■ pff= — 1— — J — i ' -JL- — | — ~t* : fH^=) M a- r . — i — — m — I* — r - ! - (O 1 4— &c IB-" ru — | — i -i ■f — m — r_ — I — — « 1 -J , IB 1 H ^4 — 1 — < — «^j— -t ~m— i fijl— 1 — ^ (• 1 ^ i. .. ~] gk^l I — — w_ i i i 1 « 1 •Celli. i 1 ^— i It looks at first sight as if this were a double fugue , that it is not so in reality is shown by the fact that the second subject, announced at first in the tenor, is only occasionally introduced in the remainder of the fugue, and does not even accompany all the entries in the exposition. 441. At other times we find an orchestral counterpoint which is quite independent of the voice parts. Hummel. 1st Mass. Soprano. Alto. Tenor. Bass. m Chap. XIII. J Accompanied Fugues. 239 W^- M. V b4 m * It^-^-FT -rfrtti* mf^f p Pj*" - „«, *r»» ^» m{ aE? = —— £t£r ^ ^ ^j fig ,b— i* — /■ £ — i 1 1 -• — 1 *"i nr r r ' st lg p^--h-p-rri iFrfTruEt? * r * tvr* ,r*s Sorffiif fffr- ~^h~'""" "' -a«iiM.ii r^#^ =5*^±^=±^ ^53*, 1 Q4 • — **_ r = * g lm. 1 «. «J J - p — {*£&- ... — : 1 ■ • - &c The subject and answer of this fugue were quoted in § 64, when we remarked on the rarity of the first voice being silent during the answer. We have selected this extract to explain what we said before, and also because it is a very good illustration of an independent accompaniment to a fugue ; but considered merely as a fugal exposition the counterpoint of the voices is pitiably weak. i 40 Fugue. 442. Our next example is much better. iChap. XIII Schubert. Mass in F. VroilNO imo. VlOLINO 2tlo. Soprano. Alto. Tenor. Bass. m P m 1 » » i *f\ 1 — r m ■ r \ -~e=(t i -m m- l 1 r * e ^ p „ p ^ , r — pn«- - N* ! B i E g 4—1-4-4 I I I L^= ^— i—n i ^= f p p p ^ : I I 9 ^3^-— i-^ B^^ P I I J3. V*nT*? g 1 * a p J^-^« ■ F » r ^j f 1 1 r - J_J1 1» PC Accompanied Fugues . — fTTTri-^F j j r gj P r-P | ^ P-^-P-Pi | j | F- V -a- UL - £r r r r r ? t # * » ■p-p- fif* m , rf= 1 1 ^ li i .c 1 _j_ ■0- 1 -4 — i i h, |_ tr F h^ — 1 r iii 1 # -• — 1 t r^ I £■ £--p- *£ r * r-r r p ^=^- i » r i p =p=p p r i r r i j \ J 1 ^ J * Jj ^^ g^jzg^- ^-rffr r !*? r 1 r T rf fTj j if 34: | | E 5 # :P: 242 Fugue. [Chap. XI II. The instruments not quoted in the above extract simply double the voice parts. These are written rather injudiciously low — the result, probably of the composer's inexperience, as he was only seventeen years of age when he wrote the mass ; but the counter- point is very good, and the moving figure for the violins gives great animation to the fugue. 443. Among modern composers, Mendelssohn has been con- spicuously successful in his treatment of the accompanied fugue. It is needless to quote examples, which would only be further illustrations of the points shown in passages already given ; but we may refer students to the fugue on the words, " Behold now total darkness covereth the nations," in the chorus, " Rise up, arise !" of 'St. Paul,' and the final chorus of the 42nd Psalm, as excellent specimens of this class of composition. 444. We have several times referred to Mozart's wonderful mastery of every scientific device. Our final example will give one more illustration of this. Mozart. Mass in F, No. 6. Violino imo. Viounq 2do. Soprano, Alto Caap. XIII.] Accompanied Fugues 243 m==E=m t= — ^^= ff^*%E^ ^ ^rrg : 244 Fugue. [Chap. xiii. This passage deserves close examination. It will be seen that in the voice parts we find not only a regular fugal exposition, but an almost strict canon, 4 in i, in the fourth and octave below, the slight deviations being those necessitated by the tonal answer. At the same time the violin parts, for the sake of which the extract is quoted, have a different canon, 2 in 1, also very nearly strict, and these close imitations are carried on in as easy and natural a manner as possible. The passage is worthy of old Bach himself. 445. It will be seen that this chapter consists almost entirely of examples. It is only in this way that assistance can be given to the student ; for in every branch of practical composition the invention of the melodies and the counterpoints must be left to the composer himself. By seeing what others have done before him, the student will be stimulated to go and do likewise. A few general inferences may, however, be drawn from the examples we have given. 446. First and foremost is the necessity of clearness, on which we have already so often insisted, the importance of which increases as we add to the number of parts. As an illustration of this, look at the passage by Bach in § 437, and note how the orchestral accompaniments are written in such a way as never to obscure the progression of the voice parts by which the fugue is carried on. The same thing will be observed in the fugue by Haydn quoted in § 440. 