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In
music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated concepts , , and ...

music
, a fugue () is a
contrapuntal In music, counterpoint is the relationship between two or more Part (music), musical lines (or voices) which are harmonically interdependent yet independent in rhythm and Pitch contour, melodic contour. It has been most commonly identified in ...

contrapuntal
compositional technique in two or more voices, built on a subject (a musical theme) that is introduced at the beginning in
imitation Imitation (from Latin ''imitatio'', "a copying, imitation") is an advanced behavior whereby an individual observes and replicates another's behavior. Imitation is also a form of social learning that leads to the "development of traditions, and ...
(repetition at different pitches) and which recurs frequently in the course of the composition. It is not to be confused with a ''
fuguing tuneThe fuguing tune (often fuging tune) is a variety of Anglo-American vernacular choral A choir (; also known as a chorale or chorus) is a musical ensemble of singers. Choral music, in turn, is the music written specifically for such an ensemble to ...
'', which is a style of song popularized by and mostly limited to early American (i.e.
shape note Shape notes are a musical notation Music notation or musical notation is any system used to visually represent aurally perceived music played with instrument (music), instruments or singing, sung by the human voice through the use of wr ...
or "
Sacred Harp Sacred Harp singing is a tradition of sacred choral music that originated in New England New England is a region comprising six states in the Northeastern United States: Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and ...
") music and
West Gallery music __NOTOC__ , Oxfordshire West gallery music, also known as Georgian era, Georgian psalmody, refers to the sacred music (metrical psalms, with a few hymns and anthems) sung and played in Church of England parish church, English parish churches, as wel ...
. A fugue usually has three main sections: an
exposition Exposition (also the French for exhibition) may refer to: * Universal exposition or World's Fair *Expository writing Rhetorical modes (also known as modes of discourse) describe the variety, conventions, and purposes of the major kinds of languag ...
, a
development Development or developing may refer to: Arts *Development hell, when a project is stuck in development *Filmmaking#Development, Filmmaking, development phase, including finance and budgeting *Development (music), the process thematic material i ...
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 In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of w ...
, the term was widely used to denote any works in canonic style; by the
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in m ...

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 The human voice consists of sound Voice production, made by a human being using the vocal tract, including Speech, talking, singing, Laughter, laughing, crying, screaming, shouting, humming or yelling. The human voice frequency is specifically a ...
(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 completed the subject, 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 Coda or CODA may refer to: Arts, entertainment, and media Films * ''Coda'' (1987 film), an Australian horror film about a serial killer, made for television * ''Coda'' (2019 film), a Canadian drama film starring Patrick Stewart, Katie Holmes, a ...
."Fugue", ''The Concise Oxford Dictionary of Music'', fourth edition, ed. Michael Kennedy (Oxford and New York:
Oxford University Press Oxford University Press (OUP) is the university press 200px, The Pitt Building in Cambridge, which used to be the headquarters of Cambridge University Press, and now serves as a conference centre for the Press. A university press is an academic ...

Oxford University Press
, 1996).
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
ricercar A ricercar (also spelled ricercare, ) is a type of late Renaissance The Renaissance ( , ) , from , with the same meanings. was a period in European history marking the transition from the Middle Ages In the history of Europe, the ...
s, capriccios,
canzona The canzona is an Italian musical form derived from the Franco-Flemish and Parisian chansons , and during Giovanni Gabrieli's lifetime was frequently spelled canzona, though both earlier and later the singular was spelled either canzon or canzone ...
s, and fantasias. The famous fugue composer
Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known for instrumental compositions such as the Cello Suites (Bach), Cello Suites and ''Brandenburg Concertos''; keyboard ...

Johann Sebastian Bach
(1685–1750) shaped his own works after those of
Jan Pieterszoon Sweelinck , the composer's brother. Jan Pieterszoon Sweelinck ( ; April or May, 1562 – 16 October 1621) was a Netherlands, Dutch composer A composer (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch ...

