Topic: Four tetrads, nine notes

6 scales

Thread (1 messages)

From: Gene Ward Smith (2004-08-30)
Subject: Four tetrads, nine notes

I went looking for scales containing four tetrads in the -1 to 1 chord
cube, one of which was [0,0,0]. I found six such scales, the first two
of which are permuation epimorphic, which I give below. I also found
six ten-note, four tetrad scales which are strictly epimorphic.

! ch9_1.scl
Four tetrads one <9 14 21 26| permutation epimorphic
9
!
21/20
6/5
5/4
21/16
3/2
12/7
7/4
9/5
2

! ch9_2.scl
Four tetrads two <9 14 21 26| permutation epimorphic
9
!
21/20
35/32
5/4
21/16
35/24
3/2
49/32
7/4
2

! ch9_3.scl
Four tetrads three
9
!
15/14
35/32
5/4
35/24
3/2
25/16
7/4
15/8
2

! ch9_4.scl
Four tetrads four
9
!
49/48
35/32
7/6
5/4
7/5
35/24
3/2
7/4
2

! ch9_5.scl
Four tetrads five
9
!
21/20
7/6
49/40
5/4
21/16
7/5
3/2
7/4
2

! ch9_6.scl
Four tetrads six
9
!
7/6
5/4
4/3
7/5
10/7
3/2
5/3
7/4
2