447. If the accompaniment to a fugue is anything more than a mere filling up of the harmony — that is, if it has independent features of its own, as in the examples to §§ 441, 442, 444, it is very desirable that it should be well contrasted with the subject and counterpoint of the fugue itself. 448. It is seldom advisable to have more than one, or at most two, free instrumental parts, in the accompaniment to a fugue, because not only is the difficulty of composing much increased, but each added part renders it less easy to preserve clearness. It is quite true that we often find more than two free parts added in Bach's vocal fugues ; but it must not be forgotten that it seems to have been about as easy to Bach to write in ten or twelve real parts as it is to the average composer to write in four. The student will do well not to overtax his strength by attempting feats too difficult for him. Unless he can write florid counterpoint fluently in at least five or six parts, he had better not try to compose an accompanied fugue at all. 449. Beyond these general hints, it is not possible for us to go. The farther we advance in this series of theoretical works, the more we are compelled to leave the student to his own resources. In our earlier volumes on Harmony and Counter- point, it was possible, at all events in most cases, to give very definite rules as to what to do, and what not to do. These subjects bear the same relation to composition that grammar Chap, xiii.] Accompanied Fugues, »45 does to poetry. The old Latin proverb, Poeta nascititr, non fit, applies equally to music. Just as a man may have a thorough knowledge of the grammar of a language, and yet not have an idea of poetry in his head, a musician may have perfectly mastered Harmony and Counterpoint, and yet be no composer. Anyone who, like the author, has ever acted as an examiner for musical degrees at one of our universities, will need no further proof of the correctness of this statement than the recollection of some of the candidates' exercises that have passed through his hands — quite correct, perhaps grammatically, but as dry as the bones in Ezekiel's vision, and without the faintest spark of musical life. As soon as the teacher approaches the higher branches of composition, his relations to his pupil become to some extent modified. From a pedagogue, whose word is " You must," or " You must not," he now becomes an adviser who can only generally indicate the direction which the student's work should take, by setting before him the best models, and showing him how to imitate them. It must not be forgotten that every great composer has begun by being an imitator. Even Bach was no exception to this ; his earlier works were modelled after those of Froberger, Pachelbel, Buxtehude, and others of his predecessors. In order that the student may have a sufficiency of good models to guide him, we shall, as we have already incidentally mentioned, follow this volume by a companion work on ( Fugal Analysis,' which will contain a selection of the finest fugues by the great composers, in various styles, put into score and fully analyzed. From an examination of these, the student who has mastered the present volume will probably learn all that is possible to be learned from books. 450. One word in conclusion. Many of che rules laid down in this volume differ materially from those given in most other treatises on fugue. The reason of this is that this work, like all the others of the series, is founded, not upon any other theoretical works whatever, but solely upon the practice of the great masters themselves. Not one rule is given which is not enforced by the example of distinguished composers. Where theory and the practice of Bach, Handel, or Mozart come into collision, theory must give way ; and the student who writes fugues according to the directions given in this book may at all events comfort himself that if he is wrong, he is in exceedingly good company. THE END. ANALYTICAL INDEX. The numbers refer to the paragraphs, not the pages. Accompanied Fugue, defined, 435 ; ex- position, accompanied — examples by Bach, 436, 437 ; filling up thin har- mony — example by Cherubini, 438 ; free parts in accompaniment, number of, 448 ; free variation of the voice parts in the accompaniment — ex- amples by Cherubini, 439 ; by Haydn, 440 ; general principles, 445-448 ; in- dependent counterpoints in accom- paniment — examples by Hummel, 441; by