Fugue
Overview
 
In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, a fugue (icon ) is a compositional technique
Musical composition
Musical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...

 (in classical music) in two or more voices, built on a subject (theme) that is introduced at the beginning in imitation
Imitation (music)
In music, imitation is when a melody in a polyphonic texture is repeated shortly after its first appearance in a different voice, usually at a different pitch. The melody may vary through transposition, inversion, or otherwise, but retain its original character...

 (repetition at different pitches) and recurs frequently in the course of the composition.

The English term fugue originated in the 16th century and is derived from either the French word fugue or the Italian fuga.
Encyclopedia
In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, a fugue (icon ) is a compositional technique
Musical composition
Musical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...

 (in classical music) in two or more voices, built on a subject (theme) that is introduced at the beginning in imitation
Imitation (music)
In music, imitation is when a melody in a polyphonic texture is repeated shortly after its first appearance in a different voice, usually at a different pitch. The melody may vary through transposition, inversion, or otherwise, but retain its original character...

 (repetition at different pitches) and recurs frequently in the course of the composition.

The English term fugue originated in the 16th century and is derived from either the French word fugue or the Italian fuga. This in turn comes from Latin, also fuga, which is itself related to both fugere (‘to flee’) and fugare, (‘to chase’). 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 usually has three sections: an exposition, a development, and a recapitulation containing the return of the subject in the fugue's tonic
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

 key, though not all fugues have a recapitulation. In the Middle Ages
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...

, the term was widely used to denote any works in canonic
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

 style; by the Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...

, 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
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

, which is often followed by closing material, the coda
Coda (music)
Coda is a term used in music in a number of different senses, primarily to designate a passage that brings a piece to an end. Technically, it is an expanded cadence...

. 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
Ricercar
A ricercar is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many ricercars serve a preludial function to "search out" the key or mode of a following piece...

s, capriccios
Capriccio (music)
A capriccio or caprice , is a piece of music, usually fairly free in form and of a lively character...

, canzona
Canzona
In the 16th century an instrumental chanson; later, a piece for ensemble in several sections or tempos...

s, and fantasias
Fantasia (music)
The fantasia is a musical composition with its roots in the art of improvisation. Because of this, it seldom approximates the textbook rules of any strict musical form ....

. The famous fugue composer Johann Sebastian Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

 (1685-1750) shaped his own works after those of Johann Jakob Froberger
Johann Jakob Froberger
Johann Jakob Froberger was a German Baroque composer, keyboard virtuoso, and organist. He was among the most famous composers of the era and influenced practically every major composer in Europe by developing the genre of keyboard suite and contributing greatly to the exchange of musical...

 (1616–1667), Johann Pachelbel
Johann Pachelbel
Johann Pachelbel was a German Baroque composer, organist and teacher, who brought the south German organ tradition to its peak. He composed a large body of sacred and secular music, and his contributions to the development of the chorale prelude and fugue have earned him a place among the most...

 (1653–1706), Girolamo Frescobaldi
Girolamo Frescobaldi
Girolamo Frescobaldi was a musician from Ferrara, one of the most important composers of keyboard music in the late Renaissance and early Baroque periods. A child prodigy, Frescobaldi studied under Luzzasco Luzzaschi in Ferrara, but was influenced by a large number of composers, including Ascanio...

 (1583–1643), Dieterich Buxtehude
Dieterich Buxtehude
Dieterich Buxtehude was a German-Danish organist and composer of the Baroque period. His organ works represent a central part of the standard organ repertoire and are frequently performed at recitals and in church services...

 (c. 1637–1707), and other composers. With the decline of sophisticated styles at the end of the baroque period, the fugue's popularity waned, eventually giving way to sonata form
Sonata
Sonata , in music, literally means a piece played as opposed to a cantata , a piece sung. The term, being vague, naturally evolved through the history of music, designating a variety of forms prior to the Classical era...

. Nevertheless, composers from the 1750s to the present day continue to write and study fugues for various purposes; they appear in the works of Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...

 (1756-1791) and Ludwig van Beethoven
Ludwig van Beethoven
Ludwig van Beethoven was a German composer and pianist. A crucial figure in the transition between the Classical and Romantic eras in Western art music, he remains one of the most famous and influential composers of all time.Born in Bonn, then the capital of the Electorate of Cologne and part of...

 (1770–1827). Many composers such as Felix Mendelssohn
Felix Mendelssohn
Jakob Ludwig Felix Mendelssohn Barthóldy , use the form 'Mendelssohn' and not 'Mendelssohn Bartholdy'. The Grove Dictionary of Music and Musicians gives ' Felix Mendelssohn' as the entry, with 'Mendelssohn' used in the body text...

 (1809–1847), Anton Reicha
Anton Reicha
Anton Reicha was a Czech-born, later naturalized French composer. A contemporary and lifelong friend of Beethoven, Reicha is now best remembered for his substantial early contribution to the wind quintet literature and his role as a teacher – his pupils included Franz Liszt and Hector Berlioz...

 (1770–1836) and Dmitri Shostakovich
Dmitri Shostakovich
Dmitri Dmitriyevich Shostakovich was a Soviet Russian composer and one of the most celebrated composers of the 20th century....

 (1906–1975) wrote cycles of fugues.

Musical outline

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

What follows is a chart displaying a fairly typical fugal outline, and an explanation of the processes involved in creating this structure.
Example of Key/Entry Structure, in a Three-Voice Baroque Fugue
Exposition 1st Middle-Entry 2nd Middle-Entry Final Entries in Tonic
Tonic Dom. T (D-redundant entry) Relative Maj/Min Dom. of Rel. Subdom. T T
Sop. Subj. CS1 C
O
D
E
T
T
A
CS² A E
P
I
S
O
D
E
CS1 CS² E
P
I
S
O
D
E
S E
P
I
S
O
D
E
CS1 Free Counterpoint C
O
D
A
Alto Ans. CS1 CS² S CS1 CS² S CS1
Bass S CS1 CS² A CS1 CS² S

The exposition

A fugue begins with the exposition of its subject in one of the voices alone in the tonic
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

 key. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another (often closely related) key, which is known as the answer. To make the music run smoothly, it may also have to be altered slightly. When the answer is an exact copy of the subject to the dominant, it is classified as a real answer; if it has to be altered in any way it is a tonal answer.
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 (music)
In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...

, 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 or double counterpoint. In tonal
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...

 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 the Well-Tempered Clavier, Book 1 by J. S. Bach. A brief codetta is often heard connecting the various statements of the subject and answer. This allows the music to run smoothly. The codetta, just as the other parts of the exposition, can be used throughout the rest of the fugue.

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
Quarter note
A quarter note or crotchet is a note played for one quarter of the duration of a whole note . Often people will say that a crotchet is one beat, however, this is not always correct, as the beat is indicated by the time signature of the music; a quarter note may or may not be the beat...

 (or crotchet) B-flat of the third beat of the second bar which harmonizes the opening G of the answer. The later codettas may be considerably longer, and often serve to (a) develop the material heard so far in the subject/answer and countersubject and possibly introduce ideas heard in the second countersubject or free counterpoint that follows (b) delay, and therefore heighten the impact of the reentry of the subject in another voice as well as modulating back to the tonic.

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). Opening with the subject stated in the bass, while unusual, is to be preferred when other actions would present illegal inversions in the exposition.

The episode

Further entries of the subject follow this initial exposition, either immediately (as for example in Fugue No. 1 in C major, BWV 846 of the Well-Tempered Clavier), or separated by episodes. Episodic material is always modulatory and is usually based upon some element heard in the exposition. Each episode has primarily the 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. Gédalge states that the episode of the fugue is generally based on a series of imitations of the subject that have been fragmented.

The development

Further entries of the subject, or middle entries, occur throughout the fugue, must state the subject or answer at least once in its entirety, and may also be heard in combination with the countersubject(s) from the exposition, new countersubjects, free counterpoint or any of these in combination. It is uncommon for the subject to enter alone in a single voice in the middle-entries just as it is in the exposition; rather it is usually heard with at least one of the countersubjects and/or other free contrapuntal accompaniments. Middle-entries tend to occur at pitches other than the initial—as shown in the typical structure above, these are often closely related keys such as the relative dominant and subdominant, but key structure of fugues varies greatly. In the fugues of J. S. Bach the first middle-entry very commonly occurs in the relative major or minor of the work's overall key, and is followed by an entry the dominant of the relative major or minor when the fugue's subject requires a tonal answer. In the fugues of earlier composers (notably Buxtehude
Dieterich Buxtehude
Dieterich Buxtehude was a German-Danish organist and composer of the Baroque period. His organ works represent a central part of the standard organ repertoire and are frequently performed at recitals and in church services...

 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
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

, retrograde
Permutation (music)
In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...

 (a less common form where the entire subject is heard back-to-front) and diminution
Diminution
In Western music and music theory, diminution has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values...

 (the reduction of the subject's rhythmic values by a certain factor), augmentation
Augmentation (music)
In Western music and music theory, the word augmentation has three distinct meanings. Augmentation is a compositional device where a melody, theme or motif is presented in longer note-values than were previously used...

 (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 J. S. Bach's
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

 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
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

 at the fourth. Arrival in E-flat major is marked by a quasi perfect cadence across the barline, from the last quarter note beat of the first bar to the first beat of the second bar in the second system, and the first middle entry. Here Bach has altered countersubject 2 to accommodate the change of mode.

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
Stretto
The term stretto comes from the Italian past participle of stringere, and means "narrow", "tight", or "close".In music the Italian term stretto has two distinct meanings:...

,
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 Bach's Mass in B Minor). In general, fugues that are densely strettoed will not contain countersubjects, and vice versa. One notable exception is the E Major fugue from Bach's Well-Tempered Clavier, Book II, which initially exposes the subject accompanied by its countersubject, followed by counterexposition of the two ideas, separated in time, and each in stretto with itself.

Final entries and coda

The closing section of a fugue often includes one or two counter-expositions, and possibly a stretto, in the tonic
Tonic (music)
In music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...

; sometimes over a tonic or dominant pedal note
Pedal point
In tonal music, a pedal point is a sustained tone, typically in the bass, during which at least one foreign, i.e., dissonant harmony is sounded in the other parts. A pedal point sometimes functions as a "non-chord tone", placing it in the categories alongside suspensions, retardations, and passing...

. Any material that follows the final entry of the subject is considered to be the final coda and is normally cadential
Cadence (music)
In Western musical theory, a cadence is, "a melodic or harmonic configuration that creates a sense of repose or resolution [finality or pause]." A harmonic cadence is a progression of two chords that concludes a phrase, section, or piece of music...

.

Double (triple, quadruple) fugue

A double fugue has two subjects that are often developed simultaneously; similarly, it follows that a triple fugue has three subjects. 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
Kyrie
Kyrie, a transliteration of Greek κύριε , vocative case of κύριος , meaning "Lord", is the common name of an important prayer of Christian liturgy, which is also called the Kýrie, eléison ....

 of Mozart’s
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...

 Requiem in D minor
Requiem (Mozart)
The Requiem Mass in D minor by Wolfgang Amadeus Mozart was composed in Vienna in 1791 and left unfinished at the composer's death. A completion by Franz Xaver Süssmayr was delivered to Count Franz von Walsegg, who had anonymously commissioned the piece for a requiem Mass to commemorate the...

), and (b) a fugue in which the second subject has its own exposition at some later point, and the two subjects are not combined until later (see for example, fugue no. 14 in f-sharp minor from Bach’s Well-Tempered Clavier Book 2, or more famously, Bach's "St. Anne" Fugue in E-flat major, BWV 552.)

Counter-fugue

A counter-fugue is a fugue in which the first answer is presented as the subject in inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

, 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
The Art of Fugue , BWV 1080, is an incomplete work by Johann Sebastian Bach . It was most likely started at the beginning of the 1740s, if not earlier. The first known surviving version, which contained 12 fugues and 2 canons, was copied by the composer in 1745...

.

Permutation 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. Each voice takes this pattern and states all the subjects/themes in the same order (and repeats the material when all the themes have been stated, sometimes after a rest). There is usually very little non-structural/thematic material. During the course of a permutation fugue, it is quite uncommon, actually, for every single possible voice-combination (or 'permutation') of the themes to be heard. This limitation exists in consequence of sheer proportionality: the more voices in a fugue, the greater the amount of possible permutations. In consequence, composers exercise editorial judgment as to the most musical of permutations and processes leading thereto. One example of permutation fugue can be seen in the opening chorus of Bach’s cantata, Himmelskönig, sei willkommen, BWV182.

