Fugue

In classical music, a fugue (, from Latin , meaning 'flight' or 'escape' ) is a contrapuntal, polyphonic compositional technique in two or more voices, built on a subject (a musical theme) that is

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 the Latin fuga, which is itself related to both fugere (“to flee”) and fugare (“to chase”). Variants include fughetta (“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 and is written according to certain rules. The composer has more freedom once the exposition ends, 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, and often accompanying key changes. The various entries may or may not be separated by episodes or occur in stretto. :: S = subject; A = answer; CS = countersubject; T = tonic; D = dominant Exposition A fugue begins with the exposition of its subject in one of the voices alone in the tonic key. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key (almost always the dominant or subdominant, with the latter being less common), which is known as the answer. To enable a natural harmonic progression, the answer may also be altered slightly (usually by changing one or a few notes near the beginning). When the answer is an exact transposition of the subject into the new key, the answer is classified as a real answer; alternatively, if the intervals of the subject are altered in any way, the answer is a tonal answer. During the answer, the voice in which the subject was previously heard accompanies 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 (two octaves). The distinction is made between the use of free counterpoint and regular countersubjects accompanying the fugue subject/answer, because in order for it to be heard accompanying the subject in more than one instance, the countersubject must be capable of sounding correctly when played above or below the subject, and must be conceived, therefore, in invertible (double) counterpoint. In tonal music, invertible contrapuntal lines must be written according to certain rules, because several intervallic combinations, while acceptable in one orientation, are not permissible when inverted. As an example, perfect fifths are contrapuntally acceptable, while the inversion of a perfect fifth results in a perfect fourth, which, unlike the perfect fifth, is considered a dissonance, requiring proper preparation and resolution. 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. It is customary in the exposition to alternate entrances of the subject (S) with entrances of the answer (A). However, this order is occasionally varied. For example, the exposition from J.S. Bach’s The Well-Tempered Clavier Fugue No. 1 in C Major, BWV 846 uses a SAAS (subject-answer-answer-subject) exposition. A brief codetta is often heard connecting the various statements of the subject and answer, smoothly connecting each and often facilitating the modulation between the tonic and the key of the answer. The codetta, like other parts of the exposition, may be reused throughout the remainder 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 absent or very short. In the example shown above of J.S. Bach’s Fugue No. 16 in G minor, BWV 861, the first codetta is absent. The subject concludes on the quarter note (or crotchet) B of the third beat of the second bar, which harmonizes the opening G of the tonal answer. The later codettas may be considerably longer, and often serve to develop the material heard in the subject/answer and countersubject and possibly introduce ideas heard in the second countersubject or free counterpoint that follows. They may also be present to delay, and therefore heighten the impact of, the reentry of the subject in another voice. Finally, they may be modulatory passages to return the fugue to the tonic. The exposition usually concludes when all voices have given a statement of the subject or answer. In some fugues, especially those with an odd number of voices, the exposition will end with a redundant entry, or an extra presentation of the theme in a voice which has already entered. Furthermore, the entry of one of the voices may not be heard until considerably later. For example, in J.S. Bach’s Fugue in C minor for Organ, BWV 549, the subject entrance in the lowest voice (played by the organ pedals), is not heard until near the end of the fugue.

Episode#

Further entries of the subject may follow the initial exposition either immediately or separated by episodes. André Gedalge, a teacher of Maurice Ravel, stated 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. The development must state the subject or answer at least once in its entirety, and may also be heard in combination with any countersubjects 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; rather, it is usually heard with at least one of the countersubjects and/or other free contrapuntal accompaniments. Middle entries tend to occur at keys other than the tonic. These are often closely related keys such as the relative dominant and subdominant, although the key structure of fugues varies greatly. In the fugues of J.S. Bach, the first middle entry occurs most often in the relative major or minor of the work’s overall key, and is followed by an entry in the dominant of the relative major or minor when the fugue’s subject requires a tonal answer. In the fugues of earlier composers (notably Buxtehude and Pachelbel), middle entries in keys other than the tonic and dominant tend to be the exception, and non-modulation the norm. One famous example 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 it. This is called a counter-exposition, which often uses the inversion of the subject, although the term is sometimes used synonymously with middle entry and may also describe the exposition of completely new subjects, such as those encountered in double fugues. In any of the entries within a fugue, the subject may be altered by inversion, retrograde (where the subject is heard back-to-front), diminution (the reduction of the subject’s rhythmic values by a certain factor), augmentation (the enlargement of the subject’s rhythmic values by a certain factor), or any combination thereof.

