Topic: Fourteen 12 note epimorphic scales with five tetrads

6 scales

Thread (1 messages)

From: Gene Ward Smith (2004-08-30)
Subject: Fourteen 12 note epimorphic scales with five tetrads

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