A secondary subject (independent coherent musical theme) that plays simultaneously with or "counter" to the main subject.
As two independent voices sing together, they meet, "point by point" (counterpoint), to create a mutual blend, a higher-level musical coherence. 1 + 1 = 3. A countersubject must appear more than once without significant modification to be regarded as such. Otherwise, it would be considered non-repeating free-counterpoint without establishing a pattern of expectation. A counter-subject is similar but less independent than a "2nd" subject, for example, in a double fugue. Most fugues have at least one countersubject. Many have two or three. Countersubjects frequently supply contrasting material for episodes.
Here is a visual representation (a timeline) of a fugal exposition with two countersubjects from Bach's Well-Tempered Clavier, Book 1, No. 21 in B flat major. Quite often, the countersubjects are revealed in the exposition as orderly as the subject entries. Notice in this example that each voice enters with the subject, continues with first countersubject then on to the second countersubject. New countersubjects can appear later in the fugue.
In order to run against the subject, to be complimentary as well as independent enough so that both voices are clear, a countersubject differs dramatically from the subject, usually in terms of rhythm and motion. Rhythmically, one will be slow, the other fast. Where one voice pauses, the other moves. Each will have distinct points of accent such that where one is strong, the other is weak. In terms of motion, the two musical themes often show similar dichotomies: where one moves up, the other goes down, where one has smooth step-wise conjunct motion, the other leaps in more jagged disjunct motion. These are course but useful generalizations. Often, these polarities shift between the voices (particularly when the subject has multiple motives) so that an exchange occurs even during a single statement of the subject.
When multiple countersubjects participate, the counterpoint becomes thrillingly dense, and even more miraculous when all voices are clear, independent and mutually complimentary. Additional countersubjects may not appear until later in the fugue, creating sections with new development and new context for the original subject. Coordinating this complexity so that the final unity is aesthetically successful, for composer or performer, is an achievement of high art.
Example: WTC, Book 1, No. 2, C-minor.
Credit goes to Siglind Bruhn for her excellent diagrams.
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