kleismic34trans

Kleismic[34] transversal (detempering)

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	34
Period	1200.0 ¢
Just	5-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19423.html#19423
Thread	3 scales

Tone	Tone (¢)	Step	Step (¢)
128/125	41	128/125	41
25/24	71	3125/3072	30
16/15	112	128/125	41
27/25	133	81/80	22
10/9	182	250/243	49
9/8	204	81/80	22
144/125	245	128/125	41
75/64	275	3125/3072	30
6/5	316	128/125	41
100/81	365	250/243	49
5/4	386	81/80	22
32/25	427	128/125	41
162/125	449	81/80	22
4/3	498	250/243	49
27/20	520	81/80	22
25/18	569	250/243	49
45/32	590	81/80	22
36/25	631	128/125	41
40/27	680	250/243	49
3/2	702	81/80	22
125/81	751	250/243	49
25/16	773	81/80	22
8/5	814	128/125	41
81/50	835	81/80	22
5/3	884	250/243	49
128/75	925	128/125	41
125/72	955	3125/3072	30
16/9	996	128/125	41
9/5	1018	81/80	22
50/27	1067	250/243	49
15/8	1088	81/80	22
48/25	1129	128/125	41
125/64	1159	3125/3072	30
2/1	1200	128/125	41

Similar scales

File	Notes	Rotation	Max diff (¢)
xen18-erlich-hanson-34	34	25	4.2
xen18-erlich-keemun-34	34	25	5.7
cata34	34	22	8.0
xen18-erlich-vishnu-34	34	30	10.2
diasynch34	34	17	11.1
edo-34	34	2	11.9
secor_34wt	34	27	12.3
xen18-erlich-tetracot-34	34	9	12.9
xen18-erlich-wurschmidt-34	34	0	15.5
xen18-erlich-pajara-34	34	14	17.4

Parent scales

File	Notes	Max diff (¢)
xen18-erlich-hanson-53	53	4.2
edo-53	53	4.2
amity53pure	53	4.4
Sp53via19lim	53	4.5
SpaRational53Coll	53	4.6
Spa53tone256Hz	53	5.5
xen18-erlich-orson-53	53	5.7
septenarian53well	53	5.8
xen15-gilson-generalized-pythagorean-3-2-53	53	5.9
xen18-erlich-orwell-53	53	5.9

Child scales

File	Notes	Max diff (¢)
fivecrys2	19	0.0
xen07-chalmers-fokker	19	0.0
xen07-chalmers-fokker-h	19	0.0
xen07-chalmers-opelt	19	0.0
xen07-chalmers-wurschmidt-1	19	0.0
xen07-chalmers-wurschmidt-2	19	0.0
JoanAlbertBan18tone	18	0.0
cw12_5	12	0.0
dodek	12	0.0
duodene	12	0.0

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

! 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
!
! 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