[seqfan] Re: "Polyrhythmic" sequences

[Antti Karttunen]

Well, at least in my own very vague way of thinking, I see "polyrhythmic"
as any sequence from which can be clearly seen two distinct periodicities
whose periods are co-prime to each other.

See e.g. https://oeis.org/A263273 "Bijective base-3 reverse: a(0) = 0; for
n >= 1, a(n) = A030102(A038502(n)) * A038500(n)."
and its graph:
https://oeis.org/A263273/graph

There are many similar constructions, e.g.: https://oeis.org/A264994

Maybe also this fits in: https://oeis.org/A266635/graph ?


Best regards,

Antti


Message: 24
> Date: Wed, 3 Feb 2016 21:10:00 +0200
> From: Veikko Pohjola <veikko at nordem.fi>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: "Polyrhythmic" sequences
> Message-ID: <EE965A78-230F-42FD-A83D-B1AA1CFCE0BC at nordem.fi>
> Content-Type: text/plain; charset=us-ascii
>
> Bob,
> Well, I guess I'm using the same definition for polyrhythmic as it is
> defined in music and, why not, as does also Robert Walker (see for instance
> http://www.science20.com/robert_inventor).
> Cheers,
> Veikko
>
>
> Bob Selcoe kirjoitti 3.2.2016 kello 0.30:
>
> > Hi Viekko,
> >
> > Sounds interesting - I'm curious to see the results because it's not
> obvious to me how A258024 relates to polyrhythmic sequences as defined in
> A267027.
> >
> > Best,
> > Bob
> >
> > --------------------------------------------------
> > From: "Veikko Pohjola" <veikko at nordem.fi>
> > Sent: Tuesday, February 02, 2016 3:58 PM
> > To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> > Subject: [seqfan] Re: "Polyrhythmic" sequences
> >
> >> Hi Bob,
> >>
> >> I'm working on polyrhythmic sequences (related to A258024) and hope to
> return after a more general description of the superposed periodicities is
> ready.
> >>
> >> Veikko Pohjola
> >>
> >>
> >> Bob Selcoe kirjoitti 2.2.2016 kello 20.38:
> >>
> >>> 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
> >>>
>