Mailing list post
From: Gene Ward Smith (2005-09-11)
Subject: A 22-note 5-limit quasi-circulating scale
Here is a JI scale curiosity constructed in a way I think is new. I
used the approach I've been using for circulating beat-ratio scales,
but I solved only for brats of 0, 3/2 and infinity, which correspond
to pure minor thirds, pure major thirds, and pure fifths respectively.
Hence, the resulting scale is really a JI rather than RI scale; one
which attempts to circulate. Of the 22 major triads, 21 have either a
pure fifth or a pure major third, and nine have both. There are 15
pure fifths, 15 pure major thirds, and 9 pure minor thirds.
! quasic22.scl
A 22 note quasi-circulating scale
22
!
25/24
140625/131072
1125/1024
9/8
75/64
1265625/1048576
5/4
125/96
4/3
5625/4096
45/32
375/256
3/2
25/16
421875/262144
5/3
28125/16384
225/128
3796875/2097152
15/8
125/64
2
Full thread (2 messages)
From: Gene Ward Smith (2005-09-11)
Subject: A 22-note 5-limit quasi-circulating scale
Here is a JI scale curiosity constructed in a way I think is new. I
used the approach I've been using for circulating beat-ratio scales,
but I solved only for brats of 0, 3/2 and infinity, which correspond
to pure minor thirds, pure major thirds, and pure fifths respectively.
Hence, the resulting scale is really a JI rather than RI scale; one
which attempts to circulate. Of the 22 major triads, 21 have either a
pure fifth or a pure major third, and nine have both. There are 15
pure fifths, 15 pure major thirds, and 9 pure minor thirds.
! quasic22.scl
A 22 note quasi-circulating scale
22
!
25/24
140625/131072
1125/1024
9/8
75/64
1265625/1048576
5/4
125/96
4/3
5625/4096
45/32
375/256
3/2
25/16
421875/262144
5/3
28125/16384
225/128
3796875/2097152
15/8
125/64
2
From: Gene Ward Smith (2005-09-11)
Subject: Re: A 22-note 5-limit quasi-circulating scale
--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Here is a JI scale curiosity constructed in a way I think is new.
It certainly doesn't look like anything I've seen before when viewed
in Tonescape. It consists of a 4x4 Euler genus, a square of 16 notes,
with a handle of six notes coming out of a corner, defined by three
pure major thirds followed by three pure fifths.