Xenharmonic Wiki

Kleismic family: Difference between revisions

← Older editNewer edit →
VisualWikitext
m →Tritikleismic: edo list (my result 87 isn't better than 72)
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,030 edits
No edit summary
Line 177: Line 177:


= Catalan =
= Catalan =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 190: Line 189:
{{Val list|legend=1| 15, 34d, 49, 132bcd }}
{{Val list|legend=1| 15, 34d, 49, 132bcd }}


[[Badness]]: 0.0949
[[Badness]]: 0.094872


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 202: Line 200:
POTE generator: ~6/5 = 318.282
POTE generator: ~6/5 = 318.282


{{Val list|legend=1| 15, 34d, 49 }}
Vals: {{Val list| 15, 34d, 49 }}


Badness: 0.0369
Badness: 0.036894


= Catakleismic =
= Catakleismic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 225: Line 222:
{{Val list|legend=1| 19, 34d, 53, 72, 197, 269c }}
{{Val list|legend=1| 19, 34d, 53, 72, 197, 269c }}


[[Badness]]: 0.0215
[[Badness]]: 0.021501


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 242: Line 238:
* strict range: [315.789, 316.981]
* strict range: [315.789, 316.981]


{{Val list|legend=1| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }}
Vals: {{Val list| 19, 34de, 53, 72, 197e, 269ce, 341ce, 610bccee }}


Badness: 0.0218
Badness: 0.021849


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 261: Line 256:
* strict range: [315.789, 316.981]
* strict range: [315.789, 316.981]


{{Val list|legend=1| 19, 34de, 53, 72, 125f, 197ef, 269cef }}
Vals: {{Val list| 19, 34de, 53, 72, 125f, 197ef, 269cef }}


Badness: 0.0169
Badness: 0.016883


== Cataclysmic ==
== Cataclysmic ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 275: Line 269:
POTE generator: ~6/5 = 317.042
POTE generator: ~6/5 = 317.042


{{Val list|legend=1| 19e, 34d, 53, 193dde, …, 352… }}
Vals: {{Val list| 19e, 34d, 53 }}


Badness: 0.0400
Badness: 0.039954


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 289: Line 282:
POTE generator: ~6/5 = 317.036
POTE generator: ~6/5 = 317.036


{{Val list|legend=1| 19e, 34d, 53, 246ddee, …, 405… }}
Vals: {{Val list| 19e, 34d, 53 }}


Badness: 0.0226
Badness: 0.022555


== Catalytic ==
== Catalytic ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 303: Line 295:
POTE generator: ~6/5 = 316.653
POTE generator: ~6/5 = 316.653


{{Val list|legend=1| 19e, 53e, 72 }}
Vals: {{Val list| 19e, 53e, 72 }}


Badness: 0.0304
Badness: 0.030422


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 317: Line 308:
POTE generator: ~6/5 = 316.639
POTE generator: ~6/5 = 316.639


{{Val list|legend=1| 19e, 53e, 72 }}
Vals: {{Val list| 19e, 53e, 72 }}


Badness: 0.0223
Badness: 0.022337


== Cataleptic ==
== Cataleptic ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 331: Line 321:
POTE generator: ~6/5 = 317.083
POTE generator: ~6/5 = 317.083


{{Val list|legend=1| 19, 34d, 53e }}
Vals: {{Val list| 19, 34d, 53e }}


Badness: 0.0443
Badness: 0.044335


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 345: Line 334:
POTE generator: ~6/5 = 317.118
POTE generator: ~6/5 = 317.118


{{Val list|legend=1| 19, 34d, 53e, 87dee }}
Vals: {{Val list| 19, 34d, 53e, 87dee }}


Badness: 0.0273
Badness: 0.027343


== Bikleismic ==
== Bikleismic ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 359: Line 347:
POTE generator: ~6/5 = 316.721
POTE generator: ~6/5 = 316.721


{{Val list|legend=1| 34d, 72, 322c, …, 610bcc }}
Vals: {{Val list| 34d, 72, 322c, …, 610bcc }}


Badness: 0.0293
Badness: 0.029319


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 373: Line 360:
POTE generator: ~6/5 = 316.726
POTE generator: ~6/5 = 316.726


{{Val list|legend=1| 34d, 72, 322cfff, …, 538… }}
Vals: {{Val list| 34d, 72 }}


Badness: 0.0218
Badness: 0.021814


= Countercata =
= Countercata =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 391: Line 377:
{{Val list|legend=1| 19d, 34, 53, 87, 140, 333, 473, 806b }}
{{Val list|legend=1| 19d, 34, 53, 87, 140, 333, 473, 806b }}


[[Badness]]: 0.0521
[[Badness]]: 0.052129


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 403: Line 388:
POTE generator: ~6/5 = 317.162
POTE generator: ~6/5 = 317.162


{{Val list|legend=1| 34, 53, 87, 140, 227, 367e, 507e }}
Vals: {{Val list| 34, 53, 87, 140, 227, 367e, 507e }}


