[seqfan] Re: SeqFan Digest, Vol 80, Issue 8

[Antti Karttunen]

On Sun, May 24, 2015 at 12:00 AM,  <seqfan-request at list.seqfan.eu> wrote:

> ------------------------------
>
> Message: 16
> Date: Sun, 24 May 2015 00:00:32 +0300
> From: Veikko Pohjola <veikko at nordem.fi>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Musical information about a sequence
> Message-ID: <2C234C13-4D18-4D6C-AC08-E57A1A0DAFB0 at nordem.fi>
> Content-Type: text/plain; charset=windows-1252
>
> Dear seqfans,
>
> Applying floor(tan(n)) repeatedly, a limiting sequence results composed of 0’s and 1’s only. The proportion of 1’s is somewhat over 12% and they distribute interestingly forming a repeating pattern. Converting the sequence of distances between the positions of 1’s into music (say piano) turns it to fascinating music manifesting a steady beat with a theme and delicate variations. Counting the number of beats in a sequence of known length permits to assess the number of individual sounds (terms) within each measure to about 42.
>
> I am wondering whether such a steady beat could be inherited from the periodic nature of the mother function (tan) and if so, should the length of the pattern thus be predicted.
> And in general, are this sort of musical findings regarded to belong to recreational domain and not at all to hard mathematics, not ...

Dear Veikko,

I don't care what other people think about what is "hard enough
mathematics" (some people have very restrictive biases), but think
that your find is very interesting.

I have been myself trying to find good examples of the general idea
behind Per Nørgård's "infinity sequence"
http://oeis.org/A004718
"invented in an attempt to unify in a perfect way repetition and variation".
(See also https://oeis.org/A056239 for another Danish comment in
another, not related sequence. Also https://oeis.org/A126759 )

In other words, anything on the sweet but rare region between (too
much) regularity (most base-sequences) and (too much) chaos. (Compare
also to some Wolfram's CA-classifications, although I'm not now
interested about Turing-capability. Also, it seems that human mind
cannot relish complete chaos until it is regularly repeated and thus
"amplified"?)

So far, my attempts have concentrated on "entanglement-permutations"
and "beanstalk-sequences" (my neologisms but not my inventions) both
of which mix together a repeating pattern with some "new material",
although in different ways. I haven't yet much experimented of
actually producing any sounds of these, except some random playing
with "Listen-button" which leaves much to be desired regarding the
actual mapping, not just to notes but to rhythm/dynamics as well (or
maybe I should learn to use its various options better?) In any case,
maybe it's better to leave their exact mapping to rhythm and sounds to
more musical talents, and for me to just keep on producing more
patterns and hope that some of them are mathematically interesting and
useful as well.


> ... even when some useful mathematical information could be obtained by listening.

For this, please see also:
http://www.moz.ac.at/sem/lehre/lib/bib/software/cm/Notes_from_the_Metalevel/chaos.html



Terveisin,

Antti

>
> Best regards,
> Veikko Pohjola
>