Tuning-Math Digests messages 6625 - 6649

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Message: 6625

Date: Sat, 22 Mar 2003 19:20:20

Subject: Re: Quartaminorthirds and muggles

From: Carl Lumma

> could i put in a request -- when you look at these, try to find 
> omnitetrachordal variants to the basic MOS scales . . .

Paul,

1. Omnitetrachordal just means the 4/3 doesn't have to be
cut in *four*, right?  The symmetry still has to be 3:2,
right?

2. How might one find such variants?

-Carl


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Message: 6626

Date: Sat, 22 Mar 2003 19:21:04

Subject: Re: Beatles[17] and squares[17]

From: Carl Lumma

> what can we say about the conditions leading to this kind of
> uniformity of the tetradic materials as a function of "root"
> scale degree number?

Paul,

Could you explain what you're asking here?  I'm not tracking
you.

-C.


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Message: 6627

Date: Sat, 22 Mar 2003 23:26:13

Subject: Re: T[n] where n is small

From: Carl Lumma

>>I don't know how many lines of maple you do this with,
>>but if they're few you can post them here and I can
>>either translate to Scheme or run them in maple myself.
>
>I could send you some Maple code I've written for various
>things if you have access to Maple.

Not sure how much of the stuff you do I can grok, but I do
have Maple, so send away!

-Carl


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Message: 6639

Date: Sat, 22 Mar 2003 15:01:07

Subject: Re: Quartaminorthirds and muggles

From: Carl Lumma

>> 1. Omnitetrachordal just means the 4/3 doesn't have to be
>> cut in *four*, right?
>
>are you sure you're phrasing that question correctly?

Mmm...

>> The symmetry still has to be 3:2,
>> right?
>
>as opposed to 4:3? i think it's more 3:2 than 4:3.

As opposed to 5:4.  I always forget the meaning of omnitetrachordal.
I think, because the tetra's still in there.

-C.


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Message: 6641

Date: Sat, 22 Mar 2003 15:14:26

Subject: this T[n] business

From: Carl Lumma

1. Paul, could you brief us on how the T[n] method compares
to what you and Kalle were using before?

2. The last version of this thread thread (see msg. 6017)
left off with how to identify important commas.  Gene's
mentioned square and triangular numbers as being better,
though I'm not sure why... though I imagine a high level of
non-primeness in general would be good, since it increases
chances of turning a simple interval into another simple
interval.  For the same reason, complexity (Tenney or
heuristic) might be good.

I suggested some measures which included size, but Paul's
probably right that size doesn't have anything to do with it.
Tangentially though, I asserted that Tenney complexity is
tainted wrt size, since smaller ratios tend to have bigger
numbers.

I got fed up with Excel and tested this assertion in Scheme.
Using all ratios with Tenney height less than 3000, I counted
how many approximated to each degree of 23-, 50-, and 100-et.
I didn't bother to plot the results, but a roughly equal
number of ratios seem to fall in all bins in each case,
whether I enforced octave equivalence or not.  So it seems my
assertion is wrong; simple ratios don't tend to be bigger.

-Carl


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Message: 6646

Date: Sat, 22 Mar 2003 20:13:16

Subject: Re: this T[n] business

From: Carl Lumma

>> 2. The last version of this thread thread (see msg. 6017)
>> left off with how to identify important commas.  Gene's
>> mentioned square and triangular numbers as being better,
>> though I'm not sure why...
>
>don't know

I suppose squareness and triangularity are types of
compositeness.

>> though I imagine a high level of
>> non-primeness in general would be good, since it increases
>> chances of turning a simple interval into another simple
>> interval.  For the same reason, complexity (Tenney or
>> heuristic) might be good.
>
>complexity would be bad (inverse complexity would be good),

Yep, that's what I meant.  Which is why n*d was in the den.
of my suggested measures.

>> I got fed up with Excel and tested this assertion in Scheme.
>> Using all ratios with Tenney height less than 3000, I counted
>> how many approximated to each degree of 23-, 50-, and 100-et.
>> I didn't bother to plot the results, but a roughly equal
>> number of ratios seem to fall in all bins in each case,
>> whether I enforced octave equivalence or not.  So it seems my
>> assertion is wrong; simple ratios don't tend to be bigger.
>
>that's the great thing about tenney complexity (as opposed to
>farey, mann, etc.)!

Ah, you've said that before, I think!

-Carl


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