Re: [tuning] RE: Re: The CPS blues...[combination product sets]

Dan! or John Chalmers!
I have asked Erv about this and with the data at hand , he does not know what letter to
John Chalmers this is. Would like to figure this one out! Carl Lumma wrote:

> >>So, Daniel, stellation is only defined for an m-out-of-n CPS if n = m*2,
> >>right?
> >
> >No -- sorry, I'm wrong about this. On page 3 of the "Letter to John
> >Chalmers", Wilson indicates five possible solutions for a "stellated
> >dekateserany". (All five are present in the stellated Eikosany.) It
> >appears that the n=2m CPSs will each have single stellations while the
> >non-2=2m CPSs will have m possible stellations.
>
> Wow- I'd like to see that. There should be exactly one complete
> stellation for every CPS, regardless the proportion of m and n.
>
> How many tones would they have? That's an interesting question.
> I don't suspect the answer would be in Pascal's triangle. For
> CPS's with 2:1 m:n, I think the answer is as simple as t + s(c),
> where t is the number of tones in the un-stellated structure, c
> is the number of un-saturated chords in the CPS, and s is the
> number of identities needed to saturate the CPS's basic chord.
> The 14 tones of the stellated hexany make sense here; each of the
> hexany's 8 triads needs 1 extra note. The something is different
> with the 70 tones of the stellated eikosany, tho; each of its 30
> tetrads needs 2 extra notes, giving 80, but according to Chalmers
> the stellated 1*3*5*7*9*11 eik. has 70 notes. So either 10 notes
> are redundant due to the composite 9-factor, or 10 points are
> getting re-used somewhere and my formula is incorrect (which is
> unlikely, since the chords of the CPS will already exploit the
> maximum number of common-tone relations in prime-factor JI: 2).
>
> For non-2:1-m:n CPS's, the answer is more difficult, since s is
> not a constant.
>
> -Carl
>
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Carl Lumma wrote,

>How many tones would they have? That's an interesting question.
>I don't suspect the answer would be in Pascal's triangle. For
>CPS's with 2:1 m:n, I think the answer is as simple as t + s(c),
>where t is the number of tones in the un-stellated structure, c
>is the number of un-saturated chords in the CPS, and s is the
>number of identities needed to saturate the CPS's basic chord.

Carl, I think you mean "complete" and not "saturate" and "saturtated".
Anyway, as simple as that formula is, I think you can simplify it further.

>The something is different
>with the 70 tones of the stellated eikosany, tho; each of its 30
>tetrads needs 2 extra notes, giving 80, but according to Chalmers
>the stellated 1*3*5*7*9*11 eik. has 70 notes. So either 10 notes
>are redundant due to the composite 9-factor, or 10 points are
>getting re-used somewhere and my formula is incorrect (which is
>unlikely, since the chords of the CPS will already exploit the
>maximum number of common-tone relations in prime-factor JI: 2).

What's that last lemma, Lumma?

>For non-2:1-m:n CPS's, the answer is more difficult, since s is
>not a constant.

I still am waiting for Daniel Wolf to reply to my post on that subject so
that we can have a better sense of what these look like.

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