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For the use of the word in psychology see fugue state

In music, a fugue is a type of piece written in counterpoint for several independent musical voices. A fugue begins with its subject (a brief musical theme) stated by one of the voices playing alone. A second voice then enters and plays the subject, while the first voice continues on with a contrapuntal accompaniment. Then the remaining voices similarly enter one by one. The remainder of the fugue further develops the material using all of the voices.

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.

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Listen to a fugue (Johann Sebastian Bach's C-minor fugue from the Well Tempered Clavier I, in 3 voices). See the music ( for this fugue (external link, requires a Macromedia Director plugin).


Characteristics and anatomy

Number of voices

The number of voices in a fugue generally ranges from three to five, but eight or even ten voices are possible in large choral or orchestral fugues. Fugues in fewer than three voices are rare, because with two voices the subject can only jump back and forth between the upper and lower voice. The best-known example of a two-voice work is the E minor fugue from Book I of Bach's Well-Tempered Clavier. Two part works which are written in a fugal manner are sometimes called "inventions".

The term "part" is often used in the context of the fugue as a synonym for "voice." Use of the term "voice" does not imply that the fugue in question is necessarily composed for voices rather than instruments.

Musical outline

The beginning of the fugue tends to be written to definite rules, whereas in the later portions the composer has considerably greater freedom.

A fugue begins with an exposition of its subject by one of the voices. After the subject, a second 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 (minor instead of major, or vice versa).

The episodes 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 a common at the end of fugues). Sometimes the voices appear in stretto, with one voice entering with the subject before the last voice has finished its entry. There also may be false 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, for example by having the voices enter in a different order.

Various devices are used to form the conclusion of a fugue. A fugue may end with a recapitulation, in which the entries of the subject are repeated in the manner it was first introduced. Stretto entries of the subject often are found near the end, usually at the point where the fugue reaches its climax of tension. The final section often includes a pedal point, either on the dominant or the tonic note. At the very end of the fugue there may be a coda section, which follows a strong Cadence on the tonic chord.

Timing of entries

The construction of a fugue is based on taking advantage of "contrapunctal devices" as J. S. 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.

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 the 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 30 minute-long Fuga IV quadruplex of Sorabji's monumental Opus clavicembalisticum is one of the few examples of a quadruple fugue.

Is the fugue a musical form?

A widespread view of the fugue is that it is not a musical form (in the sense that, say, sonata form is) but rather a technique of composition. For instance, 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.

On the other hand, composers almost never write music in a purely cumulative fashion, and usually a work will have some kind of overall formal organization--hence the rough outline given above, involving the exposition, the sequence of episodes, and the concluding coda. When scholars say that the fugue is not a musical form, what is usually meant is that there is no one single formal outline into which all fugues reliably can be fitted.

The formal organization of a fugue involves not only the arrangement of its theme and episodes, but also its harmonic structure, a point emphasized by Ratz (1951). In particular, the exposition and coda tend to emphasize the tonic key, whereas the episodes usually explore more distant tonalities.


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, whereas a fugue continued working with the same subject or subjects throughout the entire length of the piece.

Baroque era

It was in the Baroque period that the writing of fugues became central to composition, in part as a demonstration of compositional expertise. Fugues were incorporated into a variety of musical forms. Jan Pieterszoon Sweelinck, Girolamo Frescobaldi, Johann Jakob 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 featured a quick fugal section after a slow introduction. The second movement of a sonata da chiesa, as written by Arcangelo Corelli and others, was usually fugal.

The Baroque period also saw a rise in the importance of music theory. The most influential text was published by Johann Joseph Fux (1660-1741), his Gradus Ad Parnassum ("Steps to Parnassus"), which appeared in 1725. This work laid out the terms of "species" of counterpoint, and offered a series of exercises to learn fugue writing. Fux's work was largely based on the practice of Palestrina's modal fugues. It remained influential into the nineteenth century. Haydn, for example, taught counterpoint from his own summary of Fux, and thought of it as the basis for formal structure.

