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2.11.13.17.19 subgroup: Difference between revisions

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==Commas==
{{Delete|This is just a comma dump page, and the subgroup is arguably not notable.}}


==See also==
== Commas ==
Here follows a selection of commas in the 2.11.13.17.19 [[domain basis]].


[[Yer]], a hexadecatonic [[Just intonation|JI]] [[wikipedia:Euler–Fokker_genus|EFG]] in this subgroup
{| class="wikitable"
|-
! rowspan="2" | Name
! rowspan="2" | Prime-count vector
! rowspan="2" | Ratio
! rowspan="2" | Cents
! colspan="5" | As composition of other commas
! colspan="10" | Tempered by patent val for ed2?
|-
! yama
! bean
! Blumeyer
! frouggie
! pollar
! 13
! 24
! 33
! 37
! 57
! 70
! 80
! 113
! 124
! 137
|-
| Blumeyer
| {{vector| 7 0 0 0 -1 -1 -1 1 }}
| 2432 / 2431
| 0.7120024978
|
|
| 1
|
|
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
|-
| yama
| {{vector| -4 0 0 0 1 -1 0 1 }}
| 209 / 208
| 8.303296728
| 1
|
|
|
|
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
|
|
|
|
|-
| Blume
| {{vector| -11 0 0 0 2 0 1 0 }}
| 2057 / 2048
| 7.59129423
| 1
|
| −1
|
|
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
|
|
|
|
|-
|
| {{vector| 3 0 0 0 0 -2 -1 2 }}
| 2888 / 2873
| 9.015299226
| 1
|
| 1
|
|
| ✓
| ✓
| ✓
| ✓
| ✓
| ✓
|
|
|
|
|-
| eye
| {{vector| 3 0 0 0 -2 0 2 -1 }}
| 2312 / 2299
| 9.761918139
| 1
| 1
| −2
|
|
| ✓
| ✓
| ✓
| ✓
|
|
| ✓
|
|
|
|-
| lum
| {{vector| -1 0 0 0 -1 -1 2 0 }}
| 289 / 286
| 18.06521487
| 2
| 1
| −2
|
|
| ✓
| ✓
|
| ✓
|
|
|
|
|
|
|-
| ume
| {{vector| -8 0 0 0 0 0 3 -1 }}
| 4913 / 4864
| 17.35321237
| 2
| 1
| −3
|
|
| ✓
| ✓
| ✓
| ✓
|
|
|
|
|
|
|-
| mey
| {{vector| -7 0 0 0 0 3 -1 0 }}
| 2197 / 2176
| 16.62757581
| 2
|
|
|
| 1
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| -5 0 0 0 0 -2 2 1 }}
| 5491 / 5408
| 26.36851159
| 3
| 1
| −2
|
|
| ✓
| ✓
|
| ✓
|
|
|
|
|
|
|-
|
| {{vector| -5 0 0 0 -1 0 0 2 }}
| 361 / 352
| 43.7080899
| 5
| 1
| −1
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| -1 0 0 0 -2 1 0 1 }}
| 247 / 242
| 35.40479317
| 4
| 1
| −1
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| 6 0 0 0 -1 -4 3 0 }}
| 314432 / 314171
| 1.437639059
|
| 1
| −2
|
| −1
|
|
|
|
| ✓
| ✓
| ✓
|
| ✓
| ✓
|-
|
| {{vector| 14 0 0 0 -4 0 1 -1 }}
| 278528 / 278179
| 2.170623909
|
| 1
| −1
|
|
|
|
|
|
|
|
|
| ✓
| ✓
| ✓
|-
|
| {{vector| 4 0 0 0 -2 3 -2 0 }}
| 35152 / 34969
| 9.036281578
| 1
|
| 1
|
| 1
|
|
|
|
|
|
| ✓
| ✓
|
|
|-
|
| {{vector| 10 0 0 0 -3 -1 1 0 }}
