J.S. Bach: Crab Canon (from The Musical Offering)

[Martin Jonas]

Johann Sebastian Bach: "Das musikalische Opfer" (The Musical Offering), BWV 1079
Canon a 2 cancrizans (Crab Canon)

This is one of the most mathematically elegant of Bach's pieces, from the arguably most mathematical and elegant composer of all times. "The Musical Offering" is a collection of keyboard keyboard canons and fugues and other pieces of music by Johann Sebastian Bach, all based on a single musical theme given to him by Frederick the Great (King Friedrich II of Prussia). The Crab Canon is the simplest of them, and the one that sticks closest to the King's theme. It consists of a single melody line, which the second voice plays in reverse, end to beginning, as a harmony line. Thus, this piece is identical played forward or backward and has been described as a musical Moebius strip. The Crab Canon is a major point of discussion in Douglas Hofstadter's classic book "Gödel, Escher, Bach", and the reason why Bach appears in the title.

The score is at IMSLP, in multiple free editions -- I attach one of them:

https://imslp.org/wiki/Musikalisches...ann_Sebastian)

For my recording, I have played the first voice on mandolin and the second voice on tenor guitar. On completion of the canon, I am repeating it with the voices swapped, which takes each voice back to its opening phrase in perfect symmetry.

Mid-Missouri M-0W mandolin
Vintage Viaten tenor guitar



Martin

[Martin Jonas]

Johann Sebastian Bach: "Das musikalische Opfer" (The Musical Offering), BWV 1079
Canon a 2 cancrizans (Crab Canon)

This is one of the most mathematically elegant of Bach's pieces, from the arguably most mathematical and elegant composer of all times. "The Musical Offering" is a collection of keyboard keyboard canons and fugues and other pieces of music by Johann Sebastian Bach, all based on a single musical theme given to him by Frederick the Great (King Friedrich II of Prussia). The Crab Canon is the simplest of them, and the one that sticks closest to the King's theme. It consists of a single melody line, which the second voice plays in reverse, end to beginning, as a harmony line. Thus, this piece is identical played forward or backward and has been described as a musical Moebius strip. The Crab Canon is a major point of discussion in Douglas Hofstadter's classic book "Gödel, Escher, Bach", and the reason why Bach appears in the title.

There is also a very neat animation that illustrates the Moebius Strip characteristics of Bach's Crab Canon in this article:

Link

Martin