cv9

Ninth 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
8/7	231	16/15	112
7/6	267	49/48	36
5/4	386	15/14	119
4/3	498	16/15	112
10/7	617	15/14	119
32/21	729	16/15	112
8/5	814	21/20	84
5/3	884	25/24	71
25/14	1004	15/14	119
40/21	1116	16/15	112
2	1200	21/20	84

Similar scales

File	Notes	Rotation	Max diff (¢)
cv11	12	2	7.7
tertiadia5	12	6	19.6
Secor1_4TX	12	3	24.9
archytas12_tuning-math_19356_19356	12	0	24.9
xen18-erlich-srutal-12	12	1	25.0

Parent scales

File	Notes	Max diff (¢)
xen18-keenan-blackjack-guitar	21	3.8
qx2	31	0.2
rational_canasta	31	3.9
rational_canasta_tuning_22793_23190	31	3.9
xen18-erlich-miracle-31	31	4.5
keenan5_269	31	4.5
keenan5_tuning_7341_7341	31	5.0
perz	27	7.7
hemw	41	2.1
edo-31	31	7.0

Child scales

File	Notes	Max diff (¢)
CD15_10_Morocco	6	11.8
Ethiopia_Mus_02_Bati_Zafan	5	15.0
CD15_12_Morocco	7	15.8
xen09-wilson-marwa-16a-08	7	16.6
CD15_11_Morocco	7	18.1
Greece_Second_Plagal	7	18.2
Ethiopia_Tizita	5	21.2
CD15_17_Morocco	6	22.2
archytas7	7	22.4
CD17_14_Tunisia	6	23.1

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

! 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
!
! 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