Xenharmonic Wiki

2.11.13.17.19 subgroup: Difference between revisions

← Older edit
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,164 edits
m Recategorize
 
(6 intermediate revisions by 3 users not shown)
Line 1: Line 1:
==Commas==
{{Todo|inline=1|intro}}
 
== Commas ==
Here follows a selection of commas in the 2.11.13.17.19 [[domain basis]].


{| class="wikitable"
{| class="wikitable"
|+
! rowspan="2" |name
! rowspan="2" |monzo
! rowspan="2" |ratio
! rowspan="2" |cents
! colspan="5" |as composition of other commas
! colspan="10" |tempered by ed2?
|-
|-
!nothulo
! 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
|{{Monzo| 7 0 0 0 -1 -1 -1 1 }}
| {{vector| 7 0 0 0 -1 -1 -1 1 }}
|2432 / 2431
| 2432 / 2431
|0.7120024978
| 0.7120024978
|
|  
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|-
|-
|nothulo
| yama
|{{Monzo| -4 0 0 0 1 -1 0 1 }}
| {{vector| -4 0 0 0 1 -1 0 1 }}
|209 / 208
| 209 / 208
|8.303296728
| 8.303296728
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|Blume
| Blume
|{{Monzo| -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
|1
| 1
|
|  
| -1
| −1
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 3 0 0 0 0 -2 -1 2 }}
| {{vector| 3 0 0 0 0 -2 -1 2 }}
|2888 / 2873
| 2888 / 2873
|9.015299226
| 9.015299226
|1
| 1
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|eye
| eye
|{{Monzo| 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
| 1
|1
| 1
| -2
| −2
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|-
|-
|lum
| lum
|{{Monzo| -1 0 0 0 -1 -1 2 0 }}
| {{vector| -1 0 0 0 -1 -1 2 0 }}
|289 / 286
| 289 / 286
|18.06521487
| 18.06521487
|2
| 2
|1
| 1
| -2
| −2
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|ume
| ume
|{{Monzo| -8 0 0 0 0 0 3 -1 }}
| {{vector| -8 0 0 0 0 0 3 -1 }}
|4913 / 4864
| 4913 / 4864
|17.35321237
| 17.35321237
|2
| 2
|1
| 1
| -3
| −3
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|mey
| mey
|{{Monzo| -7 0 0 0 0 3 -1 0 }}
| {{vector| -7 0 0 0 0 3 -1 0 }}
|2197 / 2176
| 2197 / 2176
|16.62757581
| 16.62757581
|2
| 2
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -5 0 0 0 0 -2 2 1 }}
| {{vector| -5 0 0 0 0 -2 2 1 }}
|5491 / 5408
| 5491 / 5408
|26.36851159
| 26.36851159
|3
| 3
|1
| 1
| -2
| −2
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -5 0 0 0 -1 0 0 2 }}
| {{vector| -5 0 0 0 -1 0 0 2 }}
|361 / 352
| 361 / 352
|43.7080899
| 43.7080899
|5
| 5
|1
| 1
| -1
| −1
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -1 0 0 0 -2 1 0 1 }}
| {{vector| -1 0 0 0 -2 1 0 1 }}
|247 / 242
| 247 / 242
|35.40479317
| 35.40479317
|4
| 4
|1
| 1
| -1
| −1
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 6 0 0 0 -1 -4 3 0 }}
| {{vector| 6 0 0 0 -1 -4 3 0 }}
|314432 / 314171
| 314432 / 314171
|1.437639059
| 1.437639059
|
|  
|1
| 1
| -2
| −2
|
|  
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 14 0 0 0 -4 0 1 -1 }}
| {{vector| 14 0 0 0 -4 0 1 -1 }}
|278528 / 278179
| 278528 / 278179
|2.170623909
| 2.170623909
|
|  
|1
| 1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 4 0 0 0 -2 3 -2 0 }}
| {{vector| 4 0 0 0 -2 3 -2 0 }}
|35152 / 34969
| 35152 / 34969
|9.036281578
| 9.036281578
|1
| 1
|
|  
|1
| 1
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 10 0 0 0 -3 -1 1 0 }}
| {{vector| 10 0 0 0 -3 -1 1 0 }}
|17408 / 17303
| 17408 / 17303
|10.47392064
| 10.47392064
|1
| 1
|1
| 1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 0 0 0 0 -1 2 -2 1 }}
