cpak15

optimal tetrad pack scale

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	15
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
35/32	155	25/24	71
9/8	204	36/35	49
49/40	351	49/45	147
5/4	386	50/49	35
21/16	471	21/20	84
7/5	583	16/15	112
35/24	653	25/24	71
3/2	702	36/35	49
63/40	786	21/20	84
105/64	857	25/24	71
7/4	969	16/15	112
147/80	1053	21/20	84
15/8	1088	50/49	35
2	1200	16/15	112

Parent scales

File	Notes	Max diff (¢)
cpak19	19	0.0
euler24	24	5.1
hemball	38	1.9
tenn41a	41	4.5
xen03-wilson-partch	41	4.5
valamute	31	9.1
xen03-secor-partch	43	4.5
xen03-wilson-positive-41	41	5.8
mund45	45	4.5
xen12-wilson-15-diamond-eikosany-union	37	7.7

Child scales

File	Notes	Max diff (¢)
cx4	10	0.0
lumma_wauchope-major	8	0.0
ninelim	5	0.0
keen6	5	3.0
xen09-wilson-marwa-09-08	7	7.7
xen09-wilson-marwa-09-09	7	7.7
xen12-wilson-09-4C2-hexany-04	6	7.7
Ethiopia_Mus_02_1976	5	11.0
hemi6	6	11.4
Central_African_Republic_Guinahui	5	12.1

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

! 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
!
! 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