Fugue

For other uses, see Fugue (disambiguation).

A six-part fugue from The Musical Offering, in the hand of Johann Sebastian Bach.

In music, a fugue ( /ˈfjuːɡ/ fewg) is a compositional technique (in classical music) in two or more voices, built on a subject (theme) that is introduced at the beginning in imitation (repetition at different pitches) and recurs frequently in the course of the composition.

The English term fugue originated in the 16th century and is derived from either the French word fugue or the Italian fuga. This in turn comes from Latin, also fuga, which is itself related to both fugere (‘to flee’) and fugare, (‘to chase’).^[1] The adjectival form is fugal.^[2] Variants include fughetta (literally, 'a small fugue') and fugato (a passage in fugal style within another work that is not a fugue).^[3]

A fugue usually has three sections: an exposition, a development, and a recapitulation containing the return of the subject in the fugue's tonic key, though not all fugues have a recapitulation.^[4] In the Middle Ages, the term was widely used to denote any works in canonic style; by the Renaissance, it had come to denote specifically imitative works.^[5] Since the 17th century,^[6] the term fugue has described what is commonly regarded as the most fully developed procedure of imitative counterpoint.^[7]

Most fugues open with a short main theme, the subject,^[8] which then sounds successively in each voice (after the first voice is finished stating the subject, a second voice repeats the subject at a different pitch, and other voices repeat in the same way); when each voice has entered, the exposition is complete. This is often followed by a connecting passage, or episode, developed from previously heard material; further "entries" of the subject then are heard in related keys. Episodes (if applicable) and entries are usually alternated until the "final entry" of the subject, by which point the music has returned to the opening key, or tonic, which is often followed by closing material, the coda.^[3][9] In this sense, a fugue is a style of composition, rather than a fixed structure.

The form evolved during the 18th century from several earlier types of contrapuntal compositions, such as imitative ricercars, capriccios, canzonas, and fantasias.^[10] The famous fugue composer Johann Sebastian Bach (1685-1750) shaped his own works after those of Johann Jakob Froberger (1616–1667), Johann Pachelbel (1653–1706), Girolamo Frescobaldi (1583–1643), Dieterich Buxtehude (c. 1637–1707), and other composers.^[10] With the decline of sophisticated styles at the end of the baroque period, the fugue's popularity waned, eventually giving way to sonata form.^[11] Nevertheless, composers from the 1750s to the present day continue to write and study fugues for various purposes; they appear in the works of Wolfgang Amadeus Mozart (1756-1791)^[11] and Ludwig van Beethoven (1770–1827).^[11] Many composers such as Felix Mendelssohn (1809–1847), Anton Reicha (1770–1836) and Dmitri Shostakovich (1906–1975) wrote cycles of fugues.^[12]

Musical outline

A fugue begins with the exposition and is written according to certain predefined rules; in later portions the composer has more freedom, though a logical key structure is usually followed. Further entries of the subject will occur throughout the fugue, repeating the accompanying material at the same time.^[13] The various entries may or may not be separated by episodes.

What follows is a chart displaying a fairly typical fugal outline, and an explanation of the processes involved in creating this structure.

Example of Key/Entry Structure, in a Three-Voice Baroque Fugue

	Exposition						1st Middle-Entry			2nd Middle-Entry		Final Entries in Tonic
	Tonic	Dom.		T	(D-redundant entry)		Relative Maj/Min	Dom. of Rel.		Subdom.		T	T
Sop.	Subj.	CS1	C O D E T T A	CS²	A	E P I S O D E	CS1	CS²	E P I S O D E	S	E P I S O D E	CS1	Free Counterpoint	C O D A
Alto		Ans.		CS1	CS²		S	CS1		CS²		S	CS1
Bass				S	CS1		CS²	A		CS1		CS²	S

The exposition

A fugue begins with the exposition of its subject in one of the voices alone in the tonic key.^[14] After the statement of the subject, a second voice enters and states the subject with the subject transposed to another (often closely related) key, which is known as the answer.^[15][16] To make the music run smoothly, it may also have to be altered slightly. When the answer is an exact copy of the subject to the dominant, it is classified as a real answer; if it has to be altered in any way it is a tonal answer.^[14]

Example of a tonal answer in J.S. Bach's Fugue No. 16 in G Minor, BWV 861, from the Well-Tempered Clavier, Book 1. ( Listen )
The first note of the subject, D (in red), is a prominent dominant note, demanding that the first note of the answer (in blue) sounds as the tonic, G, rather than A.

