No-fives subgroup temperaments: Difference between revisions
→Bleu: note secund |
m Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| " Tags: Mobile edit Mobile web edit |
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Comma list: 64/63, 364/363, 1078/1053 | Comma list: 64/63, 364/363, 1078/1053 | ||
{{Mapping|legend=0| 1 0 6 21 34 | 0 1 -2 -11 -19 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 31: | Line 31: | ||
Comma list: 64/63, 209/208, 343/342, 364/363 | Comma list: 64/63, 209/208, 343/342, 364/363 | ||
{{Mapping|legend=0| 1 0 6 21 34 17 | 0 1 -2 -11 -19 -8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 57: | Line 57: | ||
[[Comma list]]: 282429536481/281974669312 | [[Comma list]]: 282429536481/281974669312 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 0| 0 5 24 }} | ||
: mapping generators: ~2, ~243/224 | : mapping generators: ~2, ~243/224 | ||
| Line 75: | Line 75: | ||
Comma list: 1331/1323, 19712/19683 | Comma list: 1331/1323, 19712/19683 | ||
{{Mapping|legend=2| 1 1 0 1 | 0 5 24 21 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 90: | Line 90: | ||
Comma list: 352/351, 729/728, 1331/1323 | Comma list: 352/351, 729/728, 1331/1323 | ||
{{Mapping|legend=2| 1 1 0 1 3 | 0 5 24 21 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 105: | Line 105: | ||
[[Comma list]]: 177147/175616 | [[Comma list]]: 177147/175616 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -3 | 0 3 11 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 -3 | 0 3 0 11 }} | ||
: mapping generators: ~2, ~81/56 | : mapping generators: ~2, ~81/56 | ||
| Line 130: | Line 130: | ||
[[Comma list]]: 1605632/1594323 | [[Comma list]]: 1605632/1594323 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 -1 | 0 2 13 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 0 -1 | 0 2 0 13 }} | ||
: mapping generators: ~2, ~2187/1792 | : mapping generators: ~2, ~2187/1792 | ||
| Line 150: | Line 150: | ||
Comma list: 243/242, 896/891 | Comma list: 243/242, 896/891 | ||
{{Mapping|legend=2| 1 1 -1 2 | 0 2 13 5 }} | |||
{{Mapping|legend=4| 1 1 0 -1 2 | 0 2 0 13 5 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 169: | Line 169: | ||
Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }} | Sval mapping: {{mapping| 1 1 -1 2 4 | 0 2 13 5 -1 }} | ||
{{Mapping|legend=4| 1 1 0 -1 2 4 | 0 2 0 13 5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 188: | Line 188: | ||
Comma list: 243/242, 896/891, 1083/1078 | Comma list: 243/242, 896/891, 1083/1078 | ||
{{Mapping|legend=2| 1 1 -1 2 0 | 0 4 26 10 29 }} | |||
: mapping generators: ~2, ~21/19 | : mapping generators: ~2, ~21/19 | ||
| Line 208: | Line 208: | ||
[[Comma list]]: 34451725707/34359738368 | [[Comma list]]: 34451725707/34359738368 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 5 | 0 4 -15 }} | ||
: mapping generators: ~2, ~567/512 | : mapping generators: ~2, ~567/512 | ||
| Line 226: | Line 226: | ||
Comma list: 243/242, 65536/65219 | Comma list: 243/242, 65536/65219 | ||
{{Mapping|legend=2| 1 1 5 2 | 0 4 -15 10 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 241: | Line 241: | ||
Comma list: 243/242, 513/512, 1083/1078 | Comma list: 243/242, 513/512, 1083/1078 | ||
{{Mapping|legend=2| 1 1 5 2 6 | 0 4 -15 10 -12 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 258: | Line 258: | ||
[[Comma list]]: 537824/531441 | [[Comma list]]: 537824/531441 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 5 12 }} | ||
: mapping generators: ~2, ~243/196 | : mapping generators: ~2, ~243/196 | ||
| Line 276: | Line 276: | ||
Comma list: 896/891, 26411/26244 | Comma list: 896/891, 26411/26244 | ||
{{Mapping|legend=2| 1 0 -1 6 | 0 5 12 -8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 291: | Line 291: | ||
Comma list: 144/143, 343/338, 729/728 | Comma list: 144/143, 343/338, 729/728 | ||
{{Mapping|legend=2| 1 0 -1 6 -2 | 0 5 12 -8 18 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 306: | Line 306: | ||
Comma list: 144/143, 232/231, 343/338, 729/728 | Comma list: 144/143, 232/231, 343/338, 729/728 | ||
{{Mapping|legend=2| 1 0 -1 6 -2 2 | 0 5 12 -8 18 9 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 321: | Line 321: | ||
Comma list: 352/351, 364/363, 26411/26244 | Comma list: 352/351, 364/363, 26411/26244 | ||
