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Art of Fugue: Stretto Fugues
and Canon at the Tenth

Theme Developed By Other Means

In the next group of three fugues, Bach appears to suspend thematic transformation in order to establish a different process of variation involving stratification of the subject. Whereas the first four fugues contained no stretti, here Bach uses stretto to the extreme, demonstrating how a well-crafted subject can be made to "counterpoint" itself in endless ways. Bach gives us a simple, but elegant, model for stretto variation in the first four canons of his Fourteen on the Goldberg Ground, where he layers the subject with its retrograde, the inverted subject with its retrograde, the subject with its inversion, and the inverted subject with its inversion.

The subject (t8) of each stretto fugue is a slight variant of t5 from Contrapunctus III. Ever so slight, the variant is not without significance to the composer. For the first time in the Art of Fugue, the subject is comprised of fourteen pitches. Reason enough for Bach (B+A+C+H=14) to dwell upon it for awhile! In Contrapuntus V this motive is stated 22 times, half of them right-side-up and half upside-down (t9). Similarly, the 28 statements of t8 in Contrapuntus VI, are evenly divided between rectus and inversus. Of the 28 statements of t8 in Contrapuntus VII, 16 are right-side-up and 12 are inverted. The stretto fugues contain 75 statements of t8 or t9. Only Contrapunctus VII transforms the subject in two minor variants which we call t10 and t11 (below). It is as if, in coming to this last stretto fugue, the composer says, "I've shown you how the subject can counterpoint itself, now let's vary it some more."

Notice how the stretti give this fugue atmospherics much different from those of the preceding simple fugues. The sound is one of sweet tenderness, with subjects caressing each other like lovers in a park. Subsequent fugues are also stratified but detailed analysis should not be necessary; they contain new tricks which shall occupy our attention.

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