Mendelssohn, 443; by Mozart, 444; by Schubert, 442 ; need of clearness — examples referred to, 446 ; need of contrast in independent accompani- ments — exa?nples referred to, 447. Additional Entry of Subject or Answer — in Exposition, when advisable, 186 ; examples, 197 ; by Bach, 296 ; by Mozart, 282 ; — in Double fugue — examples by Haydn, 373, 376 ; — in Triple fugue — example by Mozart, 407; — in Fugue on a choral — example by Buxtehude, 417, 420. Additional Voice often introduced in the Coda — examplesby Bach, 298, 306 ; sometimes as a Pedal, 347 ; examples by Bach, 329. Analysis of Complete Fugues — subject worked in Two parts, 334-339 ; subject worked in Three parts, 340-342 ; sub- ject worked in Four parts, 343-348 ; examples by Bach, 294-318. Answer :— Alteration of last note of the Subject in the Answer — example by Mendelssohn, 65 ; change of pitch of an octave in Vocal Fugues sometimes met with in the course of the Answer — example by Schumann, 154 ; defined, 9, 55 ; disregard of semitones between Subject and Answer — examples by Bach, 144 (a), (b), 145 (a) ; by Handel, 145 (b) ; by Mozart, 144 (c) ; by Winter, 143 (c) ; dissonant intervals in the Subject usually retained in the Answer ; Seventh ; Augmented and Diminished fourth ; Diminished fifth ; Diminished seventh — examples referred to, 139 ; an important exception, 140. Examples : by Albrechtsberger— an Octave answered by a Seventh, 140 (b) ; an Augmented fourth answered by a Major third, 142 (b) ; a Major third answered by an Augmented fourth, 143 ; by Bach— an Augmented fourth answered by a Major third, 142 (a) ; by Kirnberger — a Seventh an- swered by an Octave 140 (a); a Seventh answered by a Sixth, 141 ; by Mozart — an Augmented fourth answered by a Major third, 142 (c) ; entry of — examples, 59-65 ; in sub- dominant, when possible, 80, 156 (1.) ; examples {see Answers, VI. d, e ; vn. e, f) ', in the minor key [see Answer, VI. b) ; in the minor key, when the Subject ends on the third of the Tonic, the Answer may end on either the Major or Minor third of the Dom- inant, 69 ; examples by Bach, 68 ; by Handel, 103 [a) ; by Mozart, 69 (a), 103 (b) ; key relation of Subject and Answer, 9, 56, 66 ; lengthening or shortening the first or last note of the Answer is always allowed, 57 ; ex- amples by Bach, 57 [a), 89 (b) ; by Haydn, 93 (d) ; Modulations in Subject, how answered (see Answer, iv.); Real answer (see Answer, vi.) ; Real and Tonal answers sometimes met with in the same fugue (see Answer, VII., d) ; Tonal answer (see Answer, VII.). /. ANSWERS BY AUGMENT A- 248 Ana l ytica l Index. TION AND DIMINUTION. Key of such Answers, 153 ; examples re- ferred to, 153. // ANSWERS BY INVERSION. Key of such Answers, 152 ; example by Bach, 152. ///. ANSWERS TO CHROMATIC SUBJECTS. Usually Real answers unless there be a modulation expressed or implied, 149, 151 ; examples by Bach, 149 (a), (b) ; by Handel, 151 (a)", by Kirnberger, 151 (b) ; by Mozart, 149 ('). ISO {c). IV. ANSWERS TO SUBJECTS WHICH MODULATE. THE MODU- LATION : — Double significance of each degree of the scale, 122, 123 ; ex- pressed and implied, 118; examples by Bach, 119, 120; by Handel, \\<^{d); by Mozart, 129 (b) ; point of, 117, 156 (iv.) ; rule for, 116, 156 (in.) ; to be regarded as taking place at the earliest possible point, 121, 156 (iv.) ; the reason for this, 126. 1. Treatment of Third of the scale — rule, 127, 128, 134, 158 ; examples by Bach, 128, 129, 130 (b) ; by Handel, 130 (a) ; by Mozart, 129 (b). 11. Treatment of the Seventh, of the scale — rule, 127, 128, 134, 158 ; examples by Bach, 131, 132 (a), (b), 133 (a) ; by Macfarren, x 33 (fi) '< by Naumann, 132 (c). (a) Subject in Tonic modulating to Domi- nant, Answer in Dominant modulat- ing to Tonic — examples by Bach, 125, 126, 128, 129 [a), 130 (b) to 133 ; by Handel, 125 ; by Macfarren, 133 (b) ; by Mozart, 124 ; by Naumann, 132 ((). (b) Subject in Domina?it modulaiing to Tonic, Answer in Tonic modulat- ing tc Dominant — examples by Bach, answering one note by two, 136 ; by Buxtehude, 134 ; by Handel, answer- ing one note by two, 137 ; by Kirn- berger, answering one note by two, 135. (c) Subject in Tonic modulating to Domin nt and returning to Tonic, Answer in Dominant modulating to Tonic and returning to Dominant — examples by Bach, 138 (a) ; by Prout, 138 (b). (d) Subject in Dominant answered in Superlonic — examples by Bach, 148 ; by Handel, 146 ; by Leo, 147. (e) Subject in Subdominant \ modulating to Tonic, Answer in Tonic modulating to Dominant—example by Handel, 82. (/) Subject with inter- mediate modulations imitated