Permutation fugues differ from conventional fugue in that there are no connecting episodes, nor statement of the themes in related keys. The fugue of Passacaglia and Fugue in C minor, BWV 582
Passacaglia and Fugue in C minor, BWV 582
Passacaglia and Fugue in C minor 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...

 is unusual in this sense, since it does have episodes between permutation expositions.

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

Fughetta

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

Middle Ages and Renaissance Period

The term fuga was used as far back as the Middle Ages, but was initially used to refer to any kind of imitative counterpoint, including canons
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

, 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. 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
Improvisation
Improvisation is the practice of acting, singing, talking and reacting, of making and creating, in the moment and in response to the stimulus of one's immediate environment and inner feelings. This can result in the invention of new thought patterns, new practices, new structures or symbols, and/or...

, but by the 1550s, it was considered a technique of composition. The Renaissance
Renaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...

 composer Giovanni Pierluigi da Palestrina
Giovanni Pierluigi da Palestrina
Giovanni Pierluigi da Palestrina was an Italian Renaissance composer of sacred music and the best-known 16th-century representative of the Roman School of musical composition...

 (1525?-1594) wrote masses using modal
Musical mode
In the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...

 counterpoint and imitation, and fugal writing became the basis for writing motet
Motet
In classical music, motet is a word that is applied to a number of highly varied choral musical compositions.-Etymology:The name comes either from the Latin movere, or a Latinized version of Old French mot, "word" or "verbal utterance." The Medieval Latin for "motet" is motectum, and the Italian...

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
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

 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
Jan Pieterszoon Sweelinck
Jan Pieterszoon Sweelinck was a Dutch composer, organist, and pedagogue whose work straddled the end of the Renaissance and beginning of the Baroque eras. He was among the first major keyboard composers of Europe, and his work as a teacher helped establish the north German organ...

, Girolamo Frescobaldi
Girolamo Frescobaldi
Girolamo Frescobaldi was a musician from Ferrara, one of the most important composers of keyboard music in the late Renaissance and early Baroque periods. A child prodigy, Frescobaldi studied under Luzzasco Luzzaschi in Ferrara, but was influenced by a large number of composers, including Ascanio...

, Johann Jakob Froberger
Johann Jakob Froberger
Johann Jakob Froberger was a German Baroque composer, keyboard virtuoso, and organist. He was among the most famous composers of the era and influenced practically every major composer in Europe by developing the genre of keyboard suite and contributing greatly to the exchange of musical...

 and Dieterich Buxtehude
Dieterich Buxtehude
Dieterich Buxtehude was a German-Danish organist and composer of the Baroque period. His organ works represent a central part of the standard organ repertoire and are frequently performed at recitals and in church services...

 all wrote fugues, and George Frideric Handel
George Frideric Handel
George Frideric Handel was a German-British Baroque composer, famous for his operas, oratorios, anthems and organ concertos. Handel was born in 1685, in a family indifferent to music...

 included them in many of his oratorio
Oratorio
An oratorio is a large musical composition including an orchestra, a choir, and soloists. Like an opera, an oratorio includes the use of a choir, soloists, an ensemble, various distinguishable characters, and arias...

s. Keyboard suite
Suite
In music, a suite is an ordered set of instrumental or orchestral pieces normally performed in a concert setting rather than as accompaniment; they may be extracts from an opera, ballet , or incidental music to a play or film , or they may be entirely original movements .In the...

s from this time often conclude with a fugal gigue
Gigue
The gigue or giga is a lively baroque dance originating from the British jig. It was imported into France in the mid-17th century and usually appears at the end of a suite...

. The French overture
French overture
The French overture is a musical form widely used in the Baroque period. Its basic formal division is into two parts, which are usually enclosed by double bars and repeat signs. They are complementary in styles , and the first ends with a half-cadence that requires an answering structure with a...

 featured a quick fugal section after a slow introduction. The second movement of a sonata da chiesa
Sonata da chiesa
Sonata da chiesa is an instrumental composition dating from the Baroque period, generally consisting of four movements. More than one melody was often used, and the movements were ordered slow–fast–slow–fast with respect to tempo...

, as written by Arcangelo Corelli
Arcangelo Corelli
Arcangelo Corelli was an Italian violinist and composer of Baroque music.-Biography:Corelli was born at Fusignano, in the current-day province of Ravenna, although at the time it was in the province of Ferrara. Little is known about his early life...

 and others, was usually fugal.

The Baroque period also saw a rise in the importance of music theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...

. Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students. The most influential text was published by Johann Joseph Fux (1660–1741), his Gradus Ad Parnassum ("Steps to Parnassus"), which appeared in 1725. This work laid out the terms of "species" of counterpoint, and offered a series of exercises to learn fugue writing. Fux's work was largely based on the practice of Palestrina's modal fugues. It remained influential into the nineteenth century. Haydn
Joseph Haydn
Franz Joseph Haydn , known as Joseph Haydn , was an Austrian composer, one of the most prolific and prominent composers of the Classical period. He is often called the "Father of the Symphony" and "Father of the String Quartet" because of his important contributions to these forms...

, for example, taught counterpoint from his own summary of Fux, and thought of it as the basis for formal structure.

Johann Sebastian Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

 often entered into contests where he would be given a subject with which to spontaneously improvise
Improvisation
Improvisation is the practice of acting, singing, talking and reacting, of making and creating, in the moment and in response to the stimulus of one's immediate environment and inner feelings. This can result in the invention of new thought patterns, new practices, new structures or symbols, and/or...

 a fugue on the organ
Organ (music)
The organ , is a keyboard instrument of one or more divisions, each played with its own keyboard operated either with the hands or with the feet. The organ is a relatively old musical instrument in the Western musical tradition, dating from the time of Ctesibius of Alexandria who is credited with...

 or harpsichord
Harpsichord
A harpsichord is a musical instrument played by means of a keyboard. It produces sound by plucking a string when a key is pressed.In the narrow sense, "harpsichord" designates only the large wing-shaped instruments in which the strings are perpendicular to the keyboard...

