Topic: Another 12-note scale

1 scales

Thread (1 messages)

From: Gene W Smith (2002-08-01)
Subject: Another 12-note scale

Here's a 12-note scale which is comparable to the ones I just did by
tempering Carl's. I took all the JI scales built from (15/14)^3 (16/15)^4
(21/20)^3 (25/24)^2 which consisted of two indentical tetrachords
separated by a 9/8=15/14 21/20. I got two scales and their inversions,
isomorphic by the 21/20 <==> 25/24 transformation. These scales turned
out to be adapted to the {225/224, 385/384} temperament, and on tempering
I ended up with just one scale (modulo modes) and its inversion. I took
this down a fourth to get some dominant harmony, and ended up with this:

1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15

27 (7-limit) intervals, 20 triads

Tempering it, I got the following:

! tetra.scl
! [61, 83, 83, 47, 61, 83, 83, 83, 47, 61, 83, 83]
{225/224, 385/384} tempering of two-tetrachord 12-note scale
! 858-et version of 1-21/20-9/8-6/5-5/4-21/16-7/5-3/2-8/5-5/3-7/4-28/15
12
!
85.31468531
201.3986014
317.4825175
383.2167832
468.5314685
584.6153846
700.6993007
816.7832168
882.5174825
967.8321678
1083.916084
2/1

46 (11 limit) intervals 74 triads

Something for Carl to think about.