[seqfan] Re: "Polyrhythmic" sequences

[Bob Selcoe]

Hi Viekko and Seqfans,

Viekko - I see where there might have been some confusion - there are typos in the comments for A267027.  For example, it should have shown B_k == 1 mod LCM(S)/s(k), rather than B_k == 1 mod s(k).  I'll edit accordingly and add the beat-rest pattern in the previous message as an example.

Hope that will clarify things.

Cheers,
Bob

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From: "Bob Selcoe" <rselcoe at entouchonline.net>
Sent: Wednesday, February 03, 2016 3:44 PM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: "Polyrhythmic" sequences

> Hi Viekko and Seqfans,
> 
> Thanks for the link, Viekko.  I'm also using the term as it is used in 
> music - no different than Walker. Polyrhythms are very basic in music and 
> are reflected in the definition provided in A267027; I hope the definition there is clear (I can elaborate, if needed).  Walker did not invent 
> or define the concept.
> 
> 
> Walker does provide nice audio/visual examples of polyrhythms here: 
> http://bouncemetronome.com/video-resources/polyrhythms/4-3-type-polyrhythms.  
> The 4:3 example ("4 against 3") reflects the beats as they appear in 
> sequence A267027: "beats" (b) are the sounds and "rests" (r) are silences. 
> So we have b-r-r-b-b-r-b-r-b-b-r-r repeated; when repeated indefinitely, the 
> beats are on 1,4,5,7,9,10 / 13,16,17,19,21,22 / 25,28,29,31,33,34... which 
> combines numbers congruent to 1 mod 3 and 1 mod 4.  This is A267027.
> 
> A047251 reflects beats as they appear in the 3:2 example; rests are A047238.
> 
> A267027, A047251 and A047238 are the only sequences in OEIS I could find 
> which directly reflect beats or rests in polyrhythms; so again, I'm very 
> interested in seeing how A258024 also applies.
> 
> Cheers,
> Bob
> 
> 
> 
> --------------------------------------------------
> From: "Veikko Pohjola" <veikko at nordem.fi>
> Sent: Wednesday, February 03, 2016 1:10 PM
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: "Polyrhythmic" sequences
> 
>> 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