In classical music, a fugue (pronounced /fjuːɡ/, from the Latin word fuga, meaning "flight" or "escape") is a type of composition that uses multiple voices or parts. It is built around a main musical theme called the subject, which is introduced at the beginning and repeated throughout the piece in different pitches. A fugue is not the same as a fuguing tune, a style of song found in early American music, such as shape note or "Sacred Harp" music, and West Gallery music. A fugue typically has three main parts: an exposition, where the subject is introduced in each voice; a development, where the subject is explored in different keys; and a final entry, where the subject returns in the original key. Fugues may also include episodes, which are sections with new musical ideas, stretto, where the subject overlaps in different voices, or a recapitulation. Fugues were widely used during the Baroque era and showed a composer’s skill in harmony and counterpoint, which is the technique of combining multiple independent melodies.

During the Middle Ages, the term "fugue" was used for any music written in a canonic style, where parts imitate each other. By the Renaissance, it referred specifically to music with imitation. Since the 17th century, the term has described the most developed form of imitative counterpoint. Most fugues begin with the subject, which is played in each voice one after another. Once all voices have introduced the subject, the exposition is complete. This is often followed by an episode, a short passage based on the subject, and then the subject is repeated in related keys. Episodes and entries usually alternate until the final return of the subject in the original key, often followed by a coda, which is a concluding section. Because composers have freedom in how they structure a fugue, it is more of a style than a strict form.

The fugue developed in the 18th century from earlier types of music, such as ricercars, capriccios, canzonas, and fantasias. Johann Sebastian Bach, a famous Baroque composer, was influenced by earlier musicians like Jan Pieterszoon Sweelinck, Johann Jakob Froberger, and Dieterich Buxtehude. As the Baroque period ended, the fugue’s importance decreased, and styles like sonata form and the symphony orchestra became more popular. However, composers continued to use fugues in their works, including Wolfgang Amadeus Mozart, Ludwig van Beethoven, and modern composers like Dmitri Shostakovich and Paul Hindemith.

Etymology

The English word "fugue" began to be used in the 16th century. It comes from the French word "fugue" or the Italian word "fuga." These words are based on the Latin word "fuga," which is connected to the Latin verbs "fugere" (meaning "to flee") and "fugare" (meaning "to chase"). The adjective form of "fugue" is "fugal." Other related terms include "fughetta," which means a short fugue, and "fugato," which refers to a section in a musical piece that uses a fugue-like style but is not a full fugue.

Musical outline

A fugue starts with the exposition, which follows specific rules. After the exposition, the composer has more freedom, though a logical key structure is usually followed. Throughout the fugue, the subject appears again, with the same accompanying material, and often with changes in key. These entries may be separated by episodes or occur in stretto.

The exposition begins with the subject played in one voice in the tonic key. After the subject is introduced, a second voice enters with the subject transposed to another key (usually the dominant or subdominant). This is called the answer. To create natural harmonic progressions, the answer may be slightly altered (by changing one or a few notes near the beginning). If the answer is an exact copy of the subject in the new key, it is a real answer. If the intervals are changed, it is a tonal answer.

If the subject starts with a strong dominant note, a tonal answer is often needed. To avoid weakening the fugue’s key, this note is moved up a fourth to the tonic instead of up a fifth to the supertonic. In such cases, the answer may be in the subdominant key.

During the answer, the voice that first played the subject adds new material. If this material is reused later, it is called a countersubject. If it is only heard once, it is called free counterpoint.

Countersubjects are written in invertible counterpoint at the octave or fifteenth (two octaves). This is different from free counterpoint because countersubjects must work well when played above or below the subject. In tonal music, invertible lines must follow rules because some intervals are not allowed when inverted. For example, perfect fifths are acceptable, but their inversion (perfect fourths) are dissonant and require resolution. When the countersubject is played with the answer, it is transposed to match the answer’s pitch. Each voice then plays its own subject or answer, and additional countersubjects or free counterpoint may be heard.

In the exposition, the subject (S) and answer (A) usually alternate. However, this order can vary. For example, in J.S. Bach’s The Well-Tempered Clavier Fugue No. 1 in C Major, BWV 846, the order is SAAS (subject-answer-answer-subject). A brief codetta often connects the subject and answer entries, helping to transition between keys. The first codetta is often short or absent, as the first answer must follow the subject quickly. Later codettas may be longer, developing the subject’s material or introducing new ideas. They may also delay the subject’s return or help return to the tonic key.

The exposition ends when all voices have stated the subject or answer. In some fugues, especially those with an odd number of voices, an extra entry may occur. In others, a voice may enter later. For example, in J.S. Bach’s Fugue in C minor for Organ, BWV 549, the lowest voice (organ pedals) enters near the end.

