Quote:
|
Yes, I think I understand you now. I feared that you might be a constructivist!
|
I didn't really understand what a 'constructivist' was, and I decided to look it up; it turns out to be some sweeping mode of thought that may have its roots or at least its most common expression in educational methodology. When I read the method, what I got out of it was, "the students run the class and the teacher watches and makes a few comments." Sounded like chaos, really. But, back to the real purpose!
Quote:
|
Yes, I certainly think there's an interesting argument to be had concerning whether the music of the Ainur was literally music or not. As I said, I come down on the literal side. But I can certainly see the points in favor of the other and the appeal of that side.
|
I think the idea that made this particular concept resonate (so to speak) was the constant striving of certain mathematicians and astronomers (Ptolemy, Pythagoreas, Kepler, etc.) to find a harmony in the mathematical descriptions of the motions of the planets, thus my comment earlier on the "Music of the Spheres." I searched about a little a found that the mathematical models of the angular velocity of the planets had been worked out to correspond to certain musical ratios, mainly thirds (major and minor) and fifths. I cannot remember how they correspond, though. Kepler had worked out these harmonic intervals for the 6 known planets in his time, and it turned out that the other subsequently discovered planets--Uranus, Neptune, Pluto--also corresponded to musical ratios with their angular velocity.
On another note, I ran up on a mathematician who was investigating crop circles, and the circles he had looked at followed these same harmonic ratios. Kepler had derived a 'song' for each planet, based upon his mathematical descriptions of their motions and positions.
The concept of the Music of the Spheres seems to draw science, philosophy and religion together somehow in that all seek this harmony. The sacred songs of medieval times were constrained to the 'perfect' harmonic ratios (1, 5, and 6, I think, but I'm working from a 25 year old memory here!). The permeation of this idea of harmonics, music and the realization of that music through mathematical means, links it to the material through the idea that the universe can be described mathematically. And it seems the idea of the different aspects (planets in my analogy) are ruled by different musical tones and progressions. If I recall correctly as well, the angels were the ones who pushed the crystal spheres around in their perfect orbits, so that the music could be made...I don't want to draw a one to one angel-Valar comparison, but I did want to throw out these ramblings to see if anyone could put it together more adeptly than I!
Cheers!
Lyta
[ November 23, 2003: Message edited by: Lyta_Underhill ]