Math + Music Theory

I've just posted the first in a series of music-theory related posts on my math blog. For one thing, I'd like to know how much sense it makes to non-mathematicians. For another, I want to be sure that I'm not saying anything that's misleading. In order to keep the article under book-length I've had to make some simplifications and gloss a few things over. Finally, I know there are some microtonalists around here, and as the article briefly mentions 19tET and 34tET systems and their relative benefits and downsides, I thought it might spark some interesting discussion (read: internet food fight!)

http://mclaury.blogspot.com/2006/06/why-ar...per-octave.html

Actually, Leonhard Euler, a Swiss Mathematician,

wrote a very complex piece of music using complex

mathematics.

However, mathematicians said it was too musical

and musicians said it was too mathical.

Welcome back, Dan. (Are you in town? Would you mind printing up another copy of those forms? I don't have easy access to a printer.)

tenorman, I believe you're thinking of the book that Euler wrote about music, not a piece of music. As far as I know Euler never composed any music.

* * *

I've gone home for the summer, and I won't be back at Caltech until the beginning of next year. I hear the Page lab has an awesome color laser now, though, so I'll be able to print some up in full color.

I read the one page provided - couldn't find a link to another page but I'm strapped for time now and will return later.

I'm not sure of the value of asserting the mathematics of music to a composer. It may help understanding why certain things are as they are (like a perfect fifth deep in the bass has a differen (and to some, obnoxious) sound from one two octaves 4x the frequencies up. It may make simple harmonic progressions seem 'logical'. It's certain though that western tonality has had a very long reign (and will continue to do so) because its mathematical basis is somehow comprehended by the human senses.

It has also done some harm to me as a composer. E.g I wanted to unearth why minor keys sounded "sad" or "dark". Learning the most likely cause drove me away from the notion of major and minor and was the beginning of my writing "keyless"! Then again, awareness of the harmonic series and how it applies to individual instruments has been an aid.

My opener is, yes, I know the mathematics are there but I don't want to be aware of them when I compose. They might blow the magic.

M