Jan Pieterszoon Sweelinck
(1562-1621),
Johann Jakob Froberger Johann Jakob Froberger (Baptism, baptized 19 May 1616 – 7 May 1667) was a German people, German Baroque composer, Keyboard instrument, keyboard virtuoso, and organist. Among the most famous composers of the era, he was influential in developing th ...
(1616–1667),
Johann Pachelbel Johann Pachelbel (baptised 1 September 1653 – buried 9 March 1706; also Bachelbel) was a German composer, organist, and teacher who brought the south German organ schools to their peak. He composed a large body of sacred and secular Secula ...
(1653–1706),
Girolamo Frescobaldi Girolamo Alessandro Frescobaldi (; also Gerolamo, Girolimo, and Geronimo Alissandro; September 15831 March 1643) was a musician from the Duchy of Ferrara, in what is now northern Italy. He was one of the most important composer A composer (Lati ...

Girolamo Frescobaldi
(1583–1643),
Dieterich Buxtehude Dieterich Buxtehude (; ; born Diderik Hansen Buxtehude; c. 1637 – 9 May 1707)  was an organist Image:Organist at Lausanne Cathedral.jpg, A cathedral organist in Lausanne Cathedral An organist is a musician who plays any type of organ (mus ...

Dieterich Buxtehude
(c. 1637–1707) and others. With the decline of sophisticated styles at the end of the
baroque period The Baroque (, ; ) is a style of architecture File:Plan d'exécution du second étage de l'hôtel de Brionne (dessin) De Cotte 2503c – Gallica 2011 (adjusted).jpg, upright=1.45, alt=Plan d'exécution du second étage de l'hôtel de Brionn ...
, the fugue's central role waned, eventually giving way as
sonata form Sonata form (also ''sonata-allegro form'' or ''first movement form'') is a musical form, musical structure generally consisting of three main sections: an exposition, a development, and a recapitulation. It has been used widely since the middle ...
and the
symphony orchestra An orchestra (; ) is a large instrumental ensemble typical of classical music Classical music is art music produced or rooted in the traditions of Western culture, including both Religious music, liturgical (Religion, religious) and secula ...
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 Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Johannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his ra ...

Wolfgang Amadeus Mozart
(1756–1791) and
Ludwig van Beethoven Ludwig van Beethoven (, ; baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classi ...

Ludwig van Beethoven
(1770–1827), as well as modern composers such as
Dmitri Shostakovich Dmitri Dmitriyevich Shostakovich, , group=n (9 August 1975) was a Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a socialist state A socialist state, socialist republic, or socialist count ...
(1906–1975).


Etymology

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).


Musical outline

A fugue begins with the ''
exposition Exposition (also the French for exhibition) may refer to: * Universal exposition or World's Fair *Expository writing Rhetorical modes (also known as modes of discourse) describe the variety, conventions, and purposes of the major kinds of languag ...
'' 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. ::S = subject; A = answer; CS = countersubject; T = tonic; D =
dominant Domination or dominant may refer to: Society * World domination, which is mainly a conspiracy theory * Colonialism in which one group (usually a nation) invades another region for material gain or to eliminate competition * Chauvinism in which a p ...


