Re: metric stuff (Paul Hahn)

>>>1. take the prime factorization
>>>2. take the absolute values of all the exponents
>>>3. sum them all up
>>
>>The problem with this is, you end up with things like 9:8 being less
>>dissonant than 6:5.

Well, this would be a problem, if I hadn't meant "odd" instead of "prime"
in #1. This factorization should be done 'backwards', starting with the
largest number in the declared odd-limit (assigning the biggest possible
values to the composites, as you prescribe).

>Unless you discard octave equivalence and leave in all the 2s. Which, I
>realize, Carl _is_ advocating. But then it comes out the same as lg(n*d)
>again, I'm pretty sure.

I'm actually 'advocating' two independent things.

A. Don't ignore all factors in a fraction smaller than the largest one.
B. Don't ignore factors of two.

I'm willing to hear all arguments for or against either or both. I'm in
favor of weighting, but I think these may improve both normal and weighted
versions.

Here are some ways to satisfy them...

A. (n+d), (n*d)
B. whole-number limit, 2-axis on lattice

...of course, (n+d) and (n*d) typically will satisfy B as well. But one
can imagine first taking the odd limits of n and d, or taking an odd
factorization in the case of (n*d), as discussed above.

C.