2.11.13.17.19 subgroup: Difference between revisions

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==Commas==
== Commas ==
Here follows a selection of commas in the 2.11.13.17.19 [[domain basis]].
Here follows a selection of commas in the 2.11.13.17.19 [[domain basis]].
{| class="wikitable"
{| 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
! rowspan="2" | Name
!bean
! rowspan="2" | Prime-count vector
!Blumeyer
! rowspan="2" | Ratio
!frouggie
! rowspan="2" | Cents
!pollar
! colspan="5" | As composition of other commas
!13
! colspan="10" | Tempered by patent val for ed2?
!24
|-
!33
! yama
!37
! bean
!57
! Blumeyer
!70
! frouggie
!80
! pollar
!113
! 13
!124
! 24
!137
! 33
! 37
! 57
! 70
! 80
! 113
! 124
! 137
|-
|-
|Blumeyer
| Blumeyer
|{{vector| 7 0 0 0 -1 -1 -1 1 }}
| {{vector| 7 0 0 0 -1 -1 -1 1 }}
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|yama
| yama
|{{vector| -4 0 0 0 1 -1 0 1 }}
| {{vector| -4 0 0 0 1 -1 0 1 }}
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|8.303296728
| 8.303296728
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|Blume
| Blume
|{{vector| -11 0 0 0 2 0 1 0 }}
| {{vector| -11 0 0 0 2 0 1 0 }}
|2057 / 2048
| 2057 / 2048
|7.59129423
| 7.59129423
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|{{vector| 3 0 0 0 0 -2 -1 2 }}
| {{vector| 3 0 0 0 0 -2 -1 2 }}
|2888 / 2873
| 2888 / 2873
|9.015299226
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|eye
| eye
|{{vector| 3 0 0 0 -2 0 2 -1 }}
| {{vector| 3 0 0 0 -2 0 2 -1 }}
|2312 / 2299
| 2312 / 2299
|9.761918139
| 9.761918139
|1
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|lum
| lum
|{{vector| -1 0 0 0 -1 -1 2 0 }}
| {{vector| -1 0 0 0 -1 -1 2 0 }}
|289 / 286
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|18.06521487
| 18.06521487
|2
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|ume
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|{{vector| -8 0 0 0 0 0 3 -1 }}
| {{vector| -8 0 0 0 0 0 3 -1 }}
|4913 / 4864
| 4913 / 4864
|17.35321237
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|mey
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|{{vector| -7 0 0 0 0 3 -1 0 }}
| {{vector| -7 0 0 0 0 3 -1 0 }}
|2197 / 2176
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|16.62757581
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|{{vector| -5 0 0 0 0 -2 2 1 }}
| {{vector| -5 0 0 0 0 -2 2 1 }}
|5491 / 5408
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|26.36851159
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|{{vector| -5 0 0 0 -1 0 0 2 }}
| {{vector| -5 0 0 0 -1 0 0 2 }}
|361 / 352
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|43.7080899
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|{{vector| -1 0 0 0 -2 1 0 1 }}
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|35.40479317
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|{{vector| 6 0 0 0 -1 -4 3 0 }}
| {{vector| 6 0 0 0 -1 -4 3 0 }}
|314432 / 314171
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|1.437639059
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|{{vector| 14 0 0 0 -4 0 1 -1 }}
| {{vector| 14 0 0 0 -4 0 1 -1 }}
|278528 / 278179
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|2.170623909
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|{{vector| 4 0 0 0 -2 3 -2 0 }}
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|9.036281578
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|{{vector| 10 0 0 0 -3 -1 1 0 }}
| {{vector| 10 0 0 0 -3 -1 1 0 }}
|17408 / 17303
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|10.47392064
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|{{vector| 0 0 0 0 -1 2 -2 1 }}
| {{vector| 0 0 0 0 -1 2 -2 1 }}
|3211 / 3179
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|17.33957831
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|18.77721736
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|{{vector| -4 0 0 0 0 1 -2 2 }}
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|{{vector| 3 0 0 0 -3 2 0 0 }}
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|1352 / 1331