Badness: 0.0398
Badness: 0.039770


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 417: Line 401:
POTE generator: ~6/5 = 317.162
POTE generator: ~6/5 = 317.162


{{Val list|legend=1| 34, 53, 87, 140, 227, 367e, 507e }}
Vals: {{Val list| 34, 53, 87, 140, 227, 367e, 507e }}


Badness: 0.0202
Badness: 0.020156


= Metakleismic =
= Metakleismic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 435: Line 418:
{{Val list|legend=1| 34d, 87, 121, 208 }}
{{Val list|legend=1| 34d, 87, 121, 208 }}


[[Badness]]: 0.1635
[[Badness]]: 0.163519


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 447: Line 429:
POTE generator: ~6/5 = 317.311
POTE generator: ~6/5 = 317.311


{{Val list|legend=1| 34d, 53d, 87, 121, 208 }}
Vals: {{Val list| 34d, 53d, 87, 121, 208 }}


Badness: 0.0486
Badness: 0.048570


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 461: Line 442:
POTE generator: ~6/5 = 317.311
POTE generator: ~6/5 = 317.311


{{Val list|legend=1| 34d, 53d, 87, 121, 208 }}
Vals: {{Val list| 34d, 53d, 87, 121, 208 }}


Badness: 0.0244
Badness: 0.024371


= Hemikleismic =
= Hemikleismic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 472: Line 452:


[[Mapping]]: [{{val| 1 0 1 4 }}, {{val| 0 12 10 -9 }}]
[[Mapping]]: [{{val| 1 0 1 4 }}, {{val| 0 12 10 -9 }}]
{{Multival|legend=1| 12 10 -9 -12 -48 -49 }}


[[POTE generator]]: ~35/32 = 158.649
[[POTE generator]]: ~35/32 = 158.649
Line 477: Line 459:
{{Val list|legend=1| 15, 38, 53, 121 }}
{{Val list|legend=1| 15, 38, 53, 121 }}


[[Badness]]: 0.0521
[[Badness]]: 0.052054


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 489: Line 470:
POTE generator: ~11/10 = 158.677
POTE generator: ~11/10 = 158.677


{{Val list|legend=1| 15, 38, 53, 68, 121e }}
Vals: {{Val list| 15, 38, 53, 68, 121e }}


Badness: 0.0380
Badness: 0.038023


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 503: Line 483:
Mapping: [{{val| 1 0 1 4 2 0 }}, {{val| 0 12 10 -9 11 28 }}]
Mapping: [{{val| 1 0 1 4 2 0 }}, {{val| 0 12 10 -9 11 28 }}]


{{Val list|legend=1| 15, 38f, 53, 121e }}
Vals: {{Val list| 15, 38f, 53, 121e }}


Badness: 0.0260
Badness: 0.026005


= Clyde =
= Clyde =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 516: Line 495:


Mapping generators: ~2, ~9/7
Mapping generators: ~2, ~9/7
{{Multival|legend=1| 12 10 25 -12 6 30 }}


[[POTE generator]]: ~9/7 = 441.335
[[POTE generator]]: ~9/7 = 441.335
Line 528: Line 509:
{{Val list|legend=1| 19, 49, 68, 87, 155 }}
{{Val list|legend=1| 19, 49, 68, 87, 155 }}


[[Badness]]: 0.0473
[[Badness]]: 0.047261


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 540: Line 520:
POTE generator: ~9/7 = 441.355
POTE generator: ~9/7 = 441.355


{{Val list|legend=1| 19, 49e, 68, 87, 329bd, 419bd, 503bd, 590bd }}
Vals: {{Val list| 19, 49e, 68, 87, 329bd, 419bd, 503bd, 590bd }}


Badness: 0.0474
Badness: 0.047417


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 554: Line 533:
Mapping: [{{val| 1 6 6 12 -5 14 }}, {{val| 0 -12 -10 -25 23 -28 }}]
Mapping: [{{val| 1 6 6 12 -5 14 }}, {{val| 0 -12 -10 -25 23 -28 }}]


{{Val list|legend=1| 19, 49ef, 68, 87, 503bdf, 590bdf }}
{{Val list| 19, 49ef, 68, 87, 503bdf, 590bdf }}


Badness: 0.0268
Badness: 0.026842


= Tritikleismic =
= Tritikleismic =
Line 636: Line 615:


= Quadritikleismic =
= Quadritikleismic =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 649: Line 627:
{{Val list|legend=1| 68, 72, 140, 212, 776cd, 988ccd, 1200ccd }}
{{Val list|legend=1| 68, 72, 140, 212, 776cd, 988ccd, 1200ccd }}


[[Badness]]: 0.0392
[[Badness]]: 0.039231


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 661: Line 638:
POTE generator: ~6/5 = 316.925
POTE generator: ~6/5 = 316.925


{{Val list|legend=1| 68, 72, 140, 212, 284, 496, 780 }}
Vals: {{Val list| 68, 72, 140, 212, 284, 496, 780 }}


