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