exactly in the Answer — examples by Bach, 83 (b) ; by Handel, 83 (a). V. IRREGULAR ANSWERS. Ex- amples by Bach, 155 (a) ; by Beet- hoven, 155 ( (*) I b y Haydn, 93 (c), (d). (c) Subjects which commence on the Dominant — exa?nples by Bach, 102, 104 ; by Handel, 103, 104 ; by Mendelssohn, 102 ; by Mozart 103. (d) Subject i?i Tonic, Answer first Real, second Tonal — example by Bach, 109. (e) Subject in Tonic, Answer in Sub- dominant — examples by Bach, no (a); by Buxtehude, no (b), (c). (f) Subject in Tonic, Answer first i?i Dominant, second in Subdominant — examples by Bach, in (a) ; by Schumann, in (b). Answering One note by Two (see Answer, IV. b). Answering Tonic harmony by Dominant harmony and Dominant harmony by Tonic, Rule, 80, 100, 108. Augmentation and Diminution, Answer by (see Answer, I.) ; Fugue by, 20. Augmentation and Inversion, stretto by — example by Bach, 275. Cadence, Full :— When employed in a Fugue the music must never come to a standstill, 321, 330. Cadence of a Fugue Subject, 42-45. Canon, use of in writing Episodes — ex- amples by Bach, 216 ; by Prout, 242. Canon and Fugue, difference between, 4-6. Canonic Stretto {see Stretto). Canto Fermo, Fugue on (see Fugue on a Choral). Change of an octave in pitch sometimes found in the course of the Answer in vocal fugues, the reason for this, 154. Choral, Fugue on (see Fugue on a Choral). Chromatic subjects, How answered (see Answer, in.). Close Fugue :— Defined, 17, 279 ; key of Subject and Answer the same, 281 ; examples by Bach, 279 (a) ; by Han- del, 279 (b), 280 ; by Mendelssohn, 279 (c). Close Fugue on a Choral — example by Bach, 423. Close Fugue in Double Fugue— example by Bach, 387. Coda : — Defined, 305 ; introduction of an additional voice in, 306 ; examples by Bach, 298, 306, 308, 318 ; in Double fugue — example by Bach re- ferred to, 394 ; in Triple fugue — example by Mozart, 406 ; in fughetta — examples by Bach, 353 ; by Handel, 355 ; by Beethoven, 357. 2 5° Analytical Index. Codetta : — Defined, 62 ; difference be- tween Codetta and Episode, 215; when advisable, 165, 177, 188-193, 200 ; examples, 62, 69 (b), 79 (c), 163, 173, 188-195, 204, 215, 220, 224, 269, 343; ditto in Double fugue, 377, 392. Compass of subject, 47. Complete Fugues analyzed (see Analysis of Complete Fugues). Continuity, necessity of, in Fugal writing, 3 21 - 33°- Counter - exposition :— Defined, 13, 207 ; episode sometimes separates the Exposition and the Counter-exposi- tion — examples by Bach referred to, 207 ; Exposition and Counter-exposi- tion, difference between — examples by Bach referred to, 207 ; its introduc- tion purely optional, 211 ; sometimes only partial — example by Bach referred to, 208 ; Stretto sometimes intro- duced in — example by Bach referred to, 209. Counter-exposition in Double Fugue — example by Bach referred to, 388. Counter -exposition by inversion — ex- ample by Bach referred to, 210. Countersubject : — Deferred appearance of — exampleby Bach, 172 ; defined, 10, 159 ; fugue with two regular Counter- subjects — examples by Bach, 173, 174 ; fugues without regular Countersub- jects — examples by Bach referred to, 176 ; individuality of Melodic charac- ter and contrast of Rhythm, as com- pared with the Subject, most important — examples by Bach, 161, 162 (a), (0), 163 ; in Tonal fugues which modu- late, sometimes needs modification — examples by Bach, 169, 170; Inganno, defined — example by Bach, 165 ; key of, 164; material of — examples by Bach, 166, 167 ; modification of some- times necessary- example by Bach, 170 ; must be written in Double coun- terpoint, with the Subject usually in the Octave, sometimes in the Tenth or Twelfth, 160. Must make correct Two-part counterpoint with the Answer on its first appearance, 171 ; Regular countersubject not indis- pensable — examples by Bach referred to, 176 ; sometimes accompanies only part of the Subject or Answer — example by Bach, 168 ; Triple counterpoint in fugues with Two Countersubjects, 172, 173. Derivation of the word " Fugue," 2. Difference between Canon and Fugue, 4-6. Diminution, Answer by (see Answer, 1.) ; Stretto by {see Stretto). Diminution and Augmentation, Answer by (see Answer I.) ; fugue by, 20. Diminution and Inversion, Stretto by {see Stretto). Disregard of semitones between Subject and Answer (see Answer). Dissonant intervals in Subject, how answered (see Answer). Dominant key, Subject in, how answered {see Answer, VI. c). Dominant-pedal (see Final Section, Pedal- point). Double Counterpoint :— Its employ- ment in writing Countersubjects, 160 ; in Double fugue, 368, 385 ; in Epi- sode, 224, 242. Double Fugue :— (Fugue on two sub- jects)— defined, 3, 365 ; Two methods of writing, 366. /. THE FIRST METHOD, in which the two Subjects appear together. Additional entries, 373 ; Codetta, 377 ; development of the Subjects, 379 ; Episode, 379 ; Exposition — examples, by Bach, 370; by Cherubini, 377, 378 ; by Handel, 371, 374 ; by Haydn, 37 2 . 