(YouTube Link)
This video shows a selection from Johann Sebastian Bach's Musical Offering (1747) played forwards, then backwards, then both forwards and backwards at the same time. It was created by mathematical illustrator Jos Leys and science/philosophy blogger Xantox. This Bach piece has long intrigued mathematicians:
In each of these canons a musical line is played twice (or four times in Canon 10). The second version is always transformed with respect to the first by shifting in time, but it may also be shifted in pitch, turned upside-down, stretched, or played backwards. Each of these transformations occurs in the mathematics of elementary functions; they are examples of how new functions can be made out of old and of how a function can be tailored to fit a new situation.
Link via Boing Boing
Newest 5 Comments
Its a neat thing, but it sounded dissonant to me. Not a song melody I could listen to without getting annoyed. (and I do enjoy classical)
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Have to say I'm with Briananna on that one.
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Holy moly! :o
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Um... having spent about a year-and-a-half writing only imitative counterpoint and fugue, I can firmly say anybody who says "Oh it's in 4/4 so everything will sound good together" has their head firmly planted up their bung. And, btw, I write modern art music, so I am aware of the genius of Xenakis and all of his cohorts. But, when you write a successful crab canon that has interesting phrasing, apex, and form, I will remove your title as "dunderhead".
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I remember having read a nice chapter on the Musical Offering in Douglas Hofstadter's book "Gödel, Escher, Bach".
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