{{Mapping|legend=2| 1 0 -1 6 11 | 0 5 12 -8 -23 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 336: | Line 336: | ||
Comma list: 169/168, 896/891, 26411/26244 | Comma list: 169/168, 896/891, 26411/26244 | ||
{{Mapping|legend=2| 1 0 -1 6 1 | 0 10 24 -16 17 }} | |||
: mapping generators: ~2, ~143/128 | : mapping generators: ~2, ~143/128 | ||
| Line 352: | Line 352: | ||
Comma list: 784/783, 5887/5832 | Comma list: 784/783, 5887/5832 | ||
{{Mapping|legend=2| 1 0 -1 2 | 0 5 12 9 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 371: | Line 371: | ||
[[Comma list]]: 19683/19208 | [[Comma list]]: 19683/19208 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -1 -3 | 0 4 9 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 -1 0 -3 | 0 4 0 9 }} | ||
: mapping generators: ~2, ~14/9 | : mapping generators: ~2, ~14/9 | ||
| Line 391: | Line 391: | ||
Comma list: 99/98, 243/242 | Comma list: 99/98, 243/242 | ||
{{Mapping|legend=2| 1 -1 -3 -3 | 0 4 9 10 }} | |||
{{Mapping|legend=4| 1 -1 0 -3 -3 | 0 4 0 9 10 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 408: | Line 408: | ||
Comma list: 78/77, 99/98, 243/242 | Comma list: 78/77, 99/98, 243/242 | ||
{{Mapping|legend=2| 1 -1 -3 -3 -6 | 0 4 9 10 15 }} | |||
{{Mapping|legend=4| 1 -1 0 -3 -3 -6 | 0 4 0 9 10 15}} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 425: | Line 425: | ||
Comma list: 99/98, 144/143, 243/242 | Comma list: 99/98, 144/143, 243/242 | ||
{{Mapping|legend=2| 1 -1 -3 -3 5 | 0 4 9 10 -2 }} | |||
{{Mapping|legend=4| 1 -1 0 -3 -3 5 | 0 4 0 9 10 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 444: | Line 444: | ||
Comma list: 99/98, 243/242, 363/361 | Comma list: 99/98, 243/242, 363/361 | ||
{{Mapping|legend=2| 2 2 3 4 5 | 0 4 9 10 12 }} | |||
: mapping generators: ~209/147, ~21/19 | : mapping generators: ~209/147, ~21/19 | ||
| Line 462: | Line 462: | ||
[[Comma list]]: [[59049/57344]] | [[Comma list]]: [[59049/57344]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -13 | 0 1 10 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 -13 | 0 1 0 10 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 484: | Line 484: | ||
[[Comma list]]: 17496/16807 | [[Comma list]]: 17496/16807 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 | 0 5 7 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 1 0 2 | 0 5 0 7 }} | ||
: mapping generators: ~2, ~54/49 | : mapping generators: ~2, ~54/49 | ||
| Line 504: | Line 504: | ||
Comma list: 99/98, 864/847 | Comma list: 99/98, 864/847 | ||
{{Mapping|legend=2| 1 1 2 3 | 0 5 7 4 }} | |||
{{Mapping|legend=4| 1 1 0 2 3 | 0 5 0 7 4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 521: | Line 521: | ||
Comma list: 78/77, 99/98, 144/143 | Comma list: 78/77, 99/98, 144/143 | ||
{{Mapping|legend=2| 1 1 2 3 3 | 0 5 7 4 6 }} | |||
{{Mapping|legend=4| 1 1 0 2 3 3 | 0 5 0 7 4 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 545: | Line 545: | ||
[[Comma list]]: 5764801/5668704 | [[Comma list]]: 5764801/5668704 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 | 0 8 11 }} | ||
: mapping generators: ~2, ~343/342 | : mapping generators: ~2, ~343/342 | ||
| Line 563: | Line 563: | ||
Comma list: 243/242, 2401/2376 | Comma list: 243/242, 2401/2376 | ||
{{Mapping|legend=2| 1 1 2 2 | 0 8 11 20 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 578: | Line 578: | ||
Comma list: 133/132, 243/242, 343/342 | Comma list: 133/132, 243/242, 343/342 | ||
{{Mapping|legend=2| 1 1 2 2 3 | 0 8 11 20 17 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 595: | Line 595: | ||
[[Comma list]]: 2187/2048 | [[Comma list]]: 2187/2048 | ||
{{Mapping|legend= | {{Mapping|legend=3| 7 11 0 | 0 0 1 }} | ||
: mapping generators: ~9/8, ~7 | : mapping generators: ~9/8, ~7 | ||
| Line 615: | Line 615: | ||
[[Comma list]]: {{monzo| 83 -1 -29 }} | [[Comma list]]: {{monzo| 83 -1 -29 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -4 3 | 0 29 -1 }} | ||
: mapping generators: ~2, ~8/7 | : mapping generators: ~2, ~8/7 | ||
| Line 633: | Line 633: | ||
Comma list: 43923/43904, 5767168/5764801 | Comma list: 43923/43904, 5767168/5764801 | ||
{{Mapping|legend=2| 1 -4 3 5 | 0 29 -1 -8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 656: | Line 656: | ||
