Bach's Mathematical Music

Johann Sebastian Bach (born March 21, 1685) composed music with explicit mathematical structure. The Crab Canon in The Musical Offering is a single melody playable forwards and backwards simultaneously against itself. The Art of Fugue explores what is possible within a fixed mathematical framework of melodic inversion, augmentation, and retrograde. Bach's Musical Offering contains 10 canons that correspond to the 10 levels of a musical structure, and he embedded the number 14 (B+A+C+H = 2+1+3+8 = 14 in alphabetical values) as a hidden signature throughout his work.