A fugue is the most complex polyphonic musical form, involving imitation among the parts (called “voices” whether they are vocal or instrumental). The word fugue comes from fuga, meaning to chase since each voice “chases” the previous one.

The composition of a fugue starts with the choice of a musical theme of a particular kind called the subject. In the initial section of a fugue, called the exposition, this subject is presented in turn in each of the voices, with the first voice starting by itself, much the way a round is sung—this is the telltale sign of a fugue. The subject is first presented in its original form (called the dux—leader) in the home key, the tonic. The second voice presents the subject in the key of the dominant, i.e. a fifth up or fourth down. This form of the subject is called the comes, or “companion.” The comes can either be exactly like the dux, transposed to the dominant, in which case the fugue is called real, or modified so as not to stray too far harmonically, in which case the fugue is called tonal. In this latter case, used when the subject leans strongly on or goes repeatedly to the tonic and the dominant, the pitches are often changed rather than simply transposed, so that every tonic note of the dux is a dominant in the comes and vice versa. The result is a modified melodic shape. As an example, the fugue in Motet BWV 226 Der Geist hilft at “Der aber die Herzen” has as its first two (long) notes F and B-flat, that is the dominant and the tonic, in the dux. The comes instead starts with B-flat and F, the tonic followed by the dominant, and thus with a skip of a fifth rather than a fourth.

As the subject is presented in turn by each of the voices in the exposition, the voice that has just finished the subject will often have another musical phrase (called a countersubject) that functions as a melodic accompaniment to the subject. This contributes to the fugue’s interest. Some fugues, like the familiar fugue in c minor from the first volume of Bach’s Well-Tempered Klavier, have multiple countersubjects. After the exposition has presented the subject in all parts, with or without countersubject, the fugue alternates sections where the subject is present and where it is not. The latter sections are called divertimenti, or episodes, and the function of these is in part to modulate to different keys. Often, portions of the subject are used in episodes for elaboration, most often its head.

The most complex fugues display various techniques of elaboration of the theme. These include diminution and augmentation (where the durations of each of the notes of the subject are halved or doubled), inversion (where the subject is upside down), and, more rarely, retrograde (where the subject is presented backwards) or even combinations thereof (such as augmented inversion). Towards the end of the fugue there is usually a stretto (“narrow”) section, where the subject is presented in all parts, as in the exposition, but the successive voices do not wait for previous voices to finish the subject before jumping in, thus overlapping one presentation of the subject over the next. Thus, a composer wishing to write a fugue must not only possess considerable talent and skill, but also know and abide by a set of complex rules and conventions. The subject of a fugue must be a musical phrase capable of being stacked upon itself in multiple parts, and then distinctive enough to come out of a thick polyphonic texture and suitable to being compressed, expanded, and elaborated upon in varied ways.

There are examples of double fugues (of which Bach was quite fond), or fugues with two subjects. Such fugues can present the subjects together right away or, more often, present the first in a complete exposition followed after a while by an exposition of the second, and eventually in combination. An example of a double fugue is the Amen fugue in Cantata BWV 196, where the two subjects are presented immediately in combination.

A peculiar type of choral fugue that Bach also liked is the “permutation fugue,” which dispenses with episodes altogether and has a multitude of thematic fragments which circulate among the voices in immediate succession. For example, the first voice might sing subject 1 (dux form), subject 2 (comes), subject 3 (dux), subject 4 (comes) in succession and then repeat the same; the next voice to enter would sing the same succession of subjects in order but reverse the order of the form (comes, dux, comes, dux). An example of this type of fugue occurs in the first movement of cantata BWV 196.

The pleasure of composing a fugue is that of challenging oneself with writing delightful music while following the most complex and ancient rules of composition. Listening to a fugue offers multiple layers of pleasure. What upon first exposure might be the simple experience of a single line subsequently turns into the experience of a complex texture, with the excitement of picking out successive appearances of the subject. Each successive listening will reveal further layers of counterpoint, points of imitation, hidden instances of the subject… or not! Sometimes the subject, transformed, is so cleverly hidden it will only reveal itself in a Eureka! moment during an in-depth study of the piece. It’s not uncommon for performers to have played or sung a fugue for years and think they really know it inside out, and then something previously unnoticed or “mis-categorized” will pop up and make them jump in their seat. A fugue is thus a virtually endless repository of performing and listening discovery and pleasure.

—© Alexandra Amati-Camperi, 2009