catakleismic34semitransversal
17 note 2.3.7 semitransversal of Catakleismic[34]
Properties
| Notes | 17 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | 7-limit |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19423.html#19423 |
|---|
| Thread | 3 scales |
|---|
| Tone |
Tone (¢) |
Step |
Step (¢) |
| 28/27 |
63 |
28/27 |
63 |
| 243/224 |
141 |
6561/6272 |
78 |
| 9/8 |
204 |
28/27 |
63 |
| 7/6 |
267 |
28/27 |
63 |
| 243/196 |
372 |
729/686 |
105 |
| 9/7 |
435 |
28/27 |
63 |
| 4/3 |
498 |
28/27 |
63 |
| 112/81 |
561 |
28/27 |
63 |
| 81/56 |
639 |
6561/6272 |
78 |
| 3/2 |
702 |
28/27 |
63 |
| 14/9 |
765 |
28/27 |
63 |
| 392/243 |
828 |
28/27 |
63 |
| 12/7 |
933 |
729/686 |
105 |
| 16/9 |
996 |
28/27 |
63 |
| 448/243 |
1059 |
28/27 |
63 |
| 27/14 |
1137 |
6561/6272 |
78 |
| 2/1 |
1200 |
28/27 |
63 |
Similar scales
Parent scales
Child scales
Mailing list post
From: genewardsmith (2011-08-15)
Subject: Three views of Catakleismic[34]
When studying chord relationships in a MOS, it can be useful to look at a transversal. If you have a temperament like miracle or myna where 5 is relatively complex, you can take a 5-limit transversal, stick it into Scala and look at the lattice diagram, and use the triads as a guide to other chords, such as in particular the 7-limit tetrads. This works because the triads extend to tetrads.
However, consider for example catakleismic. This is a higher limit extension of kleismic which hasn't gained much traction since the 7 and 11 are so much more complex than the 5-limit, while 13, not so complex, is not as well in tune. But it's interesting at least in theory; for one thing, there's not much difference in tuning between marvel, tempering out 225/224, and catakleismic, which adds 4375/4374 to the mix. So it's one way of organizing anything in marvel temperament. But just looking at the 5-limit transversal for a catakleismic MOS is exactly the same as looking at kleismic; it's not much help for the more complex 7-limit. Below I give a kleismic transversal, but also a 2.5.7 transversal, and a 17-note 2.3.7 transversal; the latter because catakleismic is contorted as a 2.2.7 temperament. By sticking these various transversals into Scala you can get different views of Catakleismic[34].
! kleismic34trans.scl
!
Kleismic[34] transversal (detempering)
34
!
128/125
25/24
16/15
27/25
10/9
9/8
144/125
75/64
6/5
100/81
5/4
32/25
162/125
4/3
27/20
25/18
45/32
36/25
40/27
3/2
125/81
25/16
8/5
81/50
5/3
128/75
125/72
16/9
9/5
50/27
15/8
48/25
125/64
2/1
! catakleismic34semitransversal.scl
!
17 note 2.3.7 semitransversal of Catakleismic[34]
17
!
28/27
243/224
9/8
7/6
243/196
9/7
4/3
112/81
81/56
3/2
14/9
392/243
12/7
16/9
448/243
27/14
2/1
! catakleismic34trans.scl
!
Catakleismic[34] 2.5.7 transversal
34
!
128/125
401408/390625
48828125/44957696
15625/14336
125/112
28/25
3584/3125
11239424/9765625
1953125/1605632
15625/12544
5/4
32/25
100352/78125
12845056/9765625
78125/57344
625/448
7/5
896/625
114688/78125
9765625/6422528
78125/50176
25/16
8/5
25088/15625
3211264/1953125
9765625/5619712
3125/1792
25/14
224/125
28672/15625
89915392/48828125
390625/200704
125/64
2/1
Full thread (1 messages)
From: genewardsmith (2011-08-15)
Subject: Three views of Catakleismic[34]
When studying chord relationships in a MOS, it can be useful to look at a transversal. If you have a temperament like miracle or myna where 5 is relatively complex, you can take a 5-limit transversal, stick it into Scala and look at the lattice diagram, and use the triads as a guide to other chords, such as in particular the 7-limit tetrads. This works because the triads extend to tetrads.
However, consider for example catakleismic. This is a higher limit extension of kleismic which hasn't gained much traction since the 7 and 11 are so much more complex than the 5-limit, while 13, not so complex, is not as well in tune. But it's interesting at least in theory; for one thing, there's not much difference in tuning between marvel, tempering out 225/224, and catakleismic, which adds 4375/4374 to the mix. So it's one way of organizing anything in marvel temperament. But just looking at the 5-limit transversal for a catakleismic MOS is exactly the same as looking at kleismic; it's not much help for the more complex 7-limit. Below I give a kleismic transversal, but also a 2.5.7 transversal, and a 17-note 2.3.7 transversal; the latter because catakleismic is contorted as a 2.2.7 temperament. By sticking these various transversals into Scala you can get different views of Catakleismic[34].
! kleismic34trans.scl
!
Kleismic[34] transversal (detempering)
34
!
128/125
25/24
16/15
27/25
10/9
9/8
144/125
75/64
6/5
100/81
5/4
32/25
162/125
4/3
27/20
25/18
45/32
36/25
40/27
3/2
125/81
25/16
8/5
81/50
5/3
128/75
125/72
16/9
9/5
50/27
15/8
48/25
125/64
2/1
! catakleismic34semitransversal.scl
!
17 note 2.3.7 semitransversal of Catakleismic[34]
17
!
28/27
243/224
9/8
7/6
243/196
9/7
4/3
112/81
81/56
3/2
14/9
392/243
12/7
16/9
448/243
27/14
2/1
! catakleismic34trans.scl
!
Catakleismic[34] 2.5.7 transversal
34
!
128/125
401408/390625
48828125/44957696
15625/14336
125/112
28/25
3584/3125
11239424/9765625
1953125/1605632
15625/12544
5/4
32/25
100352/78125
12845056/9765625
78125/57344
625/448
7/5
896/625
114688/78125
9765625/6422528
78125/50176
25/16
8/5
25088/15625
3211264/1953125
9765625/5619712
3125/1792
25/14
224/125
28672/15625
89915392/48828125
390625/200704
125/64
2/1
Raw file
! catakleismic34semitransversal.scl
!
17 note 2.3.7 semitransversal of Catakleismic[34]
17
!
28/27
243/224
9/8
7/6
243/196
9/7
4/3
112/81
81/56
3/2
14/9
392/243
12/7
16/9
448/243
27/14
2/1
!
! https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19423.html#19423
!
! [info]
! source = Mailing lists
! file = tuning-math/messages/yahoo_tuning-math_messages_api_raw_18428-20927.json
! topic_id = 19423
! msg_id = 19423