Tuning-Math Digests messages 6901 - 6925

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Message: 6901

Date: Mon, 16 Jun 2003 15:16:44

Subject: Re: Fried Alaska

From: Carl Lumma

>>>>and for any given brat, you can get arbitrarily close to JI.
>>> 
>>>Oh yeah?  Then brats are nonsense, I say.
>>
>>wha???
>
>At the least it means we'd need to consider the error as well
>as the brat -- brats alone would not be reliable.

Ironically, you use this sort of reasoning against prime limit
all the time.

-Carl


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Message: 6903

Date: Mon, 16 Jun 2003 15:52:12

Subject: Re: Fried Alaska

From: Carl Lumma

>> >At the least it means we'd need to consider the error as well
>> >as the brat -- brats alone would not be reliable.
>> 
>> Ironically, you use this sort of reasoning against prime limit
>> all the time.
>
>you're replying to yourself here.

Yeah...

>what sort of reasoning? let's see the analogy fleshed out.

There are ratios of low prime limit that are quite dissonant.
There are chords indistinguishable from just with very high brats.

I dunno, the sort of reasoning that looks at the function over
the pitch continuum and sees if there are anomalies.

-Carl


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Message: 6905

Date: Mon, 16 Jun 2003 16:24:36

Subject: Re: Fried Alaska

From: Carl Lumma

>i thought were were talking about well-temperaments with low,
>but rational, brats?

We were, but I suggested we compare bare chords instead of
temperaments, because that's what the assumption about the larger
tunings is based on.

>you obviously don't care what the brat is for any chord close enough
>to just -- it's the significantly tempered ones where brats may or
>may not be meaningful.

Apparently so.

>also, it's not the lowness of the brat, it's the simplicity of t

Right; I've just been saying lowness.

By simplicity, don't we mean something like the Van Eck widths?

-Carl


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Message: 6906

Date: Mon, 16 Jun 2003 16:27:16

Subject: Re: Fried Alaska

From: Carl Lumma

>>you obviously don't care what the brat is for any chord close enough
>>to just -- it's the significantly tempered ones where brats may or
>>may not be meaningful.
>
>Apparently so.

Also, if we replace "just" with "interval x" in Gene's statement,
brats are completely useless without some sort of tolerance adjustment,
like we use for odd limit.

-Carl


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Message: 6908

Date: Mon, 16 Jun 2003 19:21:27

Subject: Re: Fried Alaska

From: Carl Lumma

>> By simplicity, don't we mean something like the Van Eck widths?
>
>That's tough to answer without knowing what a Van Eck width is,

I found gcdb by the way, but have no idea how it works.

The Van Eck width of ratio Ri is log(R(i-1))-log(R(i+1)), where
Ri is, say, the ith ratio in a Farey series of order n.

Unfortunately, I guess these widths just shrink to nothing as
n goes to infinity.  The harmonic entropy based on them, however,
converges to a finite value.

>but the rules of simplicity are these:
>
>(1) q and -q, 1/q, and -1/q are equally simple. In particular, 0 and
>infinity are equally simple.
>
>(2) To judge how simple q is, you need to look at how simple 5/(3-2q)
>and (3-2q)/5q are as well.
>
>(3) Low numerators and denominators are better than high ones;
>bearing in mind that infinity = 1/0 counts as low.

Since we have no idea what's supposed to make one brat better than
another, I suppose this is fine.

-Carl


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Message: 6917

Date: Tue, 17 Jun 2003 13:42:54

Subject: Re: harmonic entropy (was: Re: Fried Alaska)

From: Carl Lumma

>Why is there such a list?

Rather than ask a question like that, why not accept it with
the rest of these miserable lists, and go there, where I've
already forwarded this thread, so as to commingle it with the
extremely valuable archives there?

-Carl


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Message: 6919

Date: Tue, 17 Jun 2003 14:18:02

Subject: that name again is harmonic_entropy

From: Carl Lumma

For those of you following along at home...

Yahoo groups: /harmonic_entropy/ *

-C.


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