From: rkliman@runet.edu (Richard M Kliman) Newsgroups: sci.bio.systematics,sci.cognitive,sci.logic,sci.math,sci.philosophy.meta,sci.skeptic,comp.ai.philosophy Subject: Re: Cynics Required Date: 20 Apr 1998 18:26:59 -0400 In article <353BB2A1.MD-0.198.sfx@2fx.u-net.com>, Si wrote: > The key point here, is that there is an unfortunately rife >misconception that Western tonality is somehow founded on a set of >ideal scientific principles. Because it ain't. In fact, it's no more >powerful, valid or correct than any other system. A good example is >the music of the indigenous Javanese; these people are perhaps unique >in that they actually possess two completely different tonalities - >/Slendro,/ with five nearly equal intervals, and /Pelog,/ which >divides an octave into seven, using a mixture of small and large >intervals. Yet by popular Western reckoning, such scales would >appear incompatible and irrational.... > > Of course, there are many different systems in use all over the >world. Some theorists have tried to locate universally consistent >intervals (such as the fifth), but I believe this is a classic case of >"not seeing the wood for the trees". I will shortly explain why..... Hindemith's Series I and II, IMHO, are nice ways to defend a 12-tone scale, though I'm not really convinced that Westerners, in general, really pay attention to anything more than the first couple overtones. However, one does not have to have a very refined musical sense to hear the first couple overtones (the octave and the next fifth). [I will also add that the 12-tone scale does not actually produce a perfect fifth, but it *is* the only scale between 5 and 19 notes that comes close.] >_A Maxim?_ > > There is only one musicouniversal: *All* tonal systems obtain their >notes by subdividing octaves. There are no exceptions. That is to >say, all humans consider an octave to be the "same" note as its root >tonic. But this clearly isn't the case - they're two different tones! >And yet it /feels/ the same. Weird, innit? (Note to Einar, Sherilyn >& Charles /et al:/ This was what I originally meant when I stated >that there is presently no satisfactory explanation for octaves.) The note in an octave are, of course, different tones. However, the combination tone produced by their simultaneous sounding reinforces the lower tone. Thus, the octave is more than something that just sounds pleasing to us; it's the only interval that reinforces one of the notes sounded. [The combination tone C = the difference between the two sounded tones, A and B. C = A-B, where A is the higher sounded tone. For C to equal A, B would have to be zero; that is, there would be no interval sounded. For C to equal B, 2C = 2B = A. When A is twice B, the interval is an octave.] > As I said yesterday, the "psychological chunking" hypothesis stumbles >at the first hurdle; most popular music is in 4/4 time. It isn't >processed as 2x2/2 - that would be a blatant fudge. It feels >intuitively wrong. 4/4 is 4/4, and 4 is not a prime number - period. >So if not primes, then what? Well, try and get your head round this: Whether or not you are right with respect to rhythm, I'm a little nervous about generalizing this to tonality. > *All* rhythms are also derived from factor-two synchrony. For the >purposes of this demonstration, let's make a distinction between >_beats_ and _rhythms._ A beat is a single percussive frequency, >whereas a rhythm is made from two or more such frequencies..... >synchronized by a factor of two. I'm not willing to grant you the above definition. Are you suggesting that a series of percussive frequencies played in straight 6/8 time (scherzo) is not a legitimate rhythm? > Imagine this simple beat: over a four-second measure you hear four >kick (bass) drums - one per second. Now add a closed hi-hat; one >coinciding with every kickdrum, and another in-between each kickdrum. >Overlay a snare with the second and fourth kickdrum. So over this >four-second period you'll hear two snares, four kicks, and eight >hats, all evenly spaced. A simple 4/4 rhythm. > > You can see where this is headed, right? I believe that this >structure represents a rhythmic standard-form. IOW, all rhythms are >based on this fundamental pulse of factor-two synchrony. This is >perhaps the biggest stumbling-block in my little scheme of things - >what about 3/4? 6/8 etc? Or 5/4 or 7/4 (e.g., Pink Floyd's "Money"). Your next point, that all rhythms resolve psychologically at a frequency ratio of 2:1 would sugges that these meters are psychologically disturbing, but I wonder if this is just a personal idiosyncrasy :) > The thing to bear in mind here is that it is not the numbers >describing the key-signatures that matter. Rather, it is how and >when a rhythm is perceived to *resolve.* And virtually all rhythms >resolve psychologically at a frequency ratio of 2:1. It is set in >stone. Those few exceptions are simply a clever play on the >"legitimate" neurological foundation of rhythm - factor-two synchrony. >They are the exceptions precisely because of this general rule. >They are the exceptions that _prove_ the rule. To me, it seems more parsimonious that the "rule" to which you refer is a social construct. Most Western music is written in common time (though much is not, particularly if you're willing to stay away from Rock). Pink Floyd's "Money" may strike us as "cool" because it strays from the cultural norm -- not because our evolved "rhythm centers" are disturbed. >Some musics are predominantly atonal, and so all music can be reduced >to this description: > >*Tonal and/or rhythmic modulation of factor-two synchrony.* Is it physically impossible for, say, Schoenberg (if he were alive) to write atonal music in 17/4 time? > If I've succeeded in making this point persuasively, then I hope >you're now asking the question: WHY? Why the hell should all Human >music, irrespective of any culturally stylistic context, even that of >peoples isolated since prehistoric times, share this characteristic? It seems intuitive to me that, for an ensemble to produce something musical, the individual members must be able to count on some type of unifying principle. This may be a (possibly complex) repeating cycle of downbeats. If there is no repeating cycle, then the unifying principle must be laid *very clearly* in advance -- or there must be a great deal of practice, practice, practice... > If you can, please tear this proposition to shreds: >/The key to a general understanding of this thing we call "music" is/ >/factor-two synchrony........./ I think you've placed the burden of proof on the wrong shoulders. Rich Kliman Dept. of Biology Radford University *standard disclaimer*