source file: m1403.txt Date: Sun, 3 May 1998 09:45:06 -0500 (CDT) Subject: Re: Open letter to Ken Wauchope and Dave Hill From: mr88cet@texas.net (Gary Morrison) >While there is the octave equivalence effect for intervals >differing by a factor of 2 or 2 to the nth power, so that a 10/4 interval is >psychologically harmonically more or less the same as a 5/4 interval, there >isn't such an equivalence effect for intervals related by factors other than >2. I think that those who favor a prime-based limit scheme would agree with that, but say that you're listening for the wrong thing. They would agree that any arbitrary power of 2 produces an effect of equivalence, but that equivalence is not what arbitrary powers of 3 produce. They'd say that three produces that feeling of steely coldness we hear in 3:2 and 4:3 (for example), and you can stack up as many threes as you'd like without changing that effect much. They'd then further say that any arbitrary power of 5 produces a sensation of sweetness, any power of 7 produces that classic septimal zap, and so forth. But there would not be a feeling of octave-like equivalence between, say, 3:2 and 9:8, because equivalence is a property of powers of 2. Again, I personally am a bit ambilvalent on the topic, but that's what I suspect the counterargument would be.