cpak12

optimal tetrad pack scale = cv1

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_12984.html#12984
Thread	5 scales

Tone	Tone (¢)	Step	Step (¢)
21/20	84	21/20	84
9/8	204	15/14	119
6/5	316	16/15	112
5/4	386	25/24	71
21/16	471	21/20	84
7/5	583	16/15	112
3/2	702	15/14	119
8/5	814	16/15	112
12/7	933	15/14	119
7/4	969	49/48	36
15/8	1088	15/14	119
2	1200	16/15	112

Similar scales

File	Notes	Rotation	Max diff (¢)
cv1	12	5	0.0
archytas12_tuning-math_19356_19356	12	11	18.7
tertiadia5	12	5	19.6
xen18-erlich-pajara-12	12	6	22.1
xen18-erlich-srutal-12	12	0	24.1
Secor1_4TX	12	3	24.9

Parent scales

File	Notes	Max diff (¢)
blackjack_r	21	0.0
xen18-keenan-just-blackjack	21	0.0
perz	27	0.0
notchedcube	28	0.0
blackjack_tuning_30510_30510	21	4.9
cpak31	31	0.0
byzantine	23	7.7
keenan5_tuning_7341_7341	31	4.1
xen03-wilson-partch	41	0.0
keenan5_269	31	4.3

Child scales

File	Notes	Max diff (¢)
lumma_wauchope-major	8	0.0
hirajoshi2	5	0.0
ninelim	5	0.0
mir10	10	5.0
xen12-wilson-09-4C2-hexany-04	6	7.7
Indonesia_Lipurtambaneng	5	14.8
xen18-erlich-augmented-06	6	15.6
Indonesia_Hajanagara	5	15.8
xen18-erlich-augene-06	6	16.3
CD06_05_Egypt	7	17.5

Mailing list post

From: Gene Ward Smith (2005-10-23)
Subject: Some tetrad pack scales

I've investigated further the idea of finding scales by packing
tetrads in order, and the results are interesting. In the case of 12,
I got some
of the cv family--scales with five tetrads--discussed here:

http://groups.yahoo.com/group/tuning-math/message/11451

This invesitation was very promising, but could not be pushed to
larger scales because the computations became too heavy. The tetrad
pack scales are far easier to find, and probably zero in on some of
the same maximal tetrad scales. 

Below I give my pick of the best of the lot for 12, 15, 19, 22 and 31
notes to the octave. In the case of 22, something happened which had
concerned me as a possibility, namely that a scale was started but
there was no way to finish it correctly. Nonetheless, some good tetrad
pack scales emerged.

! cpak12.scl
optimal tetrad pack scale = cv1
12
!
21/20
9/8
6/5
5/4
21/16
7/5
3/2
8/5
12/7
7/4
15/8
2

! cpak15.scl
optimal tetrad pack scale
15
!
21/20
35/32
9/8
49/40
5/4
21/16
7/5
35/24
3/2
63/40
105/64
7/4
147/80
15/8
2

! cpak19.scl
optimal tetrad pack scale
19
!
21/20
35/32
9/8
7/6
49/40
5/4
21/16
4/3
7/5
35/24
3/2
63/40
105/64
5/3
7/4
147/80
15/8
63/32
2

! cpak22.scl
optimal tetrad pack scale
22
!
25/24
15/14
35/32
8/7
7/6
6/5
5/4
9/7
4/3
48/35
10/7
35/24
3/2
25/16
8/5
5/3
12/7
7/4
64/35
15/8
35/18
2

! cpak31.scl
optimal tetrad pack scale
31
!
36/35
21/20
15/14
35/32
9/8
8/7
7/6
6/5
60/49
5/4
9/7
21/16
4/3
48/35
7/5
10/7
72/49
3/2
54/35
25/16
8/5
105/64
5/3
12/7
7/4
9/5
64/35
15/8
48/25
96/49
2

Full thread (1 messages)

From: Gene Ward Smith (2005-10-23)
Subject: Some tetrad pack scales

I've investigated further the idea of finding scales by packing
tetrads in order, and the results are interesting. In the case of 12,
I got some
of the cv family--scales with five tetrads--discussed here:

http://groups.yahoo.com/group/tuning-math/message/11451

This invesitation was very promising, but could not be pushed to
larger scales because the computations became too heavy. The tetrad
pack scales are far easier to find, and probably zero in on some of
the same maximal tetrad scales. 

Below I give my pick of the best of the lot for 12, 15, 19, 22 and 31
notes to the octave. In the case of 22, something happened which had
concerned me as a possibility, namely that a scale was started but
there was no way to finish it correctly. Nonetheless, some good tetrad
pack scales emerged.

! cpak12.scl
optimal tetrad pack scale = cv1
12
!
21/20
9/8
6/5
5/4
21/16
7/5
3/2
8/5
12/7
7/4
15/8
2

! cpak15.scl
optimal tetrad pack scale
15
!
21/20
35/32
9/8
49/40
5/4
21/16
7/5
35/24
3/2
63/40
105/64
7/4
147/80
15/8
2

! cpak19.scl
optimal tetrad pack scale
19
!
21/20
35/32
9/8
7/6
49/40
5/4
21/16
4/3
7/5
35/24
3/2
63/40
105/64
5/3
7/4
147/80
15/8
63/32
2

! cpak22.scl
optimal tetrad pack scale
22
!
25/24
15/14
35/32
8/7
7/6
6/5
5/4
9/7
4/3
48/35
10/7
35/24
3/2
25/16
8/5
5/3
12/7
7/4
64/35
15/8
35/18
2

! cpak31.scl
optimal tetrad pack scale
31
!
36/35
21/20
15/14
35/32
9/8
8/7
7/6
6/5
60/49
5/4
9/7
21/16
4/3
48/35
7/5
10/7
72/49
3/2
54/35
25/16
8/5
105/64
5/3
12/7
7/4
9/5
64/35
15/8
48/25
96/49
2

Raw file

! cpak12.scl
optimal tetrad pack scale = cv1
12
!
21/20
9/8
6/5
5/4
21/16
7/5
3/2
8/5
12/7
7/4
15/8
2
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12984.html#12984
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_12430-15927.json
! topic_id = 12984
! msg_id = 12984