A tonal answer is usually called for when the subject begins with a prominent dominant note, or where there is a prominent dominant note very close to the beginning of the subject.^[14] To prevent an undermining of the music's sense of key, this note is transposed up a fourth to the tonic rather than up a fifth to the supertonic. Answers in the subdominant are also employed for the same reason.^[17]

While the answer is being stated, the voice in which the subject was previously heard continues with new material. If this new material is reused in later statements of the subject, it is called a countersubject; if this accompanying material is only heard once, it is simply referred to as free counterpoint.

The interval of a fifth inverts to a fourth (dissonant) and therefore cannot be employed in invertible counterpoint, without preparation and resolution.

The countersubject is written in invertible counterpoint at the octave or fifteenth.^[18] The distinction is made between the use of free counterpoint and regular countersubjects accompanying the fugue subject/answer, because in order for a countersubject to be heard accompanying the subject in more than one instance, it must be capable of sounding correctly above or below the subject, and must be conceived, therefore, in invertible or double counterpoint.^[14][19] In tonal music invertible contrapuntal lines must be written according to certain rules because several intervallic combinations, while acceptable in one particular orientation, are no longer permissible when inverted. For example, when the note "G" sounds in one voice above the note "C" in lower voice, the interval of a fifth is formed, which is considered consonant and entirely acceptable. When this interval is inverted ("C" in the upper voice above "G" in the lower), it forms a fourth, considered a dissonance in tonal contrapuntal practice, and requires special treatment, or preparation and resolution, if it is to be used.^[20] The countersubject, if sounding at the same time as the answer, is transposed to the pitch of the answer.^[21] Each voice then responds with its own subject or answer, and further countersubjects or free counterpoint may be heard.

When a tonal answer is used, it is customary for the exposition to alternate subjects (S) with answers (A), however, in some fugues this order is occasionally varied: e.g., see the SAAS arrangement of Fugue No. 1 in C Major, BWV 846, from the Well-Tempered Clavier, Book 1 by J. S. Bach. A brief codetta is often heard connecting the various statements of the subject and answer. This allows the music to run smoothly. The codetta, just as the other parts of the exposition, can be used throughout the rest of the fugue.^[22]

The first answer must occur as soon after the initial statement of the subject as possible; therefore the first codetta is often extremely short, or not needed. In the above example this is the case: the subject finishes on the quarter note (or crotchet) B-flat of the third beat of the second bar which harmonizes the opening G of the answer. The later codettas may be considerably longer, and often serve to (a) develop the material heard so far in the subject/answer and countersubject and possibly introduce ideas heard in the second countersubject or free counterpoint that follows (b) delay, and therefore heighten the impact of the reentry of the subject in another voice as well as modulating back to the tonic.^[23]

The exposition usually concludes when all voices have given a statement of the subject or answer. In some fugues, the exposition will end with a redundant entry, or an extra presentation of the theme.^[14] Furthermore, in some fugues the entry of one of the voices may be reserved until later, for example in the pedals of an organ fugue (see J. S. Bach's Fugue in C major for Organ, BWV 547). Opening with the subject stated in the bass, while unusual, is to be preferred when other actions would present illegal inversions in the exposition.^{[citation needed]}

The episode

Further entries of the subject follow this initial exposition, either immediately (as for example in Fugue No. 1 in C major, BWV 846 of the Well-Tempered Clavier), or separated by episodes.^[14] Episodic material is always modulatory and is usually based upon some element heard in the exposition.^[9][14] Each episode has primarily the function of transitioning for the next entry of the subject in a new key,^[14] and may also provide release from the strictness of form employed in the exposition, and middle-entries.^[24] Gédalge states that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented.^[25]

The development

Further entries of the subject, or middle entries, occur throughout the fugue, must state the subject or answer at least once in its entirety, and may also be heard in combination with the countersubject(s) from the exposition, new countersubjects, free counterpoint or any of these in combination. It is uncommon for the subject to enter alone in a single voice in the middle-entries just as it is in the exposition; rather it is usually heard with at least one of the countersubjects and/or other free contrapuntal accompaniments. Middle-entries tend to occur at pitches other than the initial—as shown in the typical structure above, these are often closely related keys such as the relative dominant and subdominant, but key structure of fugues varies greatly. In the fugues of J. S. Bach the first middle-entry very commonly occurs in the relative major or minor of the work's overall key, and is followed by an entry the dominant of the relative major or minor when the fugue's subject requires a tonal answer. In the fugues of earlier composers (notably Buxtehude and Pachelbel), middle entries in keys other than the tonic and dominant tend to be the exception, and non-modulation the norm. One of the famous examples of such non-modulating fugue occurs in Buxtehude's Praeludium (Fugue and Chaconne) in C, BuxWV 137.

