cv11

Eleventh 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 (¢)
15/14	119	15/14	119
9/8	204	21/20	84
6/5	316	16/15	112
9/7	435	15/14	119
21/16	471	49/48	36
7/5	583	16/15	112
3/2	702	15/14	119
8/5	814	16/15	112
12/7	933	15/14	119
9/5	1018	21/20	84
15/8	1088	25/24	71
2	1200	16/15	112

Similar scales

File	Notes	Rotation	Max diff (¢)
cv9	12	10	7.7
tertiadia5	12	4	19.6
tertiadia1	12	4	19.6
tertiadia6	12	4	19.6
tertiadia4	12	11	19.6
xen18-erlich-pajara-12	12	5	21.1
archytas12_tuning-math_19356_19356	12	4	22.4
xen18-erlich-srutal-12	12	11	24.1
rainbow	12	8	24.4

Parent scales

File	Notes	Max diff (¢)
perz	27	0.0
notchedcube	28	0.0
cpak31	31	0.0
byzantine	23	7.7
schis41	41	0.0
tenn41b	41	0.0
mircube	31	4.4
mund45	45	0.0
valamute	31	6.2
betacub	46	2.0

Child scales

File	Notes	Max diff (¢)
tet3a	8	0.0
genggong	5	0.0
hirajoshi2	5	0.0
mir8	8	3.0
xen12-wilson-09-4C2-hexany-07	6	7.7
xen10-wilson-purvi-02b-01	7	7.7
Indonesia_Pelog_Gong_Sasak	5	12.5
Indonesia_Hajanagara	5	15.8
xen17-erlich-alternate-pentachordal-minor	10	17.5
Indonesia_Pelog_01_b	7	17.6

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

! 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
!
! 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