| {{vector| 0 0 0 0 -1 2 -2 1 }}
|3211 / 3179
| 3211 / 3179
|17.33957831
| 17.33957831
|2
| 2
|
|  
|1
| 1
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 6 0 0 0 -2 -2 1 1 }}
| {{vector| 6 0 0 0 -2 -2 1 1 }}
|20672 / 20449
| 20672 / 20449
|18.77721736
| 18.77721736
|2
| 2
|1
| 1
| -1
| −1
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -4 0 0 0 0 1 -2 2 }}
| {{vector| -4 0 0 0 0 1 -2 2 }}
|4693 / 4624
| 4693 / 4624
|25.64287503
| 25.64287503
|3
| 3
|
|  
|1
| 1
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 3 0 0 0 -3 2 0 0 }}
| {{vector| 3 0 0 0 -3 2 0 0 }}
|1352 / 1331
| 1352 / 1331
|27.10149644
| 27.10149644
|3
| 3
|1
| 1
| -1
| −1
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -8 0 0 0 -1 2 1 0 }}
| {{vector| -8 0 0 0 -1 2 1 0 }}
|2873 / 2816
| 2873 / 2816
|34.69279067
| 34.69279067
|4
| 4
|1
| 1
| -2
| −2
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 14 0 0 0 2 0 -2 -3 }}
| {{vector| 14 0 0 0 2 0 -2 -3 }}
|1982464 / 1982251
| 1982464 / 1982251
|0.1860173318
| 0.1860173318
|
|  
|
|  
|
|  
|1
| 1
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 13 0 0 0 1 -1 0 -3 }}
| {{vector| 13 0 0 0 1 -1 0 -3 }}
|90112 / 89167
| 90112 / 89167
|18.2512322
| 18.2512322
|2
| 2
|1
| 1
| -2
| −2
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 7 0 0 0 -3 1 2 -2 }}
| {{vector| 7 0 0 0 -3 1 2 -2 }}
|480896 / 480491
| 480896 / 480491
|1.458621411
| 1.458621411
|
|  
|1
| 1
| -2
| −2
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|-
|-
|bean
| bean
|{{Monzo| 21 0 0 0 -5 -1 0 0 }}
| {{vector| 21 0 0 0 -5 -1 0 0 }}
|2097152 / 2093663
| 2097152 / 2093663
|2.882626407
| 2.882626407
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -3 0 0 0 -1 4 -1 -1 }}
| {{vector| -3 0 0 0 -1 4 -1 -1 }}
|28561 / 28424
| 28561 / 28424
|8.32427908
| 8.32427908
|1
| 1
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -11 0 0 0 1 2 -1 1 }}
| {{vector| -11 0 0 0 1 2 -1 1 }}
|35321 / 34816
| 35321 / 34816
|24.93087254
| 24.93087254
|3
| 3
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 3 0 0 0 4 0 -1 -3 }}
| {{vector| 3 0 0 0 4 0 -1 -3 }}
|117128 / 116603
| 117128 / 116603
|7.777311562
| 7.777311562
|1
| 1
|
|  
| -1
| −1
|1
| 1
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| -18 0 0 0 2 3 0 0 }}
| {{vector| -18 0 0 0 2 3 0 0 }}
|265837 / 262144
| 265837 / 262144
|24.21887004
| 24.21887004
|3
| 3
|
|  
| -1
| −1
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 9 0 0 0 2 -2 0 -2 }}
| {{vector| 9 0 0 0 2 -2 0 -2 }}
|61952 / 61009
| 61952 / 61009
|26.55452893
| 26.55452893
|3
| 3
|1
| 1
| -2
| −2
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 10 0 0 0 3 -1 -2 -2 }}
| {{vector| 10 0 0 0 3 -1 -2 -2 }}
|1362944 / 1356277
| 1362944 / 1356277
|8.48931406
| 8.48931406
|1
| 1
|
|  
|
|  
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| 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
|
|  
|
|  
|1
| 1
|1
| 1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -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
|
|  
|
|  
|1
| 1
| -1
| −1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -10 0 0 0 2 3 -3 1 }}
| {{vector| -10 0 0 0 2 3 -3 1 }}
|5050903 / 5030912
| 5050903 / 5030912
|6.865657669
| 6.865657669
|1
| 1
| -1
| −1
|2
| 2
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -3 0 0 0 1 2 -4 2 }}
| {{vector| -3 0 0 0 1 2 -4 2 }}
|671099 / 668168
| 671099 / 668168
|7.577660166
| 7.577660166
|1
| 1
| -1
| −1
|3
| 3
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 5 0 0 0 3 -3 0 -1 }}
| {{vector| 5 0 0 0 3 -3 0 -1 }}
|42592 / 41743
| 42592 / 41743
|34.85782565
| 34.85782565
|4
| 4
|1
| 1
| -2
| −2
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
| 4
|1
| 1
|
|  
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|pollar
| pollar
|{{Monzo| 1 0 0 0 -2 5 -1 -2 }}
| {{vector| 1 0 0 0 -2 5 -1 -2 }}
|742586 / 742577
| 742586 / 742577
|0.02098235203
| 0.02098235203
|
|  
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 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
|1
| 1
|
|  
|1
| 1
|1
| 1
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| 11 0 0 0 -3 2 -3 1 }}
| {{vector| 11 0 0 0 -3 2 -3 1 }}
|6576128 / 6539203
| 6576128 / 6539203
|9.748284075
| 9.748284075
|1
| 1
|
|  
|2
| 2
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
|1
| 1
|1
| 1
| -1
| −1
|1
| 1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| 17 0 0 0 -4 -2 0 1 }}
| {{vector| 17 0 0 0 -4 -2 0 1 }}
|2490368 / 2474329
| 2490368 / 2474329
|11.18592313
| 11.18592313
|1
| 1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 2 0 0 0 3 -1 1 -3 }}
| {{vector| 2 0 0 0 3 -1 1 -3 }}
|90508 / 89167
| 90508 / 89167
|25.84252643
| 25.84252643
|3
| 3
|1
| 1
| -3
| −3
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 16 0 0 0 1 -3 -1 -1 }}
| {{vector| 16 0 0 0 1 -3 -1 -1 }}
|720896 / 709631
| 720896 / 709631
|27.26653142
| 27.26653142
|3
| 3
|1
| 1
| -1
| −1
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -15 0 0 0 2 1 -1 2 }}
| {{vector| -15 0 0 0 2 1 -1 2 }}
|567853 / 557056
| 567853 / 557056
|33.23416926
| 33.23416926
|4
| 4
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -2 0 0 0 -3 0 2 1 }}
| {{vector| -2 0 0 0 -3 0 2 1 }}
|5491 / 5324
| 5491 / 5324
|53.47000804
| 53.47000804
|6
| 6
|2
| 2
| -3
| −3
|
|  
|1
| 1
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 8 0 0 0 -3 4 -2 -1 }}
| {{vector| 8 0 0 0 -3 4 -2 -1 }}
|7311616 / 7308521
| 7311616 / 7308521
|0.7329848499
| 0.7329848499
|
|  
|
|  
|1
| 1
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 28 0 0 0 -2 0 -1 -4 }}
| {{vector| 28 0 0 0 -2 0 -1 -4 }}
|268435456 / 268070297
| 268435456 / 268070297
|2.356641241
| 2.356641241
|
|  
|1
| 1
| -1
| −1
|1
| 1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -10 0 0 0 -4 3 0 3 }}
| {{vector| -10 0 0 0 -4 3 0 3 }}
|15069223 / 14992384
| 15069223 / 14992384
|8.850264246
| 8.850264246
|1
| 1
|
|  
|1
| 1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 6 0 0 0 4 -2 -2 -1 }}
| {{vector| 6 0 0 0 4 -2 -2 -1 }}
|937024 / 927979
| 937024 / 927979
|16.79261079
| 16.79261079
|2
| 2
|
|  
|
|  
|1
| 1
|1
| 1
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 15 0 0 0 -4 3 -3 0 }}
| {{vector| 15 0 0 0 -4 3 -3 0 }}
|71991296 / 71931233
| 71991296 / 71931233
|1.444987348
| 1.444987348
|
|  
|
|  
|2
| 2
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -17 0 0 0 3 4 -2 0 }}
| {{vector| -17 0 0 0 3 4 -2 0 }}
|38014691 / 37879808
| 38014691 / 37879808
|6.153655171
| 6.153655171
|1
| 1
| -1
| −1
|1
| 1
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 0 0 0 0 -6 0 3 2 }}
| {{vector| 0 0 0 0 -6 0 3 2 }}
|1773593 / 1771561
| 1773593 / 1771561
|1.984606577
| 1.984606577
|
|  
|1
| 1
| -1
| −1
| -1
| −1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 14 0 0 0 -5 2 -1 0 }}
| {{vector| 14 0 0 0 -5 2 -1 0 }}
|2768896 / 2737867
| 2768896 / 2737867
|19.51020221
| 19.51020221
|2
| 2
|1
| 1
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 18 0 0 0 0 3 -4 -3 }}
| {{vector| 18 0 0 0 0 3 -4 -3 }}
|575930368 / 572870539
| 575930368 / 572870539
|9.222298909
| 9.222298909
|1
| 1
|
|  
|1
| 1
|1
| 1
|2
| 2
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| -6 0 0 0 -5 4 0 2 }}
| {{vector| -6 0 0 0 -5 4 0 2 }}
|10310521 / 10307264
| 10310521 / 10307264
|0.5469675181
| 0.5469675181
|
|  
|
|  
|1
| 1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| 20 0 0 0 1 -4 1 -3 }}
| {{vector| 20 0 0 0 1 -4 1 -3 }}
|196083712 / 195899899
| 196083712 / 195899899
|1.623656391
| 1.623656391
|
|  
|1
| 1
| -2
| −2
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -14 0 0 0 3 2 -3 2 }}
| {{vector| -14 0 0 0 3 2 -3 2 }}
|81202979 / 80494592
| 81202979 / 80494592
|15.1689544
| 15.1689544
|2
| 2
| -1
| −1
|2
| 2
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -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
|
|  
|
|  
| -1
| −1
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -1 0 0 0 4 1 -3 -1 }}
| {{vector| -1 0 0 0 4 1 -3 -1 }}
|190333 / 186694
| 190333 / 186694
|33.42018659
| 33.42018659
|4
| 4
|
|  
|
|  
|1
| 1
|2
| 2
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
|1
| 1
|1
| 1
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -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
|
|  
|1
| 1
| -2
| −2
| -1
| −1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
|1
| 1
|
|  
| -1
| −1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| -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
| 1
|
|  
|
|  
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|frouggie
| frouggie
|{{Monzo| 13 0 0 0 4 -5 -1 -1 }}
| {{vector| 13 0 0 0 4 -5 -1 -1 }}
|119939072 / 119927639
| 119939072 / 119927639
|0.1650349798
| 0.1650349798
|
|  
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
| 1
| -2
| −2
|1
| 1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -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
|
|  
| -1
| −1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -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
|1
| 1
|1
| 1
| -1
| −1
| -1
| −1
| -1
| −1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| -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
|1
| 1
| -1
| −1
|1
| 1
|1
| 1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|-
|-
|
|  
|{{Monzo| 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
| 1
|1
| 1
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
| 2
| -1
| −1
|2
| 2
|1
| 1
|2
| 2
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
|
|  
|
|  
|1
| 1
|1
| 1
|2
| 2
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -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
| −1
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|-
|-
|
|  
|{{Monzo| 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
|
|  
|1
| 1
|
|  
|
|  
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|✓
| ✓
|-
|-
|
|  
|{{Monzo| -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
| −1
|1
| 1
|
|  
|
|  
|
|  
|
|  
|
|  
|✓
| ✓
|
|  
|
|  
|
|  
|
|  
|}
|}


==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:Rank-5 temperaments|#]]
[[Category:19-limit|#]]
Retrieved from "https://en.xen.wiki/w/2.11.13.17.19_subgroup"