Fugue

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In music, the term fugue (IPA: [fjuːg]) describes a type of contrapuntal composition or compositional technique, for a specific number of parts or voices (referred to as "voices" regardless of whether the work is vocal or instrumental).^[1] In common use today,^[2] fugue describes a contrapuntal model in which one main theme (the "subject") sounds in successive imitation in each voice; when each voice has entered, the exposition is complete. This is usually followed by a connecting passage, (usually termed an episode) often developed from the opening material and further "entries" of the subject (in related keys). Episodes and entries will alternate until the "final entry" of the subject, in the same key as the opening (the tonic), followed by a coda.^{[3] [1]} In this sense, fugue is a style, rather than fixed structure, of composition, and though there are certain established practices, in writing the exposition for example,^[4] composers approach the style with varying degrees of freedom and individuality.

The form evolved during the 17th century from several earlier types of contrapuntal compositions (imitative ricercars, capriccios, canzonas, fantasias, etc.).^[5] Middle and late Baroque composers such as Dieterich Buxtehude (1637–1707) and Johann Pachelbel (1653–1706) contributed greatly to the development of the fugue, and the form reached ultimate maturity in the works of Johann Sebastian Bach (1685–1750).^[5] With the decline of sophisticated contrapuntal styles at the end of the baroque period, the fugue's popularity as a compositional style waned, eventually giving way to Sonata form.^[6] Nevertheless, composers from the 1750s to the present day continue to write and study fugue for various purposes; they appear in the works of Mozart (e.g. Kyrie Eleison of the Requiem in D minor)^[6] and Beethoven (e.g. the finale of the Missa Solemnis),^[6] and many composers such as Anton Reicha (1770–1836) and Dmitri Shostakovich (1906–1975)) wrote cycles of fugues.^[7]

The English term fugue originates in the 16th century and is derived from either the French or Italian fuga, which in turn comes from Latin, also fuga, which is itself related to both fugere (‘to flee’) and fugare, (‘to chase’).^[8] The adjectival form is fugal.^[9] Variants include fughetta (literally, 'a small fugue') and fugato (a passage in fugal style within another work that is not a fugue).^[1]

[edit] Musical outline

A fugue begins with what is known as the exposition and is characteristically written according to certain predefined rules; in later portions the composer has somewhat more freedom, though some sort of logical key structure is usually followed (depending on the era/style of composition), and further "entries" of the subject will occur throughout the fugue, (and the material first heard accompanying the subject will often also be repeated at the same time). The various entries are usually separated by episodes.

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

[edit] The Exposition

A fugue begins with the exposition of its subject sounding in one of the voices alone in the tonic key.^[10] After the statement of the subject, a second voice enters with the answer (the subject transposed to the dominant — either an exact transposition or slightly altered); sometimes the answer is the tonic or subdominant (see J.S.Bach's Toccata and Fugue in D minor, BWV 565, and the opening fugato of the Partita No 2 in C minor, BWV 826); to avoid disturbing the sense of key, it may also have to be altered slightly. When the answer is an exact transposition 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. ^[10]

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 prominent dominant note at the start of the subject (marked in red), and the subsequent adjustment of the tonal answer (i.e. the first note of the answer is G — the tonic — and not A, in blue).

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.^[10] To prevent an undermining of the music's sense of key, this note is transposed to the tonic (up a fourth) rather than to the supertonic (up a fifth). Answers in the subdominant are also employed for the same reason and tend to occur in specific circumstances: a) when the subject begins with the following scale tones: 5-4-5 or 5-4-3; and b) when subjects themselves modulate to the dominant, in which case, the answer begins in the subdominant, and subsequently modulates to the tonic.^[11]

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. Each voice then responds with its own subject or answer in turn, 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 either a) return to the tonic, following an answer in the dominant, or b) to modulate to the dominant to enable a statement of the answer.

The first answer must occur as soon after the initial statement of the subject as possible, therefore the first codetta is often extremely short, and in many cases is not even needed. (In the above example this is the case: the subject finishes on the quarter note b-flat, of the third beat of the second bar, which harmonizes the opening G of the answer). The second and later codettas maybe 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.^[12]

The exposition usually concludes when all voices have given a statement of the subject or answer. In many fugues, however, there is often one more entry of the subject, with all the voices sounding simultaneously, this is known as redundant entry.^[10] Furthermore, in some fugues (e.g. for organ) the entry of one of the voices may be reserved until later (e.g. in the pedals — see for example J.S. Bach's Fugue in C major for Organ, BWV 547).