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|27.10149644
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|{{vector| -8 0 0 0 -1 2 1 0 }}
| {{vector| -8 0 0 0 -1 2 1 0 }}
|2873 / 2816
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|34.69279067
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|{{vector| 14 0 0 0 2 0 -2 -3 }}
| {{vector| 14 0 0 0 2 0 -2 -3 }}
|1982464 / 1982251
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|{{vector| 13 0 0 0 1 -1 0 -3 }}
| {{vector| 13 0 0 0 1 -1 0 -3 }}
|90112 / 89167
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|18.2512322
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|2
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|{{vector| 7 0 0 0 -3 1 2 -2 }}
| {{vector| 7 0 0 0 -3 1 2 -2 }}
|480896 / 480491
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|1.458621411
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|bean
| bean
|{{vector| 21 0 0 0 -5 -1 0 0 }}
| {{vector| 21 0 0 0 -5 -1 0 0 }}
|2097152 / 2093663
| 2097152 / 2093663
|2.882626407
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|{{vector| -3 0 0 0 -1 4 -1 -1 }}
| {{vector| -3 0 0 0 -1 4 -1 -1 }}
|28561 / 28424
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|8.32427908
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|{{vector| -11 0 0 0 1 2 -1 1 }}
| {{vector| -11 0 0 0 1 2 -1 1 }}
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|{{vector| 3 0 0 0 4 0 -1 -3 }}
| {{vector| 3 0 0 0 4 0 -1 -3 }}
|117128 / 116603
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|7.777311562
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|1
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|✓
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|{{vector| -18 0 0 0 2 3 0 0 }}
| {{vector| -18 0 0 0 2 3 0 0 }}
|265837 / 262144
| 265837 / 262144
|24.21887004
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|3
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|✓
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|{{vector| 9 0 0 0 2 -2 0 -2 }}
| {{vector| 9 0 0 0 2 -2 0 -2 }}
|61952 / 61009
| 61952 / 61009
|26.55452893
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|3
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|{{vector| 10 0 0 0 3 -1 -2 -2 }}
| {{vector| 10 0 0 0 3 -1 -2 -2 }}
|1362944 / 1356277
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|8.48931406
| 8.48931406
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|✓
| ✓
|✓
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|{{vector| 21 0 0 0 1 -1 -3 -2 }}
| {{vector| 21 0 0 0 1 -1 -3 -2 }}
|23068672 / 23056709
| 23068672 / 23056709
|0.8980198296
| 0.8980198296
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|✓
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|✓
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|{{vector| -7 0 0 0 -3 -1 1 4 }}
| {{vector| -7 0 0 0 -3 -1 1 4 }}
|2215457 / 2214784
| 2215457 / 2214784
|0.525985166
| 0.525985166
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|{{vector| -10 0 0 0 2 3 -3 1 }}
| {{vector| -10 0 0 0 2 3 -3 1 }}
|5050903 / 5030912
| 5050903 / 5030912
|6.865657669
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|{{vector| -3 0 0 0 1 2 -4 2 }}
| {{vector| -3 0 0 0 1 2 -4 2 }}
|671099 / 668168
| 671099 / 668168
|7.577660166
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|{{vector| 5 0 0 0 3 -3 0 -1 }}
| {{vector| 5 0 0 0 3 -3 0 -1 }}
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|{{vector| 6 0 0 0 -3 0 -1 2 }}
| {{vector| 6 0 0 0 -3 0 -1 2 }}
|23104 / 22627
| 23104 / 22627
|36.11679567
| 36.11679567
|4
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|✓
| ✓
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|pollar
| pollar
|{{vector| 1 0 0 0 -2 5 -1 -2 }}
| {{vector| 1 0 0 0 -2 5 -1 -2 }}
|742586 / 742577
| 742586 / 742577
|0.02098235203
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|{{vector| 17 0 0 0 2 -2 -3 -1 }}
| {{vector| 17 0 0 0 2 -2 -3 -1 }}
|15859712 / 15775643
| 15859712 / 15775643
|9.201316557
| 9.201316557
