Math and Music

Date: 4/10/96 at 11:48:40
From: Anonymous
Subject: Math in music

Dear Dr.Math,

I'm doing a project for math class and I need info. on how math is 
involved in music.  I've looked through all of the Internet sites 
and things come up for music and math individually but not 
together.  Can you help?

Date: 4/10/96 at 14:6:50
From: Melissa Dershewitz
Subject: Re: Math in music

Hi -

First off, I suggest that you get your hands on this book:

_Emblems of Mind: The Inner Life of Music and Mathematics_,
by Edward Rothstein.

It is full of interesting information, is fairly easy to 
understand without assuming too much math knowledge, and (if I 
recall correctly) has a nice bibliography that you could use to 
track down more info.

As for material on the web, I did a search of the Math Forum site 
and came up with several items. This one looks the most promising:

-------------------------
Fractal Music Project

http://www-ks.rus.uni-stuttgart.de:80/people/schulz/fmusic/   

New field of music research. "Fractal music is a result of a 
recursive process where an algorithm is applied multiple times to 
process its previous output. In wider perspective all musical 
forms, both in micro and macro level can be modelled with this 
process. Fractals provide extremely interesting musical results." 
Mailing list; Fractal Jazz; papers on fractal music and related 
topics; software; short examples of fractal music.
-------------------------

You might also find something useful in "Leonardo," a journal 
published by the International Society of the Arts, Sciences and  
Technology. It's on the Web at:

http://mitpress.mit.edu/Leonardo/home.html   

Hope this helps you out, and good luck with your project!

Dr. Melissa, The Math Forum

Date: 4/17/96 at 14:19:26
From: Doctor Patrick
Subject: Re: math in music

Hi!  Musical tones are also determined by ratios.  If you take a 
vibrating string, like the string from a guitar, it is possible to 
divide it up so as to make a musical scale by changing where you 
cut off the string.  For example, the octave will have the ratio 
of 2:1 over the next note of the same name - i.e. if one "c" is 
one meter long, then the next "c" would be either two meters or 
one half meter, depending on whether you want a higher or lower 
tone.  Longer strings produce lower tones, and shorter strings 
make higher tones.

Some other ratios are 3:2 for a perfect fith, and 4:3 for a 
perfect fourth.

I hope that this can be of some use to you.

-Doctor Patrick,  The Math Forum