Ratios and music

I've been reading Harry Partch lately. Great stuff. It became much more enjoyable after I printed my GRE vocab list and kept it nearby. Here is my book report on Partch's Genesis of a Music: This guy is neurotic.

I respect the work that he put into this stuff and all, it's just that he is overly thorough. The sad part is that his invented instruments are now quite obsolete as a result of technology.

Anyway here is the start of what may become a series of posts based on intonation.

Ratios.
Music is most correctly described as ratios. All those lines and dots and squiggles that is all the rage in today's music conservatories are misleading, erroneous, artificial, cumbersome... oh, don't get me started on notation.

The first rule of ratio music is two's are perceived as the same note. Tell a choir to sing an "A," the altos with perfect pitch, that is, all of them, will sing A440, which is a tone that vibrates at 440 times a second. The tenors will sing A220, the basses will sing A110, and the divas among the sopranos, that is, the entire soprano section will sing A880. 110, 220, 440, and 880. Halved or doubled, they're all the same note, just different octaves.

Now through a convoluted and arbitrary historical process that will wait for another day for thorough explanation, an octave on the piano contains 12 chromatic keys. This equally tempered scale is a perversion of the ratios that occur naturally in sound. The mindset behind equal temperament is, "Well, since its too hard to get most of the notes in tune, we'll just make all of them out of tune and they'll be close enough."

As a result, none of the ratios that you hear on a "well" tuned piano occur naturally except for the octave, the 2 to 1 ratio. Some knot-head about 500 years ago said to himself, "Hey, let's just forget about these inconvenient ratios and divide the octave into 12 equal segments."

Then he said. "That makes cents."