After the exposition, the subject may reappear immediately or after episodes. Episodes are modulatory and often use ideas from the exposition. They help transition to new keys and provide a break from the strict structure of the exposition. Episodic material is usually based on fragmented imitations of the subject.

Middle entries of the subject occur throughout the fugue. These entries often use the subject or answer with countersubjects from the exposition, new countersubjects, or free counterpoint. Middle entries usually occur in keys other than the tonic, such as the relative dominant or subdominant. In J.S. Bach’s fugues, the first middle entry often appears in the relative major or minor key. Earlier composers like Buxtehude and Pachelbel often avoided modulation, as seen in Buxtehude’s Praeludium in C, BuxWV 137.

When the subject is not entered, the composer may alter it. This is called a counter-exposition and may involve inversion, retrograde, diminution, or augmentation of the subject. These techniques are also used in middle entries or in double fugues with new subjects.

The excerpt from bars 7–12 of J.S. Bach’s Fugue No. 2 in C minor, BWV 847, illustrates many of these characteristics. The fugue is for keyboard and has three voices with regular countersubjects. This excerpt begins with the final entry of the exposition: the subject is in the bass, the first countersubject in the treble, and the middle voice states a second version of the subject.

Types

A simple fugue has only one subject and does not use invertible counterpoint. Invertible counterpoint means that musical lines can be played above or below each other without causing unwanted sounds.

A double fugue has two subjects that are often introduced at the same time. A triple fugue has three subjects. There are two types of double (triple) fugue: (a) a fugue where the second (third) subject is introduced together with the first subject during the exposition, as seen in the Kyrie Eleison from Mozart’s Requiem in D minor or the fugue from Bach’s Passacaglia and Fugue in C minor, BWV 582; and (b) a fugue where each subject has its own separate introduction and is combined later, as in Bach’s Fugue No. 14 in F♯ minor from The Well-Tempered Clavier Book 2 or the famous "St. Anne" Fugue in E♭ major, BWV 552, a triple fugue for organ.

A counter-fugue is a fugue where the first answer to the subject is presented as the subject flipped upside down (inverted). This inverted version of the subject continues to appear 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 fuga contraria in Latin. The term gegenfuge was first used by Johann Mattheson in his book Der vollkommene Capellmeister (1739), and some German texts still use this term to describe a counter-fugue.

A permutation fugue is a type of composition that combines elements of fugue and strict canon. In this structure, each voice enters one after another with the subject, alternating between the tonic and dominant keys. After stating the subject, each voice continues by presenting two or more themes or countersubjects that must be written in invertible counterpoint (so they can be played above or below other themes without creating dissonance). Each voice follows the same order of themes and repeats the material after all themes have been introduced, sometimes after a pause.

There is usually little non-thematic material in a permutation fugue. It is rare for every possible combination of themes (or "permutation") to be heard, as the number of combinations increases with the number of voices. Composers choose which combinations sound most musical. An example of a permutation fugue is the eighth and final chorus of Bach’s cantata Himmelskönig, sei willkommen, BWV 182.

Permutation fugues differ from regular fugues because they lack connecting episodes and do not introduce themes in related keys. For example, the fugue from Bach’s Passacaglia and Fugue in C minor, BWV 582, is not a permutation fugue because it includes episodes between sections. Invertible counterpoint is essential to permutation fugues but not used in simple fugues.

A fughetta is a short fugue that shares the same characteristics as a fugue. The counterpoint may not be as strict, and the structure may be less formal. An example is variation 24 of Beethoven’s Diabelli Variations, Op. 120.

A mirror fugue is a fugue, or two fugues, that are mirror images of each other. One fugue would be like a reflection of the other, with intervals flipped and parts reversed in texture. For example, the topmost part in one fugue becomes the lowest part in the other. This is clearly shown in the two four-part fugues of Contrapunctus 12 from The Art of Fugue. The two three-part fugues in Contrapunctus 13 also share a similar relationship, but they are not strictly mirror fugues because the order of parts is not fully reversed (e.g., SAB becomes BSA, not BAS).

History

The word "fuga" was used as early as the Middle Ages. At first, it described any type of imitative counterpoint, including canons, which are now considered different from fugues. Before the 16th century, fugue was a musical genre. It was not until the 16th century that the techniques of fugues, as understood today, began to appear in music, both for instruments and voices. Fugal writing can be found in works like fantasias, ricercares, and canzonas.

The term "fugue" first appeared as a theoretical idea in 1330 when Jacobus of Liege wrote about "fuga" in his book Speculum musicae. The fugue developed from the technique of "imitation," where the same musical material was repeated starting on a different note.

