cv13

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

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	12
Period	1200.0 ¢
Just	7-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_11451.html#11451
Thread	6 scales

Tone	Tone (¢)	Step	Step (¢)
16/15	112	16/15	112
28/25	196	21/20	84
6/5	316	15/14	119
5/4	386	25/24	71
4/3	498	16/15	112
7/5	583	21/20	84
3/2	702	15/14	119
8/5	814	16/15	112
12/7	933	15/14	119
7/4	969	49/48	36
28/15	1081	16/15	112
2	1200	15/14	119

Similar scales

File	Notes	Rotation	Max diff (¢)
12-of-blackjack	12	0	4.9
diadieorw2	12	0	5.2
diadie2	12	0	7.7
xen18-erlich-pajara-12	12	0	16.9
tertiadia1	12	5	19.6
tertiadia5	12	5	19.6
xen18-erlich-srutal-12	12	0	20.9
archytas12_tuning-math_19356_19356	12	11	21.9
jubilee12sym	12	5	24.7
Secor1_4TX	12	3	24.9

Parent scales

File	Notes	Max diff (¢)
diam7pluswoo	17	4.5
trab19marv	19	3.9
stellar	20	3.9
trab19_72	19	4.9
rosatimarv	21	3.9
blackjack_tuning_30510_30510	21	4.9
diamond9plus-marvel	21	5.1
keenan5	22	5.0
metdia	19	7.7
stellar5	20	7.7

Child scales

File	Notes	Max diff (¢)
qm2	7	4.9
xen15-chalmers-triadic-reversed-diamond-8192-6561	7	5.8
prop19_7b	7	7.4
prop19_7c	7	7.4
xen10-wilson-purvi-02b-02	7	7.7
hirajoshi2	5	7.7
ninelim	5	7.7
mavchrome1	7	7.7
mavchrome2	7	7.7
mavchrome4	7	7.7

Mailing list post

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

Full 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

Raw file

! 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
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_11451.html#11451
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_9945-12429.json
! topic_id = 11451
! msg_id = 11451