| 17408 / 17303
| 10.47392064
| 1
| 1
| −1
|
|
|
|
|
|
|
|
| ✓
|
|
|
|-
|
| {{vector| 0 0 0 0 -1 2 -2 1 }}
| 3211 / 3179
| 17.33957831
| 2
|
| 1
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| 6 0 0 0 -2 -2 1 1 }}
| 20672 / 20449
| 18.77721736
| 2
| 1
| −1
|
|
| ✓
| ✓
|
| ✓
|
|
|
|
|
|
|-
|
| {{vector| -4 0 0 0 0 1 -2 2 }}
| 4693 / 4624
| 25.64287503
| 3
|
| 1
|
| 1
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| 3 0 0 0 -3 2 0 0 }}
| 1352 / 1331
| 27.10149644
| 3
| 1
| −1
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| -8 0 0 0 -1 2 1 0 }}
| 2873 / 2816
| 34.69279067
| 4
| 1
| −2
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| 14 0 0 0 2 0 -2 -3 }}
| 1982464 / 1982251
| 0.1860173318
|
|
|
| 1
| 1
|
|
| ✓
|
|
|
| ✓
| ✓
|
| ✓
|-
|
| {{vector| 13 0 0 0 1 -1 0 -3 }}
| 90112 / 89167
| 18.2512322
| 2
| 1
| −2
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| 7 0 0 0 -3 1 2 -2 }}
| 480896 / 480491
| 1.458621411
|
| 1
| −2
|
|
|
|
|
|
|
|
|
| ✓
| ✓
| ✓
|-
| bean
| {{vector| 21 0 0 0 -5 -1 0 0 }}
| 2097152 / 2093663
| 2.882626407
|
| 1
|
|
|
|
|
|
|
|
|
|
| ✓
| ✓
| ✓
|-
|
| {{vector| -3 0 0 0 -1 4 -1 -1 }}
| 28561 / 28424
| 8.32427908
| 1
|
|
|
| 1
|
|
|
|
|
|
| ✓
| ✓
|
|
|-
|
| {{vector| -11 0 0 0 1 2 -1 1 }}
| 35321 / 34816
| 24.93087254
| 3
|
|
|
| 1
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| 3 0 0 0 4 0 -1 -3 }}
| 117128 / 116603
| 7.777311562
| 1
|
| −1
| 1
| 1
|
|
| ✓
|
| ✓
|
|
|
| ✓
|
|-
|
| {{vector| -18 0 0 0 2 3 0 0 }}
| 265837 / 262144
| 24.21887004
| 3
|
| −1
|
| 1
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| 9 0 0 0 2 -2 0 -2 }}
| 61952 / 61009
| 26.55452893
| 3
| 1
| −2
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| 10 0 0 0 3 -1 -2 -2 }}
| 1362944 / 1356277
| 8.48931406
| 1
|
|
| 1
| 1
|
| ✓
| ✓
|
| ✓
|
|
|
| ✓
|
|-
|
| {{vector| 21 0 0 0 1 -1 -3 -2 }}
| 23068672 / 23056709
| 0.8980198296
|
|
| 1
| 1
| 1
|
|
|
|
|
|
| ✓
| ✓
|
| ✓
|-
|
| {{vector| -7 0 0 0 -3 -1 1 4 }}
| 2215457 / 2214784
| 0.525985166
|
|
| 1
| −1
| −1
|
|
|
|
|
|
| ✓
| ✓
|
| ✓
|-
|
| {{vector| -10 0 0 0 2 3 -3 1 }}
| 5050903 / 5030912
| 6.865657669
| 1
| −1
| 2
|
| 1
|
|
|
|
| ✓
| ✓
|
| ✓
|
|
|-
|
| {{vector| -3 0 0 0 1 2 -4 2 }}
| 671099 / 668168
| 7.577660166
| 1
| −1
| 3
|
| 1
|
|
|
|
| ✓
| ✓
|
|
|
|
|-
|
| {{vector| 5 0 0 0 3 -3 0 -1 }}
| 42592 / 41743
| 34.85782565
| 4
| 1
| −2
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| 6 0 0 0 -3 0 -1 2 }}
| 23104 / 22627
| 36.11679567
| 4
| 1
|
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
