Hello Joe Monzo!

>I was intriguedt upon re-reading this:

[Paul Erlich:]
>> Harmonically speaking, an interval is never more
>> likely to be interpreted as a higher-odd-limit, lower-prime-limit
>> ratio than a higher-prime-limit, lower odd-limit ratio,
>> holding the approximation error constant.

[Monzo:]
>Doesn't this support my theory that primes have
>unique properties that allow them to be easily
>identified? It seems strange coming from you,
>since you say you disagree with this theory.

No, it doesn't support your theory at all.

>As an example, say we're examining an "augmented 5th"
>or "minor 6th" of 807 cents. This is exactly midway
>(in cents) between the proportions 26:16 (= 13:8)
>and 25:16. Are you saying that the interval would be
>recognized as 13 (= 13^1) rather than as 25 (= 5^2),
>because 13 is a higher prime than 5, but a lower odd
>number than 25?

I would say that this interval is more likely to be heard as 13/8 than
25/16 because 13 is a lower odd number than 25. Of course, there are
other ratios that this interval is even more likely to be heard as. I
brought in the point about primes simply to point out that simple prime
factors _don't_ count for much acoustically, and that ratios like 64:45,
despite their low prime factors, are never really the just "target" for
a harmonic interval.

>That's what it sounds like you're saying to me, and it
>seems contradictory to everything you've written on
>the subject so far.

If you really think so, then I must suppose you have really failed to
understand my views. No offense, but my honest opinion is that, rather
than trying to penetrate a theory or style of music and see it as a
logically or aesthetically consistent whole, you focus on whatever
elements fit into your point of view, whether you're talking about
Schoenberg, Robert Johnson, or me.