[edit] The Countersubject(s)

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

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.^[10][13] In tonal music invertible contrapuntal lines must be written according to certain rules because several intervallic combinations, whilst 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 (preparation and resolution) if is to be used.^[14] Likewise, the use of a 4-3 suspension is somewhat ineffectual in invertible counterpoint (in inversion it becomes 5-6, and since both the fifth and sixth are considered consonant intervals, is not a suspension at all); whereas, the 7-6 suspension may be used successfully (it inverts to 2-3).

When writing invertible countersubjects in a fugue, composers therefore usually restrict themselves to the intervals of the third (which inverts to a sixth and vice versa) and octaves (which inverts to the unison), and the careful use of the 7-6 suspension.

[edit] 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) WTC Bk 1), but more frequently, separated by episodes.^[10] Episodic material is always modulatory and is usually based upon some element heard in the exposition.^[10][3] Each episode has primarily the function of modulating for the next entry of the subject in a new key,^[10] and may also provide release from the strictness of form employed in the exposition, and middle-entries.^[15]

[edit] The Middle-Entries

The middle-entries (i.e. further entries of the subject) occur at various intervals throughout the fugue, and must state the subject or answer at least once in its entirety, and may also be heard in combination with the countersubject(s) heard in the exposition, new countersubjects, free counterpoint or any of these in combination. The subject does not enter on its own in middle-entries, as in the first exposition; it is always accompanied in some form or other. Middle-entries also usually take place in various different keys from the fugue's tonic. The structure of keys employed for a fugue's middle-entries varies greatly, but may or may not include an entry in the relative major or minor, the dominant of the relative major or minor (this is common when the fugue's subject requires a tonal answer), and the sub-dominant.

Many fugues have counter-expositions, i.e. another exposition but with the subject or answer altered in someway:^[16] often by inversion (all intervals turned upside-down, starting from the first note, for example a fourth up becomes a fourth down), although the term is sometimes used synonamously with middle-entry and may also describe the exposition of completely new subjects, in a double fugue for example. In any of the entries within a fugue the subject may be altered, by inversion, retrograde (the entire subject is heard back-to-front, less common) and diminution (the halving, or reduction by four etc. of the subject's rhythmic values) or augmentation (the doubling, quadrupling etc of the subject's rhythmic values).^[10]

[edit] Example and Analysis

The diagram below, taken from J.S. Bach's Fugue no. 2 in C minor, BWV 847, from the Well-Tempered Clavier, Book 1 (bars 7-12) illustrates many of the characteristics described above. It is a keyboard fugue in three voices^[17] with regular, invertible countersubjects^[3], (i.e the subjects and countersubjects appear in different voices each time round). The episode following that follows the last entry of the exposition modulates between the tonic and relative major, by means of sequence - in the form of an accompanied canon at the 4th.^[18] The second occurence of countersubject 2 is not an exact repetition, due to the change of mode from minor to major.^[19]

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 )

[edit] 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 only the head of the subject, (the very opening figure) and usually occur in anticipation of the subject's "true" entry, thus heightening the impact of the subject proper. ^[20]

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 (in red). It anticipates the true entry of the subject (marked in blue) by one quarter-note.

[edit] 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.^[21]

Example of stretto fugue in a quotation from Fugue in C major by Johann Caspar Ferdinand Fischer (died 1746). The subject is seen in the soprano voice, starting on beat 1, bar 1 (the subject includes an eighth note rest) 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.^[22]. 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) chorus from Bach's Mass in B minor.^[23]

[edit] Final entries and Coda

The closing section of a fugue often includes one or two counter-expositions (and sometimes a stretto where this is possible) 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.^[3]

[edit] Types of Fugue

[edit] Double (triple, quadruple) fugue

A double fugue has two subjects that are often developed simultaneously,^[24], similarly it follows that a triple fugue has three subjects.^[25] It is not widely agreed whether a double fugue can be defined as a)a fugue in which the second subject is presented simultaensouly with the subject in the exposition (as, for example, in Kyrie Eleison of Mozart's Requiem in G minor) or b) a fugue in which the second subject has its own exposition at some later point, and the two subjects are not combined till later (see for example, fugue no. 14 in f-sharp minor from Bach's Well-tempered Clavier Book 2).^[25][26]

[edit] 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,^[27] as for example in Bach's Art of Fugue, Contrapunctus IV.^[28]

[edit] Permutation Fugue

Permutation fugue describes a type of composition (or technique of composition) in which elements of fugue and strict canon are combined.^[29] 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. It is common during the course of a permutation fugue for every single possible voice-combination (or 'permutation') of the themes to be heard at some point. 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.^[29]

[edit] History

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. 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.

