source file: m1409.txt Date: Fri, 8 May 1998 18:54:59 -0400 Subject: Re: Open letter to Ken Wauchope and Dave Hill From: "Paul H. Erlich" Dave Hill wrote, >>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. Gary wrote, >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. If you're doing the stacking and maintaining the intermediary tones in the chord, then I would agree with them. Otherwise I would disagree. But there's more. "An arbitrary power of two produces an effect of equivalence." This must of course include the case where the power is zero, and the equivalence is greatest. The equivalence evidently falls off as the power increases. But what about steely coldness? Is it there when the power is zero? Does a unison contain all potential interval qualities, to a greater degree than the intervals themselves? It would seem hard to argue that way. The equivalence Dave was referring to was not a property of intervals themselves, but a similarity relation between different intevals. If there was a specific quality associated with given prime factors, than that quality might result in a similarity between different intervals with the same prime factors albeit to different powers. But it seems hard to formulate a consistent theory along those lines. What about intervals like 3/5? Does this have both steely coldness and sweetness? You can't say it has steely coldness and anti-sweetness because a 5/3 sounds the same as a 3/5. So does 15/1 (or 15/8) have the same qualities as 5/3, since the factors are still 5 and 3? It seems hard to maintain that 5/3 has a greater affective similarity to 15/8 (or 15/1) than to any other interval. But that is exactly where such an association of primes with qualities leads. No more time now, but I think any such prime-quality theory could be shown to be either logically inconsistent or severly at variance with observation.