source file: m1403.txt Date: Sun, 3 May 1998 12:52:27 -0400 Subject: prime/ odd limits From: monz@juno.com (Joseph L Monzo) > I personally am pretty much a fence-sitter on the > prime vs. odd question, but perhaps it's worth > asking: Do you perceive that there's any mechanism > in our auditory system for detecting powers of two > (i.e.,octaves)? If so, then why not powers of three or five? As anyone who reads this digest knows by now, I am someone who certainly believes that our ears/ brains calculate prime factorization as we listen to music. I think Gary Morrison's second sentence here gives the best perceptual evidence that it occurs: under normal circumstances (i.e., instruments with basically harmonic spectra), no-one will deny being able to hear the similarity of tones one or several octaves apart. Admittedly, 2 is a very special prime number, in that it is the only one which is even (not odd), so most likely, this fact can go a long way to explain why we hear these similarities. But I still maintain that each prime factor in the music is like a separate dimension in sound and feeling. I personally feel that most of those who either deny or fence-sit on prime-factorization do so simply because we are largely unfamiliar with the sounds and feelings created by most higher-prime ratios, i.e., those other than straight harmonics of the 1/1. Even today among JI microtonalists, I would say that 7 is the highest prime that's generally used in a systematic way (Partch is the big exception, along with a few others) -- higher primes are generally used only as "overtones" of the 1/1. For example, 17/8 or 19/8 may be corralled for use as the "flat 9" or "sharp 9", but most other 17- and 19-limit ratios will not be used. Following Partch's lead, I would say that the only way to decide beyond a doubt on the questions regarding higher primes in music, is to hear lots of high-prime music. As I've said before, in my theory, the sonance continuum tends to increasing dissonance as the numbers of *both* the primes *and* their exponents increase. I tend to agree with most of what's been posted here in the last week about perceptual limitations and dissonance: dissonance increases linearly as the size of the odd numbers increases, and at some point around 19, 21, or 23 our perceptual ability falters. According to my theory, intervals which are similar in size (cents) will have different "flavors" based on the prime numbers involved. The jury is still out on whether these "flavors" can be perceived in individual dyads. I tend to feel that they become more evident in more complex chords and in other situations where the context provides more to compare to. This is the essence of the matter to me. Our mental apparatus will try to simplify everything we hear (and remember -- ultimately, harmony is rhythm too, just speeded up a great deal) into its most basic components. In my opinion, if we are scrutinizing a particular dyad with a more complex ratio, it is very easy to hear it as something else which lies close by in frequency but has much simpler relationships -- simpler meaning basically lower prime numbers, or just smaller numbers period. If other surrounding musical events are present, they will help us pinpoint what that particular interval is if it is a larger-number relationship. In my "Hendrix Chord" piece, the 12-eq chord is played and then all pitches are "bent" until they form a JI chord. This JI chord is transposed slightly higher in each successive measure. Even where these "roots" are less than 1 cent apart, I hear clearly audible differences in beating. The ratios in the JI chord are always the same, so the only thing to which I can ascribe these differences is the relationship of the transposition (a high-prime ratio) to the *memory* of the original 1/1, plucked at the start of the chord before the notes slide upward. Joseph L. Monzo monz@juno.com 4940 Rubicam St., Philadelphia, PA 19144-1809, USA phone 215 849 6723 _____________________________________________________________________ You don't need to buy Internet access to use free Internet e-mail. Get completely free e-mail from Juno at http://www.juno.com Or call Juno at (800) 654-JUNO [654-5866]