In music, a fugue (/fjuːɡ/ fewg) is a contrapuntal compositional technique in two or more voices, built on a subject (a musical theme) that is introduced at the beginning in imitation (repetition at different pitches) and which recurs frequently in the course of the composition. It is not to be confused with a fuguing tune, which is a style of song popularized by and mostly limited to early American (i.e. shape note or "Sacred Harp") music and West Gallery music. A fugue usually has three main sections: an exposition, a development and a final entry that contains the return of the subject in the fugue's tonic key. Some fugues have a recapitulation.
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. Since the 17th century, the term fugue has described what is commonly regarded as the most fully developed procedure of imitative counterpoint.
Most fugues open with a short main theme, the subject, 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. 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. 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 others. With the decline of sophisticated styles at the end of the baroque period, the fugue's central role waned, eventually giving way as sonata form and the symphony orchestra rose to a dominant position. Nevertheless, composers continued to write and study fugues for various purposes; they appear in the works of Wolfgang Amadeus Mozart (1756–1791) and Ludwig van Beethoven (1770–1827), as well as modern composers such as Dmitri Shostakovich (1906–1975).
The English term fugue originated in the 16th century and is derived from 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"). The adjectival form is fugal. Variants include fughetta (literally, "a small fugue") and fugato (a passage in fugal style within another work that is not a fugue).
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. 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.
|Final entries in tonic|
|Tonic||Dom.||T||(D-redundant entry)||Relative maj/min||Dom. of rel.||Subdom.||T||T|
A fugue begins with the exposition of its subject in one of the voices alone in the tonic key. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key (usually the dominant or subdominant), which is known as the answer. 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 new key, with identical intervals to the first statement, it is classified as a real answer; if the intervals are altered to maintain the key it is a tonal answer.
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. 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.
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 countersubject is written in invertible counterpoint at the octave or fifteenth. 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 (double) counterpoint.
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. The countersubject, if sounding at the same time as the answer, is transposed to the pitch of the answer. 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 J.S. Bach's Well-Tempered Clavier, Book 1. 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.
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♭ 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.
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. 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).
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. Episodic material is always modulatory and is usually based upon some element heard in the exposition. Each episode has the primary function of transitioning for the next entry of the subject in a new key, and may also provide release from the strictness of form employed in the exposition, and middle-entries. André Gedalge states that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented.
Further entries of the subject, or middle entries, occur throughout the fugue. They 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 as 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, although the key structure of fugues varies greatly. In the fugues of J.S. Bach, the first middle-entry occurs most often in the relative major or minor of the work's overall key, and is followed by an entry in 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, 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.
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. 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. Arrival in E♭ major is marked by a quasi perfect cadence across the bar line, 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 the second countersubject to accommodate the change of mode.
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.
The counter-exposition is a second exposition. However, there are only two entries, and the entries occur in reverse order. The counter-exposition in a fugue is separated from the exposition by an episode and is in the same key as the original exposition.
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.
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. 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 J.S. Bach's Mass in B Minor).
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.
A double fugue has two subjects that are often developed simultaneously. Similarly, a triple fugue has three subjects. 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♯ minor from Bach's Well-Tempered Clavier Book 2, or more famously, Bach's "St. Anne" Fugue in E♭ major, BWV 552, a triple fugue for organ.)
A counter-fugue is a fugue in which the first answer is presented as the subject in inversion (upside down), and the inverted subject continues to feature prominently throughout the fugue. Examples include Contrapunctus V through Contrapunctus VII, from Bach's The Art of Fugue.
Permutation fugue describes a type of composition (or technique of composition) in which elements of fugue and strict canon are combined. 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. (In other words, the subject and countersubjects must be capable of being played both above and below all the other themes without creating any unacceptable dissonances.) 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 J.S. 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. So for example, the fugue of Bach's Passacaglia and Fugue in C minor, BWV 582 is not purely a permutation fugue, as it does have episodes between permutation expositions. Invertible counterpoint is essential to permutation fugues but is not found in simple fugues.
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.
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. Prior to the 16th century, fugue was originally a genre. 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. The fugue arose from the technique of "imitation", where the same musical material was repeated starting on a different note.
Gioseffo 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). 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.
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. Domenico Scarlatti has only a few fugues among his corpus of over 500 harpsichord sonatas. 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. The most influential text was Johann Joseph Fux's 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. Mozart studied from this book, and 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.