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|✓
| ✓
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|{{vector| 11 0 0 0 -3 2 -3 1 }}
| {{vector| 11 0 0 0 -3 2 -3 1 }}
|6576128 / 6539203
| 6576128 / 6539203
|9.748284075
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|{{vector| 24 0 0 0 -1 -1 -1 -3 }}
| {{vector| 24 0 0 0 -1 -1 -1 -3 }}
|16777216 / 16674229
| 16777216 / 16674229
|10.65993797
| 10.65993797
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| ✓
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|{{vector| 17 0 0 0 -4 -2 0 1 }}
| {{vector| 17 0 0 0 -4 -2 0 1 }}
|2490368 / 2474329
| 2490368 / 2474329
|11.18592313
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|{{vector| 2 0 0 0 3 -1 1 -3 }}
| {{vector| 2 0 0 0 3 -1 1 -3 }}
|90508 / 89167
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|✓
| ✓
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|{{vector| 16 0 0 0 1 -3 -1 -1 }}
| {{vector| 16 0 0 0 1 -3 -1 -1 }}
|720896 / 709631
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|27.26653142
| 27.26653142
|3
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|✓
| ✓
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|{{vector| -15 0 0 0 2 1 -1 2 }}
| {{vector| -15 0 0 0 2 1 -1 2 }}
|567853 / 557056
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|33.23416926
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|4
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|{{vector| -2 0 0 0 -3 0 2 1 }}
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|5491 / 5324
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|{{vector| 8 0 0 0 -3 4 -2 -1 }}
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|7311616 / 7308521
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|{{vector| 28 0 0 0 -2 0 -1 -4 }}
| {{vector| 28 0 0 0 -2 0 -1 -4 }}
|268435456 / 268070297
| 268435456 / 268070297
|2.356641241
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|{{vector| -10 0 0 0 -4 3 0 3 }}
| {{vector| -10 0 0 0 -4 3 0 3 }}
|15069223 / 14992384
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|8.850264246
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|{{vector| 6 0 0 0 4 -2 -2 -1 }}
| {{vector| 6 0 0 0 4 -2 -2 -1 }}
|937024 / 927979
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|16.79261079
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|{{vector| 15 0 0 0 -4 3 -3 0 }}
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|71991296 / 71931233
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|{{vector| -17 0 0 0 3 4 -2 0 }}
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|38014691 / 37879808
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|{{vector| 0 0 0 0 -6 0 3 2 }}
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|1773593 / 1771561
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|{{vector| 14 0 0 0 -5 2 -1 0 }}
| {{vector| 14 0 0 0 -5 2 -1 0 }}
|2768896 / 2737867
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|19.51020221
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|{{vector| 18 0 0 0 0 3 -4 -3 }}
| {{vector| 18 0 0 0 0 3 -4 -3 }}
|575930368 / 572870539
| 575930368 / 572870539
|9.222298909
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|{{vector| -6 0 0 0 -5 4 0 2 }}
| {{vector| -6 0 0 0 -5 4 0 2 }}
|10310521 / 10307264
| 10310521 / 10307264
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|{{vector| 20 0 0 0 1 -4 1 -3 }}
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|196083712 / 195899899
| 196083712 / 195899899
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|{{vector| -14 0 0 0 3 2 -3 2 }}
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|81202979 / 80494592
| 81202979 / 80494592
|15.1689544
| 15.1689544
|2
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|{{vector| -21 0 0 0 -2 3 1 3 }}
| {{vector| -21 0 0 0 -2 3 1 3 }}
|256176791 / 253755392
| 256176791 / 253755392
|16.44155848
| 16.44155848
|2
| 2
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|{{vector| -1 0 0 0 4 1 -3 -1 }}
| {{vector| -1 0 0 0 4 1 -3 -1 }}
|190333 / 186694
| 190333 / 186694
