Topic: Five ten-note, four tetrad epimorphic scales

4 scales

Thread (2 messages)

From: Gene Ward Smith (2004-08-30)
Subject: Five ten-note, four tetrad epimorphic scales

I thought there were six, but my list had a duplicate. The first is
known to Scala as erlich11, "Canonical JI interpretation of the
Symmetrical decatonic mode of 22-tET". 

! cx1.scl
First 10/4 scale = erlich11 <10 16 23 28| epimorphic
10
!
15/14
7/6
5/4
4/3
10/7
3/2
5/3
7/4
15/8
2

! cx2.scl
Second 10/4 scale <10 16 23 28| epimorphic
10
!
15/14
7/6
5/4
4/3
7/5
3/2
5/3
7/4
15/8
2

! cx3.scl
Third 10/4 scale <10 16 23 28| epimorphic
10
!
21/20
9/8
5/4
21/16
10/7
3/2
5/3
7/4
15/8
2

! cx4.scl
Fourth 10/4 scale <10 16 23 28| epimorphic
10
!
35/32
9/8
5/4
21/16
35/24
3/2
105/64
7/4
15/8
2

! cx5.scl
Fifth 10/4 scale <10 17 24 29| epimorphic
10
!
49/48
7/6
6/5
5/4
7/5
35/24
3/2
12/7
7/4
2

From: Carl Lumma (2004-08-30)
Subject: Re: [tuning-math] Five ten-note, four tetrad epimorphic scales

>! cx1.scl
>First 10/4 scale = erlich11 <10 16 23 28| epimorphic
>10
>!
>15/14
>7/6
>5/4
>4/3
>10/7
>3/2
>5/3
>7/4
>15/8
>2
>
>! cx2.scl
>Second 10/4 scale <10 16 23 28| epimorphic
>10
>!
>15/14
>7/6
>5/4
>4/3
>7/5
>3/2
>5/3
>7/4
>15/8
>2
>
>! cx3.scl
>Third 10/4 scale <10 16 23 28| epimorphic
>10
>!
>21/20
>9/8
>5/4
>21/16
>10/7
>3/2
>5/3
>7/4
>15/8
>2
>
>! cx4.scl
>Fourth 10/4 scale <10 16 23 28| epimorphic
>10
>!
>35/32
>9/8
>5/4
>21/16
>35/24
>3/2
>105/64
>7/4
>15/8
>2
>
>! cx5.scl
>Fifth 10/4 scale <10 17 24 29| epimorphic
>10
>!
>49/48
>7/6
>6/5
>5/4
>7/5
>35/24
>3/2
>12/7
>7/4
>2

I'd guess that these are all equivalent under pajara.

-Carl