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. 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, BWV 1080, 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 fugal sections or movements into many of his more general works. J.S. Bach's 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. —′≈
During the Classical era, the fugue was no longer a central or even fully natural mode of musical composition. 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.
Joseph Haydn was the leader of fugal composition and technique in the Classical era. 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 String 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.
In a letter to his sister, dated in Vienna on April 20, 1782, Mozart recognizes that he had not written anything in this form, but moved by the interest of Constance he composed one piece, which is sent with the letter. He begs his sister not to let anybody see the fugue and manifests the hope to write five more and then present them to Baron van Swieten. Regarding the piece, he said "I have taken particular care to write andante maestoso upon it, so that it should not be played fast – for if a fugue is not played slowly the ear cannot clearly distinguish the new subject as it is introduced and the effect is missed". 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 his opera Die Zauberflöte and the finale of his Symphony No. 41.
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, some believe, would have come at the end of the Sequentia).
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.
Nevertheless, fugues did not take on a truly central role in Beethoven's work until his late period. The finale of Beethoven's Hammerklavier Sonata contains a fugue, which was practically unperformed until the late 19th century, due to its tremendous technical difficulty and length. The last movement of his Cello Sonata, Op. 102 No. 2 is a fugue, and there are fugal passages in the last movements of his Piano Sonatas in A major, Op. 101 and A♭ major Op. 110. According to Charles Rosen (1971, p. 503) "With the finale of 110, Beethoven re-conceived the significance of the most traditional elements of fugue writing."
Fugal passages are also found in the Missa Solemnis and all movements of the Ninth Symphony, except the third . 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"). However, it is the fugue that opens Beethoven's String Quartet in C♯ minor, Op. 131 that several commentators regard as one of the composer's greatest achievements. Joseph Kerman (1966, p. 330) calls it "this most moving of all fugues". J.W.N. Sullivan (1927, p. 235) hears it as "the most superhuman piece of music that Beethoven has ever written." Philip Radcliffe (1965, p. 149) says "[a] bare description of its formal outline can give but little idea of the extraordinary profundity of this fugue ."
By the beginning of the Romantic era, fugue writing had become specifically attached to the norms and styles of the Baroque. Felix Mendelssohn wrote many fugues inspired by his study of the music of J.S. Bach. Franz Liszt's Piano Sonata in B minor (1853) contains a powerful fugue, demanding incisive virtuosity from its player:
Giuseppe Verdi included a whimsical example at the end of his opera Falstaff and his setting of the Requiem Mass contained two (originally three) choral fugues. Anton Bruckner and Gustav Mahler also included them in their respective symphonies. The exposition of the finale of Bruckner's Fifth Symphony begins with a fugal exposition. The exposition ends with a chorale, the melody of which is then used as a second fugal exposition at the beginning of the development. The recapitulation features both fugal subjects concurrently. The finale of Mahler's Symphony No. 5 features a "fugue-like" passage early in the movement, though this is not actually an example of a fugue.
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.
The second movement of Maurice Ravel's piano suite Le Tombeau de Couperin (1917) is a fugue that Roy Howat (200, p. 88) describes as having "a subtle glint of jazz". Béla Bartók's Music for Strings, Percussion and Celesta (1936) opens with a slow fugue that Pierre Boulez (1986, pp. 346–47) regards as "certainly the finest and most characteristic example of Bartók's subtle style... probably the most timeless of all Bartók's works – a fugue that unfolds like a fan to a point of maximum intensity and then closes, returning to the mysterious atmosphere of the opening."
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 (1930), he lays out a fugue that is much like that of the Baroque era. 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.
It expresses the Creation of All Things: space, time, stars, planets – and the Countenance (or rather, the Thought) of God behind the flames and the seething – impossible even to speak of it, I have not attempted to describe it ... Instead, I have sheltered behind the form of the Fugue. Bach's Art of Fugue and the fugue from Beethoven's Opus 106 (the Hammerklavier sonata) have nothing to do with the academic fugue. Like those great models, this one is an anti-scholastic fugue.