|33.42018659
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|✓
| ✓
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|{{vector| 8 0 0 0 1 -3 2 -2 }}
| {{vector| 8 0 0 0 1 -3 2 -2 }}
|813824 / 793117
| 813824 / 793117
|44.61974379
| 44.61974379
|5
| 5
|2
| 2
| -4
| -4
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| 1
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| ✓
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|{{vector| -7 0 0 0 -5 1 4 1 }}
| {{vector| -7 0 0 0 -5 1 4 1 }}
|20629687 / 20614528
| 20629687 / 20614528
|1.272604079
| 1.272604079
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|
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|{{vector| 2 0 0 0 6 -5 0 -1 }}
| {{vector| 2 0 0 0 6 -5 0 -1 }}
|7086244 / 7054567
| 7086244 / 7054567
|7.75632921
| 7.75632921
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|{{vector| -17 0 0 0 -3 4 1 2 }}
| {{vector| -17 0 0 0 -3 4 1 2 }}
|175278857 / 174456832
| 175278857 / 174456832
|8.138261748
| 8.138261748
|1
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|frouggie
| frouggie
|{{vector| 13 0 0 0 4 -5 -1 -1 }}
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|119939072 / 119927639
| 119939072 / 119927639
|0.1650349798
| 0.1650349798
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|{{vector| 16 0 0 0 2 -5 1 -2 }}
| {{vector| 16 0 0 0 2 -5 1 -2 }}
|134807552 / 134036773
| 134807552 / 134036773
|9.926953119
| 9.926953119
|1
| 1
|1
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| -2
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|{{vector| -24 0 0 0 -2 5 2 1 }}
| {{vector| -24 0 0 0 -2 5 2 1 }}
|2038769863 / 2030043136
| 2038769863 / 2030043136
|7.42625925
| 7.42625925
|1
| 1
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| -1
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|{{vector| -4 0 0 0 -5 -1 3 3 }}
| {{vector| -4 0 0 0 -5 -1 3 3 }}
|33698267 / 33498608
| 33698267 / 33498608
|10.28790331
| 10.28790331
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|{{vector| -4 0 0 0 7 -1 -3 -1 }}
| {{vector| -4 0 0 0 7 -1 -3 -1 }}
|19487171 / 19416176
| 19487171 / 19416176
|6.31869015
| 6.31869015
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|{{vector| 18 0 0 0 -6 3 -1 -1 }}
| {{vector| 18 0 0 0 -6 3 -1 -1 }}
|575930368 / 572214203
| 575930368 / 572214203
|11.20690549
| 11.20690549
|1
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|{{vector| 0 0 0 0 5 2 -5 -1 }}
| {{vector| 0 0 0 0 5 2 -5 -1 }}
|27217619 / 26977283
| 27217619 / 26977283
|15.35497173
| 15.35497173
|2
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| -1
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|{{vector| 22 0 0 0 -1 4 -4 -4 }}
| {{vector| 22 0 0 0 -1 4 -4 -4 }}
|119793516544 / 119729942651
| 119793516544 / 119729942651
|0.9190021816
| 0.9190021816
|
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| 1
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|{{vector| -18 0 0 0 -4 3 3 2 }}
| {{vector| -18 0 0 0 -4 3 3 2 }}
|3896583821 / 3838050304
| 3896583821 / 3838050304
|26.20347661
| 26.20347661
|3
| 3
|1
| 1
| -2
| -2
| -1
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|{{vector| 22 0 0 0 -7 4 -1 -2 }}
| {{vector| 22 0 0 0 -7 4 -1 -2 }}
|119793516544 / 119592768427
| 119793516544 / 119592768427
|2.903608759
| 2.903608759
|
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|✓
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|{{vector| -27 0 0 0 -1 7 -2 3 }}
| {{vector| -27 0 0 0 -1 7 -2 3 }}
|430392078103 / 426678157312
| 430392078103 / 426678157312
|15.00391942
| 15.00391942
|2
| 2
| -1
| -1
|2
| 2
| -1
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|1
| 1
|
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|✓
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|}
|}


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


[[Hilim13]], a tridecatonic JI tuning in this subgroup
[[Category:Subgroup]]
[[Category:Subgroup]]

Revision as of 15:15, 3 February 2025

Commas

Here follows a selection of commas in the 2.11.13.17.19 domain basis.