373 1 b y Hummel, 375, 377; form of this kind of Double fugue, 379 ; isolated entries, 382 ; Middle entries, 380 ; necessity for contrast, Melodic and Rhythmic, in the two subjects, 368 ; need of clearness, 378 ; number of parts requisite in Double fugue, 369 ; Stretto, 381 ; the two Subjects should always finish together, 374 ; should be written in Double counterpoint with each other, 368; should commence shortly after each other, 374. //. THE SECOND METHOD, in which each Subject has its own separate Exposition. Coda — example by Bach referred to, 394 ; Codetta, 392 ; Counter-exposition — example by Bach, 388 ; defined, 384, 385 ; difference A NA L YTICA L 2ND EX. 251 between the two varieties, 385 ; Episode— example referred to by Bach, 392 ; exposition of First subject, 387 ; of Second subject, 389 ; examples by Bach, 387-389 ; isolated entries, 392 ; limits of variation of this form, 395; modulation, small amount of, 397 ; Second exposition sometimes only partial— examples by Bach, 387; by Handel, 386; Ternary form applied to Double fugue, 396 ; the two Ex- positions, 386 ; the two Subjects com- bined -examples by Bach, 390-394. Double fugue on a Choral — example by Mendelssohn, 431 ; by Bach, 433. Ecclesiastical scales in connection with Tonal answer, 84. Entry of Subject in a fugue best preceded by a rest, or where this is not possible, by a leap— the reason for this, 320. Episode : — All the voices should not be employed continuously, 219 ; chief essentials of good Episodes, 243 ; defined, 12, 213 ; Double counterpoint in — examples by Bach, 222 ; by Handel, 224 ; Episode and Codetta, difference between — example by Bach, 215; fugues without Episodes —ex- amples by Bach referred to, 235 ; how to obtain Unity, 217, 231 ; how to write, 230-234 ; exercise worked in Three parts, 237-239 ; in Four parts, 240-242 ; Imitation, use of, 217 ; length of, variable — examples by Bach referred to, 234 ; material for, Se- quence, 216 ; Modulation by means of — example by Bach, 214, 216 ; need of variety in each episode, 231 ; number of Episodes variable — ex- amples by Bach referred to, 233 ; number of parts in, 219, 221 ; one Episode sometimes the Inversion of another — example by Bach, 229 ; Se- quence, its importance, 230 ; Triple counterpoint in — examples by Bach, 229 ; by Handel, 226. /. EPISODES FORMED FROM THE SUBJECT. Examples (a) by Bach : Canon, Modulation, Se- quential treatment, 216 ; (b) by B ch : Imitation, Modulation, 218 ; (c) by Bach : Imitation by Contrary motion, 219. //. EPISODES FORMED FROM THE COUNTER SUBJECT. Ex- amples by Bach : free parts, imitation, sequential treatment, 220, 221. ///. EPISODES FORMED FROM THE COD E TTA . Examples by Bach : Imitation by augmentation, modula- tion, sequential imitation, 222, 223. IV. EPISODES FORMED FROM SUBJECT AND COUNTERSUB- J ECT. Examples (a) by Handel : double counterpoint in the Tenth, imi- tation, sequential treatment, 224; (b) by Handel : sequential treatment, 225 ; (c) by Handel : treatment by Inverse contrary movement, triple counter- point, 226. V. EPISODES FORMED FROM ENTIRELY NEW MATERIAL. Examples by Bach, 227 ; by Beet- hoven, 228. Episode in Double Fugue (see Double Fugue, I. and n.); in Triple fugue {see Triple Fugue) ; in Fugue on a Choral (see Fugue on a Choral) ; in Fughetta {see Fughetta). Exposition — (First section of a Fugue). Additional entry of Subject or Answer — when advisable — example by Bach referred to, 186, 187 ; Alternation of Subject and Answer, 200 ; cases in which all the voices do not appear in the Exposition — examples by Bach re- ferred to, 203 ; choice of voice for the Answer, 179-182; Codetta when neces- sary — (a) before the Entry of the Answer — examples, 188- 191 ; (b) be- tween the Second and Third entries — examples, 192, 193; defined, 11, 178, 293 ; ends in either Tonic or Domi- nant key, 202 ; Irregular Expositions — examples by Handel: an Octave fugue, 206 ; Keys of, 115 ; Last entry best in an outer part— the reasons for this, 182 ; Length of— Limits of, 178, 293, 294 ; Order of entry of the different voices, 179; (a) in & Two-part fugue, 183; (b) in a Three-part fugue, 184 ; (c) in a Four-part fugue, 199 ; relative distance of voices, 180. /. EXPOSITION OF A TWO- PART FUGi E. Either voice may lead — example of, Exposition ends at bar 9, 334, 335. 