musical complexity and Scala

>>How about, when given a number, with prime factorisation
>>
>>2^a * 3^b * 5^c * 7^d * ...
>>
>>we define something like the "musical complexity" of that number as
>>
>>2^(a*k_2) * 3^(b*k_3) * 5^(c*k_5) * 7^(d*k_7) * ...
>
>
>You betcha! That's Barlow's Indigenstibility Function!

I'm glad you said that, because I've heard of it but didn't know what it
was. I was actually playing with this in July, when I was in Berkeley. I
gave up when the only workable version I could find returned, after an
ungainly computation, odd-limit!

Does anybody know if this is the same as the "Barlow's harmonicity" stuff
that Scala returns? Or what the "Wilson harmonic complexity" is?

>Maybe even determined the factors by experiment?

While I personally find...

3=openess
5=sweetness
7=florescent lightingness

...and 15/8 to sound remarkably like its prime factorization would suggest,
I doubt there's really anything going on here, at least that an experiment
could turn up. If there was, I think you'd find the primes above 3
weighted out of the formula.

I also hear 9 as a type of 3ness, and in ratios with a 5 or 7 in one half
and a 9 in the other, I find the character dominated by the prime number.
But there's just not enough primes and odds in the low numbers to test
this. The next odd number above 9 is 15, which is already too high to give
these effects (i.e. 15/11 and 15/13 will approximate other lower-numbered
ratios at least well-enough to mask any 15-ness).

C.

> Does anybody know if this is the same as the "Barlow's harmonicity" stuff
> that Scala returns? Or what the "Wilson harmonic complexity" is?

Yes, I know :) and it is. I refer to Daniel's post for the explanation.
The prime weights implied by the Indigestibility function can be changed
to your own liking (SET HARMCONST). Together with SET WEIGHTING it can be
used in the rational approximation of intervals.

Manuel Op de Coul coul@ezh.nl

Carl Lumma wrote,

>While I personally find...

>3=openess
>5=sweetness
>7=florescent lightingness

>...and 15/8 to sound remarkably like its prime factorization would
suggest,

how would that differ from what 6/5's prime factorization would suggest?

> 3=openess
> 5=sweetness
> 7=florescent lightingness

That very closely coincides with my impressions of those prime factors.

To that I would add that 11 gives me a feeling of ambiguity.