Name Prime-count vector Ratio Cents As composition of other commas Tempered by patent val for ed2?
yama bean Blumeyer frouggie pollar 13 24 33 37 57 70 80 113 124 137
Blumeyer [7 0 0 0 -1 -1 -1 1⟩ 2432 / 2431 0.7120024978 1 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
yama [-4 0 0 0 1 -1 0 1⟩ 209 / 208 8.303296728 1 ✓ ✓ ✓ ✓ ✓ ✓
Blume [-11 0 0 0 2 0 1 0⟩ 2057 / 2048 7.59129423 1 -1 ✓ ✓ ✓ ✓ ✓ ✓
[3 0 0 0 0 -2 -1 2⟩ 2888 / 2873 9.015299226 1 1 ✓ ✓ ✓ ✓ ✓ ✓
eye [3 0 0 0 -2 0 2 -1⟩ 2312 / 2299 9.761918139 1 1 -2 ✓ ✓ ✓ ✓ ✓
lum [-1 0 0 0 -1 -1 2 0⟩ 289 / 286 18.06521487 2 1 -2 ✓ ✓ ✓
ume [-8 0 0 0 0 0 3 -1⟩ 4913 / 4864 17.35321237 2 1 -3 ✓ ✓ ✓ ✓
mey [-7 0 0 0 0 3 -1 0⟩ 2197 / 2176 16.62757581 2 1 ✓
[-5 0 0 0 0 -2 2 1⟩ 5491 / 5408 26.36851159 3 1 -2 ✓ ✓ ✓
[-5 0 0 0 -1 0 0 2⟩ 361 / 352 43.7080899 5 1 -1 1 ✓
[-1 0 0 0 -2 1 0 1⟩ 247 / 242 35.40479317 4 1 -1 1 ✓
[6 0 0 0 -1 -4 3 0⟩ 314432 / 314171 1.437639059 1 -2 -1 ✓ ✓ ✓ ✓ ✓
[14 0 0 0 -4 0 1 -1⟩ 278528 / 278179 2.170623909 1 -1 ✓ ✓ ✓
[4 0 0 0 -2 3 -2 0⟩ 35152 / 34969 9.036281578 1 1 1 ✓ ✓
[10 0 0 0 -3 -1 1 0⟩ 17408 / 17303 10.47392064 1 1 -1 ✓
[0 0 0 0 -1 2 -2 1⟩ 3211 / 3179 17.33957831 2 1 1 ✓
[6 0 0 0 -2 -2 1 1⟩ 20672 / 20449 18.77721736 2 1 -1 ✓ ✓ ✓
[-4 0 0 0 0 1 -2 2⟩ 4693 / 4624 25.64287503 3 1 1 ✓
[3 0 0 0 -3 2 0 0⟩ 1352 / 1331 27.10149644 3 1 -1 1 ✓
[-8 0 0 0 -1 2 1 0⟩ 2873 / 2816 34.69279067 4 1 -2 1 ✓
[14 0 0 0 2 0 -2 -3⟩ 1982464 / 1982251 0.1860173318 1 1 ✓ ✓ ✓ ✓
[13 0 0 0 1 -1 0 -3⟩ 90112 / 89167 18.2512322 2 1 -2 1 1 ✓
[7 0 0 0 -3 1 2 -2⟩ 480896 / 480491 1.458621411 1 -2 ✓ ✓ ✓
bean [21 0 0 0 -5 -1 0 0⟩ 2097152 / 2093663 2.882626407 1 ✓ ✓ ✓
[-3 0 0 0 -1 4 -1 -1⟩ 28561 / 28424 8.32427908 1 1 ✓ ✓
[-11 0 0 0 1 2 -1 1⟩ 35321 / 34816 24.93087254 3 1 ✓
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See also

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