[edit] 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, 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. 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 and the 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 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.

[edit] 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 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 symponies, including No. 88, No. 95, and No. 101.

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 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; he also left behind a sketch for an Amen fugue which would have come at the end of the Sequentia).

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). 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).

[edit] 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, in particular the conclusion of the second act. The finale of Giuseppe Verdi's opera Falstaff is a ten-voice fugue. Felix Mendelssohn was obsessed with fugal writing, as it can be found prominently in the Scottish Symphony, Italian Symphony, and the Hebrides Overture.

Robert Schumann, 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). The recapitulation of Liszt's B minor sonata is cast in the form of a 3-part fugue. The Quasi-Faust movement of Charles-Valentin Alkan's Grande Sonate contains a bizarre but musically convincing fugue in 8 parts. 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. 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. Alexander Glazunov wrote a very difficult Prelude and Fugue in D minor, his Op. 62, for the piano.

[edit] 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. 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, Concerto for Orchestra, and Piano Concerto No. 3. The second movement of his Sonata for Solo Violin is also a fugue. 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 a superb example.

Igor Stravinsky also incorporated fugues into his works, including the Symphony of Psalms and the Dumbarton Oaks concerto. The last movement of Samuel Barber's famous Sonata for Piano is a sort of "modernized" fugue, which, instead of obeying the constraint of a fixed number of voices, develops the fugue subject and its head-motif in various contrapuntal situations. In a different direction, the tonal fugue movement of Charles Ives' fourth symphony evokes a nostalgia for an older, halcyon time. 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, although the order of Shostakovich's pieces follows the cycle of fifths, whereas Bach's progressed chromatically). Several Bachianas Brasileiras of Heitor Villa-Lobos feature a fugue as one of the movements. Ástor Piazzolla also wrote a number of fugues in his Nuevo tango style. György Ligeti wrote a Fugue for his "Requiem" (1966), 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.

Benjamin Britten composed a fugue for orchestra in his The Young Person's Guide to the Orchestra, consisting of subject entries by each instrument once. Leonard Bernstein wrote a "Cool Fugue" as part of his musical West Side Story. Stephen Schwartz wrote a song from his 1974 Broadway hit The Magic Show called "The Goldfarb Variations" which uses fugue-like vocal counterpoint. Jazz musician Alec Templeton even wrote a fugue (recorded subsequently by Benny Goodman): Bach Goes to Town. 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.

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.

[edit] 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. 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.

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.

Ratz argues that the formal organization of a fugue involves not only the arrangement of its theme and episodes, but also its harmonic structure. In particular, the exposition and coda tend to emphasize the tonic key, whereas the episodes usually explore more distant tonalities. However, 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 as much as Ratz would have us believe. For example, a fugue may not even explore the dominant, one of the most closely related keys to the tonic. Bach's Fugue in Bb from 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).

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. Fugual technique is really just a way to develop pieces of a particular contrapuntal style.

[edit] Perceptions and aesthetics

Fugue is the most complex of contrapuntal forms and as a result, gifted composers have used it to express the profound. The complexity of fugue has foiled lesser composers who have produced only the banal. The philosopher Theodor Adorno, a skilled pianist and interpreter of Beethoven's music, expressed a sense of the arduousness and also the inauthenticity of modern fugue composition, or any composing of fugue in a contemporary context, i.e., as an anachronism. Adorno's conservative and historically bound view of Bach is not found among most modern fugue composers, such as David Diamond, Paul Hindemith or Dmitri Shostakovich. The most classicist fugues that have appeared after Beethoven are those of Felix Mendelssohn, who as a child impressed Goethe and others with his mastery of counterpoint while improvising at the piano. 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 term "school fugue" is used for a very strict form of the fugue that was created to facilitate teaching. 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, 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 improvisatory 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".

[edit] References

• Kivy, Peter (1990). Music Alone: Philosophical Reflections on the Purely Musical Experience. Ithaca: Cornell University Press. ISBN 0-8014-2331-7.
• Ratz, Erwin (1951). 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.

[edit] External links

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