<span class="Apple-style-span" style="font-family: arial, sans-serif; font-size: 13px; white-space: pre-wrap; ">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.</span><br><div> <div><br><div class="gmail_quote">
2010/1/17 Matt Barber <span dir="ltr"><<a href="mailto:brbrofsvl@gmail.com">brbrofsvl@gmail.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">This is interesting, but unfortunately it isn't a correct analysis --<br>
for it to be a real mobius strip it would need inversional symmetry,<br>
not symmetry in time -- the topology of this piece does not match that<br>
of a mobius strip (to visualize the topology of the music itself, you<br>
have to imagine it being written on a transparent strip). With an<br>
opaque strip, you can actually just write any music whatsoever -- this<br>
would have worked fine with no twists in the strip (and no music on<br>
the inside).<br>
<br>
<br>
><br>
> Canon 1 a 2 from J. S. Bach as a M?bius strip<br>
<div class="im">> <a href="http://strangepaths.com/canon-1-a-2/2009/01/18/en/" target="_blank">http://strangepaths.com/canon-1-a-2/2009/01/18/en/</a><br>
<br>
</div>_______________________________________________<br>
<a href="mailto:Pd-list@iem.at">Pd-list@iem.at</a> mailing list<br>
UNSUBSCRIBE and account-management -> <a href="http://lists.puredata.info/listinfo/pd-list" target="_blank">http://lists.puredata.info/listinfo/pd-list</a><br>
</blockquote></div><br></div></div>