## Silver Ratio・銀の比2013/05/09 | [MP3] [FLAC] | |||

For Pierre Laurent Wantzel, 1814-1848. "Ordinarily he worked evenings, not lying down until late; then he read, and took only a few hours of troubled sleep, making alternately wrong use of coffee and opium, and taking his meals at irregular hours until he was married. He put unlimited trust in his constitution, very strong by nature, which he taunted at pleasure by all sorts of abuse. He brought sadness to those who mourn his premature death." (Adhémar Jean Claude Barré de Saint-Venant) Project: Year of the Dragon. Wantzel is best known for proving that certain geometric tasks cannot be accomplished with straightedge and compass. The sounds in here sound to me like pipe organs and bells, but they are purely synthetic, derived from Mandelbrot and Julia sets. If you put a cosine wave into the horizontal coordinate of an oscilloscope, and a sine wave (which is the same thing, shifted 90 degrees) into the vertical, then the 'scope will trace out a circle. If instead it traced out a Julia set, or the boundary of the Mandelbrot set, what kind of wave would cause that and how would such a wave sound? Well, not as interesting as I'd hoped, until I layered a whole bunch of them; this is the result. The real and imaginary parts, which I had expected to be quite different, actually sound pretty much the same; see if you can figure out why. In the case of Julia sets, the waveforms contain only odd harmonics because of symmetry about the origin. The Bohlen-Pierce scale is supposed to be good for odd harmonics, and is nicely weird, so that's used throughout. The bells are a little self-indulgent, and not really very mathematically relevant, but even they have some connection to the rest of it because they are the Mandelbrot waveform again disguised with single sideband AM. |