source file: m1533.txt
Date: Wed, 23 Sep 1998 14:47:51 +0200

Subject: Re: scale derived by intersection of sets

From: Manuel.Op.de.Coul@ezh.nl

The smallest scale I could find which is a superset of Perry's scale is a
19-tone JI-scale by Max Meyer.

Max Meyer, see Doty, David, 1/1 August 1992 (7:4) p.1 and 10-14

 16/15 10/9 9/8 8/7 7/6 6/5 5/4 4/3 7/5 10/7 3/2 8/5 5/3 12/7 7/4 16/9 9/5
 15/8 2/1

This scale is inversionally symmetric so if Perry's scale is made
symmetrical
by adding the missing octave inverted tones then the resulting 17-tone
scale is
also a subset of this scale.
 16/15 10/9 9/8 8/7 7/6 6/5 5/4 4/3 3/2 8/5 5/3 12/7 7/4 16/9 9/5 15/8 2/1
I wrote a Scala program for creating Perry's scale:

harmonic 1 16
collapse
copy 0 1
invert
reverse
merge 1
copy 0 1
move 3/2
normalize
swap 1
normalize
intersect 1
clear 1
show

This program can be parametrised as follows:
! perry.cmd
echo Create a Perry-scale, an intersection of two harmonic/subharmonic
scales
echo Enter first and last harmonic
harmonic ? ?
collapse
copy 0 1
invert
reverse
merge 1
copy 0 1
echo Enter intersection interval
move ?
normalize
swap 1
normalize
intersect 1
clear 1
show

Manuel Op de Coul    coul@ezh.nl