Fugue

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

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

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

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

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

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

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

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

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

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

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

CHAPTER XIII.—Accompanied Fugues
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.