Exposition

A fugue begins with the exposition of its subject in one of the voices alone in the tonic key. 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). After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key (usually the
dominant Domination or dominant may refer to: Society * World domination, which is mainly a conspiracy theory * Colonialism in which one group (usually a nation) invades another region for material gain or to eliminate competition * Chauvinism in which a p ...
or
subdominant In music Music is the art of arranging sounds in time through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural aspects of all human societies. General definitions of music include common elements su ...
), 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 Key or The Key may refer to: Common meanings * Key (cryptography), a piece of information that controls the operation of a cryptography algorithm * Key (lock), device used to control access to places or facilities restricted by a lock * Key (map) ...
, this note is transposed up a fourth to the tonic rather than up a fifth to the
supertonic In music, the supertonic is the second Degree (music), degree () of a diatonic scale, one Steps and skips, step above the Tonic (music), tonic. In the Solfège#Movable do solf%C3%A8ge, movable do solfège system, the supertonic note is sung as ''re ...
. 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 In music, a subject is the material, usually a recognizable melody, upon which part or all of a musical composition, composition is based. In forms other than the fugue, this may be known as the theme. Characteristics A subject may be perceivab ...
''; if this accompanying material is only heard once, it is simply referred to as '' free counterpoint''. The countersubject is written in
invertible counterpoint In music theory, the word inversion describes certain types of changes to intervals, chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a p ...
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 Tonal may refer to: * Tonal (mythology), a concept in the belief systems and traditions of Mesoamerican cultures, involving a spiritual link between a person and an animal * Tonal language, a type of language in which pitch is used to make phonemic ...
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 '' Well-Tempered Clavier, Book 1''. A brief
codetta In music, a coda () (Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citizen of the Italian Republic ** Italian language, a Romance language *** Regional Ital ...
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 300px, Four quarter notes. Quarter notes are the smallest note value not beamed together. A quarter note (American) or crotchet (British) is a note Note, notes, or NOTE may refer to: Music and entertainment * Musical note In music, a note is ...

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).


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 ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is a collection of two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys, composed for solo keyboard b ...
'') 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. states that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented.


Development

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 key In music Music is the art of arranging sounds in time to produce a composition through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural Culture () is an umbrella term which encompasses the socia ...
s such as the relative dominant and
subdominant In music Music is the art of arranging sounds in time through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural aspects of all human societies. General definitions of music include common elements su ...
, 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 Relative may refer to: General use *Kinship In anthropology, kinship is the web of social relationships that form an important part of the lives of all humans in all societies, although its exact meanings even within this discipline are ofte ...
or
minor Minor may refer to: * Minor (law), a person under the age of certain legal activities. ** A person who has not reached the age of majority * Academic minor, a secondary field of study in undergraduate education Music theory *Minor chord ** Barbe ...
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 Buxtehude (), officially the Hanseatic City of Buxtehude (german: Hansestadt Buxtehude, nds, Hansestadt Buxthu ()), is a town on the Este River in Northern Germany, belonging to the district of Stade in Lower Saxony Lower Saxony (german: Ni ...

Buxtehude
and
Pachelbel Johann Pachelbel (baptised 1 September 1653 – buried 9 March 1706; also Bachelbel) was a German composer, organistImage:Organist at Lausanne Cathedral.jpg, A cathedral organist in Lausanne Cathedral An organist is a musician who plays any ty ...

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 Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * Inversion (artwork), ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and mus ...
'', 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 In Western music Music is the art of arranging sounds in time to produce a composition through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural Culture () is an umbrella term which encompass ...
(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.


Example and analysis

The excerpt below, bars 7–12 of 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 , a sequence is an enumerated collection of in which repetitions are allowed and matters. Like a , it contains (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is called the ''length'' of the sequence. Unl ...
, in the form of an accompanied
canon Canon or Canons may refer to: Places * Canon, Georgia Canon is a city in Franklin County, Georgia, Franklin and Hart County, Georgia, Hart counties in the U.S. state of Georgia (U.S. state), Georgia. The population was 804 at the 2010 census. His ...
at the fourth. Arrival in E major is marked by a quasi
perfect cadence In Western musical theory Music theory is the study of the practices and possibilities of music Music is the art of arranging sounds in time to produce a composition through the elements of melody, harmony, rhythm, and timbre. It is on ...
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 Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Language * Grammatical mode or grammatical mood, a category of verbal inflections that expresses an attitude of mind ** Imperative mood ** Subjunctive mo ...
.


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.


Counter-exposition

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.


Stretto

Sometimes counter-expositions or the middle entries take place in ''
stretto In music, the Italian term ''stretto'' (plural: ''stretti'') has two distinct meanings: # In a fugue, ''stretto'' (german: Engführung) is the imitation of the subject in close succession, so that the answer enters before the subject is complet ...
,'' 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 ' choruses from J.S. Bach's
Mass in B Minor The Mass in B minor (), BWV 232, is an extended setting of the Mass ordinary by Johann Sebastian Bach. The composition was completed in 1749, the year before the composer's death, and was to a large extent based on earlier work, such as a Sanctus ...
).


