Topic: Detempering Sensi[27]

2 scales

Thread (1 messages)

From: Gene Ward Smith (2006-08-28)
Subject: Detempering Sensi[27]

Sensi[27] is a MOS containing the 7-limit diamond. Detempering it
gives the following 27-note JI scale containing the diamond:

! sensidia.scl
Detempered Sensi[27]; contains 7-limit diamond
27
!
28/27
21/20
15/14
10/9
8/7
7/6
6/5
56/45
5/4
9/7
4/3
27/20
7/5
10/7
40/27
3/2
14/9
8/5
45/28
5/3
12/7
7/4
9/5
28/15
40/21
27/14
2

The scale is not as regular as one might hope, having intervals
ranging from 225/224 down to 28/27. It has six otonal and six utonal
tetrads, and the subscale consisting only of those tetrads has 21
notes, also containins the diamond, and also has superparticular scale
steps:

! sentdia.scl
Consists of the tetrads of detempered Sensi[27] = sensidia.scl
21
!
21/20
15/14
10/9
8/7
7/6
6/5
5/4
9/7
4/3
7/5
10/7
3/2
14/9
8/5
5/3
12/7
7/4
9/5
28/15
40/21
2
! [[0, -2, -1], [0, -1, -2], [0, -1, 0], [0, -1, -1], [0, 0, -1], [-1,
0, -1], 
! [-1, 0, 1], [-1, 1, 0], [0, 0, 0], [-1, -1, 0], [-1, 0, 0], [-1, -1,
-1]]

This has six o and six u tetrads, and three each complete quintads.
One more of each kind if you marvel temper. Scale steps range from
50/49 down to 21/20, with all superparticular step sizes.