2 5 2 Anal ytica l Index. U. EXPOSITION OF A THREE- PART FUGUE. Exercise worked — additional entry — Codetta — Counter- subject— Free part, 194-197. ///. EXPOSITION OF A FOUR- PART FUGUE— how it differs from one in Three parts, 201 — exercise worked — Codetta — Countersubject — two free parts, 204, 205. Exposition of a Double fugue {see Double Fugue) ; of a Triple fugue {see Triple Fugue) ; of a Quadruple fugue {see Quadruple Fugue) ; of an Accom- panied fugue {see Accompanied Fugue) ; of a Fugue on a Choral {see Fugue on a Choral, 1. and 11.) ; of a Fughetta {see Fughetta). Final Section of a Fugue :— Addi- tional voices sometimes introduced in the Coda, 306, 329 ; Coda, 294, 296, 3°5< 3°6i 308, 318, 347 ; defined, 291- 294 ; examples by Bach, 294, 296, 298, 3°5. 3° 8 - 3 l8 : b Y Prout, 335, 339, 34°. 343. 347; key of, 29 c, 292; length of, 305 ; Pedal-point, 272, 329, 347 ; Strrtto maestrale, 318, 347. First section of a Fugue {see Exposition). Form in Fugue (simple), 291-293 ; in Double fugue, 379, 396 ; in Triple fugue, 403, 406 ; in Fugue on a Choral, 424 ; in Fughetta, 351, 353, 355. 356. Four-part Fugue (see Simple Fugue, in.). Free Fugue defined, 18. Free parts in Simple fugue in Three parts, 194, 196, 340 ; in Simple fugue in Four parts, 204, 343. Fugato : — Defined, 358 ; Difference be- tween Fugue and Fugato, 359, 360 ; examples by Bach, 359 ; by Beethoven, 391; by Haydn, 360; by Macken- zie, 363 ; by Mendelssohn, 362 ; by Mozart, 361 ; in Fugue on Choral — example by Bach, 423. Fughetta : — Coda in, 353, 355, 357 ; de- fined, 350; Episode in, 353. 354; Expo- sition of, 351, 352, 354, 356, 357 ; Form in > 35 x > 353. 355- 35 6 l Middle entries j i n > 353» 355; Stretto in, 356; examples by Bach, 352-354 ; by Beethoven, 357; by Handel, 355 ; by Mozart, 356. Fugue : — Accompanied {see Accompanied Fugue) ; Answer in {see Answer) ; by Augmentation, Diminution, and Infer- sion — defined, 20 ; Close {see Close Fugue) ; Coda in {see Coda) ; Codetta in (see Codetta) ; Counter-exposition in (see Counter-exposition) ; Countersub- ject in (see Countersubject) ; defined, 2 ; Derivation of the word ' 'fugue," 2 ; Double fugue (see Double Fugue) ; Episode in (see Episode); Exposition of {see Exposition). Final Section of a (see Final Section of a Fugue). First Section of a (see Exposition). Free Fugue, defined, 18. Fugue and Canon, difference between, 4-6 ; general plan of, 291-.-5.05; may be in any number of parts, 11; Middle entries in (see Middle Entries) ; Middle section of a (see Middle Section) ; on a Choral (see separate paragraph below) ; on One Subject (see Simple Fugue) ; on Two Subjects (see Double Fugue) ; on Three Subjects (see Triple Fugue) ; on Four Subjects (see Quad- ruple Fugue ; Pedal-point in (see Final Section of a Fugue) ; Quadruple fugue (see Quadruple Fugue) ; Real fugue, defined, 9 ; Ricercare, defined, 19 ; Simple (see Simple Fugue) ; Stretto in (see Stretto) ; Strict fugue, defined, 18 ; Subject in (see Subject) ; Tonal, defined, 9. Fugue on a Choral: — Two methods of writing, 415. I. THE FIRST METHOD. Ad- ditional entries, 420 ; Canto Fermo, entry of, 415, 418, 420, 423, 425, 426 ; Close fugue, 423 ; defined, 415, 416 ; entries not always at regular intervals, 423 ; Exposition, 416, 418, 419, 421 ; form of, 416, 424 ; Fugato, 423 ; modulation, 424 ; plan mostly fol- lowed, 416; Stretto, 419; Subjects taken from the Choral itself, 416 ; examples by Bach analyzed, 422, 423 ; by Buxtehude analyzed, 417-421 ; Modern examples, by Macfarren, re- ferred to, 426. //. THE SECOND METHOD. Canto fermo, 427, 429, 433 ; defined, 416, 427; Double fugue, 431, 433; Episodes, 430 ; first line of a choral taken as a Fugue subject, 433 ; Fugato, 427 ; interval of Reply seldom strict, 427 ; modulations, 429 ; Subject quite anal vi ica l Index. 