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Sharing intervals with the 7-limit diamond

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

8/28/2006 4:58:28 PM

The scale consisting of all tetrads sharing an interval with the
7-limit diamond consists of 43 notes, but two of its steps are
2401/2400s. If we breed-reduce it, we get a 41-note scale with 18
otonal and 18 utonal tetrads, and 10 each quintads, which compares
favoribly to Ennealimmal[45]. Of course some of these are off by
2401/2400 if you want to worry about that, and of course you can temper.

! dint.scl
Breed reduction of 43 note scale of all tetrads sharing interval with
7-limit diamond
41
!
49/48
36/35
25/24
21/20
16/15
15/14
35/32
10/9
28/25
8/7
7/6
25/21
6/5
49/40
5/4
9/7
21/16
4/3
48/35
7/5
10/7
35/24
3/2
32/21
14/9
8/5
49/30
5/3
42/25
12/7
7/4
25/14
9/5
64/35
28/15
15/8
40/21
48/25
35/18
49/25
2