György Ligeti wrote a five-part double fugue for his Requiem's second movement, the Kyrie, in which each part (SMATB) is subdivided in four-voice "bundles" 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 simultaneous 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. According to Tom Service, in this work, Ligeti
takes the logic of the fugal idea and creates something that’s meticulously built on precise contrapuntal principles of imitation and fugality, but he expands them into a different region of musical experience. Ligeti doesn’t want us to hear individual entries of the subject or any subject, or to allow us access to the labyrinth through listening in to individual lines… He creates instead a vastly dense texture of voices in his choir and orchestra, a huge stratified slab of terrifying visionary power. Yet this is music that’s made with a fine craft and detail of a Swiss clock maker. Ligeti’s so-called 'micro-polyphony': the many voicedness of small intervals at small distances in time from one another is a kind of conjuring trick. At the micro level of the individual lines, and there are dozens and dozens of them in this music...there’s an astonishing detail and finesse, but the overall macro effect is a huge overwhelming and singular experience.
Fugues (or fughettas/fugatos) have been incorporated into genres outside Western classical music. Several examples exist within jazz, such as Bach goes to Town, composed by the Welsh composer Alec Templeton and recorded by Benny Goodman in 1938, and Concorde composed by John Lewis and recorded by the Modern Jazz Quartet in 1955.
In "Fugue for Tinhorns" from the Broadway musical Guys and Dolls, written by Frank Loesser, the characters Nicely-Nicely, Benny, and Rusty sing simultaneously about hot tips they each have in an upcoming horse race.
A widespread view of the fugue is that it is not a musical form but rather a technique of composition.
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. 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.
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." 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" and argues that "there seems to be some rational justification for their doing so."
This is related to the idea that restrictions create freedom for the composer, by directing their efforts. He also points out that fugal 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.
Alice or the Last Escapade (French: Alice ou la dernière fugue) is a 1977 French film written and directed by Claude Chabrol. The film is very loosely inspired by Alice's Adventures in Wonderland by Lewis Carroll, including the protagonist's name being Alice Carroll (a combination of the Alice character and the author's pseudonymous surname).Bach-Werke-Verzeichnis
The Bach-Werke-Verzeichnis (BWV; lit. Bach works catalogue) is a catalogue of compositions by Johann Sebastian Bach. It was first published in 1950, edited by Wolfgang Schmieder. The catalogue's second edition appeared in 1990. An abbreviated version of that second edition, known as BWV2a, was published in 1998.
1126 compositions were assigned a BWV number in the 20th century. More compositions were added to the catalogue in the 21st century. The Anhang (Anh.; Annex) of the BWV lists over 200 lost, doubtful and spurious compositions.Chromatic Fantasia and Fugue
The Chromatic Fantasia and Fugue in D minor, BWV 903, is a work for harpsichord by Johann Sebastian Bach. Bach probably composed it during his time in Köthen from 1717 to 1723. The piece was already regarded as a unique masterpiece during his lifetime. It is now often played on piano.Exposition (music)
In musical form and analysis, exposition is the initial presentation of the thematic material of a musical composition, movement, or section. The use of the term generally implies that the material will be developed or varied.
In sonata form, the exposition is "the very first major section, incorporating at least one important modulation to the dominant or other secondary key and presenting the principal thematic material."
In a fugue, the exposition is "the statement of the subject in imitation by the several voices; especially the first such statement, with which the fugue begins."Fugue in G minor, BWV 131a
The Fugue in G minor, BWV 131a, is a piece of organ music attributed to Johann Sebastian Bach.
It is a transcription of the last movement of his cantata Aus der Tiefen rufe ich, Herr, zu dir, BWV 131.
The cantata is definitely by Bach, while the arrangement for organ is regarded by some authorities (from Spitta onwards) as spurious.
The cantata dates from 1707 or 1708, which almost certainly provides a terminus ante quem for the organ arrangement.The key of G minor, sometimes associated with sadness, is used extensively in the cantata, which sets one of the penitential psalms. In the cantata the fugue (a permutation fugue) is sung by the choir.
The score of the cantata does not feature an organ part as such, but the basso continuo (for which a figured bass is provided) may well have been played on the organ.Fugue in G minor, BWV 578
Fugue in G minor, BWV 578, (popularly known as the Little Fugue), is a piece of organ music written by Johann Sebastian Bach during his years at Arnstadt (1703–1707). It is one of Bach's best known fugues and has been arranged for other voices, including an orchestral version by Leopold Stokowski.Early editors of Bach's work attached this title to distinguish it from the later Great Fantasia and Fugue in G minor, BWV 542, which is longer in duration and more challenging to play.Fugue state
Dissociative fugue, formerly fugue state or psychogenic fugue, is a dissociative disorder and a rare psychiatric disorder characterized by reversible amnesia for personal identity, including the memories, personality, and other identifying characteristics of individuality. The state can last days, months or longer. Dissociative fugue usually involves unplanned travel or wandering, and is sometimes accompanied by the establishment of a new identity. It is a facet of dissociative amnesia, according to the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5).