When there is no entrance of the subject and answer material, the composer can develop the subject by altering the subject . This is called an episode,^[26] often by inversion, although the term is sometimes used synonymously with middle-entry and may also describe the exposition of completely new subjects, as in a double fugue for example (see below). In any of the entries within a fugue the subject may be altered, by inversion, retrograde (a less common form where the entire subject is heard back-to-front) and diminution (the reduction of the subject's rhythmic values by a certain factor), augmentation (the increase of the subject's rhythmic values by a certain factor) or any combination of them.^[14]

Example and analysis

The excerpt below, bars 7–12 of J. S. Bach's Fugue no. 2 in C minor, BWV 847, from the Well-Tempered Clavier, Book 1 illustrates the application of most of the characteristics described above. The fugue is for keyboard and in three voices, with regular countersubjects.^[9][27] This excerpt opens at last entry of the exposition: the subject is sounding in the bass, the first countersubject in the treble, while the middle-voice is stating a second version of the second countersubject, which concludes with the characteristic rhythm of the subject, and is always used together with the first version of the second countersubject. Following this an episode modulates from the tonic to the relative major by means of sequence, in the form of an accompanied canon at the fourth.^[28] Arrival in E-flat major is marked by a quasi perfect cadence across the barline, from the last quarter note beat of the first bar to the first beat of the second bar in the second system, and the first middle entry. Here Bach has altered countersubject 2 to accommodate the change of mode.^[29]

Visual Analysis of J.S. Bach's Fugue no. 2 in C minor, BWV 847, from the Well-Tempered Clavier, Book 1(bars 7–12)( Listen )

False entries

At any point in the fugue there may be false entries of the subject, which include the start of the subject but are not completed. False entries are often abbreviated to the head of the subject, and anticipate the "true" entry of the subject, heightening the impact of the subject proper.^[17]

Example of a false answer in J. S. Bach's Fugue no. 2 in C minor, BWV 847, from the Well-Tempered Clavier, Book 1. This passage is bars 6/7, at the end of the codetta before the first entry of the third voice, the bass, in the exposition. The false entry occurs in the alto, and consists of the head of the subject only, marked in red. It anticipates the true entry of the subject, marked in blue, by one quarter-note.

Counter-exposition

The counter-exposition is a second exposition. However, there are only two entries, and the entries occur in reverse order.^[30] The counter-exposition in a fugue is separated from the exposition by an episode, and is in the same key as the original exposition.^[30]

Stretto

Sometimes counter-expositions or the middle entries take place in stretto, whereby one voice responds with the subject/answer before the first voice has completed its entry of the subject/answer, usually increasing the intensity of the music.^[31]

Example of stretto fugue in a quotation from Fugue in C major by Johann Caspar Ferdinand Fischer who died in 1746. The subject, including an eighth note rest, is seen in the alto voice, starting on beat 1 bar 1 and ending on beat 1 bar 3, which is where the answer would usually be expected to begin. As this is a stretto the answer already takes place in the tenor voice, on the third quarter note of the first bar, therefore coming in "early".

Only one entry of the subject must be heard in its completion in a stretto. However, a stretto in which the subject/answer is heard in completion in all voices is known as stretto maestrale or grand stretto.^[32] Strettos may also occur by inversion, augmentation and diminution. A fugue in which the opening exposition takes place in stretto form is known as a close fugue or stretto fugue (see for example, the Gratias agimus tibi and Dona nobis pacem choruses from Bach's Mass in B Minor).^[33] In general, fugues that are densely strettoed will not contain countersubjects, and vice versa. One notable exception is the E Major fugue from Bach's Well-Tempered Clavier, Book II, which initially exposes the subject accompanied by its countersubject, followed by counterexposition of the two ideas, separated in time, and each in stretto with itself.^{[citation needed]}

Final entries and coda

The closing section of a fugue often includes one or two counter-expositions, and possibly a stretto, in the tonic; sometimes over a tonic or dominant pedal note. Any material that follows the final entry of the subject is considered to be the final coda and is normally cadential.^[9]

