A fugue is a polyphonic piece with a short melody traded between the voices (typically three or four voices). This melody is called a subject. Statements of the subject are frequently connected by episodes, which often use motives from the subject. Statements of the subject (together with any episodes) are grouped into longer passages, the first of which is called the exposition. A double fugue is a fugue with two subjects that are heard together at some point. There are also triple and even quadruple fugues.

History and etymology

Fugue started to take shape in the sixteenth century and reached a high point of artistry in the early eighteenth century with J. S. Bach. It became less prominent during the late eighteenth and nineteenth centuries and regained some prominence in the twentieth century. Notable examples of twentieth-century fugues are:

• Samuel Barber, Piano Sonata in E-flat minor, op. 26 (1949), IV (scroll to 14:00)
• Béla Bartók, Music for Strings, Percussion, and Celesta, Sz. 106, BB 114 (1936), I
• Paul Hindemith, Ludus Tonalis (1942)
• Several works by Alan Hovhaness
• Dmitri Shostakovich, 24 Preludes and Fugues (1950–1951)
• Igor Stravinsky, Symphony of Psalms (1930), II

Fugue admirably exemplifies the artistic potential of polyphony, just as sonata form admirably exemplifies the potential of homophony.

The term fugue derives from the Latin fugere, to flee. The voices chase each other, as it were. This etymology points to the dynamism that is particular to fugue. Because the phrases in the different voices do not typically begin and end together, and because there is typically a kind of tour of different tonics, there is a high and unremitting degree of mental tension running through a fugue, the same as physically with a run.

Particular features

Typically, the voices enter one at a time in the exposition, switching back and forth between the tonic and dominant keys. The subject can simply be transposed up a perfect fifth, in which case it is called a real answer (the subject here is from J. S. Bach’s The Art of Fugue, BWV 1080 (1743–1750):

Or the subject can be transposed by a fifth, except that the dominant (and possibly some other notes) are answered at the fourth above, such that the tonality-defining dyad do-sol is retained (as sol-do), in which case it is called a tonal answer:

Whichever kind of answer is used initially will generally alternate with the original form of the subject throughout a fugue.

If there are melodies that are heard regularly together with the subject, they are called countersubjects.

Example: J. S. Bach, Contrapunctus 3, from The Art of Fugue, BWV 1080 (1743–1750), mm. 1–12:

At some point, or throughout, the subject can be inverted (turned upside down). Notice that the above-quoted fugue uses an inversion of the subject quoted previously. Often inversions are crafted to retain the do-sol dyad, somewhat as with tonal answers. So in this case, the original subject starts with do sol (D–A), and the inversion also starts with do-sol (D–A), adjusting the fifth to a fourth.

At some point, or throughout, the subject can be augmented (stretched out). Here augmentation is shown together with inversion, but they need not occur together:

Example: J. S. Bach, Contrapunctus 9, from The Art of Fugue, BWV 1080 (1743–1750): The initial subject is joined partway through by the main subject of The Art of Fugue in augmentation.

Toward the end of a fugue, the subject often appears in close imitation, which is called stretto. Here it is shown with inversion, but stretto need not feature inversion:

Example: Dmitri Shostakovich, Fugue No. 5 in D major, from 24 Preludes and Fugues (1950–1951) (scroll to 3:18): The subject appears in stretto toward the end.

There is no standard plan for using inversion, augmentation, and stretto, nor is there a standard form for a fugue. A fugue is an exploration of the polyphonic possibilities of its particular subjects, so the course of that exploration will depend on the constitution of the subjects and the insight of the composer.

Further reading

External links

The Wikipedia article on fugue is okay.