Example and analysis#

The excerpt below, bars 7–12 of J.S. Bach’s Fugue No. 2 in C minor, BWV 847, from The Well-Tempered Clavier, Book 1 illustrates the application of most of the characteristics described above. The fugue is for keyboard and in three voices, with regular countersubjects. This excerpt opens at last entry of the exposition: the subject is sounding in the bass, the first countersubject in the treble, while the middle-voice is stating a second version of the second countersubject, which concludes with the characteristic rhythm of the subject, and is always used together with the first version of the second countersubject. Following this, an episode modulates from the tonic to the relative major by means of sequence, in the form of an accompanied canon at the fourth.

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, 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).

Final entries and coda#

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

Simple fugue#

A simple fugue has only one subject, and does not utilize invertible counterpoint.

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 of Mozart’s Requiem in D minor or the fugue of Bach’s Passacaglia and Fugue in C minor, BWV 582), 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, 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 (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. During the Baroque period, counter-fugues were sometimes called by the Latin name fuga contraria. German composer Johann Mattheson coined the term gegenfuge to refer to a counter-fugue construct in his Der vollkommene Capellmeister (1739), and some German-language texts use that name to refer to a counter-fugue.

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. (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.

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.

Mirror fugue#

A mirror fugue is a fugue, or rather two fugues, one of which is the mirror image of the other. It is as though a mirror were placed above or below an existing fugue, producing inversions of each interval in each part, as well as inverting the position of the parts within the texture, so that, for example, the topmost part in one fugue is inverted to produce the lowest part in the other. This is well demonstrated by the two four-part fugues of Contrapunctus 12 in The Art of Fugue. The two three-part fugues of Contrapunctus 13 exhibit a similar relationship to each other, but this cannot strictly be called a mirror fugue, since the position of each inverted part is not itself inverted in the texture, SAB becoming not BAS, but BSA.

Middle Ages and Renaissance#

The term fuga was used as far back as the Middle Ages, but was initially used to refer to any kind of imitative counterpoint, including canons, which are now thought of as distinct from fugues. Prior to the 16th century, fugue was originally a genre. It was not until the 16th century that fugal technique as it is understood today began to be seen in pieces, both instrumental and vocal. Fugal writing is found in works such as fantasias, ricercares and canzonas. “Fugue” as a theoretical term first occurred in 1330 when Jacobus of Liege wrote about the fuga in his Speculum musicae. The fugue arose from the technique of “imitation”, where the same musical material was repeated starting on a different note. Gioseffo Zarlino, a composer, author, and theorist in the Renaissance, was one of the first to distinguish between the two types of imitative counterpoint: fugues and canons (which he called imitations). Palestrina’s imitative motets differed from fugues in that each phrase of the text had a different subject which was introduced and worked out separately, whereas a fugue continued working with the same subject or subjects throughout the entire length of the piece.

Baroque era#

It was in the Baroque period that the writing of fugues became central to composition, in part as a demonstration of compositional expertise. Jan Pieterszoon Sweelinck, Girolamo Frescobaldi, Johann Jakob Froberger and Dieterich Buxtehude all wrote fugues. Fugues were incorporated into a variety of musical genres, and are found in most of George Frideric Handel’s oratorios. Keyboard suites from this time often conclude with a fugal gigue. Domenico Scarlatti has only a few fugues among his corpus of over 500 harpsichord sonatas. The French overture featured a quick fugal section after a slow introduction. The second movement of a sonata da chiesa, as written by Arcangelo Corelli and others, was usually fugal. The Baroque period also saw a rise in the importance of music theory. Some fugues during the Baroque period were pieces designed to teach contrapuntal technique to students. The most influential text was Johann Joseph Fux’s Gradus Ad Parnassum (“Steps to Parnassus”), which appeared in 1725. This work laid out the terms of “species” of counterpoint, and offered a series of exercises to learn fugue writing. Fux’s work was largely based on the practice of Palestrina’s modal fugues. Mozart studied from this book, and it remained influential into the nineteenth century. Haydn, for example, taught counterpoint from his own summary of Fux and thought of it as the basis for formal structure. Bach’s most famous fugues are those for the harpsichord in The Well-Tempered Clavier, which many composers and theorists look at as the greatest model of fugue. The Well-Tempered Clavier comprises two volumes written in different times of Bach’s life, each comprising 24 prelude and fugue pairs, one for each major and minor key. Bach is also known for his organ fugues, which are usually preceded by a prelude or toccata. The Art of Fugue, BWV 1080, is a collection of fugues (and four canons) on a single theme that is gradually transformed as the cycle progresses. Bach also wrote smaller single fugues and put fugal sections or movements into many of his more general works. J.S. Bach’s influence extended forward through his son C.P.E. Bach and through the theorist Friedrich Wilhelm Marpurg (1718–1795) whose Abhandlung von der Fuge (“Treatise on the fugue”, 1753) was largely based on J.S. Bach’s work.

Genre family: Choral music genres