Great Example of a Great Form

Bach's "Die Kunst der Fuge" (BWV 1080), though incomplete, is arguably the greatest example of the purest abstract form of Western Classical Music, the Fugue. It consists of 14 contrapuncti & 4 canons in D minor.

The Fugue is a musical form in which the stated subject is followed by an answer, an imitation of the subject, a perfect fifth above or a perfect fourth below it. Interestingly, the subject also continues simultaneously with the answer, providing a contrary melodic line, in harmony, which is now called the counter-subject. A Fugue can have four voices.

The Fugue also uses the mathematical concepts of the Fibonacci numbers & the Golden Ratio. The Fibonacci numbers 1, 3 & 5 are also the semitones used in the C major chord, C, E & G. A piano octave consists of a total of 13 keys, 8 white & 5 black. The ratio of 13/8 is approximately equal to the Golden Ratio of mathematics.

Though it was presumably written for a keyboard instrument, versions featuring a string quartet, orchestra & vocal versions are available.

Though Bach composed his monumental set of "The 48" comprising preludes & Fugues in all the semitones of an octave (12) in both major & minor keys (24) twice over (48), "The Art of Fugue" occupies a special space in his ouvre.