Quote:
|
Originally Posted by John Henry
Numbers do not exist in nature, they exist in our heads. any numbers we see in nature are an artefacft of the seeing, not the nature. They are a simple way of describing relations between measurements we make.
|
Sorry, this is ridiculous. While the symbols we use for numbers are of purely human origin, the symbol is not the number, but rather a means of representing mathematical aspects of nature. Take a physics course.
Quote:
|
Originally Posted by 666
It has to do with how the systems scale, and without the supporting math it sounds pretty much like mysticism.
|
I've completed one semester of Differential Equations, and while there is still much higher math for me to explore, I would be surprised if this were insufficient for the purposes of our discussion.
Quote:
|
Originally Posted by 666
If you have two systems based on the same harmonic ratio, but at a different scale... in all probability the interactions between the systems where they overlap will be destructive. But when you overlay systems based on Phi (and sqrt(2) and e) you can end up with a third harmonic, also based on Phi (or sqrt(2) or e), in the overlapping region... because of the way that complex mathematical functions on these values are analogous to simpler functions. So the individual systems, and the combined systems remain coherent and stable... rather than fighting it out, each trying to overpower the resonance of the other system.
How clear is that?
|
It's clear enough - but it's also clear from your explanation (assuming for the moment that it is true) that Phi is not the only possible "base" for a musical system. Yet the Neanderthals used it, the Chinese used it, the Greeks used it, and we use it, when to my knowledge no musical systems on earth have been based on either
e or
v2. Your claim was that "harmonic systems based on Phi outperform non-harmonic systems or systems based on some other harmonic," but here you write that both
e and
v2 could be used, when, to my knowledge, they never were. (It is interesting to speculate on what such music would sound like. I hypothesize that, even though the wave forms would combine appropriately, humans would still find them unappealing.)
Additionally, why do you think that Phi so appealing to humans on a purely visual level? Conflicting wavelengths of light are not an issue, here. Humans did not evolve alongside pentagrams and golden rectangles, after all; assuming that natural selection programmed this aesthetic into human beings, how do you believe that it did so? What is so interesting to me is that Phi seems to underlie human aesthetics
in general, not merely the aesthetics of a single area. I'll expound on this further, but I want to see your response first.
--Mark