Types of fugue

Double (triple, quadruple) fugue

A double fugue has two subjects that are often developed simultaneously; similarly, it follows that a triple fugue has three subjects.^[34][35] There are two kinds of double fugue: (a) a fugue in which the second subject is presented simultaneously with the subject in the exposition (e.g. as in Kyrie Eleison of Mozart’s Requiem in D minor), and (b) a fugue in which the second subject has its own exposition at some later point, and the two subjects are not combined until later (see for example, fugue no. 14 in f-sharp minor from Bach’s Well-Tempered Clavier Book 2, or more famously, Bach's "St. Anne" Fugue in E-flat major, BWV 552.)^[34][36]

Counter-fugue

A counter-fugue is a fugue in which the first answer is presented as the subject in inversion, and the inverted subject continues to feature prominently throughout the fugue.^[37] Examples include Contrapunctus V through Contrapunctus VII, from Bach's The Art of Fugue.^[38]

Permutation fugue

Permutation fugue describes a type of composition (or technique of composition) in which elements of fugue and strict canon are combined.^[39] Each voice enters in succession with the subject, each entry alternating between tonic and dominant, and each voice, having stated the initial subject, continues by stating two or more themes (or countersubjects), which must be conceived in correct invertible counterpoint. Each voice takes this pattern and states all the subjects/themes in the same order (and repeats the material when all the themes have been stated, sometimes after a rest). There is usually very little non-structural/thematic material. During the course of a permutation fugue, it is quite uncommon, actually, for every single possible voice-combination (or 'permutation') of the themes to be heard. This limitation exists in consequence of sheer proportionality: the more voices in a fugue, the greater the amount of possible permutations. In consequence, composers exercise editorial judgment as to the most musical of permutations and processes leading thereto. One example of permutation fugue can be seen in the opening chorus of Bach’s cantata, Himmelskönig, sei willkommen, BWV182.

Permutation fugues differ from conventional fugue in that there are no connecting episodes, nor statement of the themes in related keys.^[39] The fugue of Passacaglia and Fugue in C minor, BWV 582 is unusual in this sense, since it does have episodes between permutation expositions.

Invertible counterpoint is one of the main technical devices used in permutation fugue not in the conventional fugue.^[40]

Fughetta

A fughetta is a short fugue that has the same characteristics as a fugue. Often the contrapuntal writing is not strict, and the setting less formal. See for example, variation 24 of Beethoven's "Diabelli Variations" Op. 120.

History

Middle Ages and Renaissance Period

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.^[41] Prior to the 16th century, fugue was originally a genre.^[42] 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.

"Fugue" as a theoretical term first occurred in 1330 when Jacobus of Liege wrote about the fuga in his Speculum musicae.^[43] The fugue arose from the technique of "imitation", where the same musical material was repeated starting on a different note. Zarlino, a composer, author, and theorist in the Renaissance, was one of the first to distinguish between the two types of imitative counterpoint; fugues and canons(which he called imitations).^[42] 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.^[44] Palestrina's imitative motets differed from fugues 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 Dieterich Buxtehude all wrote fugues,^[45] 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. Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students.^[46] The most influential text was published by Johann Joseph Fux (1660–1741), his Gradus Ad Parnassum ("Steps to Parnassus"), which appeared in 1725.^[47] This work laid out the terms of "species" of counterpoint, and offered a series of exercises to learn fugue writing.^[48] Fux's work was largely based on the practice of Palestrina's modal fugues.^[49] 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 often entered into contests where he would be given a subject with which to spontaneously improvise a fugue on the organ or harpsichord.^{[citation needed]} This musical form was also apparent in chamber music he would later compose for Weimar; the famous Concerto for Two Violins in D Minor (BWV 1043) (although not contrapuntal in its entirety) has a fugal opening section to its first movement.

Bach's most famous fugues are those for the harpsichord in The Well-Tempered Clavier, which many composers and theorists look at as the greatest model of fugue.^[50] 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 is also known for 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. Bach also wrote smaller single fugues, and put fugues into 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.^[51] Nevertheless, both Haydn and Mozart had periods of their careers in which they in some sense "rediscovered" fugal writing and used it frequently in their work.

Haydn was the leader of fugal composition and technique in the Classical era.^[52] Haydn's most famous fugues can be found in his Sun quartets (op. 20, 1772), of which three have fugal finales. This was a practice that Haydn repeated only once later in his quartet-writing career, with the finale of his quartet op. 50 no. 4 (1787). Some of the earliest examples of Haydn's use of counterpoint, however, are in three symphonies (No. 3, No. 13, and No. 40) that date from 1762–63. The earliest fugues, in both the symphonies and in the baryton trios, exhibit the influence of Joseph Fux's treatise on counterpoint, Gradus ad Parnassum (1725), which Haydn studied carefully. Haydn's second fugal period occurred after he heard, and was 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, as well as several of his later symphonies, including No. 88, No. 95, and No. 101.