. This musical form was also apparent in chamber music he would later compose for Weimar; the famous Concerto for Two Violins in D Minor
Double Violin Concerto (Bach)
The Concerto for 2 Violins, Strings and Continuo in D Minor, BWV 1043, also known as the Double Violin Concerto or "Bach Double", is perhaps one of the most famous works by J. S. Bach and considered among the best examples of the work of the late Baroque period. Bach wrote it between 1730 and 1731...

(BWV 1043) (although not contrapuntal in its entirety) has a fugal opening section to its first movement.

Bach's most famous fugues are those for the harpsichord in The Well-Tempered Clavier
The Well-Tempered Clavier
The Well-Tempered Clavier , BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach...

, 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
Prelude (music)
A prelude is a short piece of music, the form of which may vary from piece to piece. The prelude can be thought of as a preface. It may stand on its own or introduce another work...

 or toccata
Toccata
Toccata is a virtuoso piece of music typically for a keyboard or plucked string instrument featuring fast-moving, lightly fingered or otherwise virtuosic passages or sections, with or without imitative or fugal interludes, generally emphasizing the dexterity of the performer's fingers...

. The Art of Fugue is a collection of fugues (and four canons
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

) on a single theme that is gradually transformed as the cycle progresses. Bach also wrote smaller single fugues, and put fugues into many of his works that were not fugues per se.

Although J. S. Bach was not well known as a composer in his lifetime, his influence extended forward through his son C.P.E. Bach
Carl Philipp Emanuel Bach
right|250pxCarl Philipp Emanuel Bach was a German Classical period musician and composer, the fifth child and second son of Johann Sebastian Bach and Maria Barbara Bach...

 and through the theorist Friedrich Wilhelm Marpurg
Friedrich Wilhelm Marpurg
Friedrich Wilhelm Marpurg was a German music critic, music-theorist and composer. He was friendly and active with many figures of the Enlightenment of the 18th century.-Life:...

 (1718–1795) whose Abhandlung von der Fuge ("Treatise on the fugue", 1753) was largely based on J. S. Bach's work.

Classical era

During the Classical era, the fugue was no longer a central or even fully natural mode of musical composition. Nevertheless, both Haydn
Joseph Haydn
Franz Joseph Haydn , known as Joseph Haydn , was an Austrian composer, one of the most prolific and prominent composers of the Classical period. He is often called the "Father of the Symphony" and "Father of the String Quartet" because of his important contributions to these forms...

 and Mozart
Wolfgang Amadeus Mozart
Wolfgang Amadeus Mozart , baptismal name Johannes Chrysostomus Wolfgangus Theophilus Mozart , was a prolific and influential composer of the Classical era. He composed over 600 works, many acknowledged as pinnacles of symphonic, concertante, chamber, piano, operatic, and choral music...

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

Haydn was the leader of fugal composition and technique in the Classical era. Haydn's most famous fugues can be found in his Sun quartets
String Quartets, Op. 20 (Haydn)
The six string quartets opus 20 by Joseph Haydn are among the works that earned Haydn the sobriquet "the father of the string quartet." The quartets are considered a milestone in the history of composition; in them, Haydn develops compositional techniques that were to define the medium for the next...

 (op. 20, 1772), of which three have fugal finales. This was a practice that Haydn repeated only once later in his quartet-writing career, with the finale of his quartet op. 50 no. 4 (1787). Some of the earliest examples of Haydn's use of counterpoint, however, are in three symphonies (No. 3
Symphony No. 3 (Haydn)
Joseph Haydn's Symphony No. 3 in G major, Hoboken I/3, is believed to have been written between 1760 and 1762.It is scored for 2 oboes, bassoon, 2 horns, strings and continuo...

, No. 13
Symphony No. 13 (Haydn)
Joseph Haydn's Symphony No. 13 in D major was written in 1763 for the orchestra of Haydn's patron, Prince Nikolaus Esterházy, in Eisenstadt.The work can be precisely dated thanks to a dated score in Haydn's own hand in the National Library of Budapest. Two other Haydn symphonies are known to have...

, and No. 40
Symphony No. 40 (Haydn)
The Symphony No. 40 in F major, Hoboken I/40, is a symphony by Joseph Haydn. Despite its number, Haydn had composed this symphony by 1763, long before the other symphonies numbered in the 30s and 40s in Hoboken's catalog Chronologically, the symphony belongs with no...

) 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 oratorio
Oratorio
An oratorio is a large musical composition including an orchestra, a choir, and soloists. Like an opera, an oratorio includes the use of a choir, soloists, an ensemble, various distinguishable characters, and arias...

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 and The Seasons
The Seasons (Haydn)
The Seasons is an oratorio by Joseph Haydn .-Composition, premiere, and reception:Haydn was led to write The Seasons by the great success of his previous oratorio The Creation , which had become very popular and was in the course of being performed all over Europe...

,
as well as several of his later symphonies, including No. 88
Symphony No. 88 (Haydn)
The Symphony No. 88 in G major was written by Joseph Haydn. It is occasionally referred to as The Letter V referring to an older method of cataloguing Haydn's symphonic output.The symphony was completed in 1787...

, No. 95
Symphony No. 95 (Haydn)
The Symphony No. 95 in C minor is the third of the so-called twelve London symphonies written by Joseph Haydn. It is the only one of the twelve London symphonies in a minor key....

, and No. 101
Symphony No. 101 (Haydn)
The Symphony No. 101 in D major is the ninth of the twelve so-called London Symphonies written by Joseph Haydn. It is popularly known as The Clock because of the "ticking" rhythm throughout the second movement....

.

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
Gottfried van Swieten
Gottfried, Freiherr van Swieten was a diplomat, librarian, and government official who served the Austrian Empire during the 18th century...

 in Vienna around 1782. Van Swieten, during diplomatic service in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...

