Text: WHAT DIFFERENCE DOES IT MAKE? Posted By: somtum Date: Sunday, 27 June 2004, 2:59 a.m. In Response To: PYTHAGORAS AS RIEMANN KNEW HIM (Rosalinda) "What difference does it make what basic pitch we choose, as long as the other notes are properly tuned relative to that pitch? After all, musical tones are just frequencies, they are all essentially alike. So, why choose one pitch rather than another?" Compare the measurement of lengths on a straight line with that of arcs on the circumference of a circle. A straight line has no intrinsic measure; before we can measure length, we must first choose some unit, some interval with which to compare any given segment. The choice of the unit of measurement, however, is purely arbitrary. The circle, on the contrary, possesses by its very nature an intrinsic, absolute measure, namely one complete cycle of rotation. Each arc has an absolute value as an angle, and the regular self-divisions of the circle define certain specific angles and arcs in a lawful fashion. Just as the process of rotation, which creates the circle, imposes an absolute metric upon the circle, so also the process of creation of our universe determines an absolute value for every existence in the universe, including musical tones. Sound is not a vibration of the air. A sound wave, we know today, is an electromagnetic process involving the rapid assembly and disassembly of geometrical configurations of molecules. In modern physics, this kind of self-organizing process is known as a "soliton." Although much more detailed experimental work needs to be done, we know in principle that different frequencies of coherent solitons correspond to distinct geometries on the microscopic or quantum level of organization of the process. The bel canto human voice is for sound what a laser is for light: The voice is an acoustical laser, generating the maximum density of electromagnetic singularities per unit action. It is this property which gives the bel canto voice its special penetrating characteristic, but also determines it as uniquely beautiful and uniquely musical. By contrast, electronic instruments typically produce Helmholtzian sine-wave tones, which are ugly, "dead," and unmusical exactly to the extent that they are incoherent and inefficient as electromagnetic processes. -------- Let us now return to our soprano. She makes the first register shift, from first to second register, exactly at this point of division. The first tetrachord, C--D--E--F, is sung in the first register, while G--A--B--C are sung in the second register. The register shift divides the scale exactly at the geometrical-mean or halfway point in the cycle of conical spiral action. The same process repeats in the next-higher octave, where the shift from second to third register of the soprano comes once again at F-sharp, the geometric mean. The bel canto shift is a physical event of fundamental importance, and not merely a technical question for the voice. In physical terms, the register shift constitutes a singularity, a nonlinear phase change comparable to the transformation from ice to water or water to steam. Our solar system also makes a "register shift." It has long been noted that the inner planets (Mercury, Venus, Earth, and Mars) all share such common features as relatively small size, solid silico-metallic surface, few moons, and no rings. The outer planets (Jupiter, Saturn, Uranus, and Neptune) share a second, contrasting set of characteristics: large size, gaseous composition, many moons, and rings. The dividing-point between these two sharply contrasting "registers" is the asteroid belt, a ring-like system of tens of thousands of fragmentary bodies believed to have arisen from an exploded planet. The Golden Section To understand the well-tempered system better, we must first examine the reason why certain specific proportions, especially the Golden Section, predominate in our universe, whereas others do not. There is nothing mysterious or mystical about the appearance of the Golden Section as an "absolute value" for living processes. Space itself‹that is, the visual space in which we perceive things‹has a specific "shape" coherent with the Golden Section. all the above are snippets, not necessarily in sequence, from http://www.schillerinstitute.org/fid_91-96/fid_911_jbt_tune.html It's about sanity. There are so many, many things to do to fight. http://www.rumormillnews.com/cgi-bin/forum.cgi?read=51192

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