Wolfgang Amadeus Mozart studied counterpoint when young with Padre Martini in Bologna. 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 Die Zauberflöte. The parts of the Requiem he completed also contain several fugues (most notably the Kyrie, and the three fugues in the Domine Jesu;^[53] he also left behind a sketch for an Amen fugue which, some believe, would have come at the end of the Sequentia).

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.^{[citation needed]} It was also characteristic to abandon fugal texture just before the end of a work, providing a purely homophonic resolution.^{[citation needed]} This is found, for instance, in the final fugue of the chorus "The Heavens are Telling" in Haydn's The Creation (1798). Ludwig van 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 second and fourth movements of the Eroica Symphony (1805). Beethoven incorporated fugues in his sonatas, and reshaped the episode’s purpose and compositional technique for later generations of composers.^[54] Nevertheless, fugues did not take on a truly central role in Beethoven's work until his "late period." A massive, dissonant fugue forms the finale of his String Quartet, Op. 130 (1825); the latter was later published separately as Op. 133, the Große Fuge ("Great Fugue"). His Cello Sonata, Op. 102,2 have fugue movements. Fugues are also found in the Missa Solemnis and in the finale of the Ninth Symphony.

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.^{[citation needed]} 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.^{[citation needed]} 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.^{[citation needed]}

Examples of fugal writing in the Romantic era are found in the last movement of Berlioz's Symphonie Fantastique, and Wagner's Meistersinger, in particular the triple fugue at the conclusion of the second act.^{[citation needed]} The finale of Giuseppe Verdi's opera Falstaff is a ten-voice fugue.^{[citation needed]} Felix Mendelssohn was obsessed with fugal writing, as it can be found prominently in the Scottish Symphony, Italian Symphony, and the Hebrides Overture.^{[citation needed]} In the last movement of his Fifth Symphony Anton Bruckner wrote the development section in form of a big double fugue.^{[citation needed]} The unfinished Finale of his Ninth Symphony has a fugue section, too.^{[citation needed]} Another composer of this time, whose work is strongly influenced by fugal textures, was Felix Draeseke. Especially in his church music highly artificial fugues could be found.^{[citation needed]}

Robert Schumann, and Johannes Brahms also included fugues in many of their works. 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. Sergei Rachmaninoff, despite writing in a lush post-romantic idiom, was highly skilled in counterpoint (as is highly evident in his Vespers); a well known fugue occurs in his Symphony No. 2.^{[citation needed]} Alexander Glazunov wrote a very difficult Prelude and Fugue in D minor, his Op. 62, for the piano.^{[citation needed]}

20th century

Twentieth-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."^{[citation needed]}

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.^{[citation needed]} Twentieth-century composers brought fugue back to its position of prominence, realizing its uses in full instrumental works, its importance in development and introductory sections, and the developmental capabilities of fugal composition.^[51]

A number of other 20th-century composers made extensive use of the fugue. Béla Bartók opened his Music for Strings, Percussion and Celesta with a fugue based on alternating ascending and descending fifth series. He also included fugal sections in the final movements of his String Quartet No. 1, String Quartet No. 5, Concerto for Orchestra, and Piano Concerto No. 3. The second movement of his Sonata for Solo Violin is also a fugue.^{[citation needed]} The Czech composer Jaromir Weinberger studied fugue with Max Reger, and had an uncommonly facile skill in fugal writing. The fugue of the "Polka and Fugue" from his opera "Schwanda the Bagpiper" is an example.^{[citation needed]}

Igor Stravinsky also incorporated fugues into his works, including the Symphony of Psalms and the Dumbarton Oaks concerto. Stravinsky recognized the compositional techniques of Bach, and in the second movement of his Symphony of Psalms, he lays out a fugue that is much like that of the Baroque era.^[55] It employs a double fugue with two distinct subjects, the first beginning in C and the second in E♭. Techniques such as stretto, sequencing, and the use of subject incipits are frequently heard in the movement.

