reply to Erlich: prime/ odd again

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.

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?

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. I'd be flabbergasted if I found
out you actually really agree with me for once --
I can't object to anything you're saying here, except
that, in real music, I'd rather *hear* 13/8 or 25/16 than
any old 807-cent ET approximation.

Joseph L. Monzo
monz@juno.com

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