Canon 1 a 2

xantox, 18 January 2009 in Gallery

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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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  1. Animation created in POV-Ray by Jos Leys. Music performed by xantox with Post Flemish Harpsichord, upper manual. []

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5 Comments to “Canon 1 a 2”

View Comments in: Français (12) Italiano (10)

  1. 1
    John Footen

    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!

  2. 2
    William Innes

    I have never seen a clearer presentation of the structure and logic of a great work of art. Congratulations and thank you.

  3. 3

    The Music Animation Machine, an insightful view of music.
    See the animation on YouTube.

  4. 4
    Sajith Shetty

    I always loved Bach’s mathematical treatment of Canons and Fugues. This was heartening to see. Great work and thank you.

  5. 5
    John Baez « This Week's Finds in Mathematical Physics (Week 291)

    […] 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 […]

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