, had taken the opportunity to collect as many manuscripts by Bach and Handel as he could, and he invited Mozart to study his collection and also encouraged him to transcribe various works for other combinations of instruments. Mozart was evidently fascinated by these works, and wrote a set of transcriptions for string trio of fugues from Bach's Well-Tempered Clavier, introducing them with preludes of his own. Mozart then set to writing fugues on his own, mimicking the Baroque style. These included the fugues for string quartet, K. 405 (1782) and a fugue in C Minor K. 426 for two pianos (1783). Later, Mozart incorporated fugal writing into the finale of his Symphony No. 41
Symphony No. 41 (Mozart)
Wolfgang Amadeus Mozart completed his Symphony No. 41 in C major, K. 551, on 10 August 1788. It was the last symphony that he composed.The work is nicknamed the Jupiter Symphony...

and his opera Die Zauberflöte. The parts of the Requiem
Requiem (Mozart)
The Requiem Mass in D minor by Wolfgang Amadeus Mozart was composed in Vienna in 1791 and left unfinished at the composer's death. A completion by Franz Xaver Süssmayr was delivered to Count Franz von Walsegg, who had anonymously commissioned the piece for a requiem Mass to commemorate the...

 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
Amen
The word amen is a declaration of affirmation found in the Hebrew Bible and New Testament. Its use in Judaism dates back to its earliest texts. It has been generally adopted in Christian worship as a concluding word for prayers and hymns. In Islam, it is the standard ending to Dua and the...

 fugue which, some believe, would have come at the end of the Sequentia).

A common characteristic of the Classical composers is that they usually wrote fugues not as isolated works but as part of a larger work, often as a sonata-form development section or as a finale. It was also characteristic to abandon fugal texture just before the end of a work, providing a purely homophonic resolution. This is found, for instance, in the final fugue of the chorus "The Heavens are Telling" in Haydn's The Creation (1798).
Ludwig van Beethoven
Ludwig van Beethoven
Ludwig van Beethoven was a German composer and pianist. A crucial figure in the transition between the Classical and Romantic eras in Western art music, he remains one of the most famous and influential composers of all time.Born in Bonn, then the capital of the Electorate of Cologne and part of...

 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
The Well-Tempered Clavier , BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach...

. During his early career in Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...

, 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
Symphony No. 3 (Beethoven)
Ludwig van Beethoven's Symphony No. 3 in E flat major , also known as the Eroica , is a landmark musical work marking the full arrival of the composer's "middle-period," a series of unprecedented large scale works of emotional depth and structural rigor.The symphony is widely regarded as a mature...

(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." A massive, dissonant fugue forms the finale of his String Quartet, Op. 130
String Quartet No. 13 (Beethoven)
The String Quartet No. 13 in B major, op. 130, by Ludwig van Beethoven was completed in November 1825. The number traditionally assigned to it is based on the order of its publication; it is actually the fourteenth quartet in order of composition. It was premiered in March 1826 by the Schuppanzigh...

 (1825); the latter was later published separately as Op. 133, the Große Fuge
Große Fuge
The Große Fuge , Op. 133, is a single-movement composition for string quartet by Ludwig van Beethoven. A massive double fugue, it originally served as the final movement of his Quartet No. 13 in B major but he replaced it with a new finale and published it separately in 1827 as Op...

("Great Fugue"). His Cello Sonata, Op. 102,2 have fugue movements. Fugues are also found in the Missa Solemnis
Missa Solemnis (Beethoven)
The Missa solemnis in D Major, Op. 123 was composed by Ludwig van Beethoven from 1819-1823. It was first performed on April 7, 1824 in St. Petersburg, under the auspices of Beethoven's patron Prince Nikolai Galitzin; an incomplete performance was given in Vienna on 7 May 1824, when the Kyrie,...

and in the finale of the Ninth Symphony
Symphony No. 9 (Beethoven)
The Symphony No. 9 in D minor, Op. 125, is the final complete symphony of Ludwig van Beethoven. Completed in 1824, the symphony is one of the best known works of the Western classical repertoire, and has been adapted for use as the European Anthem...

.

Romantic era

By the beginning of the Romantic
Romantic music
Romantic music or music in the Romantic Period is a musicological and artistic term referring to a particular period, theory, compositional practice, and canon in Western music history, from 1810 to 1900....

 era, fugue writing had become specifically attached to the norms and styles of the Baroque.

One manual explicitly stated that the hallmark of contrapuntal style was the style of J. S. Bach. The 19th century's taste for academicism–setting of forms and norms by explicit rules–found Marpurg
Friedrich Wilhelm Marpurg
Friedrich Wilhelm Marpurg was a German music critic, music-theorist and composer. He was friendly and active with many figures of the Enlightenment of the 18th century.-Life:...

, and the fugue, to be a congenial topic. The writing of fugues also remained an important part of musical education throughout the 19th century, particularly with the publication of the complete works of Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

 and Handel
George Frideric Handel
George Frideric Handel was a German-British Baroque composer, famous for his operas, oratorios, anthems and organ concertos. Handel was born in 1685, in a family indifferent to music...

, and the revival of interest in Bach's music.

Examples of fugal writing in the Romantic
Romantic music
Romantic music or music in the Romantic Period is a musicological and artistic term referring to a particular period, theory, compositional practice, and canon in Western music history, from 1810 to 1900....

 era are found in the last movement of Berlioz
Hector Berlioz
Hector Berlioz was a French Romantic composer, best known for his compositions Symphonie fantastique and Grande messe des morts . Berlioz made significant contributions to the modern orchestra with his Treatise on Instrumentation. He specified huge orchestral forces for some of his works; as a...

's Symphonie Fantastique
Symphonie Fantastique
Symphonie Fantastique: Épisode de la vie d'un Artiste...en cinq parties , Op. 14, is a program symphony written by the French composer Hector Berlioz in 1830. It is one of the most important and representative pieces of the early Romantic period, and is still very popular with concert audiences...

, and Wagner
Richard Wagner
Wilhelm Richard Wagner was a German composer, conductor, theatre director, philosopher, music theorist, poet, essayist and writer primarily known for his operas...

's Meistersinger
Die Meistersinger von Nürnberg
Die Meistersinger von Nürnberg is an opera in three acts, written and composed by Richard Wagner. It is among the longest operas still commonly performed today, usually taking around four and a half hours. It was first performed at the Königliches Hof- und National-Theater in Munich, on June 21,...

