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For the use of the word in psychology see fugue state

In music, a fugue is a process in which a subject is stated and developed in imitative counterpoint. Because the fugal process may yield various forms, it is not technically a form (although it is often referred to as such). Donald Tovey wrote that "Fugue is not so much a musical form as a musical texture," that can be introduced anywhere as a distinctive and recognizable technique, often to produce intensification in musical development.

The word fugue comes from the Latin fuga (flight) and fugere (to flee). Variants include fughetta (a small fugue) and fugato (a work or section of a work resembling a fugue but not necessarily adhering to the rules of one). The adjectival form of fugue is fugal.

(Johann Sebastian Bach's C-minor fugue from the Well Tempered Clavier I, in 3 voices)

Table of contents
1 Characteristics and anatomy of fugues
2 History of the fugue
3 Perceptions and aesthetics of the fugue
4 References

Characteristics and anatomy of fugues

Fugues are said to be in a number of voices or parts (the term voices may be used even if the fugue is not written for singers), that is, independent melodic lines. Fugues are generally in from three to five parts, but eight or even ten parts are possible in large choral or orchestral fugues. Fugues in fewer than three parts are rare, because with two parts the subject can only jump back and forth between the upper and lower part. The best-known example of a two-voice work is the E minor fugue from Book 1 of The Well-Tempered Clavier by Johann Sebastian Bach.

While compositions that qualify as fugues admit of considerable variation, there is broad agreement that all fugues adhere to certain characteristics. A typical fugue will manifest the following pattern.

A fugue begins with an exposition of its subject. This is the main theme that will be developed throughout the work. After the subject, another voice "answers" the subject. The answer mimics the subject at a different pitch (interval), usually a fifth or fourth higher or lower. In a tonal answer, some of the intervals may be altered to keep the answer in the same key. In a real answer, the subject is literally transposed to another key. As the answer is passed to each new voice, the prior voice will sometimes accompany the subject with a counter-subject. It is customary for the exposition to alternate subjects (S) with answers (A) as follows: SASA. But in some fugues the order is varied: e.g. SAAS of the first fugue in Bach's Well-Tempered Clavier. The fugue's exposition concludes when all voices have stated or answered the subject.

The fugue rarely stops after its initial exposition, more often continuing to one or more developmental episodes. Episodic material is usually based upon some element of the exposition - for example, a melodic motif may be taken and repeated sequentially. There may also be middle entries: these are entries of the subject by fewer than all the voices in the fugue, often varied in some way. They are often given in keys other than the tonic or dominant, or in a different mode (that is, in D minor instead of D major, or vice versa). They may also vary the subject by giving it in inversion (upside-down), retrograde (back-to-front), diminution (with shorter note values) or augmentation (with longer note values; the subject in augmentation entering in the bass is quite a common device used at the end of fugues). Sometimes the voices enter in stretto, with one voice entering with the subject before the last voice has finished its entry (this is also particularly common at the end of fugues). Stretto, from the Italian word for "strict," originally described a treatment of the subject in close, Renaissance style counterpoint, after the manner of Palestrina. Sometimes there may be false entires - entries which begin the fugue subject, but do not give it in full.

Episodes may be interspersed with repeated expositions in which all voices give subjects and answers as at the beginning of the fugue, though these may be also be varied, by the voices entering in a different order to how they did at the start of the fugue, for example. the use of episodes was considered by many to be essential to a properly constructed fugue, and the best procedure was to use the theme itself as the source of the episodes.

A fugue may end with a recapitulation in which the entires of the subject are repeated in the manner it was first introduced. There may also be a coda to conclude the fugue. Another common device is the entrance of the theme in each voice in a short space of time, called "stretto" treatment of the theme. In the Baroque, this was almost always at the point where the fugue was reaching its climax of tension.

The construction of a fugue is based on taking advantage of "contrapunctal devices" as JS Bach called them - places where an "entrance" of a theme or subject could occur. In each fugue theme, then, there is an implied structure of where and at what intervals the theme can begin in another voice. Bach was sufficiently expert that he could tell exactly what entrances could occur simply by hearing the first playing of a theme.

Although fugues are often described in purely contrapuntal terms, tonally-centered fugues also manifest a fundamental harmonic structure (Ratz, 1951). As with most classical music, this structure is ternary, with an initial exposition of the subject in the tonic, subsequent developments in related keys, concluding with a return to the tonic.

Double (Triple, Quadruple) fugue

A double fugue has two subjects that are often developed simultaneously. Sometimes the second subject is initially presented as the counter-subject of the first, while in other examples, the second subject has its own exposition. In this latter case, the work has the structure: fugue on subject A; fugue on subject B; combination of subjects A and B.

While triple fugues are not uncommon (see Bach C# minor WTC I and F# minor WTC II), quadruple fugues are rare. The surviving pages of Contrapunctus XIV from Bach's Die Kunst der Fuge (The Art of Fugue) represent a triple fugue that was undoubtedly quadruple by conception. The missing fourth exposition would have brought back he main theme of DKdF. Reconstructions of this fugue, such as by Tovey, interpret it as such. While tradition holds that this fugue was "unfinished," Christoph Wolff and others have shown that it was certainly completed, but the final exposition and development were lost by the executors of Bach's estate.

