Fugue

A theme appears alone, in one voice. Soon another voice repeats it at a different pitch while the first carries on with a new line. A third comes in, then a fourth, until all of them are playing, each with its own melody. That is how a fugue begins.

Where it comes from

The fugue as we know it is a product of the Baroque, appearing around the 1620s; before that, the word was used for any imitative music. Its most important precursor is the ricercar, a fifteenth-century instrumental piece related to the vocal motet, highly contrapuntal, with a distinctive thematic figure passed among the voices in imitation (Blatter 2007, part 5, art. 4).

For students today, the definition and structure of the fugue are bound up with Bach, although Handel and many other composers of the time, and earlier, wrote important fugues (Blatter 2007, part 5, art. 4).

Subject and answer

A fugue is an imitative, contrapuntal piece in which a theme, usually a single one, the subject, is introduced in one voice and followed by entries of the same theme in the other voices until all have entered. There can be six voices or more, but three to five is most common (Blatter 2007, part 5, art. 4).

The entries alternate in pitch. The first, third and fifth voices state the theme in the tonic; the second, fourth and sixth, in the dominant. That transposed version of the subject is called the answer (Blatter 2007, part 5, art. 4).

A subject often has a head, with distinctive features that make it easy to spot whenever it appears, and a tail, more utilitarian, leading into what follows (Blatter 2007, part 5, art. 4). A subject in C major, its head the leap from C to G:

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Real answer and tonal answer

To find the answer, it seems enough to transpose the subject up a fifth. That exact transposition is called a real answer:

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But Bach often altered the answer, and the altered version is called a tonal answer (Blatter 2007, part 5, art. 4). Theorists have observed when this happens (Blatter 2007, part 5, art. 4):

• when the subject begins with a leap from tonic to dominant, or from dominant to tonic;
• when the subject modulates;
• when the subject emphasises the dominant.

The subject above begins with a tonic-to-dominant leap, C to G. A real answer would begin G to D, dominant to the second degree of the key. The tonal answer swaps the leap: it begins G to C, dominant to tonic, and adjusts what follows:

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The reason is tonal. If the real answer went from G to D, the fugue would start sounding in G major too soon; by swapping the leap, the answer responds to the subject without taking the music out of C. With a modulating subject the logic is the same: a real answer would modulate even further from the tonic and make the third entry, which has to return to the tonic, impossible (Blatter 2007, part 5, art. 4).

The exposition

A fugue usually has two main parts, the exposition and the body. In the exposition each voice presents its version of the theme, subject or answer, and once it has entered goes on to accompany the following voices with counterpoints called countersubjects. The exposition usually ends on a tonic or dominant chord (Blatter 2007, part 5, art. 4). In a four-voice fugue:

Entry	Soprano	Alto	Tenor	Bass
1st		subject (I)
2nd	answer (V)	countersubject 1
3rd	countersubject 1	countersubject 2	subject (I)
4th	countersubject 2	countersubject 3	countersubject 1	answer (V)

The order of voices varies from fugue to fugue; what stays is the alternation of subject and answer. Countersubjects are usually written in invertible counterpoint, so they can appear above or below the theme (Blatter 2007, part 5, art. 4).

The body and the episodes

The body of the fugue begins at the chord that closes the exposition and is made of entries of the subject or answer, in various keys, with episodes between them. Like the development of sonata form, the body is unpredictable: the composer may bring in the theme in any key at all (Blatter 2007, part 5, art. 4).

An episode is a passage containing neither subject nor answer. It is contrapuntal, made of material drawn from the subject, the answer or the countersubjects, and often presents that material in sequence, in invertible counterpoint (Blatter 2007, part 5, art. 4). Episodes give the ear a rest from the theme and carry the music from one key to another, towards the next entry.

Special devices

Some devices appear in many fugues without being required (Blatter 2007, part 5, art. 4).

Stretto. An entry of the theme begins before the previous one has finished, and the voices tumble over each other. The subject in C, and a second entry starting halfway through the first bar, an octave higher:

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Pedal point. A note held for several bars in one voice, usually the tonic or the dominant, most often near the end of the body.

Augmentation and diminution. The theme appears in longer or shorter note values.

Counter-exposition. A new exposition inside the body, with the voices entering one by one again, sometimes in a different order.

Delayed entry. In the exposition one voice, usually the last, comes in later than expected, so its arrival becomes a surprise.

Coda. An ending added to the body, which may bring one last entry of the theme.

Double and triple fugues. In some large fugues the composer uses two or three subjects, with two expositions, or with two themes presented together from the start.

What comes next

The fugue gathers almost everything counterpoint has: imitation, invertible counterpoint, sequence, augmentation and diminution, modulation. Listening to a fugue knowing where each voice comes in is one of the best ways to hear counterpoint for real.