Our last two blog posts looked at how two or more distinct melodies can be juxtaposed in counterpoint. But it is also possible to juxtapose a melody against a copy of itself that is displaced in time – a kind of time travel story in music. Most of us are familiar with how that works in a round like “Row, row, row your boat.”
This idea is developed further in the classical-music form known as the fugue. In the beginning (“exposition”) of a typical fugue, the fugue “subject” is introduced by (say) the bass voice. The tenor then enters with its “answer,” which is the subject transposed (usually) to a different pitch level, while the bass proceeds with a countersubject. Later the alto enters with the subject, while the other two voices proceed, and so on.
If the answers use exactly the same intervals as the original subject, they are known as “real” answers. Perhaps more commonly, though, the subject will emphasize both the tonic and dominant (melody notes 1 and 5), which are interchanged in the answers. The interchange causes slight alterations to the intervals within such “tonal” answers.
A good example of a fugue with tonal answers appears in my Piano Sonata No. 4, at the climax of the development section. The fugue begins in the secondary key center of A Minor, so the tonic is A and the dominant is E. The first full measure of the subject features E and A prominently. The answering entry replaces them with A and E, and the next entry presents them as E and A again.
The whole fugue is not quite two minutes long and includes such advanced fugal techniques as augmentation (where the subject is “stretched out” to twice its initial length) and inversion (where the subject is turned upside-down). It begins around 16:40 in this recording:
My Rhapsody for Woodwinds and Piano contains a six-part grand fugue, this one in D minor, where the individual “voices” are carried by these instruments in this order: flute, clarinet, bassoon, oboe, piano left hand, and piano right hand. The answers in this case are again tonal, and somewhat irregular, but again we can see how the dominant (A) is echoed by the tonic (D), and vice versa. Notice that the clarinet part sounds a whole step lower than written, since it is a B-flat instrument, so its first two notes are heard as D and A.
The fugue begins around 8:35 in this recording: