2.11.13.17.19 subgroup: Difference between revisions

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{{Todo|inline=1|intro}}
== 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]].
Line 73: Line 75:
| 1
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Line 113: Line 115:
| 1
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| 2
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Line 153: Line 155:
| 2
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Line 193: Line 195:
| 3
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Line 213: Line 215:
| 5
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| 4
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Line 253: Line 255:
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Line 273: Line 275:
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Line 313: Line 315:
| 1
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Line 353: Line 355:
| 2
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Line 393: Line 395:
| 3
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Line 413: Line 415:
| 4
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Line 453: Line 455:
| 2
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Line 473: Line 475:
|  
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Line 553: Line 555:
| 1
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Line 573: Line 575:
| 3
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Line 593: Line 595:
| 3
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Line 654: Line 656:
|  
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Line 672: Line 674:
| 6.865657669
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| 1
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| 2
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Line 692: Line 694:
| 7.577660166
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| 1
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| 3
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Line 713: Line 715:
| 4
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Line 813: Line 815:
| 1
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Line 853: Line 855:
| 3
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| 1
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Line 873: Line 875:
| 3
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| 1
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Line 913: Line 915:
| 6
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| 2
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Line 953: Line 955:
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Line 974: Line 976:
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Line 1,032: Line 1,034:
| 6.153655171
| 6.153655171
| 1
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Line 1,053: Line 1,055:
|  
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Line 1,114: Line 1,116:
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Line 1,133: Line 1,135:
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Line 1,152: Line 1,154:
| 15.1689544
| 15.1689544
| 2
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Line 1,174: Line 1,176:
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Line 1,213: Line 1,215:
| 5
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| 1
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Line 1,233: Line 1,235:
|  
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Line 1,253: Line 1,255:
| 1
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Line 1,274: Line 1,276:
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Line 1,313: Line 1,315:
| 1
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Line 1,333: Line 1,335:
| 1
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Line 1,353: Line 1,355:
| 1
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Line 1,372: Line 1,374:
| 6.31869015
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Line 1,412: Line 1,414:
| 15.35497173
| 15.35497173
| 2
| 2
| -1
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| 2
| 2
| 1
| 1
Line 1,453: Line 1,455:
| 3
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Line 1,492: Line 1,494:
| 15.00391942
| 15.00391942
| 2
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| -1
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| 2
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| 1
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Line 1,513: Line 1,515:
* [[Hilim13]], a tridecatonic JI tuning in this subgroup
* [[Hilim13]], a tridecatonic JI tuning in this subgroup


[[Category:Subgroup]]
[[Category:Just intonation subgroups|#]]
[[Category:Rank-5 temperaments|#]]
[[Category:19-limit|#]]

