prime/odd limits

> you appear to agree with me that the "limit" is best defined as the
> largest odd, not prime, factor, in the ratios, when the intention is to
> characterize the complexity of an interval's sound.

I gave the example of a 19/13 being easier for me to hear a cessation
of beats than a 21/13, and to that extent, yes, the fact that 21/13 is
a 3*7 compound didn't seen to give it any special advantage. From the
strictly "monophonic" standpoint of listening for harmonic fusion
against a 1/1, I ranked the 21/13 as harder to hear.

Another example is the pair of neighbors 24/13 - 13/7, which I heard
as respectively "medium" - "easy" despite 24 being just an even
multiple of 3. So I would go a step beyond odd/prime and allow as how
evenness can't be ignored in this either -- it all just seems to boil
down to how many partials are involved and how faint and far out in the
spectrum they are.

However this was a very narrowly defined exercise concentrating only
on beating, roughness and harmonic fusion, without addressing any
other aspects of interval recognition, such as whether it's easier to
tune a 15/8 than a 13/7 based on affect, and if so, why. On the prime/odd
controversy, I'm still an agnostic. I've certainly noticed how 7, 11 and
13 sound exotic to me and 9 and 15 sound familiar, but just why that is,
I haven't decided. All I know that as far as a sense of harmonic fusion
against a 1/1 goes, a 15/8 doesn't win any prizes over a 13/7 or a 17/9
to my ear.

--Ken