History of the fugue

The term fuga was used as far back as the Middle Ages, but was initially used to refer to any kind of imitative counterpoint, including canons, which are now thought of as distinct from fugues. It was not until the 16th century that fugal technique as it is understood today began to be seen in pieces, both instrumental and vocal. Fugal writing is found in works such as fantasias, ricercares and canzonas.

The fugue arose from the technique of "imitation", where the same musical material was repeated starting on a different note. Originally this was to aid improvisation, but by the 1550s, it was considered a technique of composition. The Renaissance composer Giovanni Pierluigi da Palestrina (1525?-1594) wrote masses using modal counterpoint and imitation, and fugal writing became the basis for writing motets as well. A motet differed from a fugue in that each phrase of the text had a different subject which was introduced and worked out separately, where as a fugue continued working with the same subject or subjects throughout the entire length of the piece.

The fugue in the Baroque era

It was in the Baroque period that the writing of fugues became really popular. Jan Pieterszoon Sweelinck, Girolamo Frescobaldi, Johann Jacob Froberger and Dietrich Buxtehude all wrote fugues, and George Frideric Handel included them in many of his oratorios. Keyboard suites from this time often conclude with a fugal gigue. The French overture, used by French Baroque composers as well as by Handel to open his oratorios and operas and Bach to open his orchestral suites, features a quick fugal section after a slow introduction. The second movement of a sonata da chiesa, as written by Arcangelo Corelli (opus numbers one and three) among others, was usually fugal.

The Baroque period also saw an rise in music theory, and the most influential text on fugue writing was based on Renaissance counterpoint and fugue writing. Johann Joseph Fux (1660-1741), writing almost a century after Palestrina, published Gradus Ad Paransum - meaning "Steps to Parnasus" or steps to perfection - in 1725. This work laid out the terms of "species" of counterpoint, and laid out a series of exercises to learn fugue writing. His work was largely based on the practice of Palestrina's modal fugues, and remained an influential text all the way into the 19th Century. Haydn, for example, taught counterpoint from his own summary of Fux, and thought of it as the basis for formal structure.

The 18th century composer Johann Sebastian Bach is generally regarded as the greatest composer of fugues. He often entered into contests where he would be given a subject with which to spontaneously improvise a fugue on the organ or harpsichord.

Bach's most famous fugues are those in the unfinished Art of Fugue, The Well-Tempered Clavier (keyboard), and his organ fugues, which are usually preceded by a prelude or toccata. The Art of Fugue is a collection of fugues (and four canons) on a single theme that is gradually transformed as the cycle progresses. The Well-Tempered Clavier is two volumes written in different times of his life, each comprising 24 prelude and fugue pairs, one for each major and minor key. Bach also wrote smaller single fugues, and incorporated fugal writing in many of his works that were not fugues per se.

While not well known as a composer in his lifetime, his influence extendd forward through his son CPE Bach and through the theorist Marpurg who wrote a book on fugues which was largely based on Bach's work.

The fugue in the Classical era

During the Classical era, the fugue was no longer a central or even fully natural mode of musical composition. Nevertheless, the three greatest composers of the Classical era, Haydn, Mozart, and Beethoven, all had periods of their careers in which they in some sense "rediscovered" fugal writing and used it frequently in their work.

Haydn's first spell of fugue-writing occurred when he composed his Sun quartets, (op. 20, 1772) of which four have fugal finales. This was an practice that Haydn only repeated once later in his quartet-writing career, with the finale of his quartet Op. 50 no. 4 (1787). However, a second period of fugue writing for Haydn occurred after he had heard, and been greatly inspired by, the oratorios of Handel during his visits to London (1791-1793, 1794-1795). As a result, Haydn studied Handel's techniques and incorporated Handelian fugal writing into the choruses of his mature oratorios The Creation and The Seasons.

Mozart went to Rome to study under Padre Martini when young, who introduced him to the modal counterpoint based on Fux of church music, but the major impetus to fugal writing can be clearly identified: the influence of Baron Gottfried van Swieten, in Vienna around 1782. Van Swieten, during diplomatic service in Berlin, had taken the opportunity to collect as many manuscripts by Bach and Handel as he could, and he invited Mozart to study his collection and also encouraged him to transcribe various works for other combinations of instruments. Mozart was evidently fascinated by these works, and wrote a set of string trios in which he took fugues from Bach's Well-Tempered Clavier, transcribed them for this combination of instruments, and introduced them with preludes of his own. He soon set to writing fugues on his own, mimicking the Baroque style. These included the fugues for string quartet, K. 405 (1782) and a fugue in C Minor K. 426 for two pianos (1783). Later, Mozart incorporated fugal writing into the finale of his Symphony No. 41 and his opera The Magic Flute.

