How does a double fugue differ from a triple fugue?

In the study of counterpoint, the primary difference between a double fugue and a triple fugue lies in the number of principal themes, or subjects, utilized by the composer.

• Double Fugue: This form is built upon two subjects. Composers may present these subjects simultaneously, which functions similarly to a simple fugue featuring a countersubject. Alternatively, and more commonly, the composer provides separate, complete expositions for each subject before eventually combining them.12
• Triple Fugue: This form utilizes three distinct subjects. Similar to the double fugue, these subjects are treated both separately and simultaneously. In a triple fugue, each subject typically receives its own separate exposition, often in a different metre, before they are eventually integrated into the texture of the piece.31

While both forms rely on the systematic development of multiple themes, the triple fugue requires the management of an additional subject, increasing the complexity of the contrapuntal structure.13