After recovery from a fugue state, previous memories usually return intact, and further treatment is unnecessary. Additionally, an episode of fugue is not characterized as attributable to a psychiatric disorder if it can be related to the ingestion of psychotropic substances, to physical trauma, to a general medical condition, or to dissociative identity disorder, delirium, or dementia. Fugues are precipitated by a series of long-term traumatic episodes. It is most commonly associated with childhood victims of sexual abuse who learn over time to dissociate memory of the abuse (dissociative amnesia).Große Fuge
The Große Fuge (or Grosse Fuge, also known in English as Great Fugue or Grand Fugue), Op. 133, is a single-movement composition for string quartet by Ludwig van Beethoven. An immense double fugue, it was universally condemned by contemporary critics. A reviewer writing for Allgemeine musikalische Zeitung in 1826 described the fugue as "incomprehensible, like Chinese" and "a confusion of Babel". However, critical opinion of the work has risen steadily since the beginning of the 20th century. The work is now considered among Beethoven's greatest achievements. Igor Stravinsky said of it, "[it is] an absolutely contemporary piece of music that will be contemporary forever."The Große Fuge originally served as the final movement of his Quartet No. 13 in B♭ major (Op. 130), written in 1825. But Beethoven's publisher, who was concerned about the dismal commercial prospects of the piece, urged Beethoven to replace the fugue with a new finale. Beethoven complied, and the Große Fuge was published separately in 1827 as Op. 133. It was composed when Beethoven was almost completely deaf, and is considered to be part of his set of late quartets. It was first performed in 1826, as the finale of the B♭ quartet, by the Schuppanzigh Quartet.
Analysts describe the Große Fuge as "inaccessible", "eccentric", "filled with paradoxes", and "Armaggedon". "[It] stands out as the most problematic single work in Beethoven's output and … doubtless in the entire literature of music," writes critic and musicologist Joseph Kerman of the fugue. Moreover, according to violinist and composer David Matthews, "it is fiendishly difficult to play."List of compositions by Franz Schubert by genre
Franz Schubert (31 January 1797 – 19 November 1828) was an extremely prolific Austrian composer. He composed some 1500 works (or, when collections, cycles and variants are grouped, some thousand compositions). The largest group are the lieder for piano and solo voice (over six hundred), and nearly as many piano pieces. Schubert also composed some 150 part songs, some 40 liturgical compositions (including several masses) and around 20 stage works like operas and incidental music. His orchestral output includes a dozen symphonies (seven completed) and several overtures. Schubert's chamber music includes over 20 string quartets, and several quintets, trios and duos.
This article constitutes a complete list of Schubert's known works organized by their genre. The complete output is divided in eight series, and in principle follows the order established by the Neue Schubert-Ausgabe printed edition. The works found in each series are ordered ascendingly according to Deutsch numbers, the information of which attempts to reflect the most current information with regards to Schubert's catalogue.
The list below includes the following information:
D – the catalogue number assigned by Otto Erich Deutsch or NSA authorities
Genre – the musical genre to which the piece belongs. This has been omitted when the genre is self-explanatory or unnecessary, i.e. piano dances
Title – the title of the work
Incipit – the first line(s) of text, as pertaining to vocal works
Scoring – the instrumentation and/or vocal forces required for the work
Informal Title – any additional names by which the work is known, when applicable
Former Deutsch Number – information on Deutsch numbers that have been reassigned, when applicable
Date – the known or assumed date of composition, when available; or date of publication
Opus Number – the opus number of the original publication of the work, when applicable
Setting – the order of setting as it pertains to vocal works that have numerous settings of the same text
Version – the number of version as it pertains to works or vocal settings that have more than one existing version
Notes – any additional information concerning the work: alternate titles, completeness, relation to other works, authorship, etc.List of fugal works by Johann Sebastian Bach
This page lists the fugal works of Johann Sebastian Bach, defined here as the fugues, fughettas, and canons, as well as other works containing fugal expositions but not denoted as fugues, such as some choral sections of the Mass in B minor, the St Matthew Passion, the St John Passion, and the cantatas.
This sub-list of the complete list of compositions by Johann Sebastian Bach is intended to facilitate the study of Bach's counterpoint techniques. Each work cited in this list will be annotated with the fugal subject(s) and any countersubjects in musical notation.List of keyboard and lute compositions by Johann Sebastian Bach
Keyboard and Lute Works is the topic of the fifth series of the New Bach Edition.Keyboard Works (Klavierwerke) by Johann Sebastian Bach traditionally refers to the Nos. 772 to 994, Chapter 8 in the BWV catalogue, listing compositions for a solo keyboard instrument like the harpsichord or the clavichord. Despite the fact that organ is also a keyboard instrument, and that in Bach's time the distinction wasn't always made whether a keyboard composition was for organ or another keyboard instrument, Wolfgang Schmieder ranged organ compositions in a separate section of the Bach-Werke-Verzeichnis (Nos. 525-771). Also other compositions for keyboard, like compositions for lute-harpsichord and fortepiano were listed outside the "Klavierwerke" range by Schmieder. Lute works are in the range 995–1000, Chapter 9 in the BWV catalogue.Bach was a prodigious talent at the keyboard, well known during his lifetime for both his technical and improvisational abilities. Many of Bach's keyboard works started out as improvisations. Bach wrote widely for the harpsichord, producing numerous inventions, suites, fugues, partitas, overtures, as well as keyboard arrangements of concerto music by his contemporaries. The fortepiano is an instrument Bach would have encountered once, by the end of his life when it was recently invented, while visiting his son in Potsdam. The visit resulted in Das Musikalische Opfer, parts of which may have been intended for the new instrument.
Several of Bach's works for keyboard were published in print in his own lifetime. Four such publications were given the name Clavier-Übung (Keyboard Practice) by the composer. Bach was not the first to use that name, for example Bach's Leipzig predecessor Johann Kuhnau had used it for two volumes published in the late 17th century. The first volume, Bach's Opus 1, was published in 1731, while the last was published a decade later. The first, second and last volume contain music written for harpsichord, while the third was written for the organ, only four duets contained in that volume ending up in the BWV 772–994 range.
The Well-Tempered Clavier, a collection of forty-eight Preludes and Fugues, was not printed until half a century after Bach's death, although it had circulated in manuscript form before that. Before the extensive rediscovery of his works in the nineteenth century, Bach was known almost exclusively through his music for the keyboard, in particular his highly influential Well-Tempered Clavier, which were regularly assigned as part of musicians' training. Composers and performers such as Ludwig van Beethoven and Camille Saint-Saëns first showed off their skills as child prodigies playing the entire cycle of Bach's forty-eight Preludes and Fugues.
Modern composers have continued to draw inspiration from Bach's keyboard output. Dmitri Shostakovich, for example, wrote his own set of Preludes and Fugues after the Bach model. Jazz musicians and composers, in particular, have been drawn to the contrapuntal style, harmonic expansion and rhythmic expression of Bach's compositions, especially the works for keyboard.
The first section below lists all compositions in the BWV 772–994 range, then follows a section listing other compositions for keyboard instruments, excluding the organ.
After the composer's death most of his keyboard compositions, and many others, are, or were, often performed on the piano, played either directly from a score for the instruments as the composer knew them, or from a score that was a transcription for piano. The latter is sometimes needed even for harpsichord scores while for instance a composition intended for a two-manual harpsichord (like the Goldberg Variations) can present difficulties for the crossing of hands when performed on a single-keyboard instrument like the piano. Some of the transposers/arrangers of Bach's work added their own inspiration, like Busoni in his arrangement and expansion of Bach's Chromatische Fantasie und Fuge, BWV 903. The fourth section of this list refers to such transcriptions and arrangements for the piano.Passacaglia and Fugue in C minor, BWV 582
Passacaglia and Fugue in C minor (BWV 582) is an organ piece by Johann Sebastian Bach. Presumably composed early in Bach's career, it is one of his most important and well-known works, and an important influence on 19th and 20th century passacaglias: Robert Schumann described the variations of the passacaglia as "intertwined so ingeniously that one can never cease to be amazed."Prelude and Fugue in A minor, BWV 543
Prelude and Fugue in A minor, BWV 543 is a piece of organ music written by Johann Sebastian Bach sometime around his years as court organist to the Duke of Saxe-Weimar (1708–1717).Prelude and Fugue in C major, BWV 846
The Prelude and Fugue in C Major, BWV 846, is a keyboard composition written by Johann Sebastian Bach. It is the first prelude and fugue in the first book of The Well-Tempered Clavier, a series of 48 preludes and fugues by the composer. An early version of the prelude, BWV 846A, is found in the Klavierbüchlein für Wilhelm Friedemann Bach.Prelude and Fugue in C major, BWV 870
Prelude and Fugue in C major, BWV 870, is a keyboard composition written by Johann Sebastian Bach. It is the first prelude and fugue in the second book of The Well-Tempered Clavier, a series of 48 preludes and fugues in every major and minor key.Subject (music)
In music, a subject is the material, usually a recognizable melody, upon which part or all of a composition is based. In forms other than the fugue, this may be known as the theme.The Art of Fugue
The Art of Fugue (or The Art of the Fugue; German: Die Kunst der Fuge), BWV 1080, is an incomplete musical work of unspecified instrumentation by Johann Sebastian Bach (1685–1750). Written in the last decade of his life, The Art of Fugue is the culmination of Bach's experimentation with monothematic instrumental works.
