Cv scales

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From http://tech.groups.yahoo.com/group/tuning-math/message/11451

It turns out there are a lot of five tetrad scales involving only 11 notes (I've got a list of 132 of them) but none I've found are strictly epimorphic. Checking for permutation epimorphic scales may be a good plan.

Of course, there are even more five tetrad scales with 12 notes, but here I give only ones which are epimorphic--all, as it turns out, with the standard val. I cataloged these in pairs, where the odd numbers have three major and two minor tetrads, and the even pairs the reverse. Marvel tempering removes this distinction, and I only list the odd, with the three major tetrads.

I found two scales I've found before, "pris" and "hen12". The latter is an adjusted version of the Hahn reduction of a chain of fifths.

! cv1.scl

First 12/5 <12 19 28 34| epimorphic

12

!

16/15

8/7

7/6

5/4

4/3

7/5

3/2

8/5

5/3

7/4

28/15

2

! cv3.scl

Third 12/5 scale <12 19 28 34| epimorphic = pris

12

!

16/15

28/25

7/6

5/4

4/3

7/5

3/2

8/5

5/3

7/4

28/15

2

! cv5.scl

Fifth 12/5 scale <12 19 28 34| epimorphic = inverse hen12

12

!

15/14

9/8

6/5

5/4

21/16

7/5

3/2

8/5

12/7

7/4

15/8

2

! cv7.scl

Seventh 12/5 scale <12 19 28 34| epimorphic

12

!

21/20

9/8

6/5

9/7

21/16

7/5

3/2

8/5

12/7

9/5

15/8

2

! cv9.scl

Ninth 12/5 scale <12 19 28 34| epimorphic

12

!

15/14

8/7

7/6

5/4

4/3

10/7

32/21

8/5

5/3

25/14

40/21

2

! cv11.scl

Eleventh 12/5 scale <12 19 28 34| epimorphic

12

!

15/14

9/8

6/5

9/7

21/16

7/5

3/2

8/5

12/7

9/5

15/8

2

! cv13.scl

Thirteenth 12/5 scale <12 19 28 34| epimorphic

12

!

16/15

28/25

6/5

5/4

4/3

7/5

3/2

8/5

12/7

7/4

28/15

2