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 Opus clavicembalisticum, and Dmitri Shostakovich in his Preludes and Fugues, Op. 87 (which, like the Well-Tempered Clavier, contains a prelude and fugue in each key, although the order of Shostakovich's pieces follows the cycle of fifths, whereas Bach's progressed chromatically).^{[citation needed]} Several Bachianas Brasileiras of Heitor Villa-Lobos feature a fugue as one of the movements.^{[citation needed]} Ástor Piazzolla also wrote a number of fugues in his Nuevo tango style.^{[citation needed]} György Ligeti wrote a fugue for his "Requiem’s" (1966) second movement, the Kyrie/Christe, which consists of a 5-part fugue in which each part (S,M,A,T,B) is subsequently divided in four voices that make a canon. The melodic material in this fugue is totally chromatic, with melismatic (running) parts overlaid onto skipping intervals, and use of polyrhythm (multiple simulataneous subdivisions of the measure), blurring everything both harmonically and rhythmically so as to create an aural aggregate, thus highlighting the theoretical/aesthetic question of the next section as to whether fugue is a form or a texture.

John Lewis, pianist and musical director for the American jazz ensemble The Modern Jazz Quartet, used the group as a vehicle to explore the possibilities of fugue in jazz. Examples of Lewis's fugues include "Vendome" (1952), "Concorde" (1955), "Versailles" (1956), and "Three Windows" (1957).^{[citation needed]}

Canadian pianist Glenn Gould composed So You Want to Write a Fugue?, a full-scale fugue set to a text that cleverly explicates its own musical form.^[56]

Is the fugue a musical form or texture?

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.^[57] For instance, Donald Francis 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.^{[citation needed]}

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 single formal outline into which all fugues reliably can be fitted.^{[citation needed]}

The Austrian musicologist Erwin Ratz argues that the formal organization of a fugue involves not only the arrangement of its theme and episodes, but also its harmonic structure.^[58] In particular, the exposition and coda tend to emphasize the tonic key, whereas the episodes usually explore more distant tonalities. Ratz stressed, however, that this is the core, underlying form ("Urform") of the fugue, from which individual fugues may deviate. Thus it is to be noted that while certain related keys are more commonly explored in fugal development, the overall structure of a fugue does not limit its harmonic structure. For example, a fugue may not even explore the dominant, one of the most closely related keys to the tonic. Bach's Fugue in B♭ major from book one of the Well Tempered Clavier explores the relative minor, the supertonic and the subdominant. This is unlike later forms such as the sonata, which clearly prescribes which keys are explored (typically the tonic and dominant in an ABA form). Then, many modern fugues dispense with traditional tonal harmonic scaffolding altogether, and either use serial (pitch-oriented) rules, or (as the Kyrie/Christe in György Ligeti’s Requiem, Witold Lutosławski works), use panchromatic or even denser harmonic spectra.

Fugues are also not limited in the way the exposition is structured, the number of expositions in related keys, or the number of episodes (if any). So, the fugue may be considered a compositional practice rather than a compositional form, similar to the invention. The fugue, like the invention and sinfonia, employs a basic melodic subject and spins out additional melodic material from it to develop an entire piece.^{[citation needed]}

Perceptions and aesthetics

Fugue is the most complex of contrapuntal forms. In Ratz's words, "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."^[59] An indication of this is that in the 19th century Simon Sechter composed over 5,000 fugues, but none of them is in today's concert repertoire,^{[citation needed]} while another is the enduring success of the organ fugues of Felix Mendelssohn and Johannes Brahms.

In presenting Bach's fugues as among the greatest of contrapuntal works, Peter Kivy points out that "counterpoint itself, since time out of mind, has been associated in the thinking of musicians with the profound and the serious"^[60] and argues that "there seems to be some rational justification for their doing so."^[61] Because of the way fugue is often taught, the form can be seen as dry and filled with laborious technical exercises. The term "school fugue" is used for a very strict form of the fugue that was created to facilitate teaching.^{[citation needed]}

Others, such as Alfred Mann, argued that fugue writing, by focusing the compositional process actually improves or disciplines the composer towards musical ideas.^{[citation needed]} 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 Renaissance, practiced as an improvisatory art. Writing in 1555, Nicola Vicentino, for example, suggests that

the composer, having completed the initial imitative entrances, take the passage which has served as accompaniment to the theme and make it the basis for new imitative treatment, so that 'he will always have material with which to compose without having to stop and reflect'. This formulation of the basic rule for fugal improvisation anticipates later sixteenth-century discussions which deal with the improvisational technique at the keyboard more extensively.^[62]

