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An 18 note permutation epimorphic scale containing the 7-limit diamond

🔗Gene Ward Smith <gwsmith@svpal.org>

7/8/2005 5:02:34 PM

This is a permutation epimorphic 7-limit scale, both Hahn and TM
reduced, for <18 29 42 50|. Since this val does not order the 7-limit
diamond in increasing order (it makes 7/4 come before 12/7 and 7/6
before 8/7) it can't give an epimorphic scale in the strict sense--for
that, you need to go to 27 notes. Similarly, with 51 (or 52) notes you
can't linearly order the 11-limit diamond, so for a strictly
epimorphic scale, you need 58 notes.

This scale has 4 otonal and 4 utonal tetrads, and marvel tempering it
gives an additional otonal and utonal tetrad. Below I give three
versions of it.

! diamin7.scl
permutation epimorphic scale with 7-limit diamond, Hahn and TM reduced
<18 29 42 50|
18
!
16/15
10/9
7/6
8/7
6/5
5/4
4/3
27/20
7/5
10/7
3/2
8/5
5/3
7/4
12/7
9/5
15/8
2

! diamin7marv.scl
1/4 kleismic tempered diamin7
18
!
115.587047
184.331593
268.798786
231.174094
315.641287
384.385833
499.972880
515.695527
584.440073
615.559927
700.027120
815.614167
884.358713
968.825906
931.201214
1015.668407
1084.412953
1200.000000

! diamin7_72.scl
diamin7 in 72-et
18
!
116.666667
183.333333
266.666667
233.333333
316.666667
383.333333
500.000000
516.666667
583.333333
616.666667
700.000000
816.666667
883.333333
966.666667
933.333333
1016.666667
1083.333333
1200.000000