Beethoven was familiar with fugal writing from childhood, as an important part of his training was playing the preludes and fugues from The Well-Tempered Clavier. During his early career in Vienna, Beethoven attracted notice for his performance of these works. There are fugal sections in Beethoven's early piano sonatas, and fugal writing is to be found in the slow movement of the Eroica Symphony (1805). Nevertheless, fugues did not take on a truly central role in Beethoven's work until his "late period." A fugue forms the development section of the last movement of his piano sonata op. 101 (1816), and massive, dissonant fugues form the finales of his Hammerklavier piano sonata (1818) and string quartet op. 130 (1825); the latter was later published separately as op. 133, the Grosse Fuge ("Great Fugue")). Beethoven's last piano sonata, op. 111 (1822) integrates fugal texture throughout the first movement, written in sonata form. Fugues are also found in the Missa Solemnis and in the finale of the Ninth Symphony.

A common characteristic of the Classical composers is that they usually wrote fugues not as isolated works but as part of a larger work, often as a sonata-form development section or as a finale. It was also characteristic to abandon fugal texture just before the end of a work, providing a purely homophonic resolution. This is found, for instance, in the final fugue of the chorus "The Heavens are Telling" in Haydn's The Creation (1798) and the final fugal section of Beethoven's piano sonata op. 110 (1822).

The fugue in the Romantic era and later

Fugues became somewhat less popular in the Romantic era, although examples of fugal writing are found in the last movement of Berlioz's Sinfonie Fantastique, and Wagner's Meistersinger overture. The finale of Giuseppe Verdi's opera Falstaff is a ten-voice fugue. Robert Schumann, Felix Mendelssohn and Johannes Brahms also included fugues in many of their works. The final part of Schumann's Piano Quintet is a double fugue, and his opus numbers 126, 72 and 60 are all sets of fugues for the piano (opus 60 based on the BACH motif). Brahms' Variations and Fugue on a Theme of Handel ends with a fugue, as does his Cello Sonata No. 1. The writing of fugues also remained an important part of musical education throughout the 19th century, particularly with the publication of the complete works of Bach and Handel, and the revival of interest in Bach's music.

A number of twentieth century composers made extensive use of the fugue. Béla Bartók opened his Music for Strings, Percussion and Celesta with a fugue in which the tritone, rather than the fifth, is the main structural interval. He also included fugal sections in the final movements of his String Quartet No. 1, String Quartet No. 5 and Piano Concerto No. 3 and the second movement of his Sonata for Solo Violin is also a fugue.

Igor Stravinsky also incorporated fugues into his works, including the Symphony of Psalms and the Dumbarton Oaks concerto. The practice of writing fugue cycles in the manner of Bach's Well-Temepred Clavier was perpetuated by by Paul Hindemith in his Ludus Tonalis, and Dmitri Shostakovich in his Preludes and Fugues, opus 87 (which, like the Well-Tempered Clavier, contains a prelude and fugue in each key, be it ordered along the cycle of fifths rather than chromatically). Leonard Bernstein wrote a "Cool Fugue" as part of his musical West Side Story, and the musical comedy composer Frank Loesser included a Fugue for Tinhorns in his musical Guys and Dolls. Jazz musician Benny Goodman even wrote a fugue: Bach Goes to Town.

Perceptions and aesthetics of the fugue

Fugue is the most complex of contrapuntal forms. As such, gifted composers have used it to express the profound. The complexity of fugue has foiled lesser composers who have produced only the banal. In the words of the Austrian musicologist (and Schoenberg student) Erwin Ratz (1951, p. 259), "Many lay people, but many musicians as well, believe that in the realm of musical works of art something is of a higher status through the mere fact of being a fugue. In truth things are similar here to the situation with twelve-tone technique, where the fateful misunderstanding arose that something is music simply because it uses this technique. Arnold Schoenberg's greatness consisted rather in being able to write music despite using twelve-tone technique, which provides as little guarantee for the value of the musical substance created with it as does the application of fugal technique or the C major scale. Thus Bach's greatness consisted in being able to create a musical art work although it was a fugue. It must be grasped that Bach's fugues belong to the greatest works of art not because they are fugues but rather despite their being fugues. Like twelve-tone technique, fugal technique significantly burdens the shaping of musical ideas, and it was given only to the greatest geniuses, such as Bach and Beethoven, to breathe life into such an unwieldy form and make it the bearer of the highest thoughts."

In presenting Bach's fugues as among the greatest of contrapuntal works, Peter Kivy (1990) points out (p. 206) that "counterpoint itself, since time out of mind, has been associated in the thinking of musicians with the profound and the serious" and argues (p. 210) that "there seems to be some rational justification for their doing so." Because of the way fugue is often taught, the form can be seen as dry and filled with laborious technical exercises. The derogatory term school fugue is sometimes applied to fugues (MIDI File), which have no real musical interest and have been merely written to demonstrate technical ability. The works of the Austrian composer Simon Sechter, who was a teacher of Schubert and Bruckner, include several thousand fugues, but they are not found in the standard repertory, again not because they are fugues but because of Sechter's limitations as a musical artist.