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 . Any material that follows the final entry of the subject is considered to be the final
coda Coda or CODA may refer to: Arts, entertainment, and media Films * ''Coda'' (1987 film), an Australian horror film about a serial killer, made for television * ''Coda'' (2019 film), a Canadian drama film starring Patrick Stewart, Katie Holmes, a ...
and is normally cadential.


Types


Simple fugue

A simple fugue has only one subject, and does not utilize
invertible counterpoint In music theory, the word inversion describes certain types of changes to intervals, chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a p ...
.


Double (triple, quadruple) fugue

A double fugue has two subjects that are often developed simultaneously. Similarly, a triple fugue has three subjects. There are two kinds of double (triple) fugue: (a) a fugue in which the second (third) subject is (are) presented simultaneously with the subject in the exposition (e.g. as in
Kyrie Eleison Kyrie, a transliteration Transliteration is a type of conversion of a text from one script Script may refer to: Writing systems * Script, a distinctive writing system, based on a repertoire of specific elements or symbols, or that repe ...

Kyrie Eleison
of Requiem in D minor or the fugue of Bach's Passacaglia and Fugue in C minor,
BWV 582 ''Passacaglia and Fugue in C minor'' (BWV 582) is an Pipe organ, 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 c ...
), and (b) a fugue in which all subjects have their own expositions at some point, and they are not combined until later (see for example, the three-subject 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 The (BWV; ; ) is a catalogue of compositions by Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the Baroque music, Baroque period. He is known for instrumental compositions such as the ''Bra ...
, a triple fugue for organ.)


Counter-fugue

A counter-fugue is a fugue in which the first answer is presented as the subject in
inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * Inversion (artwork), ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and mus ...
(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 ''The Art of Fugue'' (or ''The Art of the Fugue''; german: Die Kunst der Fuge, links=no), Bach-Werke-Verzeichnis, BWV 1080, is an Unfinished creative work, incomplete musical work of unspecified instrumentation by Johann Sebastian Bach (1685–1 ...
''.


Permutation fugue

Permutation fugue describes a type of composition (or technique of composition) in which elements of fugue and strict
canon Canon or Canons may refer to: Places * Canon, Georgia Canon is a city in Franklin County, Georgia, Franklin and Hart County, Georgia, Hart counties in the U.S. state of Georgia (U.S. state), Georgia. The population was 804 at the 2010 census. His ...
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 music theory, the word inversion describes certain types of changes to intervals, chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a p ...
. (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 number 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 eighth and final chorus of J.S. Bach's cantata, ''Himmelskönig, sei willkommen'', BWV 182. 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 ''Passacaglia and Fugue in C minor'' (BWV 582) is an organ piece by Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the Baroque music, Baroque period. He is known for instrumental composition ...
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.


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 's ''Diabelli Variations'' Op. 120.


History


Middle Ages and Renaissance

The term ''fuga'' was used as far back as the
Middle Ages In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of ...
, 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,
ricercar A ricercar (also spelled ricercare, ) is a type of late Renaissance The Renaissance ( , ) , from , with the same meanings. was a period in European history marking the transition from the Middle Ages In the history of Europe, the ...
es and
canzona The canzona is an Italian musical form derived from the Franco-Flemish and Parisian chansons , and during Giovanni Gabrieli's lifetime was frequently spelled canzona, though both earlier and later the singular was spelled either canzon or canzone ...
s. "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 Gioseffo Zarlino (31 January or 22 March 1517 – 4 February 1590) was an Italian music theorist Music theory is the study of the practices and possibilities of music Music is the of arranging s in time through the of melody, harmony, ...

Gioseffo Zarlino
, a composer, author, and theorist in the
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in ...
, 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 Improvisation is the activity of making or doing something not planned beforehand, using whatever can be found. Improvisation in the performing arts is a very spontaneous performance without specific or scripted preparation. The skills of imp ...
, but by the 1550s, it was considered a technique of composition. The composer
Giovanni Pierluigi da Palestrina Giovanni Pierluigi da Palestrina ( 1525 – 2 February 1594) was an Italian Renaissance The Renaissance ( , ) , from , with the same meanings. is a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or ...

Giovanni Pierluigi da Palestrina
(1525?–1594) wrote masses using modal counterpoint and imitation, and fugal writing became the basis for writing
motet In Western classical music Classical music generally refers to the art music, formal musical tradition of the Western world, considered to be #Relationship to other music traditions, distinct from Western folk music or popular music traditio ...
s 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.


Baroque era

It was in the
Baroque period The Baroque (, ; ) is a style Style is a manner of doing or presenting things and may refer to: * Architectural style, the features that make a building or structure historically identifiable * Design, the process of creating something * Fashi ...
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 , the composer's brother. Jan Pieterszoon Sweelinck ( ; April or May, 1562 – 16 October 1621) was a Netherlands, Dutch composer A composer (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch ...

Jan Pieterszoon Sweelinck
,
Girolamo Frescobaldi Girolamo Alessandro Frescobaldi (; also Gerolamo, Girolimo, and Geronimo Alissandro; September 15831 March 1643) was a musician from the Duchy of Ferrara, in what is now northern Italy. He was one of the most important composer A composer (Lati ...

Girolamo Frescobaldi
,
Johann Jakob Froberger Johann Jakob Froberger (Baptism, baptized 19 May 1616 – 7 May 1667) was a German people, German Baroque composer, Keyboard instrument, keyboard virtuoso, and organist. Among the most famous composers of the era, he was influential in developing th ...
and
Dieterich Buxtehude Dieterich Buxtehude (; ; born Diderik Hansen Buxtehude; c. 1637 – 9 May 1707)  was an organist Image:Organist at Lausanne Cathedral.jpg, A cathedral organist in Lausanne Cathedral An organist is a musician who plays any type of organ (mus ...

Dieterich Buxtehude
all wrote fugues, and
George Frideric Handel George Frideric (or Frederick) Handel (; baptised , ; 23 February 1685 – 14 April 1759) was a German-British Baroque The Baroque (, ; ) is a of , , , , and other arts that flourished in Europe from the early 17th century until the 1740 ...
included them in many of his
oratorio An oratorio () is a large musical composition Musical composition can refer to an piece or work of , either or , the of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions ar ...

oratorio
s. Keyboard suites from this time often conclude with a fugal
gigue The gigue (; ) or giga () is a lively baroque dance Baroque dance is dance Dance is a performing art art form, form consisting of sequences of movement, either improvised or purposefully selected. This movement has aesthetic and often s ...

gigue
.
Domenico Scarlatti Giuseppe Domenico Scarlatti, also known as Domingo or Doménico Scarlatti (26 October 1685, in Naples23 July 1757, in Madrid), was an Italy, Italian composer. He is classified primarily as a Baroque music, Baroque composer chronologically, alth ...

Domenico Scarlatti
has only a few fugues among his corpus of over 500 harpsichord sonatas. The
French overture The French overture is a musical form widely used in the Baroque music, Baroque period. Its basic formal division is into two parts, which are usually enclosed by double bars and repeat signs. They are complementary in style (slow in dotted rhythms ...
featured a quick fugal section after a slow introduction. The second movement of a
sonata da chiesa Sonata (; Italian: , pl. ''sonate''; from Latin and Italian: ''sonare'' rchaic Italian; replaced in the modern language by ''suonare'' "to sound"), in music, literally means a piece ''played'' as opposed to a cantata A cantata (; ; literally ...
, as written by
Arcangelo Corelli Arcangelo Corelli (, also , , ; (17 February 1653 – 8 January 1713) was an Italian violin The violin, sometimes known as a ''fiddle A fiddle is a Bow (music), bowed String instrument, string musical instrument, most often a violi ...

