Fugue
A musical genre featuring sections of imitative polyphony based on a single theme, which alternate with free sections.

[Example 1: Handel, Concerto Grosso, Op. 6, No. 7,mvt.2.]

A fugue is a musical genre featuring sections of imitative polyphony based on a single theme, these sections alternating with free sections. Fugue is associated particularly with the late Baroque period, but continued in use during the Classical period and into the Romantic era. It has enjoyed periodic revivals during the twentieth century.

Despite a superficial resemblance, fugue differs from the imitative polyphony of the Renaissance era in two respects: (1) imitative polyphony uses a succession of themes (or "points of imitation"), whereas fugue uses just one theme, and (2) imitative polyphony does not alternate free sections on a regular basis.

1. Subject and Answer

A fugue begins with a solo presentation of the theme. This theme is called the subject. It is then restated in a second voice, this restatement being called the answer. The answer usually appears at a different pitch -- typically a 5th or 4th higher or lower. The answer is otherwise either identical with the subject or only slightly modified.

Listen to the opening of Beethoven's String Quartet in C-sharp minor, Op. 131 (1826). The diagram below shows the entrances of the theme.

[Fig 1: Beethoven: succession of subject-answer-subject-answer.]

[Example 2: Beethoven, String Quartet in C-sharp minor, Op 131, mvt.1.]

2. Subject and Countersubject

In many cases the subject is followed by a second phrase called the countersubject that is heard along with the answer. The fifth movement of Bach's cantata God's Time is the Very Best Time (c1707) offers an example. Its subject accompanies the words "Es ist der alte Bund" ("It is the ancient law"). The second part of this sentence, "Mensch, du musst sterben" ("Man, thou art mortal"), is sung to the countersubject.

[Fig 2: Bach: subject and countersubject.]

[Example 3: Bach, Gottes Zeit ist der allerbeste Zeit, mvt.5.]

A countersubject is rarely as audible as this. In most cases, it is a subtle agent that flavors the overall texture rather than a distinct entity.

3. Exposition and Episode

Sections with the subject are called expositions, and the free sections episodes. (The latter often quote or allude to parts of the subject.) A typical fugue follows this pattern:

[Fig 3: Expositions and episodes.]

Listen to the following passage from a concerto grosso by Handel (1739). The subject starts off with a single pitch played 14 times (2 slow, 4 medium, then 8 fast) before spiraling away:

[Fig 4: Handel: succesion of expositions and episodes.]

[Example 4: Handel, Concerto Grosso, Op. 6, No. 7,mvt.2.]

The order in which the subject appears varies from fugue to fugue. In many cases, all the voices enter in turn with the subject or answer, before the first episode intervenes. The number of voices is equally variable. Most fugues have three or four, but fugues do exist with five, six, or even more voices. Many possibilities exist, in fact. Unlike forms such as the rondo or minuet, which prescribe a strict order of events from beginning to end, fugue is best understood as a manner of composition based on a set of general conventions. Here are just a few of the more common such conventions.

4. Stretto

Fugue often uses stretto, a device that introduces the answer before the subject has run its course -- that is, the answer overlaps the subject. Stretto may occur at any point, but it is used most often as a way to build tension or excitement at a climactic point, such as the ending.

[Fig 5: stretto.]

5. Inversion, Augmentation, Diminution

Some fugues invert the intervals of the subject at some point.

[Fig 6: inversion of subject.]

The answer may also be inverted. A fugue that does this throughout is called a counterfugue or a fugue in contrary motion. When the subject is played at half-speed (that is, its note values are doubled) it is said to be in augmentation. (This often happens right at the end of the fugue.) Vice versa, when the subject is played twice as fast (its note values being halved), it is in diminution.

[Fig 7: augmentation/diminution.]

Interesting combinations of augmentation, diminution, inversion, and stretto may be heard in several fugues, such as the seventh "counterpoint" from Bach's The Art of the Fugue (pub. 1751), which is based on the following subject:

[Example 5: Subject from The Art of the Fugue: Play Contrapunctus I, bb.1-5 on a keyboard at pitch.]

