A fugue with two subjects.
A double fugue is distinctly different from a fugue with a single subject and one or more countersubjects. Where a countersubject is almost always subservient to the main subject, a second subject usually enjoys its own independant exposure in a full exposition where the initial subject is absent. Most double fugues have a strong sectional organization, with different sections highlighting one or the other subject. Like a countersubject, however, the second subject combines with the first subject so that both ideas blend into synergistic counterpoint. The essence of the double fugue depends on the independence of the subjects as well as their successful combination in counterpoint.
There are double fugues where the second subject is exposed against and in the presense of the first subject; the second subject has no independent exposition. However, unlike a countersubject which appears very early in the fugue (often in the exposition against the second subject entry), the second subject in this kind of double fugue appears later where it emerges as a fresh idea, a new and dramatic development. There are also fugues where the interpretation is not clear: one analyst calls it a double fugue, another merely a single fugue with a strong countersubject. The final designation is less important than the appreciation of artful counterpoint in general, where each part has its own musical integrity alone as well as the miraculous ability to combine with others in pleasing counterpoint.
A fugue can have even more than two subjects, hence the terms triple fugue, quadruple fugue, etc..
Example fugues with multiple subjects:
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