Arcangelo Corelli
and others, was usually fugal. The Baroque period also saw a rise in the importance of
music theory Music theory is the study of the practices and possibilities of music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elem ...
. Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students. The most influential text was ''
Gradus Ad Parnassum The Latin phrase ''gradus ad Parnassum'' means "steps to Parnassus". It is sometimes shortened to ''gradus''. The name ''Parnassus Mount Parnassus (; el, Παρνασσός, ''Parnassós'') is a mountain of limestone Limestone is a comm ...
'' ("Steps to
Parnassus Mount Parnassus (; el, Παρνασσός, ''Parnassós'') is a mountain of limestone Limestone is a common type of carbonate rock, carbonate sedimentary rock. It is composed mostly of the minerals calcite and aragonite, which are differ ...

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 Palestrina (ancient ''Praeneste''; grc, Πραίνεστος, ''Prainestos'') is a modern Italian city and ''comune The (; plural: ) is a Administrative division, local administrative division of Italy, roughly equivalent to a township ...

Palestrina
's modal fugues.
Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Johannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical periodClassical period may refer to: *Classical Greece, speci ...

Mozart
studied from this book, and it remained influential into the nineteenth century.
Haydn Franz Joseph Haydn (; ; 31 March 173231 May 1809) was an Austrian composer A composer (Latin wikt:compono, ''compōnō''; literally "one who puts together") is a person who writes musical composition, music, especially classical music in an ...

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 ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys for keyboard by Johann Sebastian Bach. In th ...
'', 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 A prelude (music), prelude is a musical form. It may also refer to: Music *Prelude (band), an English-based folk band *Prelude Records (record label), a former New York-based dance independent record label *Chorale prelude, a short liturgical compo ...
or
toccata Toccata (from Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citizen of the Italian Republic ** Italian language, a Romance language *** Regional Italian ...
. ''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 Carl Philipp Emanuel Bach (8 March 1714 – 14 December 1788), also formerly spelled Karl Philipp Emmanuel Bach, and commonly abbreviated C. P. E. Bach, was a German Classical period musician and composer, the fifth child and seco ...

C.P.E. Bach
and through the theorist
Friedrich Wilhelm Marpurg Friedrich Wilhelm Marpurg (21 November 1718 – 22 May 1795) was a German Music criticism, music critic, Music theory, music theorist and composer. He was friendly and active with many figures of the Age of Enlightenment, Enlightenment of the 18 ...

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 Classical antiquity (also the classical era, classical period or classical age) is the period of cultural history History (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, ...
, the fugue was no longer a central or even fully natural mode of musical composition. Nevertheless, both
Haydn Franz Joseph Haydn (; ; 31 March 173231 May 1809) was an Austrian composer A composer (Latin wikt:compono, ''compōnō''; literally "one who puts together") is a person who writes musical composition, music, especially classical music in an ...

Haydn
and
Mozart Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Johannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical periodClassical period may refer to: *Classical Greece, speci ...

Mozart
had periods of their careers in which they in some sense "rediscovered" fugal writing and used it frequently in their work.


Haydn

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, Symphony No. 13 (Haydn), No. 13, and Symphony No. 40 (Joseph Haydn), No. 40) that date from 1762 to 1763. The earliest fugues, in both the symphonies and in the Baryton trios (Haydn), 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
oratorio An oratorio () is a large musical composition Musical composition can refer to an piece or work of , either or , the of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions ar ...

oratorio
s 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 (Haydn), The Creation'' and ''The Seasons (Haydn), The Seasons,'' as well as several of his later symphonies, including Symphony No. 88 (Haydn), No. 88, Symphony No. 95 (Haydn), No. 95, and Symphony No. 101 (Haydn), No. 101; and the late string quartets, Opus 71 no. 3 and (especially) Opus 76 no. 6.