Latest revision as of 10:27, 11 February 2026

Todo: intro

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 ✓
[3 0 0 0 4 0 -1 -3⟩ 117128 / 116603 7.777311562 1 −1 1 1 ✓ ✓ ✓
[-18 0 0 0 2 3 0 0⟩ 265837 / 262144 24.21887004 3 −1 1 ✓
[9 0 0 0 2 -2 0 -2⟩ 61952 / 61009 26.55452893 3 1 −2 1 1 ✓
[10 0 0 0 3 -1 -2 -2⟩ 1362944 / 1356277 8.48931406 1 1 1 ✓ ✓ ✓ ✓
[21 0 0 0 1 -1 -3 -2⟩ 23068672 / 23056709 0.8980198296 1 1 1 ✓ ✓ ✓
[-7 0 0 0 -3 -1 1 4⟩ 2215457 / 2214784 0.525985166 1 −1 −1 ✓ ✓ ✓
[-10 0 0 0 2 3 -3 1⟩ 5050903 / 5030912 6.865657669 1 −1 2 1 ✓ ✓ ✓
[-3 0 0 0 1 2 -4 2⟩ 671099 / 668168 7.577660166 1 −1 3 1 ✓ ✓
[5 0 0 0 3 -3 0 -1⟩ 42592 / 41743 34.85782565 4 1 −2 1 1 ✓
[6 0 0 0 -3 0 -1 2⟩ 23104 / 22627 36.11679567 4 1 1 ✓
pollar [1 0 0 0 -2 5 -1 -2⟩ 742586 / 742577 0.02098235203 1 ✓ ✓
[17 0 0 0 2 -2 -3 -1⟩ 15859712 / 15775643 9.201316557 1 1 1 1 ✓ ✓ ✓
[11 0 0 0 -3 2 -3 1⟩ 6576128 / 6539203 9.748284075 1 2 1 ✓ ✓
[24 0 0 0 -1 -1 -1 -3⟩ 16777216 / 16674229 10.65993797 1 1 −1 1 1 ✓ ✓
[17 0 0 0 -4 -2 0 1⟩ 2490368 / 2474329 11.18592313 1 1 ✓
[2 0 0 0 3 -1 1 -3⟩ 90508 / 89167 25.84252643 3 1 −3 1 1 ✓
[16 0 0 0 1 -3 -1 -1⟩ 720896 / 709631 27.26653142 3 1 −1 1 1 ✓
[-15 0 0 0 2 1 -1 2⟩ 567853 / 557056 33.23416926 4 1 ✓
[-2 0 0 0 -3 0 2 1⟩ 5491 / 5324 53.47000804 6 2 −3 1 ✓
[8 0 0 0 -3 4 -2 -1⟩ 7311616 / 7308521 0.7329848499 1 1 ✓ ✓
[28 0 0 0 -2 0 -1 -4⟩ 268435456 / 268070297 2.356641241 1 −1 1 1 ✓ ✓
[-10 0 0 0 -4 3 0 3⟩ 15069223 / 14992384 8.850264246 1 1 −1 ✓ ✓ ✓ ✓
[6 0 0 0 4 -2 -2 -1⟩ 937024 / 927979 16.79261079 2 1 1 ✓ ✓
[15 0 0 0 -4 3 -3 0⟩ 71991296 / 71931233 1.444987348 2 1 ✓ ✓
[-17 0 0 0 3 4 -2 0⟩ 38014691 / 37879808 6.153655171 1 −1 1 1 ✓ ✓
[0 0 0 0 -6 0 3 2⟩ 1773593 / 1771561 1.984606577 1 −1 −1 −1 ✓ ✓
[14 0 0 0 -5 2 -1 0⟩ 2768896 / 2737867 19.51020221 2 1 1 ✓
[18 0 0 0 0 3 -4 -3⟩ 575930368 / 572870539 9.222298909 1 1 1 2 ✓ ✓ ✓
[-6 0 0 0 -5 4 0 2⟩ 10310521 / 10307264 0.5469675181 1 −1 ✓
[20 0 0 0 1 -4 1 -3⟩ 196083712 / 195899899 1.623656391 1 −2 1 ✓
[-14 0 0 0 3 2 -3 2⟩ 81202979 / 80494592 15.1689544 2 −1 2 1 ✓ ✓
[-21 0 0 0 -2 3 1 3⟩ 256176791 / 253755392 16.44155848 2 −1 ✓ ✓ ✓
[-1 0 0 0 4 1 -3 -1⟩ 190333 / 186694 33.42018659 4 1 2 ✓
[8 0 0 0 1 -3 2 -2⟩ 813824 / 793117 44.61974379 5 2 −4 1 1 ✓
[-7 0 0 0 -5 1 4 1⟩ 20629687 / 20614528 1.272604079 1 −2 −1 −1 ✓
[2 0 0 0 6 -5 0 -1⟩ 7086244 / 7054567 7.75632921 1 −1 1 ✓
[-17 0 0 0 -3 4 1 2⟩ 175278857 / 174456832 8.138261748 1 −1 ✓ ✓
frouggie [13 0 0 0 4 -5 -1 -1⟩ 119939072 / 119927639 0.1650349798 1 ✓ ✓
[16 0 0 0 2 -5 1 -2⟩ 134807552 / 134036773 9.926953119 1 1 −2 1 ✓
[-24 0 0 0 -2 5 2 1⟩ 2038769863 / 2030043136 7.42625925 1 −1 −1 ✓ ✓
[-4 0 0 0 -5 -1 3 3⟩ 33698267 / 33498608 10.28790331 1 1 −1 −1 −1 ✓
[-4 0 0 0 7 -1 -3 -1⟩ 19487171 / 19416176 6.31869015 1 −1 1 1 1 ✓
[18 0 0 0 -6 3 -1 -1⟩ 575930368 / 572214203 11.20690549 1 1 1 ✓
[0 0 0 0 5 2 -5 -1⟩ 27217619 / 26977283 15.35497173 2 −1 2 1 2 ✓
[22 0 0 0 -1 4 -4 -4⟩ 119793516544 / 119729942651 0.9190021816 1 1 2 ✓
[-18 0 0 0 -4 3 3 2⟩ 3896583821 / 3838050304 26.20347661 3 1 −2 −1 ✓
[22 0 0 0 -7 4 -1 -2⟩ 119793516544 / 119592768427 2.903608759 1 1 ✓ ✓
[-27 0 0 0 -1 7 -2 3⟩ 430392078103 / 426678157312 15.00391942 2 −1 2 −1 1 ✓

See also

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