253 independent ot the Choral, 427 ; ex- amples by Bach analyzed, 427, 428 ; by Bach — Double fugue, 433 ; by Mendelssohn — E oub!e fugue, 431. General Plan of a Fugue, 334; ex- ercises worked- (a) in Two parts 335, and analyzed, 336-339 ; (b) in Three parts, 340, and analyzed, 341, 342 ; (c) in Four parts, 343, and analyzed, 344-347- How to determine the limits of the Ex- position 293; of the Subject, 53. How to obtain Unity in iugal writing, 217, 231. Imitation, use of, in writing Episodes, 217. Implied modulation in a Subject (see Subject). Incidental modulation in Sibject (see Subject, Vlll.); how answered (see Answer, IV. (/). Incomplete entries of Subject or Answer in S retto, 252. Incomplete Exposition, 203. Incomplete Counter-exposition, 208. Inganno : — Defined — example by Bach, ,65. Inversion : — A^werby (see Answer, 11.); Counter-exposition by (see Counter- exposition) ; Stretto by (see Stretto (A (*). [h)- Irregular — Answers (see Answer, v.) ; Ex- position (see Exposition). Isolated entries (see Middle Section of a Fugue). Key : — Of Answer (see Answer) ; of Countersubject (see Countersubject) ; of Subject (see Subject) ; of Subject and Answer in Close fugue (see Close Fugue). Keys : — Of Exposition (see Exposition) ; of Middle section — order of modula- tion (see Middle Section) ; of final section (see Final Section). Leading Note :— Subject commencing on (see Subject, How to Commence) ; treatment of, in Answers to Subjects which modulate (see Answers, IV.). Length of Episodes (see Episode) ; of Exposition (see Expositi< n) ; of Final section (see Final Section) ; of Middle section (see Middle Section) ; of Sub- ject (see Subject). Limits of exposition, how to find (see Exposition); of Subject, how to deter- mine (see Subject). Material of Countersubject (see Counter- subject) ; of Episode (see Episode). Mediant, Subject commencing on (see Subject, How to Commence). Melody and Rhythm in Subject, im- portance of (see Subject). Middle Entries : — All voices need not take part in, 327 ; general Rule for treatment of, 325, 326 ; how to dis- tinguish Subject and Answer in, 297 ; in Stretto, 313, 314, 316-318 ; number of Middle entries variable, 328. Middle entries in Double fugue (see Double Fugue, I.) ; in Fughetta (see Fughetta). Middle Section of a Fugue : — Cadences in, 321; defined, 14; entries of the Subject best preceded by a rest, or, if this is not possible, by a leap — the reason for this, 320 ; free- dom of treatment in, 290 ; how to distinguish Subject and Answer in, 2^7 ; individuality in the voices to be carefully preserved, 332 ; isolated en- tries, 301 ; length of, variable, 294, 295 ; Middle entries in (see Middle Entries) ; occasional rests in some of the voices desirable, 319; order of modulation in, 322-324; Stretto in (see Stretto) ; where it com- mences, 293 ; where it ends, 294.. Exercise worked and analyzed — (a) in Two parts, 335-339 ; (b) in Three parts, 340-342 ; (c) in Four parts, 343-347- Examples — (a) by Bach analyzed, 298-307 ; (b) by Bach an- alyzed, 308-318 ; (c) by Bach referred to and analyzed, 294, 295 ; (d) by Bach referred to and analyzed, 296. Example of how not to write by Mozart, 330. Modulation : — In Double fugue (see Double Fugue, 11.) ; in a Fugue sub- ject (see Subject, III., iv., v., VI., viii.); in a Fugue subject, how an- swered (see Answer, iv. ) ; in Fugue 254 Analytical Index. on a Choral (see Fugue on a Choral, I. and II.); in Middle section (see Middle Section, Order of Modulation) ; in Triple fugue (see Triple Fugue) ; use of Episode to effect (see Episode). Need of clearly defined Tonality in the Subject, 26. Need of contrast in Counter subject, 161 ; in the Subjects of a Double fugue, 368 ; of a Triple fugue, 398. Need of variety in Episodes, 231. Occasional rests to some of the voices desirable in a Fugue, 219-222, 319, 331. Octave Fugue defined — example by Handel, 206. Order of entry of the different voices in the exposition (see Exposition). Order of modulation in Middle section of a Fugue (see Middle Section). Pedal-point (see Final Section of a Fugue). Plagal scale in connection with Tonal Answer, 84. Point of modulation in a Fugue subject, how to determine and how to Answer (see Answer, IV.). Quadruple Counterpoint (see Quad- ruple Fugue). Quadruple Fugue : — Four Subjects to be written in Quadruple counter- point, 411. Examples by Cherubini, 413, 414; by Haydn, 411; by Handel, discussed 412. Real answer (see Answer, VI.). Real and Tonal answer sometimes met with in the same Fugue, 109. Real fugue (see Fugue). Rests before re-entry of Subject, 197. Rests in some of the voices desirable occasionally, 219-222, 319, 331. Rhythm and Melody in the Subject, im- portance of, 52. Ricercare fugue defined (see Fugue). Semitones, disregard of, between Subject and Answer (see Answer). Sequence, its employment in Episode (see Episode). Short Subjects — Examples by Bach, 46 (a), (b) ; by Mozart, 46 (c). Simple Fugue :— General plan of, 334. /. FUGUE IN TWO PARTS. Exercise worked of a complete Fugue, 335 ; analysis of, 336-339. //. FUGUE IN THREE PARTS. Exercise worked of a complete Fugue, 340 ; analysis of, 341, 342 ; examples of complete Fugues (a) by Bach, analysis of, 297-307 ; (b) by Bach, referred to, analysis