Fugue - A contrapuntal piece with spaced entries of a theme, usually in three or more parts.
Musical examples where the term 'Fugue' is used:
The most fixed part of a fugue occurs at the beginning or exposition. Here each voice in turn presents the main theme or subject. On finishing, the next voice presents the subject, the first voice continuing on to some new material. When this material is regular – i.e. it appears in subsequent voices – it is labelled countersubject. The process continues until all three voices are playing:
Subject (redundant entry)
The second entry of the subject is also called the answer. It occurs on the dominant, a fifth above or a fourth below the entry in the first voice. Since it occupies a different position in the scale, often the notes of the answer need to be slightly modified in order fit the prevailing tonality. This is called a tonal answer. If, however, the intervals are exactly transposed it is called a real answer. Sometimes, as in the example here, there will also be an extra entry of the subject at the end of the exposition. This is labelled as a redundant entry. When the subject can be presented above or below the countersubject without modification and still make tonal sense, this is known as invertible counterpoint.
Once the exposition is complete the fugue presents episodes of free counterpoint, normally developing elements already presented in the exposition. These are alternated with further entries of subject and countersubject, labelled middle entries. The keys may modulate freely in this middle section.
In the final section the subject renters in the original key, leading towards the close of the fugue. There are many variations upon this basic pattern. Double fugues, for example, present two subjects. An example of this would be the Kyrie form Mozart’s Requiem, where the subject is immediately answered by a distinct theme and not by the initial subject. There are also a variety of technical devices associated with fugues, including:
Stretto, where entries of the subject occur closer together in order to create greater excitement.
Augmentation, where notes of the subject and/or countersubject are doubled in rhythmic value.
Diminution, where notes of the subject and/or countersubject are halved in rhythmic value.
Inversion, where the intervals of theme are flipped.
The form has a long history and examples exist until the present day. Fugue form is most perfectly realized, however, in the music of J.S. Bach, for example in his Well Tempered Clavier, also known as the 48 Preludes and Fugues:
Here also is a useful video exploring "What is a fugue":