Re: 351 possible scales? - but I can't prove it

on 12/12/00 10:46 AM, tuning@egroups.com at tuning@egroups.com wrote:

> Message: 9
> Date: 11 Dec 2000 21:28:04 +0100
> From: monxmood@free.fr
> Subject: RE: FW: [MusicTheory] 351 possible scales? - but I can't prove it.
>

>
> I have a system of choosing them using the I ching coins. Using three coins
> with a value of 3 heads or 2 tails, the result table below tells us how to
> play the tubes of a whole tone panpipe.
> The panpipe in this example gives us one of two tones, open (nominal pitch)
> and shaded (a halftone lower). Six pipes cover an octave.
> So:
> 6 (2+2+2) Don't play the pipe
> 7 (2+2+3) Play the open sound
> 8 (2+3+3) Play the shaded sound
> 9 (3+3+3) Play both open and shaded sounds.
>
> Do it six times and you have a scale which can be any one of 4096
> possibilities. (this includes those which dont contain your starting note.)

I like this, have to try it later.

All this talk about scales reminds me of a beautiful concept regarding
Melodic and Position Permutations on page 2 of Lou Harrison's Music Primer.

"For two tones there are two positions, i.e. high-low or low-high. For three
tones there are 6 positions, i.e. low-mid-high, hi-mid-low, low-hi-mid,
mid-hi-low, mid-low-high, hi-low-mid. One multiplies the digits,
successively, of the total number of tones. Thus, for four, 1x2x3x4=24
positions for four tones."

This can easily keep me busy for a few hours... Enjoy,

Seth

--
Seth Austen

http://www.sethausten.com
email; seth@sethausten.com