Well, yes, but the crab-canon symmetry here has nothing to do with the mobius strip -- it still needed two "playheads" running in the opposite direction to accomplish the task, and it could be written on any (opaque) two-dimensional surface with the same parameters. I actually had two points:
- You can put any piece on an opaque two-dimensional surface,
including a mobius strip. In the case of the Bach piece the relevant contrapuntal thing is the retrograde symmetry, so the mobius strip adds nothing.
- If you wanted an analogous piece where the mobius strip was
actually relevant, you would need to craft the piece so that it was syntactically well-formed in inversion. Imagine it being written on a transparent mobius strip where the playhead plays the "front" and the "back" of each note at different times as it passes them -- the playhead will be upside down on one of the passes. As a bonus, if you could craft it with retrograde-inversional symmetry, you could use the two playheads running in opposite directions as in the video and make what is usually called a "flip" canon -- a piece that can be played by two players looking at the same music from opposite sides of a table.
To put this another way -- imagine the Bach piece is written on a window. To play it correctly, you would need a player on each side of the glass. A mobius-strip piece with one playhead would sound like a piece followed by its inversion. With two playheads running in the opposite direction would have one of two properties depending on which side the playheads start, and in which orientation: 1) it would be the piece followed by its inversion in one voice accompanied by the retrograde inversion of the whole thing in the other voice (a flip canon), or 2) the piece followed by its inversion in one voice accompanied by the retrograde of the whole thing (a crab canon).
If it's played with the same timbre, the Bach piece (a crab canon) sounds like a piece in two voices followed by its retrograde. A piece with a real mobius strip topology with two playheads running in opposite directions like the video would sound like either a flip canon or a crab canon followed by its inversion.
Matt
On Sun, Jan 17, 2010 at 6:51 PM, Mario Mora maredmo@gmail.com wrote:
if you check that video with the volume on, you will hear that the intervalic relationships between the notes are perfect, this means that the beginning works perfectly in conjunction with the end, and that means that what can be melody, can also be accompaniment, so you can do any inversion of the music and it will work as a musical piece because it is perfectly symmetrical, to put any music whatsoever, in your words, does not guarantee a musical result, and in fact, does not guarantee music in a coherent sense, and obviously, does not garantee any symmetry at all. In this example, the musical result is accomplished by laws of complex intervalic relationships between the notes, called counterpoint, and Bach was a master on that. It is about what you hear, not about what you see, the score is just a graphic way of to write relations of time and frequency of a music so that can be read and performed by a human being.
2010/1/17 Matt Barber brbrofsvl@gmail.com
This is interesting, but unfortunately it isn't a correct analysis -- for it to be a real mobius strip it would need inversional symmetry, not symmetry in time -- the topology of this piece does not match that of a mobius strip (to visualize the topology of the music itself, you have to imagine it being written on a transparent strip). With an opaque strip, you can actually just write any music whatsoever -- this would have worked fine with no twists in the strip (and no music on the inside).
Canon 1 a 2 from J. S. Bach as a M?bius strip http://strangepaths.com/canon-1-a-2/2009/01/18/en/
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