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Johann Sebastian Bach 1685 - 1750 |
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"CRAB" CANON The "crab" is the second of five canons in the Musical Offering, in which the imitating part proceeds backwards. Bach 的 Canon有一段充滿數學色彩，Crab Canon 曲譜從尾到頭演奏是一模一樣的，甚至也可以構成一條 Möbius Strip。 |
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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. | ||
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The Art of Fugue, BWV 1080 | ||
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Musical Offering, BWV 1079 | ||
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