References

1. ^ "Fugue, n." The Concise Oxford English Dictionary, eleventh edition, revised, ed. Catherine Soanes and Angus Stevenson (Oxford and New York: Oxford University Press, 2006). "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t23.e22155. Retrieved 2007-03-16. 
2. ^ "Fugal, adj." The Concise Oxford English Dictionary, eleventh edition, revised, ed. Catherine Soanes and Angus Stevenson (Oxford and New York: Oxford University Press, 2006). "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t23.e22149. Retrieved 2007-03-16. 
3. ^ ^{a b} "Fugue", The Concise Oxford Dictionary of Music, fourth edition, ed. Michael Kennedy (Oxford and New York: Oxford University Press, 1996). ISBN 019280037X "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t76.e3627. Retrieved 2007-03-16. 
4. ^ Bruce Benward, Music in Theory and Practice, 3rd ed. Vol. 2 (Dubuque: Wm. C. Brown Publishers, 1985), 45. ISBN 0697036332.
5. ^ "Fugue [Fr. fugue; Ger. Fuge; Lat., It., Sp., fuga]." The Harvard Dictionary of Music (Cambridge: Harvard University Press, 2003), "credo Reference". http://www.xreferplus.com/entry.jsp?xrefid=4663031&secid=.3.2.. Retrieved 2008-05-06. 
6. ^ Paul Walker. "Fugue", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access). for discussion of the changing use of the term throughout Western music history.
7. ^ Leonard G. Ratner, Classic Music: Expression, Form, and Style (London: Collier Macmillan Publishers, 1980), 263.
8. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 7.
9. ^ ^{a b c d} Paul Walker. "Fugue, §1: A classic fugue analysed", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
10. ^ ^{a b} Paul Walker. "Fugue", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
11. ^ ^{a b c} Paul Walker. "Fugue, §6: Late 18th century", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
12. ^ Paul Walker. "Fugue, §8: 20th century", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
13. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 70.
14. ^ ^{a b c d e f g h i} G. M. Tucker and Andrew V. Jones, "Fugue", in The Oxford Companion to Music, ed. Alison Latham (Oxford and New York: Oxford University Press, 2002). ISBN 0198662122 "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e2723. Retrieved 2007-03-16. 
15. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964),12.
16. ^ R. O. Morris, Contrapuntal Technique in the Sixteenth Century (London: Oxford University Press, 1958), 47.
17. ^ ^{a b} John W. Verrall, Fugue and Invention in Theory and Practice (Palo Alto: Pacific Books, 1966), 12.
18. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 59.
19. ^ "Invertible Counterpoint" The Oxford Companion to Music, ed. Alison Latham (Oxford and New York: Oxford University Press, 2002) "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e3465. Retrieved 2007-03-16. 
20. ^ Drabkin, William. "Invertible Counterpoint", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
21. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 61.
22. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 71–72.
23. ^ Paul Walker, "Fugue, §1: A Classic Fugue Analysed" "Grove Music Online". http://www.grovemusic.com/shared/views/article.html?section=music.51678.1. Retrieved 2007-02-18. 
24. ^ John W. Verrall, Fugue and Invention in Theory and Practice (Palo Alto: Pacific Books, 1966), 33.
25. ^ André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964).
26. ^ Paul Walker. "Counter-exposition", Grove Music Online, ed. L. Macy (accessed 19 March 2007), grovemusic.com (subscription access).
27. ^ Johann Sebastian Bach, 'Fuge Nr. 2', Das Wohltemperierte Klavier I, ed. Ernst-Günter Heinemann (Munich: G. Henle Verlag, 1997).
28. ^ John W. Verrall, Fugue and Invention in Theory and Practice (Pacific, California, 1966), 33.
29. ^ See Laurence Dreyfus, "Figments of the Organicist Imagination", in his Bach and the Patterns of Invention (Cambridge, Mass., and London: Harvard University Press, 1996), 178.
30. ^ ^{a b} André Gédalge, Treatise on Fugue, trans. A. Levin (Mattapan: Gamut Music Company, 1964), 108.
31. ^ Paul Walker. "Stretto (i)", Grove Music Online, ed. L. Macy (accessed 16 March 2007), grovemusic.com (subscription access).
32. ^ John W. Verrall, Fugue and Invention in Theory and Practice (Palo Alto: Pacific Books, 1966), 77.