Gioseffo Zarlino, a Renaissance composer, writer, and theorist, was one of the first to separate fugues and canons (which he called imitations). This distinction helped musicians improvise at first, but by the 1550s, fugues became a formal composition method. The composer Giovanni Pierluigi da Palestrina (1525?–1594) used modal counterpoint and imitation in his masses. Fugal writing later became the foundation for motets. Palestrina’s motets differed from fugues because each phrase of the text had a unique subject introduced separately, while fugues used the same subject throughout the entire piece.

During the Baroque period, fugues became central to composition, often used to show a composer’s skill. Composers like Jan Pieterszoon Sweelinck, Girolamo Frescobaldi, Johann Jakob Froberger, and Dieterich Buxtehude wrote fugues.

Fugues were used in many musical styles. They appear in most of George Frideric Handel’s oratorios. Keyboard suites from this time often ended with a fugal gigue. Domenico Scarlatti wrote only a few fugues among his more than 500 harpsichord sonatas. The French overture included a fast fugal section after a slow introduction. The second movement of a sonata da chiesa, written by Arcangelo Corelli and others, was usually fugal.

The Baroque period also saw more focus on music theory. Some fugues were written to teach students about counterpoint. The most important book was Gradus ad Parnassum ("Steps to Parnassus") by Johann Joseph Fux, published in 1725. This book explained the "species" of counterpoint and provided exercises to learn fugue writing. Fux’s work was based on Palestrina’s modal fugues. Mozart studied this book, and it remained influential until the 19th century. Haydn, for example, taught counterpoint using his own summary of Fux and considered it the basis for musical structure.

Bach’s most famous fugues are in The Well-Tempered Clavier, which many composers and theorists regard as the greatest model of fugue. This work includes two volumes with 24 prelude and fugue pairs, one for each major and minor key. Bach also wrote organ fugues, often preceded by a prelude or toccata. The Art of Fugue, BWV 1080, is a collection of fugues and four canons based on a single theme that changes gradually. Bach also wrote smaller fugues and included fugal sections in many of his works. Bach’s influence continued through his son C.P.E. Bach and the theorist Friedrich Wilhelm Marpurg, whose Treatise on the Fugue (1753) was based on Bach’s work.

During the Classical era, fugues were not as central to composition as they had been before. However, both Haydn and Mozart used fugues in their work at certain times.

Joseph Haydn was a leading figure in fugal composition during the Classical era. His most famous fugues are in his "Sun" Quartets (op. 20, 1772), where three have fugal finales. He used this technique again later in his career with the finale of his String Quartet, Op. 50 No. 4 (1787). Some of Haydn’s earliest examples of counterpoint appear in three symphonies (No. 3, No. 13, and No. 40) from 1762 to 1763. These early fugues show the influence of Fux’s Gradus ad Parnassum, which Haydn studied carefully.

Haydn’s second period of fugal writing began after he heard and was inspired by Handel’s oratorios during his time in London (1791–1793, 1794–1795). He then used Handel’s fugal techniques in his oratorios The Creation and The Seasons, as well as in several symphonies, including No. 88, No. 95, and No. 101, and in his late string quartets, Opus 71 No. 3 and Opus 76 No. 6.

Wolfgang Amadeus Mozart studied counterpoint with Padre Martini in Bologna. Under the influence of his father, Leopold Mozart, and other composers, Mozart wrote fugues and contrapuntal passages in Catholic choral works like the Mass in C minor, K. 139 "Waisenhaus" (1768), and other masses. His father warned him in 1777 to demonstrate his skills in "fugue, canon, and contrapunctus."

Later, Baron Gottfried van Swieten in Vienna inspired Mozart to write fugues. Van Swieten had collected many manuscripts by Bach and Handel and encouraged Mozart to study and transcribe them. Mozart wrote five transcriptions for string quartet, K. 405 (1782), of fugues from *The Well-Tempered Cl

Discussion

A common belief about the fugue is that it is a method of composing music, not just a type of musical structure.

Erwin Ratz, an Austrian music expert, explains that the structure of a fugue includes how the main theme and other parts are arranged, as well as how the music's harmony is built. The beginning and ending sections usually focus on the main key, while other parts explore different keys. However, he notes that this is the basic structure, and individual fugues might differ.

Although some keys are often used in fugues, the overall structure does not limit the harmony. For example, Bach's Fugue in B♭ major from The Well-Tempered Clavier uses the related minor key, the supertonic, and the subdominant. This is different from the sonata form, which follows a strict pattern. Some modern fugues avoid traditional harmony and use other methods, such as serial rules or complex harmonies.

The fugue is the most complex type of contrapuntal music. Ratz said that creating fugues is very challenging, and only great composers like Bach and Beethoven could make them work well. Peter Kivy notes that counterpoint has always been linked with serious music, and there is a reason for this.

This idea connects to how rules can help composers by giving them direction. Fugal writing started as an improvisational art during the Renaissance. In 1555, Nicola Vicentino wrote about this, for example.