of, 295, 296. III. FUGUE IN FOUR PARTS. Exercise worked of a complete Fugue, 343 ; analysis of, 344-347 ; examples of complete Fugues (a) by Bach, analysis of, 308-318 ; by Bach, re- ferred to, analysis of, 294, 295. Stretto: — Canonic, 270; Close fugue, 279, 280 ; closest Stretti should come last, 251 ; defined, 16, 244 ; imitation, may be at any interval, 248, and in any number of parts, 251 ; in the exposition, Subject and Answer in the same key, Close fugue, 279 ; in the Counter exposition, 269, 270 ; incomplete entries, 252 ; interest should be cumu- lative, 251, 328 ; last entering voice should have the Subject complete, 252, 271 ; last notes of the Subject sometimes slightly altered, 285 ; later entries should be either in more parts, or at shorter distances, or both, 251 ; met with mostly in the Middle and Final sections of a Fugue, 269 ; necessity for analysis, 288 ; not in- dispensable, 246 ; one voice may dis- continue the Subject as soon as another voice enters with it, 252, 271 ; regularity desirable in the entries of the Stretti, 271 ; slight modifications of the Subject allowable in Close Stretti, 277 ; Stretto ma^-strale defined, 277, 278 ; Subject and Countersub- ject sometimes treated in Stretto, 272; Subject or Answer of a Tonal fugue may be used, 253 ; Subjects should be specially designed for Stretto — ex- ample of Subject not so designed, 247-250 ; the Old rule, 245 ; varieties of, 253. Exercise worked : — /. IN TWO PARTS. Subject specially designed for Stretto, 254 ; (a) Treatment of the Subject — (i.) At three bars' distance, 255; (ii.) af Analy tic a l Ind ex. 255 two and a half bars', 256; (iii.) at two bars', 257; (iv.) at one bar's, 258; (v.) at half a bar's, 259. (b) Treatment of the Answer— (i.) At three bars' distance, 260; (ii.) at two bars' distance, 261 ; (iii.) at one bar's distance, 262; (iv.) at half a bar's distance, 263. //. IN THREE PARTS. InteivalS of entry irregular — (i.) At one bar's distance, 264 ; (ii. ) at two and one bars' distance, 265. 111. IN FOUR PARTS. Intervals of Entry irregular — (i.) at one bar's distance, 266; (ii.) at half a bar's distance, 267. Examples : — (a) by Bach, Stretto in the Ex- position, close fugue, 279 ; (b) by Bach, Stretto in the Counter-expo- sition, 269 ; (c) by Bach, Canonic Stretto in the Counter-exposition, 270; (d) by Bach, Stretto in the Middle section, 271 ; (e) by Bach, Stretto in the Final Section above a pedal, 272 ; (/) by Bach, Stretto by Inversion, 274 ; (g) by Bach, Stretto by Aug- mentation and Inversion, 275 ; (h) by Bach, Stretto by Diminution and In- version, 276 ; (i) by Bach, Stretto Maestrale, 277, 278 ; (/') by Brahms, Modern freedom, 287 ; (k) by Handel, Stretto made from altered Subject, 2 73 1 (J) by Handel, Stretto in the Exposition, Close fugue, 279 (b), 280; (m) by Mendelssohn, Stretto in the Exposition, Close fugue, 279 (c) ; (n) by Mendelssohn, alteration of the last notes of the Subject, 285 ; (o) by Mozart, Stretto in the Exposition, 282 (a) ; entries per Arsin et Thesin, 283 (a) ; Closest stretti, 283 (b) ; (p) by Mozart, 284 ; (q) by Spohr, 286. Stretto in Double fugue (see Double Fugue, I.) ; in Triple fugue (see Triple Fugue) ; in Fughetta (see Fughetta) ; in Fugue on a Choral (see Fugue on a Choral). Strict fugue (see Fugue). Subdominant, Answer in (see Answer, VI. (d), (), 134 ; Fugue on a Choral, 417 ; Organ Fugue in G minor, no (c). Cherubini, Credo a 8 voci, 413; First Mass, 438, 439 ; Second Mass, 377 ; Fourth Mass, 48 (d) ; Treatise on Fugue, 98. Clementi, Gradus ad Parnassum, No. 25. 69 (b) ; No. 45, 99 (a). Handel, "Alexander's Feast," 38 {a), 82 ; Anthem, " Have mercy upon me, O God," 107 (e) ; Anthem, "I will magnify Thee," 137 (a); Anthem, "In the Lord put I my trust," 41 (c) ; An- them, " Let God arise," 105 (c) ; Anthem, "O come, let us sing," 106 (b) ; ' Belshazzar,' 137 (b) ; ' Choice of Hercules,' 155 (b) ; Concerto Grosso in C, 130 ; Dettingen Anthem, 49 (a), 146, 386 ; First Grand Con- certo, 95 (d) ; Fourth Oboe Concerto, 105 (b) ; ' Hercules,' 34 (c), 100 (b) ; ' Israel in Egypt,' 95 (b), 125 (a), 279 (P) < ' Jephthah,' 39, 81, 151 (a) ; Jubilate, 280 ; ' Judas Maccabaeus, ' 28 (b), 374; ' Messiah,' 28 (a), 41 (a), 103 (a), 104 (b), 273 ; Muzio Scevola, 32 (a), 145 (b) ; Ninth Organ Con- certo, 95 (c) ; Ricardo Primo, 62 ; ' Rinaldo,' 36 (b) ; 'Samson,' 33 (c), 70 (b) ; ' Saul,' 91 (c) ; 107 (d), ng(d); 'Semele,' 40 (b), 83 (a) ; Six Fugues, No. 2, 224-226 ; Six Fugues for Harp- sichord, No. i, 371 ; ' Solomon,' 79 (a), 206 ; ' Susanna,' 91 (b) ; ' Theo- dora,' 95 (a); 'Tolomeo,' 95 (