, in particular the triple fugue at the conclusion of the second act. The finale of Giuseppe Verdi
Giuseppe Verdi
Giuseppe Fortunino Francesco Verdi was an Italian Romantic composer, mainly of opera. He was one of the most influential composers of the 19th century...

's opera Falstaff
Falstaff (opera)
Falstaff is an operatic commedia lirica in three acts by Giuseppe Verdi, adapted by Arrigo Boito from Shakespeare's plays The Merry Wives of Windsor and scenes from Henry IV. It was Verdi's last opera, written in the composer's ninth decade, and only the second of his 26 operas to be a comedy...

is a ten-voice fugue. Felix Mendelssohn
Felix Mendelssohn
Jakob Ludwig Felix Mendelssohn Barthóldy , use the form 'Mendelssohn' and not 'Mendelssohn Bartholdy'. The Grove Dictionary of Music and Musicians gives ' Felix Mendelssohn' as the entry, with 'Mendelssohn' used in the body text...

 was obsessed with fugal writing, as it can be found prominently in the Scottish Symphony, Italian Symphony, and the Hebrides Overture
Hebrides Overture
The Hebrides Overture , Op. 26, also known as Fingal's Cave , is a concert overture composed by Felix Mendelssohn. Written in 1830, the piece was inspired by a cavern known as Fingal's Cave on Staffa, an island in the Hebrides archipelago located off the west coast of Scotland...

. In the last movement of his Fifth Symphony
Symphony No. 5 (Bruckner)
The Symphony No. 5 in B flat major of Anton Bruckner was written in 1875–1876, with a few minor changes over the next few years. It was first performed in public on two pianos by Joseph Schalk and Franz Zottmann on 20 April 1887 at the Bösendorfersaal in Vienna...

Anton Bruckner
Anton Bruckner
Anton Bruckner was an Austrian composer known for his symphonies, masses, and motets. The first are considered emblematic of the final stage of Austro-German Romanticism because of their rich harmonic language, complex polyphony, and considerable length...

 wrote the development section in form of a big double fugue. The unfinished Finale of his Ninth Symphony
Symphony No. 9 (Bruckner)
Anton Bruckner's Symphony No. 9 in D minor is the last Symphony upon which he worked, leaving the last movement incomplete at the time of his death in 1896. The symphony was premiered under Ferdinand Löwe in Vienna in 1903, after Bruckner's death...

has a fugue section, too. Another composer of this time, whose work is strongly influenced by fugal textures, was Felix Draeseke
Felix Draeseke
Felix August Bernhard Draeseke was a composer of the "New German School" admiring Liszt and Richard Wagner. He wrote compositions in most forms including eight operas and stage works, four symphonies, and much vocal and chamber music.-Life:Felix Draeseke was born in the Franconian ducal town of...

. Especially in his church music highly artificial fugues could be found.

Robert Schumann
Robert Schumann
Robert Schumann, sometimes known as Robert Alexander Schumann, was a German composer, aesthete and influential music critic. He is regarded as one of the greatest and most representative composers of the Romantic era....

, and Johannes Brahms
Johannes Brahms
Johannes Brahms was a German composer and pianist, and one of the leading musicians of the Romantic period. Born in Hamburg, Brahms spent much of his professional life in Vienna, Austria, where he was a leader of the musical scene...

 also included fugues in many of their works. Towards the end of the Romantic era, Richard Strauss
Richard Strauss
Richard Georg Strauss was a leading German composer of the late Romantic and early modern eras. He is known for his operas, which include Der Rosenkavalier and Salome; his Lieder, especially his Four Last Songs; and his tone poems and orchestral works, such as Death and Transfiguration, Till...

 included a fugue in his tone poem, Also sprach Zarathustra, to represent the high intelligence of science. Sergei Rachmaninoff
Sergei Rachmaninoff
Sergei Vasilievich Rachmaninoff was a Russian composer, pianist, and conductor. Rachmaninoff is widely considered one of the finest pianists of his day and, as a composer, one of the last great representatives of Romanticism in Russian classical music...

, despite writing in a lush post-romantic idiom, was highly skilled in counterpoint (as is highly evident in his Vespers); a well known fugue occurs in his Symphony No. 2
Symphony No. 2 (Rachmaninoff)
Symphony No. 2 in E minor, Op. 27 is a music piece by Russian composer Sergei Rachmaninoff, created in 1906–07. The premiere was conducted by the composer himself in St. Petersburg on 8 February 1908. Its duration is approximately 60 minutes when performed uncut; cut performances can be as...

. Alexander Glazunov
Alexander Glazunov
Alexander Konstantinovich Glazunov was a Russian composer of the late Russian Romantic period, music teacher and conductor...

 wrote a very difficult Prelude and Fugue in D minor, his Op. 62, for the piano.

20th century

Twentieth-century fugue writing explored many of the directions implied by Beethoven's Große Fuge, and what came to be termed "free counterpoint" as well as "dissonant counterpoint."

The late-Romantic composer Max Reger
Max Reger
Johann Baptist Joseph Maximilian Reger was a German composer, conductor, pianist, organist, and academic teacher.-Life:...

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

A number of other 20th-century composers made extensive use of the fugue. Béla Bartók
Béla Bartók
Béla Viktor János Bartók was a Hungarian composer and pianist. He is considered one of the most important composers of the 20th century and is regarded, along with Liszt, as Hungary's greatest composer...

 opened his Music for Strings, Percussion and Celesta
Music for Strings, Percussion and Celesta
Music for Strings, Percussion and Celesta, Sz. 106, BB 114 is one of the best-known compositions by the Hungarian composer Béla Bartók. Commissioned by Paul Sacher to celebrate the tenth anniversary of the Basel Chamber Orchestra, the score is dated September 7, 1936...

with a fugue based on alternating ascending and descending fifth series. He also included fugal sections in the final movements of his String Quartet No. 1
String Quartet No. 1 (Bartók)
The String Quartet No. 1 in A minor by Béla Bartók was completed in 1909. The score is dated January 27 of that year.The work is in three movements, played without breaks between each:#Lento...

, String Quartet No. 5
String Quartet No. 5 (Bartók)
The String Quartet No. 5 Sz. 102, BB 110 by Béla Bartók was written between August 6 and September 6, 1934.The work is in five movements:#Allegro#Adagio molto#Scherzo: alla bulgarese#Andante#Finale: Allegro vivace...

