Definition
A crab canon is a contrapuntal form in which one voice plays a theme forwards while another plays the same theme backwards — the two voices retrograde mirror images of each other. Bach included one in the Musical Offering (1747). The form is named after the supposed sideways gait of a crab. Hofstadter's Crab Canon dialogue in GEB is structurally a palindrome at the level of speeches — readable the same way forwards and backwards.
Why it matters
How it works
Compose a melody A. Reverse A note-by-note to get retrograde-A. Play both simultaneously, with A in one voice and retrograde-A in another, at a chosen interval. For the result to be euphonious, you must select pitches so that every simultaneous pair (A note i against retrograde-A note i) is harmonically acceptable. This is severely constrained, which is why crab canons are rare. Bach's example threads the constraint successfully across 18 bars.