| pollar
| {{vector| 1 0 0 0 -2 5 -1 -2 }}
| 742586 / 742577
| 0.02098235203
|
|
|
|
| 1
|
|
|
|
|
|
|
|
| ✓
| ✓
|-
|
| {{vector| 17 0 0 0 2 -2 -3 -1 }}
| 15859712 / 15775643
| 9.201316557
| 1
|
| 1
| 1
| 1
|
|
| ✓
|
| ✓
|
|
|
| ✓
|
|-
|
| {{vector| 11 0 0 0 -3 2 -3 1 }}
| 6576128 / 6539203
| 9.748284075
| 1
|
| 2
|
| 1
|
|
|
|
|
|
| ✓
| ✓
|
|
|-
|
| {{vector| 24 0 0 0 -1 -1 -1 -3 }}
| 16777216 / 16674229
| 10.65993797
| 1
| 1
| −1
| 1
| 1
|
|
|
|
|
|
| ✓
|
| ✓
|
|-
|
| {{vector| 17 0 0 0 -4 -2 0 1 }}
| 2490368 / 2474329
| 11.18592313
| 1
| 1
|
|
|
|
|
|
|
|
|
| ✓
|
|
|
|-
|
| {{vector| 2 0 0 0 3 -1 1 -3 }}
| 90508 / 89167
| 25.84252643
| 3
| 1
| −3
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| 16 0 0 0 1 -3 -1 -1 }}
| 720896 / 709631
| 27.26653142
| 3
| 1
| −1
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| -15 0 0 0 2 1 -1 2 }}
| 567853 / 557056
| 33.23416926
| 4
|
|
|
| 1
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| -2 0 0 0 -3 0 2 1 }}
| 5491 / 5324
| 53.47000804
| 6
| 2
| −3
|
| 1
| ✓
|
|
|
|
|
|
|
|
|
|-
|
| {{vector| 8 0 0 0 -3 4 -2 -1 }}
| 7311616 / 7308521
| 0.7329848499
|
|
| 1
|
| 1
|
|
|
|
|
|
|
|
| ✓
| ✓
|-
|
| {{vector| 28 0 0 0 -2 0 -1 -4 }}
| 268435456 / 268070297
| 2.356641241
|
| 1
| −1
| 1
| 1
|
|
|
|
|
|
|
| ✓
|
| ✓
|-
|
| {{vector| -10 0 0 0 -4 3 0 3 }}
| 15069223 / 14992384
| 8.850264246
| 1
|
| 1
| −1
|
|
|
|
| ✓
|
| ✓
| ✓
| ✓
|
|
|-
|
| {{vector| 6 0 0 0 4 -2 -2 -1 }}
| 937024 / 927979
| 16.79261079
| 2
|
|
| 1
| 1
|
|
| ✓
|
| ✓
|
|
|
|
|
|-
|
| {{vector| 15 0 0 0 -4 3 -3 0 }}
| 71991296 / 71931233
| 1.444987348
|
|
| 2
|
| 1
|
|
|
|
|
|
|
|
| ✓
| ✓
|-
|
| {{vector| -17 0 0 0 3 4 -2 0 }}
| 38014691 / 37879808
| 6.153655171
| 1
| −1
| 1
|
| 1
|
|
|
|
| ✓
| ✓
|
|
|
|
|-
|
| {{vector| 0 0 0 0 -6 0 3 2 }}
| 1773593 / 1771561
| 1.984606577
|
| 1
| −1
| −1
| −1
|
|
|
|
|
|
|
| ✓
|
| ✓
|-
|
| {{vector| 14 0 0 0 -5 2 -1 0 }}
| 2768896 / 2737867
| 19.51020221
| 2
| 1
|
|
| 1
|
|
|
|
|
|
| ✓
|
|
|
|-
|
| {{vector| 18 0 0 0 0 3 -4 -3 }}
| 575930368 / 572870539
| 9.222298909
| 1
|
| 1
| 1
| 2
|
|
|
|
|
|
| ✓
| ✓
| ✓
|
|-
|
| {{vector| -6 0 0 0 -5 4 0 2 }}
| 10310521 / 10307264
| 0.5469675181
|
|
| 1
| −1
|
|
|
|
|
|
|
|
|
|
| ✓
|-
|
| {{vector| 20 0 0 0 1 -4 1 -3 }}
| 196083712 / 195899899
| 1.623656391
|
| 1
| −2
| 1
|
|
|
|
|
| ✓
|
|
|
|
|
|-
|
| {{vector| -14 0 0 0 3 2 -3 2 }}
| 81202979 / 80494592
| 15.1689544
| 2
| −1
| 2
|
| 1
|
|
|
|
| ✓
| ✓
|
|
|
|
|-
|
| {{vector| -21 0 0 0 -2 3 1 3 }}
| 256176791 / 253755392
| 16.44155848
