source file: m1415.txt Date: Thu, 14 May 1998 15:23:32 -0400 Subject: Prime/Odd and harmonic complexity From: monz@juno.com (Joseph L Monzo) After describing a list of ratios between 399.1 and 415.7 cents, with their prime limits, Paul Erlich wrote: > If you have a way of tuning intervals with 0.1 cent > precision, hold one note constant and sweep the other one > through this range. Without looking, stop the sweep where you > hear 3-ness. Do the same for 7-ness,... As I stated in a post a few weeks ago, I think you're missing the point here, Paul. I agree with you totally here: to my ears, it's difficult if not _impossible_ to isolate _exact_ prime qualities in a _dyad_. But add some more notes, and it becomes fairly easy to compare the qualities heard in comparing various intervals. To my ears, fairly subtle pitch shadings can be distinguished in a complex harmonic environment, and the only thing to which I can attribute this ability to distinguish, is prime factorization. I agree with what most subscribers have said (and you have said that you can agree with this too), that in a _very general_ sense, humanity has historically expanded its familiarity with prime qualities in music in an evolving manner, certainly beginning with prime-base 2, then continuing with 3, much later 5, and more recently 7 and higher primes. But these prime qualities don't mean much if you're talking about a harmonic context of less than 3 notes. It seems that, again in a general sense, people's aural sensibilities reach a point where they're ready to embrace the particular quality exhibited by a "new" prime. Recognizing the unique quality of 2 gives us a scale of octaves -- not very useful musically. Stacking powers of 3 gives a scale of 12 obviously different notes, and if continued, new notes which are only a small distance (a "Pythagorean Comma" or 23.46 cents) away from those 12. Of course, since 9=3^2, this 3-Limit scale gives exact harmonic 9-identities. Prime-base 5 became accepted as a harmonic interval because it gave a new sound to the musical interval of a "3rd", a sound which was "sweeter", "softer", "more mellow", but at any rate very different, from the sound of the 81/64 or 3-Limit "3rd". In expanding pitch resources, rather than create new scales by stacking powers of 5, a few powers of 5 were used as bases from which were created other new scales by stacking powers of 3. At this point in history (today), I don't think anyone will dispute that 7 is implied very strongly in most new tonal music in our culture. This is because of a similar process of prime-base 7 giving a harmonic "minor 7th" which is much more consonant, in contexts where the minor 7th is used in tbe manner of a consonance (as in the blues). Certainly, there is still a place, even in contemporary music, for 3- and 5-limit minor 7ths and minor 3rds, but just as certainly, 7/4 and the "septimal minor 3rd" 7/6 have been enthusiastically accepted. Harry Partch put 11 out there, Jon Catler's using 13, Ben Johnston has gone as far as 31, Ezra Sims implies up to 37, and La Monte Young's current Dream House goes up to 283, but alas, all this music is so little known... I'm coming to think more and more that this prime-factor interplay is most expressive when it clashes against 12-Eq accompaniment. Perhaps this is why I'm so attracted to certain blues performers. Robert Palmer, in his book "Deep Blues", characterizes the "deep blues" of the title as that blues style deriving from the (Mississippi) "Delta" (the area south of Memphis). Palmer emphasizes again and again throughout the book that one of the primary ingredients that sets this style apart from other blues styles is its best performers's (Robert Johnson, Muddy Waters, Otis Rush) subtle use of microtonality in the high bottleneck guitar lines and especially in the vocals. What's important to remember is that the rest of this music, meaning the strummed guitar notes, the bass lines, and piano if present, would be in 12-Eq (or something very close, depending on how well-tuned the instruments were). This clash also figures importantly in the style of Hendrix, and of course, is at the bottom of the dispute to Schoenberg's claims of the 12-Eq scale's implied ratios. I'm beginning to have a lot more respect for Johnny Reinhard's concept of "polymicrotonality", partly for this reason (and partly because Reinhard's own compositions exploit the idea so effectively, regardless of what Anthony Tommasini thinks). The point, as far as a response to Erlich, is that _complexity_ of harmonic resources gives lots of intervals, odd numbers, and primes to compare, and I think that as the harmonic resources become more complex, we rely more and more on prime factorization to delineate the differences, to "put together what goes together". (I'd really like to see more feedback about microtonality in the blues.) Joseph L. Monzo monz@juno.com _____________________________________________________________________ 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]