This work consists of 14 fugues and 4 canons in D minor, each using some variation of a single principal subject, and generally ordered to increase in complexity. "The governing idea of the work", as put by Bach specialist Christoph Wolff, "was an exploration in depth of the contrapuntal possibilities inherent in a single musical subject." The word "contrapunctus" is often used for each fugue.The Well-Tempered Clavier
The Well-Tempered Clavier, BWV 846–893, is a collection of two sets of preludes and fugues in all 24 major and minor keys, composed for solo keyboard by Johann Sebastian Bach. In Bach's time Clavier (keyboard) was a generic name indicating a variety of keyboard instruments, most typically a harpsichord or clavichord – but not excluding an organ either.
The modern German spelling for the collection is Das wohltemperierte Klavier (WTK; German pronunciation: [das ˌvoːlˌtɛmpəˈʁiːɐ̯tə klaˈviːɐ̯]). Bach gave the title Das Wohltemperirte Clavier to a book of preludes and fugues in all 24 major and minor keys, dated 1722, composed "for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study". Some 20 years later Bach compiled a second book of the same kind, which became known as The Well-Tempered Clavier, Part Two (in German: Zweyter Theil, modern spelling: Zweiter Teil).
Modern editions usually refer to both parts as The Well-Tempered Clavier, Book I (WTC I) and The Well-Tempered Clavier, Book II (WTC II), respectively. The collection is generally regarded as being among the most important works in the history of classical music.Toccata and Fugue in D minor, BWV 565
The Toccata and Fugue in D minor, BWV 565, is a piece of organ music written, according to its oldest extant sources, by Johann Sebastian Bach. The piece opens with a toccata section, followed by a fugue that ends in a coda. It is one of the most famous works in the organ repertoire.
Scholars differ as to when it was composed. It could have been as early as c.1704 (when the presumed composer was still in his teens), which would be one explanation for the unusual features; alternatively a date as late as the 1750s has been suggested (Bach died in 1750).
To a large extent the piece conforms to the characteristics deemed typical for the north German organ school of the baroque era with divergent stylistic influences, such as south German characteristics, described in scholarly literature on the piece.
Despite a profusion of educated guesswork, there is not much that can be said with certainty about the first century of the composition's existence other than that it survived that period in a manuscript written by Johannes Ringk. The first publication of the piece, in the Bach Revival era, was in 1833, through the efforts of Felix Mendelssohn, who also performed the piece in an acclaimed concert in 1840. Familiarity with the piece was enhanced in the second half of the 19th century by a fairly successful piano version by Carl Tausig, but it was not until the 20th century that its popularity rose above that of other organ compositions by Bach. That popularity further increased, due for example to its inclusion in Walt Disney's Fantasia (in Stokowski's orchestral transcription), until this composition came to be considered the most famous work in the organ repertoire.
A wide, and often conflicting, variety of analyses has been published about the piece: for instance, in literature on organ music, it is often described as some sort of program music depicting a storm, while in the context of Disney's Fantasia, it was promoted as absolute music, nothing like program music depicting a storm. In the last quarter of the 20th century, scholars like Peter Williams and Rolf-Dietrich Claus published their studies on the piece, and argued against its authenticity. Bach-scholars like Christoph Wolff defended the attribution to Bach. Other commentators ignored the authenticity doubts or considered the attribution issue undecided. No edition of the Bach-Werke-Verzeichnis listed the Toccata and Fugue among the doubtful works, nor does its entry on the website of the Bach Archiv Leipzig even mention alternative views on the attribution issue.