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a cool crab canon
"Crab canons", or "retrograde canons", are musical pieces in which you get one part by reading a different part backwards, from end to beginning. (There's a variant in which you actually rotate the sheet music 180 degrees so not only is the first note of one part the last note of the other, but also high notes in one part become low notes in the other -- for example, if both parts are in modern treble clef, a high F in one part, on the top line, becomes a low E, on the bottom line, in the other.) There's a well-known one by Bach, which inspired Douglas Hofstadter to write a crab canon in prose as one of the interludes in Gödel, Escher, Bach: an Eternal Golden Braid. And the earliest one I know of is Guillaume de Machaut's "Ma Fin Est Mon Commencement".
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shalmestere was sorting through photocopied sheet music a few weeks ago and came across an anonymous "Retrograde Canon" from the mid-15th-century Trent codices (in modern edition; we haven't tried reading the original notation yet). We tried it on recorders and were utterly charmed. It's unusual in that the beats are offset: the "reflection point" is between beats 3 and 4 of a 4/4 measure, so every note that falls on a downbeat half note in the forward direction is on an upbeat half note in the retrograde direction. And the third part, written to go against the two canonic parts, is not a palindrome (as it is in the Machaut and Bach examples), but rather does different things with the same harmonies forward and backward. And when we played through it, putting breaths where they seemed to make sense in our individual parts, miraculously most of the breaths matched up. Anyway, last night we decided to do a multi-tracked recording of it: we recorded the two canonic parts (and yes, I read the "forward" line from end to beginning, rather than the editor's helpful reversal of it), then I recorded the third part while listening to the first two through earbuds, then combined the two recordings. Take a listen.
So
shalmestere was sorting through photocopied sheet music a few weeks ago and came across an anonymous "Retrograde Canon" from the mid-15th-century Trent codices (in modern edition; we haven't tried reading the original notation yet). We tried it on recorders and were utterly charmed. It's unusual in that the beats are offset: the "reflection point" is between beats 3 and 4 of a 4/4 measure, so every note that falls on a downbeat half note in the forward direction is on an upbeat half note in the retrograde direction. And the third part, written to go against the two canonic parts, is not a palindrome (as it is in the Machaut and Bach examples), but rather does different things with the same harmonies forward and backward. And when we played through it, putting breaths where they seemed to make sense in our individual parts, miraculously most of the breaths matched up. Anyway, last night we decided to do a multi-tracked recording of it: we recorded the two canonic parts (and yes, I read the "forward" line from end to beginning, rather than the editor's helpful reversal of it), then I recorded the third part while listening to the first two through earbuds, then combined the two recordings. Take a listen.
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I didn't know about this kind of piece.
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There are pieces from the 14th-15th centuries in which two or three parts are exactly the same but written in different time signatures (which, considering the effect of medieval time signatures, makes them sound quite different!). There's a famous Josquin piece in which every note is dotted, making it half again as long as it would otherwise be, which means it would sound exactly the same if you left off all the dots and played it at 2/3 speed. There's a famous J.S. Bach piece based on the four-note melody "B, A, C, H" (in German music theory, the note "H" is what we call "B-natural" and the note "B" is what we call "B-flat"). And my early-notation teacher once gave us a piece in which one part is produced from another part by starting two bars later and reading all the whole notes as quarter notes and vice versa, leaving half notes as they are. They played a lot of these games starting in about the 14th century.
Moving more into science-fiction territory, there's a famous segment in Rachmaninoff's "Rhapsody on a Theme of Paganini" in which he takes the "demonic"-sounding theme that you've heard a thousand times by that point in the piece, turns it upside down (but not backwards), and gets a beautiful, sweet, pastoral melody.
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Cool piece! Thanks for the recording.
I didn't know these kinds of palindromes/upside-down/etc compositions had a name -- hadn't heard "crab canon" before. Why "crab"?
The 14th century brought some wild and wacky stuff. Years ago our choir sang Le Ray Au Soleyl (here's a recording by people who are way better than we are), in which the same line proceeds at three different speeds. It's the sort of thing that music geeks appreciate, but can be hard for general audiences. (And yeah, we struggled with it.)
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Something I hadn't realized until that attempt: the textual rule in the original manuscript is more complicated than just "play this part at speed ratios of 1:3:4"; in one of the parts you're also supposed to replace all the white notes with rests, while playing the black notes. This is presumably to avoid some otherwise unavoidable dissonances.
I don't know who invented the term "crab canon" -- I thought it was Bach, but the Wikipedia page doesn't address this question. The idea is that a crab walks sideways (and in principle could walk either left or right) rather than straight forward.