Canon 1 a 2
xantox, 18 January 2009 in GalleryOther Languages:
In the enigmatic Canon 1 a 2 from J. S. Bach’s “Musical Offering” (1747) (also known as “crab canon” or “canon cancrizans”), the manuscript shows a single score, whose beginning joins with the end. This space is topologically equivalent to a bundle of the line segment over the circle, known as a Möbius strip. The simultaneous performance of the deeply related forward and backward paths gives appearance to two voices, whose symmetry determines a reversible evolution. A musical universe is built and then is “unplayed” back into silence.1
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29 April 2009, 1:58 am
Simply amazing! BothBach’s work and your presentation of it. I am deeply moved by this illustration. Thank you very much for this lesson in music. It made understaning this form of canon easy. Thanks again!
31 August 2009, 11:08 pm
I have never seen a clearer presentation of the structure and logic of a great work of art. Congratulations and thank you.
7 October 2009, 9:12 pm
The Music Animation Machine, an insightful view of music.
See the animation on YouTube.
13 October 2009, 5:56 pm
I always loved Bach’s mathematical treatment of Canons and Fugues. This was heartening to see. Great work and thank you.
23 January 2010, 8:36 am
[…] While it’s fun to read about crab canons, and fun to listen to them, you may have trouble fully appreciating them unless you see the score while you’re listening. And that’s one reason the video by Jos Leys and Xantox is so great.
For more on the Musical Offering, try these:
4) Timothy A. Smith, Canons of the Musical Offering […]