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### Math and Music

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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

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
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

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