Johann Sebastian Bach (1685-1750) 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 for the harpsichord in The Well-Tempered Clavier and the (unfinished) Art of Fugue, 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 comprises two volumes written in different times of Bach's 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.

Although J. S. Bach was not well known as a composer in his lifetime, his influence extended forward through his son C.P.E. Bach and through the theorist Friedrich Wilhelm Marpurg (1718-1795) whose Abhandlung von der Fuge ("Treatise on the fugue", 1753) was largely based on J. S. Bach's work.

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 three have fugal finales. This was a 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). Haydn then studied Handel's techniques and incorporated Handelian fugal writing into the choruses of his mature oratorios The Creation and The Seasons.

Mozart studied counterpoint when young with Padre Martini in Rome. However, the major impetus to fugal writing for Mozart was 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 transcriptions for string trio of fugues from Bach's Well-Tempered Clavier, introducing them with preludes of his own. Mozart then 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 from The Well-Tempered Clavier. During his early career in Vienna, Beethoven attracted notice for his performance of these fugues. 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).

Romantic era

By the beginning of the Romantic era, fugue writing had become specifically attached to the norms and styles of the Baroque. One manual explicitly stated that the hallmark of contrapuntal style was the style of J. S. Bach. The 19th century's taste for academicism - setting of forms and norms by explicit rules - found Marpurg, and the fugue, to be a congenial topic. 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.

Examples of fugal writing in the Romantic era are found in the last movement of Berlioz's Symphonie 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. Towards the end of the Romantic era, Richard Strauss included a fugue in his tone poem, Also sprach Zarathustra, to represent the high intelligence of science.

20th century

The late Romantic composer Max Reger had the closest association with the fugue among his contemporaries. Many of his organ works contain, or are themselves fugues. Two of Reger's most-played orchestral works, the Hiller variations and the Mozart variations, end with a large-scale orchestral fugue.

A number of other twentieth century composers made extensive use of the fugue. Bla Bartk 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-Tempered Clavier was perpetuated by Paul Hindemith in his Ludus Tonalis, Kaikhosru Sorabji in a number of his works including the Opus clavicembalisticum, 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 Alec Templeton even wrote a fugue (recorded subsequently by Benny Goodman): Bach Goes to Town.

20th Century fugue writing explored many of the directions implied by Beethoven's Grosse Fuge, and what came to be termed free counterpoint as well as dissonant counterpoint. Fugal technique as described by Marpurg became part of the theoretical basis for Schoenberg's twelve tone technique.

Perceptions and aesthetics

Fugue is the most complex of contrapuntal forms and, 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 Erwin Ratz (1951, p. 259), "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 Missing image

like this (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.

Others, such as Alfred Mann, argued that fugue writing, by focusing the compositional process actually improves or disciplines the composer towards musical ideas. This is related to the idea that restrictions create freedom for the composer, by directing their efforts. He also points out that fugue writing has its roots in improvisation, and was, during the baroque, practiced as an improvisitory art.

The fugue is perceived, then, not merely as itself, but in relation to the idea of the fugue, and the greatest of examples from the Baroque era forward. As a musical idea with a history, which includes its use in liturgical music of Christianity, a device in teaching composition, a favored form by one of the greatest, if not the greatest, composer of classical music, and as a form which can be thought of as distinctly antique - there are a whole range of expectations brought to bear on any piece of music labelled "fugue".


  • Kivy, Peter (1990). Music Alone: Philosophical Reflections on the Purely Musical Experience. Ithaca: Cornell University Press. ISBN 0-8014-2331-7.
  • Ratz, Erwin (1951). Einfhrung in die Musikalische Formenlehre: ber Formprinzipien in den Inventionen J. S. Bachs und ihre Bedeutung fr die Kompositionstechnik Beethovens {"Introduction to Musical Form: On the Principles of Form in J. S. Bach's Inventions and their Import for Beethoven's Compositional Technique", first edition with supplementary volume. Vienna: sterreichischer Bundesverlag fr Unterricht, Wissenschaft und Kunst.


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