In the opening exposition of Counterpoint VII, the tenor first presents the subject, in diminution (that is, twice as fast as normal). The soprano immediately restates the subject in stretto, now at normal speed but inverted, and the alto promptly answers it in stretto, inverted and in diminution. Then the bass plays the answer, inverted and in augmentation (extremely slowly!). And while this is being sounded (i.e. in stretto), the tenor plays the answer and the alto plays the subject, both in diminution and the right way up. (All this information is given in the diagram below.) In this performance, the first three voices are played on string instruments (viols). Try to spot when the bass enters: it is played on a wind instrument (a bassoon):

[Fig 8: Bach: exposition, stretto.]

[Example 6: Bach, The Art of the Fugue, Contrapunctus VII.]

6. Double Fugues, Invertible Counterpoint, and Pedal

Some fugues have two subjects rather than one, and are called double fugues. Some double fugues present the two subjects simultaneously from the beginning. Others present the first alone, then the second, only combining them near the end. Similarly, composers have written triple, and even quadruple fugues.

Most fugues contain several instances of invertible counterpoint. This term refers to melodic lines that can change places with one another, the top line becoming the bottom line, and the bottom the top. It takes special skill to construct lines so that they will work in this way.

[Fig 9: invertible counterpoint.]

Invertible counterpoint involving two lines is usually called double counterpoint. Examples of triple, or even quadruple or quintuple counterpoint also exist.

One final convention: the closing moments of a fugue are often marked by the use of a sustained note, called a pedal, in one of the voices, most often the bass.

7. Instrumental and Vocal Fugues

We have so far listened to fugues for orchestra, for chamber ensemble, and for chorus. There are fugues also for solo keyboard instruments, notably for church organ, for harpsichord, and later for piano. Arguably the most famous of all collections of fugues is for keyboard: Johann Sebastian Bach's The Well-tempered Clavier (1722, 1742), comprises 48 preludes and fugues in two books, each book containing 24 -- one in each major and minor key.

Many fugues for chorus, especially in the Baroque, have an independent bass line in the orchestra, which simply underpins the vocal fugue without taking part in it. Listen again to the Bach fugue "It is the Ancient Law." This time, instead of listening for subject and countersubject, try to hear the bass line, which is a basso continuo part, plodding constantly on, at about twice the speed of the voices.

[Example 7: Bach, Gottes Zeit ist der allerbeste Zeit, mvt.5.]

8. Fugato

The term fugato describes a passage within a larger work that displays fugal features -- such as an exposition -- but is not, properly speaking, a fugue. The first movement of Stravinsky's Dumbarton Oaks Concerto (1938) contains several examples of fugato. Here is one of them, which occurs about midway through the movement:

[Example 8: Stravinsky, Concerto in E Flat, Dumbarton Oaks, mvt.1.]

Summary:

• A fugue is a musical genre that features sections of imitative polyphony based on a single theme, which alternate with free sections.
• A fugue has several principal components:
  • It begins with the solo presentation of the subject, repetition of which, in another voice, is called an answer.
  • Often, the subject is followed by a second phrase called a countersubject, which is heard along with the answer.
  • Sections with the subject and answer are expositions; free sections are called episodes.
• A fugue comprises a series of expositions and episodes.
• Fugues have many special conventions:
  • Subject and answer may appear in augmentation, diminution, or inversion.
  • Fugue makes frequent use of invertible counterpoint and stretto, and often employs a pedal in the concluding moments.
• Fugues are most commonly written for chorus, for orchestra, for ensemble, and for solo keyboard instruments.
• Fugato is a passage in a larger work that displays some characteristics of a fugue.

Copyright © Columbia University, Visual & Sound Materials from the Gabe M. Wiener Music & Arts Library of Columbia University
Fugue written by: Michael Von der Linn Recording & Mixing: Christopher Bailey	Narration: Mark Burford Technology & Design: Maurice Matiz