Date: Jun 17, 1996 4:50 PM
Author: Dave Rusin
Subject: Re: Fundamentals of music



In article <4pm64j$au4@eccles.dsbc.icl.co.uk>,
Roy Lakin <roy@dsbc.icl.co.uk> wrote:

>Helmholtz's "Sensations of Tone" showed a 53-keys-to-the-octave keyboard
>where you would have to move backwards and forwards to transpose keys, so
>as to position your hands above a slightly different subset.
>

The 'best' number of tones per interval can be deduced from a
continued-fraction argument, as another poster noted, although in
practice there have been some reasonably successful experiments with,
say, a 19-tone scale. After a 12-tone scale, a 'best' candidate would
be a 41-tone scale. I once rigged my PC keyboard to play the 41-tone
octave. You might wish to play with it; look in

http://www.math.niu.edu/~rusin/uses-math/music/

(where you will find summaries of previous threads on this theme, too).

dave