33. ^ Paul Walker. "Stretto (i)", Grove Music Online, ed. L. Macy (accessed 29 March 2007), grovemusic.com (subscription access).
34. ^ ^{a b} Paul Walker. "Double Fugue", Grove Music Online, ed. L. Macy (accessed 29 March 2007), grovemusic.com (subscription access).
35. ^ "double fugue" The Oxford Companion to Music, Ed. Alison Latham, Oxford University Press, 2002, "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t114.e2059. Retrieved 2007-03-29. 
36. ^ "Double Fugue", The Concise Oxford Dictionary of Music, fourth edition, ed. Michael Kennedy (Oxford and New York: Oxford University Press, 1996) "Oxford Reference Online, subscription access". http://www.oxfordreference.com/views/ENTRY.html?subview=Main&entry=t76.e2780. Retrieved 2007-03-29. 
37. ^ Paul Walker. "Counter-fugue", Grove Music Online, ed. L. Macy (accessed 31 March 2007), grovemusic.com (subscription access).
38. ^ Johann Sebastian Bach (1992). Alfred Dörffel. ed. The Art of Fugue & A Musical Offering. Courier Dover. p. 56. ISBN 9780486270067. http://books.google.com/books?id=6JY6sH5E94oC&pg=PA56. 
39. ^ ^{a b} Paul Walker. "Permutation Fugue", Grove Music Online, ed. L. Macy (accessed 31 March 2007), grovemusic.com (subscription access).
40. ^ Paul Walker, The Origin of Permutation Fugue (New York: Broude Brothers Limited, 1992), 56.
41. ^ Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 7.
42. ^ ^{a b} Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 9-10.
43. ^ Alfred Mann, The Study of Fugue (London: Oxford University Press, 1960), 9
44. ^ Leeman L. Perkins, Music in the Age of the Renaissance (New York: W. W. Norton & Company, Inc., 1999), 880–81.
45. ^ Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 165.
46. ^ David Schulenberg, Music of the Baroque (New York: Oxford University Press, 2001), 243.
47. ^ Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 316.
48. ^ Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 317.
49. ^ Alfred Mann, The Study of Fugue (London: Oxford University Press, 1960), 53.
50. ^ Paul Mark Walker, Theories of Fugue from the Age of Josquin to the Age of Bach (Rochester: University of Rochester Press, 2000), 2.
51. ^ ^{a b} William L. Graves, Jr., Twentieth Century Fugue (Washington, D.C.: The Catholic University of America Press, 1962), 64.
52. ^ Leonard G. Ratner, Classic Music: Expression, Form, and Style (London: Collier Macmillan Publishers, 1980), 263.
53. ^ Leonard G. Ratner, Classic Music: Expression, Form, and Style (London: Collier Macmillan Publishers, 1980), 266.
54. ^ William L. Graves, Jr., Twentieth Century Fugue (Washington, D.C.: The Catholic University of America Press, 1962), 65.
55. ^ William L. Graves, Jr., Twentieth Century Fugue (Washington, D.C.: The Catholic University of America Press, 1962), 67.
56. ^ Bazzana, Kevin (2004). Wondrous Strange: The Life and Art of Glenn Gould. New York: Oxford University Press. ISBN 0195174402. OCLC 54687539. 
57. ^ Donald Francis Tovey, Essays in Music Analysis Volume I: Symphonies (London: Oxford University Press, 1962), 17.
58. ^ Erwin Ratz, Einführung in die Musikalische Formenlehre: Über Formprinzipien in den Inventionen J. S. Bachs und ihre Bedeutung für 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: Österreichischer Bundesverlag für Unterricht, Wissenschaft und Kunst, 1951), Chapter 3.
59. ^ Erwin Ratz, Einführung in die Musikalische Formenlehre: Über Formprinzipien in den Inventionen J. S. Bachs und ihre Bedeutung für 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: Österreichischer Bundesverlag für Unterricht, Wissenschaft und Kunst, 1951), 259.
60. ^ Peter Kivy, Music Alone: Philosophical Reflections on the Purely Musical Experience (Ithaca: Cornell University Press, 1990), 206. ISBN 0-8014-2331-7.
61. ^ Peter Kivy, Music Alone: Philosophical Reflections on the Purely Musical Experience (Ithaca: Cornell University Press, 1990), 210. ISBN 0-8014-2331-7.
62. ^ Alfred Mann, The Study of Fugue (New York: W. W. Norton & Company, Inc., 1965): 16.

Further reading

• Horsley, Imogene. 1966. Fugue: History and Practice. New York: Free Press; London: Collier-Macmillan.

External links

• Downloadable PDFs of J.S. Bach's Well-Tempered Clavier on Mutopia
• Analysis of the Well-Tempered Clavier (requires Shockwave)
• Theory on fugues
• Fugues and Fugue Sets