| 2
|
|
| −1
|
|
|
| ✓
| ✓
|
| ✓
|
|
|
|
|-
|
| {{vector| -1 0 0 0 4 1 -3 -1 }}
| 190333 / 186694
| 33.42018659
| 4
|
|
| 1
| 2
|
|
| ✓
|
|
|
|
|
|
|
|-
|
| {{vector| 8 0 0 0 1 -3 2 -2 }}
| 813824 / 793117
| 44.61974379
| 5
| 2
| −4
| 1
| 1
|
| ✓
|
|
|
|
|
|
|
|
|-
|
| {{vector| -7 0 0 0 -5 1 4 1 }}
| 20629687 / 20614528
| 1.272604079
|
| 1
| −2
| −1
| −1
|
|
|
|
|
| ✓
|
|
|
|
|-
|
| {{vector| 2 0 0 0 6 -5 0 -1 }}
| 7086244 / 7054567
| 7.75632921
| 1
|
| −1
| 1
|
|
|
|
|
|
|
|
|
| ✓
|
|-
|
| {{vector| -17 0 0 0 -3 4 1 2 }}
| 175278857 / 174456832
| 8.138261748
| 1
|
|
| −1
|
|
|
|
| ✓
|
| ✓
|
|
|
|
|-
| frouggie
| {{vector| 13 0 0 0 4 -5 -1 -1 }}
| 119939072 / 119927639
| 0.1650349798
|
|
|
| 1
|
|
|
|
| ✓
|
| ✓
|
|
|
|
|-
|
| {{vector| 16 0 0 0 2 -5 1 -2 }}
| 134807552 / 134036773
| 9.926953119
| 1
| 1
| −2
| 1
|
|
|
|
| ✓
|
|
|
|
|
|
|-
|
| {{vector| -24 0 0 0 -2 5 2 1 }}
| 2038769863 / 2030043136
| 7.42625925
| 1
|
| −1
| −1
|
|
|
|
| ✓
|
| ✓
|
|
|
|
|-
|
| {{vector| -4 0 0 0 -5 -1 3 3 }}
| 33698267 / 33498608
| 10.28790331
| 1
| 1
| −1
| −1
| −1
|
|
|
|
|
|
| ✓
|
|
|
|-
|
| {{vector| -4 0 0 0 7 -1 -3 -1 }}
| 19487171 / 19416176
| 6.31869015
| 1
| −1
| 1
| 1
| 1
|
|
|
|
|
|
|
|
| ✓
|
|-
|
| {{vector| 18 0 0 0 -6 3 -1 -1 }}
| 575930368 / 572214203
| 11.20690549
| 1
| 1
|
|
| 1
|
|
|
|
|
|
|
| ✓
|
|
|-
|
| {{vector| 0 0 0 0 5 2 -5 -1 }}
| 27217619 / 26977283
| 15.35497173
| 2
| −1
| 2
| 1
| 2
|
|
|
|
| ✓
|
|
|
|
|
|-
|
| {{vector| 22 0 0 0 -1 4 -4 -4 }}
| 119793516544 / 119729942651
| 0.9190021816
|
|
| 1
| 1
| 2
|
|
|
|
|
|
|
|
|
| ✓
|-
|
| {{vector| -18 0 0 0 -4 3 3 2 }}
| 3896583821 / 3838050304
| 26.20347661
| 3
| 1
| −2
| −1
|
|
|
|
| ✓
|
|
|
|
|
|
|-
|
| {{vector| 22 0 0 0 -7 4 -1 -2 }}
| 119793516544 / 119592768427
| 2.903608759
|
| 1
|
|
| 1
|
|
|
|
|
|
|
|
| ✓
| ✓
|-
|
| {{vector| -27 0 0 0 -1 7 -2 3 }}
| 430392078103 / 426678157312
| 15.00391942
| 2
| −1
| 2
| −1
| 1
|
|
|
|
|
| ✓
|
|
|
|
|}


[[Gjaeck]], a [[Tridecatonic MOS|tridecatonic MOS]] of [[57edo|57ed2]] in this subgroup
== See also ==
* [[Yer]], a hexadecatonic [[Just intonation|JI]] [[wikipedia:Euler–Fokker_genus|EFG]] in this subgroup
* [[Gjaeck]], a [[Tridecatonic MOS|tridecatonic MOS]] of [[57edo|57ed2]] in this subgroup
* [[Hilim13]], a tridecatonic JI tuning in this subgroup


[[Hilim13]], a tridecatonic JI tuning in this subgroup
[[Category:Just intonation subgroups|#]]
[[Category:Rank-5 temperaments|#]]
[[Category:19-limit|#]]
Retrieved from "https://en.xen.wiki/w/2.11.13.17.19_subgroup"