cpak31

optimal tetrad pack scale

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	31
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 (¢)
36/35	49	36/35	49
21/20	84	49/48	36
15/14	119	50/49	35
35/32	155	49/48	36
9/8	204	36/35	49
8/7	231	64/63	27
7/6	267	49/48	36
6/5	316	36/35	49
60/49	351	50/49	35
5/4	386	49/48	36
9/7	435	36/35	49
21/16	471	49/48	36
4/3	498	64/63	27
48/35	547	36/35	49
7/5	583	49/48	36
10/7	617	50/49	35
72/49	666	36/35	49
3/2	702	49/48	36
54/35	751	36/35	49
25/16	773	875/864	22
8/5	814	128/125	41
105/64	857	525/512	43
5/3	884	64/63	27
12/7	933	36/35	49
7/4	969	49/48	36
9/5	1018	36/35	49
64/35	1045	64/63	27
15/8	1088	525/512	43
48/25	1129	128/125	41
96/49	1164	50/49	35
2	1200	49/48	36

Similar scales

File	Notes	Rotation	Max diff (¢)
xen18-erlich-orson-31	31	10	9.7
xen18-erlich-orwell-31	31	3	9.7
xen18-erlich-luna-31	31	4	10.8
xen18-erlich-myna-31	31	22	12.0
vala	31	9	12.1
xen18-erlich-meantone-31	31	2	12.1
xen18-erlich-wurschmidt-31	31	21	12.2
cbrat31	31	20	12.4
woz31	31	12	13.1
circle31	31	23	13.1

Parent scales

File	Notes	Max diff (¢)
xen18-erlich-wurschmidt-34	34	12.2
hemball	38	12.2
41cosine	41	11.4
edo-41	41	12.1
Sp53Ragismatic	53	8.4
edo-33	33	15.6
SpDyadRat53	53	8.8
SpDyadRat53_tuning_89066_89410	53	8.8
edo-57	57	7.8
red72_11	72	4.5

Child scales

File	Notes	Max diff (¢)
metdia	19	0.0
15highschool2	15	0.0
xen12-wilson-06d-diamond	13	0.0
12highschool1	12	0.0
12highschool2	12	0.0
Spa_s_s_7_lim	12	0.0
cpak12	12	0.0
cv11	12	0.0
cv5	12	0.0
cv7	12	0.0

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

! 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
!
! 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