, Concerto for Orchestra
Concerto for Orchestra (Bartók)
Concerto for Orchestra, Sz. 116, BB 123, is a five-movement musical work for orchestra composed by Béla Bartók in 1943. It is one of his best-known, most popular and most accessible works. The score is inscribed "15 August – 8 October 1943", and it premiered on December 1, 1944 in Boston Symphony...

, and Piano Concerto No. 3
Piano Concerto No. 3 (Bartók)
Béla Bartók's Piano Concerto No. 3 in E major, Sz. 119, BB 127 is a musical composition for piano and orchestra. The piece was composed in 1945 by Hungarian composer Béla Bartók during the final months of his life. It consists of three movements.-Context:...

. The second movement of his Sonata for Solo Violin
Sonata for Solo Violin (Bartók)
The Sonata for Solo Violin Sz. 117, BB 124, is a sonata for unaccompanied violin composed by Béla Bartók. It was premiered by Yehudi Menuhin, to whom it was dedicated, in New York on 26 November, 1944.-Composition:...

is also a fugue. The Czech composer Jaromir Weinberger
Jaromír Weinberger
- Biography :Weinberger was born in Prague, from a family of Jewish origin. He heard Czech folksongs from time spent at his grandparents' farm as a youth. He started to play the piano at age 5, and was composing and conducting by age 10. He began musical studies with Jaroslav Křička. Later teachers...

 studied fugue with Max Reger, and had an uncommonly facile skill in fugal writing. The fugue of the "Polka and Fugue" from his opera "Schwanda the Bagpiper" is an example.

Igor Stravinsky
Igor Stravinsky
Igor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....

 also incorporated fugues into his works, including the Symphony of Psalms
Symphony of Psalms
The Symphony of Psalms by Igor Stravinsky was written in 1930 and was commissioned by Serge Koussevitzky to celebrate the 50th anniversary of the Boston Symphony Orchestra. This piece is a three-movement choral symphony and was composed during Stravinsky's neoclassical period. The symphony derives...

and the Dumbarton Oaks
Concerto in E-flat (Dumbarton Oaks)
Concerto in E-flat , subtitled “Dumbarton Oaks 8-v-1938,” is a chamber concerto by Igor Stravinsky, named for the Dumbarton Oaks estate of Robert Woods Bliss and Mildred Barnes Bliss in Washington, DC, who commissioned it for their thirtieth wedding anniversary...

concerto. Stravinsky recognized the compositional techniques of Bach, and in the second movement of his Symphony of Psalms
Symphony of Psalms
The Symphony of Psalms by Igor Stravinsky was written in 1930 and was commissioned by Serge Koussevitzky to celebrate the 50th anniversary of the Boston Symphony Orchestra. This piece is a three-movement choral symphony and was composed during Stravinsky's neoclassical period. The symphony derives...

, 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.

The practice of writing fugue cycles in the manner of Bach's Well-Tempered Clavier was perpetuated by Paul Hindemith
Paul Hindemith
Paul Hindemith was a German composer, violist, violinist, teacher, music theorist and conductor.- Biography :Born in Hanau, near Frankfurt, Hindemith was taught the violin as a child...

 in his Ludus Tonalis
Ludus Tonalis
Ludus Tonalis , subtitled Kontrapunktische, tonal, und Klaviertechnische Übungen , is a piano work by Paul Hindemith that was composed in 1942 during his stay in the United States.The piece starts with a three-part Praeludium in C resembling Bach's toccatas, and ends with a Postludium...

, Kaikhosru Sorabji
Kaikhosru Shapurji Sorabji
Kaikhosru Shapurji Sorabji was an English composer, music critic, pianist, and writer.-Biography:...

 in a number of his works including Opus clavicembalisticum
Opus Clavicembalisticum
Opus clavicembalisticum is a solo piano piece composed by Kaikhosru Shapurji Sorabji, completed on June 26, 1930.The piece is notable for its length and difficulty: at the time of its completion it was the longest piano piece in existence. Its duration is around four hours, depending on tempo...

, and Dmitri Shostakovich
Dmitri Shostakovich
Dmitri Dmitriyevich Shostakovich was a Soviet Russian composer and one of the most celebrated composers of the 20th century....

 in his Preludes and Fugues
24 Preludes and Fugues (Shostakovich)
The 24 Preludes and Fugues, Op. 87 by Dmitri Shostakovich is a set of 24 piano pieces, one in each of the major and minor keys of the chromatic scale. While the musical style and ideas are Shostakovich's own, it follows the form of Frederic Chopin's Op. 28 preludes.Each piece is in two parts: a...

, Op. 87 (which, like the Well-Tempered Clavier, contains a prelude and fugue in each key, although the order of Shostakovich's pieces follows the cycle of fifths, whereas Bach's progressed chromatically). Several Bachianas Brasileiras
Bachianas Brasileiras
The Bachianas Brasileiras constitute a series of nine suites by the Brazilian composer Heitor Villa-Lobos, written for various combinations of instruments and voices between 1930 and 1945...

 of Heitor Villa-Lobos
Heitor Villa-Lobos
Heitor Villa-Lobos was a Brazilian composer, described as "the single most significant creative figure in 20th-century Brazilian art music". Villa-Lobos has become the best-known and most significant Latin American composer to date. He wrote numerous orchestral, chamber, instrumental and vocal works...

 feature a fugue as one of the movements. Ástor Piazzolla
Ástor Piazzolla
Ástor Pantaleón Piazzolla was an Argentine tango composer and bandoneón player. His oeuvre revolutionized the traditional tango into a new style termed nuevo tango, incorporating elements from jazz and classical music...

 also wrote a number of fugues in his Nuevo tango
Nuevo tango
Tango Nuevo - either a form of music in which new elements are incorporated into traditional Argentine tango, or an evolution of tango dance that began to develop in the 1980s...

 style. György Ligeti
György Ligeti
György Sándor Ligeti was a composer of contemporary classical music. Born in a Hungarian Jewish family in Transylvania, Romania, he briefly lived in Hungary before becoming an Austrian citizen.-Early life:...

 wrote a fugue for his "Requiem’s" (1966) second movement, the Kyrie/Christe, which consists of a 5-part fugue in which each part (S,M,A,T,B) is subsequently divided in four voices that make a canon
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

. The melodic material in this fugue is totally chromatic, with melismatic (running) parts overlaid onto skipping intervals, and use of polyrhythm
Polyrhythm
Polyrhythm is the simultaneous sounding of two or more independent rhythms.Polyrhythm in general is a nonspecific term for the simultaneous occurrence of two or more conflicting rhythms, of which cross-rhythm is a specific and definable subset.—Novotney Polyrhythms can be distinguished from...