Mozart

The young Wolfgang Amadeus Mozart studied counterpoint with Padre Martini in Bologna. Under the employment of Hieronymus von Colloredo, Archbishop Colloredo, and the musical influence of his predecessors and colleagues such as Johann Ernst Eberlin, Anton Cajetan Adlgasser, Michael Haydn, and his own father, Leopold Mozart at the Salzburg Cathedral, the young Mozart composed ambitious fugues and contrapuntal passages in Catholic choral works such as Mass in C minor, K. 139 "Waisenhaus" (1768), Mass in C major, K. 66 "Dominicus" (1769), Mass in C major, K. 167 "in honorem Sanctissimae Trinitatis" (1773), Mass in C major, K. 262 "Missa longa" (1775), Mass in C major, K. 337 "Solemnis" (1780), various litanies, and vespers. Leopold admonished his son openly in 1777 that he not forget to make public demonstration of his abilities in "fugue, canon, and contrapunctus"
Konrad
. Later in life, 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 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 ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is a collection of two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys, composed for solo keyboard b ...
'', introducing them with preludes of his own. In a letter to his sister Nannerl Mozart, dated in Vienna on 20 April 1782, Mozart recognizes that he had not written anything in this form, but moved by his wife's interest he composed one piece, which is sent with the letter. He begs her 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 (Mozart), Symphony No. 41. The parts of the Requiem (Mozart), 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).


Beethoven

Ludwig van Beethoven Ludwig van Beethoven (, ; baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classi ...

Ludwig van Beethoven
was familiar with fugal writing from childhood, as an important part of his training was playing from ''
The Well-Tempered Clavier ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys for keyboard by Johann Sebastian Bach. In th ...
''. 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 ''Symphony No. 3 (Beethoven), 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 Piano Sonata No. 29 (Beethoven), ''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 Sonatas Nos. 4 and 5 (Beethoven)#Sonata No. 5.2C Op. 102.2C No. 2, Cello Sonata, Op. 102 No. 2 is a fugue, and there are fugal passages in the last movements of his Piano Sonatas in Piano Sonata No. 28 (Beethoven), A major, Op. 101 and Piano Sonata No. 31 (Beethoven), 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 (Beethoven), Missa Solemnis'' and all movements of the Symphony No. 9 (Beethoven), Ninth Symphony, except the third. A massive, dissonant fugue forms the finale of his String Quartet No. 13 (Beethoven), 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 No. 14 (Beethoven), 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, 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 ."]


Romantic era

By the beginning of the Romantic music, 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
Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known for instrumental compositions such as the Cello Suites (Bach), Cello Suites and ''Brandenburg Concertos''; keyboard ...

Johann Sebastian Bach
. Johannes Brahms' ''Variations and Fugue on a Theme by Handel'', Op. 24, is a work for solo piano written in 1861. It consists of a set of twenty-five variations and a concluding fugue, all based on a theme from George Frideric Handel's ''Harpsichord Suite No. 1 in B♭ major'', HWV 434. Franz Liszt's Piano Sonata in B minor (Liszt), Piano Sonata in B minor (1853) contains a powerful fugue, demanding incisive virtuosity from its player:] Richard Wagner included several fugues in his opera ''Die Meistersinger von Nürnberg''. Giuseppe Verdi included a whimsical example at the end of his opera ''Falstaff (opera), Falstaff'' and his setting of the Requiem (Verdi), 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 Symphony No. 5 (Bruckner), Symphony No. 5 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 (Mahler), Symphony No. 5 features a "fugue-like" passage early in the movement, though this is not actually an example of a fugue.


