Contrapunctus VI a 4, in Stylo Francese
As a youth Johann Sebastian lived for three years in Lüneburg. This city was famous for its Ritteracademie where young noblemen studied the French language, social graces (fencing and dancing), and, most important, listened to French music. Young Bach was able, also, to visit the city of Celle, fifty miles to the south, where Duke Wilhelm of Brunswick-Lüneburg maintained a bevy of French musicians. It was probably in Celle where Sebastian first heard the music of Couperin, Lully, Muffat, Fischer, and Raison.
With its clipped dotted rhythms and flights of thirty-second notes, Contrapunctus VI represents a fusion of the French Mannier with solid north German counterpoint to produce a one-of-a-kind fugue in stile francese. The subject of this fugue consists of francophile versions of t8 and t9. But, for the first time in the Art of Fugue, Bach employs rhythmic proportions. Both versions of the subject are stated in normal values (half notes) and in diminution (quarter notes). The inversus (t8) and rectus (t9) forms of the subject are each stated 14 times. No two stretti are alike, and nearly every proportional or inversional permutation is represented.
This fugue is about the subject accompanying itself in rhythmic proportions of double and half its normal values. The subject is stated four times in half notes (its normal pace), four times in whole notes (+), and twenty times in quarter notes (-). The fugue contains seven episodes in stretto (left). See if you can locate the following:
and sixteen times upside-down 
. The four statements in augmentation alternate rectus and inversus. Similarly, the first two statements of the normal subject (mm. 2 & 14) are upside-down, while the second two (m. 36 & 38) are right-side-up.