 (multiple simulataneous subdivisions of the measure), blurring everything both harmonically and rhythmically so as to create an aural aggregate, thus highlighting the theoretical/aesthetic question of the next section as to whether fugue is a form or a texture.

John Lewis
John Lewis (pianist)
John Aaron Lewis was an American jazz pianist and composer best known as the musical director of the Modern Jazz Quartet.- Early life:...

, pianist and musical director for the American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 jazz
Jazz
Jazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...

 ensemble The Modern Jazz Quartet, used the group as a vehicle to explore the possibilities of fugue in jazz. Examples of Lewis's fugues include "Vendome" (1952), "Concorde" (1955), "Versailles" (1956), and "Three Windows" (1957).

Canadian pianist Glenn Gould
Glenn Gould
Glenn Herbert Gould was a Canadian pianist who became one of the best-known and most celebrated classical pianists of the 20th century. He was particularly renowned as an interpreter of the keyboard music of Johann Sebastian Bach...

 composed So You Want to Write a Fugue?, a full-scale fugue set to a text that cleverly explicates its own musical form.

Is the fugue a musical form or texture?

A widespread view of the fugue is that it is not a musical form (in the sense that, say, sonata form
Sonata form
Sonata form is a large-scale musical structure used widely since the middle of the 18th century . While it is typically used in the first movement of multi-movement pieces, it is sometimes used in subsequent movements as well—particularly the final movement...

 is) but rather a technique of composition. For instance, Donald Francis Tovey
Donald Francis Tovey
Sir Donald Francis Tovey was a British musical analyst, musicologist, writer on music, composer, conductor and pianist...

 wrote that "Fugue is not so much a musical form as a musical texture," that can be introduced anywhere as a distinctive and recognizable technique, often to produce intensification in musical development.

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

The Austrian musicologist Erwin Ratz
Erwin Ratz
Erwin Ratz was an Austrian musicologist and music theorist. He studied musicology with Guido Adler and composition with Arnold Schoenberg and was active in the Schoenberg circle. In the 1920s he worked at the Bauhaus. After World War II he was a professor of musical form and analysis in Vienna...

 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
Closely related key
In music, a closely related key is one sharing many common tones with an original key, as opposed to a distantly related key...

 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
Supertonic
In music or music theory, the supertonic is the second degree or note of a diatonic scale, one step above the tonic. In music theory, the supertonic chord is symbolized by the Roman numeral ii in a major scale, indicating that the chord is a minor chord , or ii in a natural minor scale, indicating...

 and the subdominant
Subdominant
In music, the subdominant is the technical name for the fourth tonal degree of the diatonic scale. It is so called because it is the same distance "below" the tonic as the dominant is above the tonic - in other words, the tonic is the dominant of the subdominant. It is also the note immediately...

. 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
György Ligeti
György Sándor Ligeti was a composer of contemporary classical music. Born in a Hungarian Jewish family in Transylvania, Romania, he briefly lived in Hungary before becoming an Austrian citizen.-Early life:...

’s Requiem, Witold Lutosławski works), use panchromatic or even denser harmonic spectra.

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

Perceptions and aesthetics

Fugue is the most complex of contrapuntal forms. In Ratz's words, "fugal technique significantly burdens the shaping of musical ideas, and it was given only to the greatest geniuses, such as Bach and Beethoven, to breathe life into such an unwieldy form and make it the bearer of the highest thoughts." An indication of this is that in the 19th century Simon Sechter
Simon Sechter
Simon Sechter was an Austrian music theorist, teacher, organist, conductor and composer.Sechter was born in Friedberg , Bohemia, then part of the Austrian Empire, and moved to Vienna in 1804, succeeding Jan Václav Voříšek as court organist there in 1824. In 1810 he began teaching piano and voice...

 composed over 5,000 fugues, but none of them is in today's concert repertoire, while another is the enduring success of the organ fugues of Felix Mendelssohn
Felix Mendelssohn
Jakob Ludwig Felix Mendelssohn Barthóldy , use the form 'Mendelssohn' and not 'Mendelssohn Bartholdy'. The Grove Dictionary of Music and Musicians gives ' Felix Mendelssohn' as the entry, with 'Mendelssohn' used in the body text...

 and Johannes Brahms
Johannes Brahms
Johannes Brahms was a German composer and pianist, and one of the leading musicians of the Romantic period. Born in Hamburg, Brahms spent much of his professional life in Vienna, Austria, where he was a leader of the musical scene...

.

In presenting Bach's fugues as among the greatest of contrapuntal works, Peter Kivy
Peter Kivy
Peter Kivy is a professor of philosophy at Rutgers University. He studies aesthetics and the philosophy of art, particularly the philosophy of music....

 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." Because of the way fugue is often taught, the form can be seen as dry and filled with laborious technical exercises. The term "school fugue" is used for a very strict form of the fugue that was created to facilitate teaching.

Others, such as Alfred Mann
Alfred Mann (musicologist)
Alfred Mann , was a writer in musical theory and Professor Emeritus of Musicology at the Eastman School of Music, University of Rochester.-Biography:...

, argued that fugue writing, by focusing the compositional process actually improves or disciplines the composer towards musical ideas. This is related to the idea that restrictions create freedom for the composer, by directing their efforts. He also points out that fugue writing has its roots in improvisation, and was, during the Renaissance, practiced as an improvisatory art. Writing in 1555, Nicola Vicentino
Nicola Vicentino
Nicola Vicentino was an Italian music theorist and composer of the Renaissance. He was one of the most visionary musicians of the age, inventing, among other things, a microtonal keyboard, and devising a practical system of chromatic writing two hundred years before the rise of equal...

, for example, suggests that

Further reading

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

External links

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