20th century

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." ''Schwanda the Bagpiper'' (Czech: Švanda dudák), written in 1926, an opera in two acts (five scenes), with music by Jaromír Weinberger, includes a ''Polka'' followed by a powerful ''Fugue'' based on the Polka theme. Igor Stravinsky also incorporated fugues into his works, including the Symphony of Psalms and the Concerto in E-flat (Dumbarton Oaks), 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.
Dmitri Shostakovich Dmitri Dmitriyevich Shostakovich, , group=n (9 August 1975) was a Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a socialist state A socialist state, socialist republic, or socialist count ...
's 24 Preludes and Fugues (Shostakovich), 24 Preludes and Fugues is the composer's homage to Bach's two volumes of
The Well-Tempered Clavier ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys for keyboard by Johann Sebastian Bach. In th ...
. In the first movement of his Symphony No. 4 (Shostakovich), Fourth Symphony, starting at rehearsal mark 63, is a gigantic fugue in which the 20-bar subject (and tonal answer) consist entirely of semiquavers, played at the speed of quaver = 168. Olivier Messiaen, writing about his ''Vingt regards sur l'enfant-Jésus'' (1944) wrote of the sixth piece of that collection, "''Par Lui tout a été fait''" ("By Him were all things made"): György Ligeti wrote a five-part double fugue for his ''Requiems second movement, the Kyrie, in which each part (SMATB) is subdivided in four-voice "bundles" that make a canon (music), canon. The melodic material in this fugue is totally Diatonic and chromatic, 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 Benjamin Britten used a fugue in the final part of ''The Young Person's Guide to the Orchestra'' (1946). The Henry Purcell theme is triumphantly cited at the end, making it a choral fugue. Canadian pianist and musical thinker 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.


Outside classical music

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 (album), Concorde'' composed by John Lewis (pianist), 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 racing, horse race. In "West Side Story", the dance sequence following the song "Cool" is structured as a fugue. Interestingly, Leonard Bernstein quotes Beethoven's monumental "Grosse Fugue" for string quartet and employs Arnold Schoenberg's twelve tone technique, all in the context of a jazz infused Broadway show stopper. A few examples also exist within progressive rock, such as the central movement of "Trilogy (Emerson, Lake & Palmer album)#Track listing, The Endless Enigma" by Emerson, Lake & Palmer and "Free Hand#Track listing, On Reflection" by Gentle Giant. On their EP of the same name, Vulfpeck has a composition called "Fugue State", which incorporates a fugue between Theo Katzman (guitar), Joe Dart (bass), and Woody Goss (Wurlitzer keyboard). The composer Matyas Seiber included an atonal or twelve-tone fugue, for flute trumpet and string quartet, in his score for the 1953 film ''Graham Sutherland'' The film composer John Williams includes a fugue in his score for the 1990 film, ''Home Alone'', at the point where Kevin, accidentally left at home by his family, and realizing he is about to be attacked by a pair of bumbling burglars, begins to plan his elaborate defenses. Another fugue occurs at a similar point in the 1992 sequel film, ''Home Alone 2: Lost in New York''. The jazz composer and film composer, Michel Legrand, includes a fugue as the climax of his score (a classical theme with variations, and fugue) for Joseph Losey's 1972 film ''The Go-Between'', based on the 1953 novel by British novelist, L.P. Hartley.


Discussion


Musical form or texture

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. Although certain closely related key, 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 1 of the ''Well Tempered Clavier'' explores the relative minor, the
supertonic In music, the supertonic is the second Degree (music), degree () of a diatonic scale, one Steps and skips, step above the Tonic (music), tonic. In the Solfège#Movable do solf%C3%A8ge, movable do solfège system, the supertonic note is sung as ''re ...
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.


Perceptions and aesthetics

The 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:


References


Sources

* * * * * * * * * *


Further reading

* *


External links

* Downloadabl
PDFs
of
Well-Tempered Clavier ''The Well-Tempered Clavier'', Bach-Werke-Verzeichnis, BWV 846–893, is a collection of two sets of Prelude and fugue, preludes and fugues in Music written in all major and/or minor keys, all 24 major and minor keys, composed for solo keyboard b ...
on Mutopia
Fugues of the Well-Tempered Clavier
(viewable in Adob

o






Analyses of J.S. Bach's ''Well-Tempered Clavier'' with accompanying recordings
*
Video Visualization of Bach's "Little" Fugue in G minor, OrganAnalyses of J. S. Bach's Fugue for Solo Violin in C major BWV 1005 (Tutorial video with score)
{{Authority control Fugues, Polyphonic form Classical music styles