2.11.13.17.19 subgroup: Difference between revisions

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==Commas==
{{Todo|inline=1|intro}}
 
== 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
!37
!57
!70
!80
!113
!124
!137
|-
|-
|Blumeyer
! yama
|{{vector| 7 0 0 0 -1 -1 -1 1 }}
! bean
|2432 / 2431
! Blumeyer
|0.7120024978
! frouggie
|
! pollar
|
! 13
|1
! 24
|
! 33
|
! 37
|✓
! 57
|✓
! 70
|✓
! 80
|✓
! 113
|✓
! 124
|✓
! 137
|✓
|✓
|✓
|✓
|-
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|yama
| Blumeyer
|{{vector| -4 0 0 0 1 -1 0 1 }}
| {{vector| 7 0 0 0 -1 -1 -1 1 }}
|209 / 208
| 2432 / 2431
|8.303296728
| 0.7120024978
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|Blume
| yama
|{{vector| -11 0 0 0 2 0 1 0 }}
| {{vector| -4 0 0 0 1 -1 0 1 }}
|2057 / 2048
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|7.59129423
| 8.303296728
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| {{vector| -11 0 0 0 2 0 1 0 }}
|2888 / 2873
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|9.015299226
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|lum
| eye
|{{vector| -1 0 0 0 -1 -1 2 0 }}
| {{vector| 3 0 0 0 -2 0 2 -1 }}
|289 / 286
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|18.06521487
| 9.761918139
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|{{vector| -8 0 0 0 0 0 3 -1 }}
| {{vector| -1 0 0 0 -1 -1 2 0 }}
|4913 / 4864
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|17.35321237
| 18.06521487
|2
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|mey
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|{{vector| -7 0 0 0 0 3 -1 0 }}
| {{vector| -8 0 0 0 0 0 3 -1 }}
|2197 / 2176
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|16.62757581
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| {{vector| -7 0 0 0 0 3 -1 0 }}
|5491 / 5408
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|26.36851159
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|361 / 352
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|43.7080899
| 26.36851159
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|247 / 242
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| {{vector| -1 0 0 0 -2 1 0 1 }}
|314432 / 314171
| 247 / 242
|1.437639059
| 35.40479317
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|{{vector| 14 0 0 0 -4 0 1 -1 }}
| {{vector| 6 0 0 0 -1 -4 3 0 }}
|278528 / 278179
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|2.170623909
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|{{vector| 4 0 0 0 -2 3 -2 0 }}
| {{vector| 14 0 0 0 -4 0 1 -1 }}
|35152 / 34969
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|9.036281578
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|{{vector| 10 0 0 0 -3 -1 1 0 }}
| {{vector| 4 0 0 0 -2 3 -2 0 }}
|17408 / 17303
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|10.47392064
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|{{vector| 0 0 0 0 -1 2 -2 1 }}
| {{vector| 10 0 0 0 -3 -1 1 0 }}
|3211 / 3179
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|17.33957831
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|{{vector| -4 0 0 0 0 1 -2 2 }}
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|1352 / 1331
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|{{vector| 14 0 0 0 2 0 -2 -3 }}
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|1982464 / 1982251
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|480896 / 480491
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|{{vector| 21 0 0 0 -5 -1 0 0 }}
| {{vector| 7 0 0 0 -3 1 2 -2 }}
|2097152 / 2093663
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|{{vector| -11 0 0 0 1 2 -1 1 }}
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|265837 / 262144
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|61952 / 61009
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|1362944 / 1356277
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|8.48931406
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|{{vector| 21 0 0 0 1 -1 -3 -2 }}
| {{vector| 10 0 0 0 3 -1 -2 -2 }}
|23068672 / 23056709
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|0.8980198296
| 8.48931406
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|{{vector| -7 0 0 0 -3 -1 1 4 }}
| {{vector| 21 0 0 0 1 -1 -3 -2 }}
|2215457 / 2214784
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|0.525985166
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|{{vector| -10 0 0 0 2 3 -3 1 }}
| {{vector| -7 0 0 0 -3 -1 1 4 }}
|5050903 / 5030912
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|{{vector| -3 0 0 0 1 2 -4 2 }}
| {{vector| -10 0 0 0 2 3 -3 1 }}
|671099 / 668168
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|36.11679567
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|742586 / 742577
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|0.02098235203
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| pollar
|{{vector| 17 0 0 0 2 -2 -3 -1 }}
| {{vector| 1 0 0 0 -2 5 -1 -2 }}
|15859712 / 15775643
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|9.201316557
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|6576128 / 6539203
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|9.748284075
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|{{vector| 24 0 0 0 -1 -1 -1 -3 }}
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|16777216 / 16674229
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|3896583821 / 3838050304
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|26.20347661
| 0.9190021816
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|430392078103 / 426678157312
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|15.00391942
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| 430392078103 / 426678157312
| 15.00391942
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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:Just intonation subgroups|#]]
[[Category:Subgroup]]
[[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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