source file: m1422.txt Date: Wed, 20 May 1998 15:19:59 -0400 Subject: Hello Joe Monzo! From: "Paul H. Erlich" >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.