[seqfan] mailto:rselcoe at entouchonline.net

[Tom Johnson]

Dear Seqfans,

Jean-Paul Allouche forwarded to me the letter below from Bob Selcoe. I don¹t
know anything about the work you have been doing so far with polyrhythms,
but I have the impression you are mostly doing three-against-four and
five-against-seven and things like that, and I suppose that from a
mathematical point of view there are interesting sequences that result. As a
musician I am quite familiar with these sorts of things, and with the
difficulty of performing them, but I am more interested in polyrhythms in
less well known senses. A very important recent evolution has to do with
one-dimensional tiling. I found recently that there are 452 ways to tile
tata in eight different tempos in eight voices in the time of  16 beats. And
you can double that if you wish to listen to the retrogrades. Jean-Paul
Davalan found that the shortest tiling of tatatata that is perfect (each
voice in a different tempo in ratios from 1 to 24), requires 24 voices in 96
beats. Nothing shorter. Then there are ³self-replicating² melodies, which I
discuss in my book ³Self-Similar Melodies². The simplest example of that is
the Alberti bass which we can describe with numbers as 1323132313231323...
If you just listen to every third note you get 1__3__2__3__1__3__2__3__1_,
the same thing, a self-replication, and of course, you could have a third
person playing every ninth note and they would be doing the same thing. But
one can construct much more interesting examples, as I have in several
compositions.

Do my interests have anything to do with yours? Should we continue this
discussion?

Best wishes,
Tom Johnson

tom.johnson at editions75.com
     
www.editions75.com

Editions 75
75 rue de la Roquette
75011 Paris (France)

Tel 33 1 43489057





Hi Seqfans,

A while ago there was some interest here in relating music to OEIS
sequences.  Apparently there is a general interest in applying or relating
sequences to areas outside of mathematics, music being one such area.

In December I proposed using the concept of "polyrhythmic" sequences for
this purpose; they combine certain sequences congruent to 1 mod k, which
reflect where beats are played in what are called "polyrhythms" in music.
Seems to me that this is one of the easiest and most intuitive applications
of sequences to music; in general, I think rhythm-related concepts may be
easier to apply than melody or harmony-related ones.

A267027 is the P(3,4) polyrhythmic sequence; a brief description of the
concept is shown there.  A047251 is the P(2,3) sequence.  As far as I can
tell, these are the only two polyrhythmic sequences in OEIS.

Since there was very little response to the December post, I took it to mean
there was little interest in the idea.  If there is some interest, might
anyone want to pursue this or perhaps some related ideas further?

Cheers,
Bob Selcoe 


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