cpak19

optimal tetrad pack scale

Open in Scale Workshop Scala analysis Download scl

Properties

Notes19
Period1200.0 ¢
Just7-limit
Source Mailing lists
Referencehttps://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12984.html#12984
Thread5 scales
Tone Tone (¢) Step Step (¢)
21/20 84 21/20 84
35/32 155 25/24 71
9/8 204 36/35 49
7/6 267 28/27 63
49/40 351 21/20 84
5/4 386 50/49 35
21/16 471 21/20 84
4/3 498 64/63 27
7/5 583 21/20 84
35/24 653 25/24 71
3/2 702 36/35 49
63/40 786 21/20 84
105/64 857 25/24 71
5/3 884 64/63 27
7/4 969 21/20 84
147/80 1053 21/20 84
15/8 1088 50/49 35
63/32 1173 21/20 84
2 1200 64/63 27

Similar scales

FileNotesRotationMax diff (¢)
xen07-chalmers-two-ninth-comma 19 2 10.1
xen07-chalmers-lst 19 2 11.3
xen07-chalmers-rvf-2 19 2 11.5
xen07-chalmers-19-31-equal 19 2 12.2
xen18-erlich-meantone-19 19 7 12.7
scott 19 18 12.7
mandelbaum7keemun 19 18 13.8
xen07-chalmers-chalmers 19 13 13.8
xen07-chalmers-fokker 19 7 13.8
xen07-chalmers-fokker-h 19 7 13.8

Parent scales

FileNotesMax diff (¢)
tenn41a 41 4.5
xen03-wilson-partch 41 5.8
xen03-wilson-positive-41 41 5.8
caleb46_tuning_92330_92333 46 4.5
rodan41 41 6.3
xen03-secor-partch 43 5.8
xen18-erlich-cynder-31 31 10.7
xen18-erlich-miracle-41 41 6.6
studwacko 41 7.0
miracle41 41 7.0

Child scales

FileNotesMax diff (¢)
cpak15 15 0.0
parizek_ji1 12 0.0
10highschool1 10 0.0
cx4 10 0.0
xen12-wilson-40-5C2-dekany-00 10 0.0
ch9_5 9 0.0
08_wauchope_symmetrical 8 0.0
kirkwood 8 0.0
lumma_wauchope-major 8 0.0
mavchrome7 7 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

! 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
!
! 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