[seqfan] Re: XronoMorph - Overlaid polygons and music

[Charles Greathouse]

Perhaps being about half binomial(2^16, 3) means that the author reduced
for reversal but not for circular shifts?

Charles Greathouse
Case Western Reserve University

On Tue, Jul 19, 2016 at 1:31 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hi Charles,
>
> I think the article may be wrong; the way it's worded suggests 3
> overlapping rhythms with any combination of 16 "taps" allowed for each
> rhythm; presuming there are no repeated rhythms allowed (standard with
> polyrhythms) then we have (2^16-1)*(2^15-1)*(2^14-1) ~ 35 trillion
> combinations.  I guess the author sees this as divided by 2 (around 2^44
> instead of 2^45) but I'm not sure why.
>
> Cheers,
> Bob Selcoe
>
> --------------------------------------------------
> From: "Charles Greathouse" <charles.greathouse at case.edu>
> Sent: Monday, July 18, 2016 11:33 PM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] XronoMorph - Overlaid polygons and music
>
> I found an interesting article:
>>
>> http://theconversation.com/how-a-little-mathematics-can-help-create-some-beautiful-music-61812
>>
>> It discusses music generated from fairly simple mathematical structures:
>> (small) subsets of the vertices of a polygon. Each subset is displayed as
>> a
>> polygon of a different color.
>>
>> From the article: "There are more than 17 trillion different rhythms, and
>> that is only counting rhythms with three levels where every beat occurs at
>> one of 16 distinct time locations (16 being a very common temporal
>> subdivision in music)."
>>
>> I'm trying to figure out how this number is computed. I've tried a few
>> different ways but none are close enough. binomial(2^16, 3) is too big,
>> but
>> reducing it by circular shift makes it a bit more than 1/16th the size
>> which is too small. Any ideas? (I assume that by "more than 17 trillion"
>> they mean between 17e12 and 18e12.)
>>
>> Charles Greathouse
>> Case Western Reserve University
>>
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>>
>>
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