Badness: 0.0234
Badness: 0.023406


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 675: Line 651:
POTE generator: ~6/5 = 316.989
POTE generator: ~6/5 = 316.989


{{Val list|legend=1| 68, 72, 140, 212 }}
Vals: {{Val list| 68, 72, 140, 212 }}


Badness: 0.0187
Badness: 0.018731


= Kleiboh =
= Kleiboh =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 686: Line 661:


[[Mapping]]: [{{val| 1 6 6 6 }}, {{val| 0 -18 -15 -13 }}]
[[Mapping]]: [{{val| 1 6 6 6 }}, {{val| 0 -18 -15 -13 }}]
{{Multival|legend=1| 18 15 13 -18 -30 -12 }}


[[POTE generator]]: ~25/21 = 294.303
[[POTE generator]]: ~25/21 = 294.303
{{Multival|legend=1| 18 15 13 -18 -30 -12 }}


{{Val list|legend=1| 49, 53, 314d }}
{{Val list|legend=1| 49, 53, 314d }}


[[Badness]]: 0.0765
[[Badness]]: 0.076460


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 705: Line 679:
POTE generator: ~25/21 = 294.181
POTE generator: ~25/21 = 294.181


{{Val list|legend=1| 49, 53, 102d, 155d }}
Vals: {{Val list| 49, 53, 102d, 155d }}


Badness: 0.0528
Badness: 0.052805


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 719: Line 692:
POTE generator: ~13/11 = 294.187
POTE generator: ~13/11 = 294.187


{{Val list|legend=1| 49f, 53, 102df, 155d }}
Vals: {{Val list| 49f, 53, 102df, 155d }}
 
Badness: 0.031074
 
= Marfifths =
The ''marfifths'' temperament (19&140, named by [[User:Xenllium|Xenllium]]) tempers out the [[hemimage comma]], 10976/10935. It splits the interval of major tenth (~10/3) into three marvelous fifth ([[112/75]]) intervals, and uses it for a generator.
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 10976/10935, 15625/15552
 
[[Mapping]]: [{{val| 1 -6 -4 -17 }}, {{val| 0 18 15 47 }}]
 
{{Multival|legend=1| 18 15 47 -18 24 67 }}
 
[[POTE generator]]: ~75/56 = 505.705
 
{{Val list|legend=1| 19, 121, 140, 579, 719, 859bcd, 999bcd, 1858bbccdd }}
 
[[Badness]]: 0.063448
 
== 11-limit ==
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 6250/6237, 10976/10935
 
Mapping: [{{val| 1 -6 -4 -17 22 }}, {{val| 0 18 15 47 -44 }}]
 
POTE generator: ~75/56 = 505.684
 
Vals: {{Val list| 19, 140, 159, 299 }}
 
Badness: 0.058902
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 385/384, 625/624, 10976/10935
 
Mapping: [{{val| 1 -6 -4 -17 22 -14 }}, {{val| 0 18 15 47 -44 42 }}]
 
POTE generator: ~75/56 = 505.686
 
Vals: {{Val list|19, 140, 159, 299 }}
 
Badness: 0.030082
 
== Diatessic ==
The ''marfifths'' temperament (121&140, named by [[User:Xenllium|Xenllium]]) is closely related to the '''diatess tuning''' (generator: 505.727281 cents).
 
Subgroup: 2.3.5.7.11
 
Comma list: 1375/1372, 2200/2187, 5632/5625
 
Mapping: [{{val| 1 -6 -4 -17 -37 }}, {{val| 0 18 15 47 96 }}]
 
POTE generator: ~75/56 = 505.740
 
Vals: {{Val list|19e, 121, 140, 261, 401, 662bd }}
 
Badness: 0.061172
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 352/351, 625/624, 1375/1372
 
Mapping: [{{val| 1 -6 -4 -17 -37 -14 }}, {{val| 0 18 15 47 96 42 }}]
 
POTE generator: ~75/56 = 505.740
 
Vals: {{Val list| 19e, 121, 140, 261, 401, 662bd }}
 
Badness: 0.028671
 
== Marf ==
The ''marf'' temperament (19&121, named by [[User:Xenllium|Xenllium]]) has a POTE generator which strongly approximates the marvelous fifth interval of 112/75.
 
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 896/891, 15625/15552
 
Mapping: [{{val| 1 -6 -4 -17 14 }}, {{val| 0 18 15 47 -25 }}]
 
POTE generator: ~75/56 = 505.769
 
Vals: {{Val list| 19, 102d, 121 }}
 
Badness: 0.075112
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 325/324, 540/539, 625/624, 896/891
 
Mapping: [{{val| 1 -6 -4 -17 14 -14 }}, {{val| 0 18 15 47 -25 42 }}]
 
POTE generator: ~75/56 = 505.771
 
Vals: {{Val list| 19, 121 }}


Badness: 0.0311
Badness: 0.038317


= Novemkleismic =
= Novemkleismic =
Retrieved from "https://en.xen.wiki/w/Kleismic_family"