[[Comma list]]: 14680064/14348907 | [[Comma list]]: 14680064/14348907 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -21 | 0 1 15 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 -21 | 0 1 0 15 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 676: | Line 676: | ||
Comma list: 896/891, 1331/1323 | Comma list: 896/891, 1331/1323 | ||
{{Mapping|legend=2| 1 0 -21 -14 | 0 1 15 11 }} | |||
{{Mapping|legend=4| 1 0 0 -21 -14 | 0 1 0 15 11 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 693: | Line 693: | ||
Comma list: 169/168, 352/351, 364/363 | Comma list: 169/168, 352/351, 364/363 | ||
{{Mapping|legend=2| 1 0 -21 -14 -9 | 0 1 15 11 8 }} | |||
{{Mapping|legend=4| 1 0 0 -21 -14 -9 | 0 1 0 15 11 8 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 710: | Line 710: | ||
Comma list: 169/168, 208/207, 352/351, 364/363 | Comma list: 169/168, 208/207, 352/351, 364/363 | ||
{{Mapping|legend=2| 1 0 -21 -14 -9 -5 | 0 1 15 11 8 6 }} | |||
{{Mapping|legend=4| 1 0 0 -21 -14 -9 0 0 -5 | 0 1 0 15 11 8 0 0 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 727: | Line 727: | ||
Comma list: 169/168, 208/207, 232/231, 352/351, 364/363 | Comma list: 169/168, 208/207, 232/231, 352/351, 364/363 | ||
{{Mapping|legend=2| 1 0 -21 -14 -9 -5 -38 | 0 1 15 11 8 6 27 }} | |||
{{Mapping|legend=4| 1 0 0 -21 -14 -9 -5 0 0 -38 | 0 1 0 15 11 8 0 0 6 27 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 756: | Line 756: | ||
[[Comma list]]: 17294403/16777216 | [[Comma list]]: 17294403/16777216 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 3 | 0 8 -1 }} | ||
: mapping generators: ~2, ~8/7 | : mapping generators: ~2, ~8/7 | ||
| Line 770: | Line 770: | ||
=== Hectosaros leap week === | === Hectosaros leap week === | ||
This temperament may be described as the {{nowrap| 320 & 1803 }} temperament, in the 2.3.7.13.17.19 | This temperament may be described as the {{nowrap| 320 & 1803 }} temperament, in the 2.3.7.13.17.19. It is named after the fact that 1803 tropical years make up almost exactly 100 saros cycles. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
| Line 776: | Line 776: | ||
[[Comma list]]: {{monzo| -50 -746 439 }} | [[Comma list]]: {{monzo| -50 -746 439 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -126 -214 | 0 439 746 }} | ||
: mapping generators: ~2, ~{{monzo| -16 -243 143 }} | : mapping generators: ~2, ~{{monzo| -16 -243 143 }} | ||
| Line 794: | Line 794: | ||
Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }} | Comma list: {{monzo| -42 -2 -5 16 }}, {{monzo| 10 -46 29 -5 }} | ||
{{Mapping|legend=2| 1 -126 -214 -80 | 0 439 746 288 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 809: | Line 809: | ||
Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }} | Comma list: 39337984/39328497, {{monzo| 0 -14 7 4 -3 }}, {{monzo| -18 -24 14 -1 5 }} | ||
{{Mapping|legend=2| 1 -126 -214 -80 -18 | 0 439 746 288 76 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 824: | Line 824: | ||
Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256 | Comma list: 10081799/10077696, 10754912/10744731, 39337984/39328497, 480024727/480020256 | ||
{{Mapping|legend=2| 1 -126 -214 -80 -18 -171 | 0 439 746 288 76 603 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 843: | Line 843: | ||
[[Comma list]]: 243/242, 1083/1078 | [[Comma list]]: 243/242, 1083/1078 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 0 2 1 | 0 4 0 10 3 | 0 0 1 0 1 }} | ||
: mapping generators: ~2, ~21/19, ~7 | : mapping generators: ~2, ~21/19, ~7 | ||
| Line 867: | Line 867: | ||
[[Comma list]]: 33/32 | [[Comma list]]: 33/32 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 | 0 1 -1 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 887: | Line 887: | ||
[[Comma list]]: 131769/131072 | [[Comma list]]: 131769/131072 | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 1 8 | 0 2 -1 }} | ||
: mapping generators: ~363/256, ~16/11 | : mapping generators: ~363/256, ~16/11 | ||
| Line 907: | Line 907: | ||
[[Comma list]]: 214990848/214358881 | [[Comma list]]: 214990848/214358881 | ||
{{Mapping|legend= | {{Mapping|legend=3| 8 0 15 | 0 1 1 }} | ||
: mapping generators: ~12/11, ~3 | : mapping generators: ~12/11, ~3 | ||
| Line 927: | Line 927: | ||
[[Comma list]]: 264627/262144 | [[Comma list]]: 264627/262144 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 9 | 0 2 -7 }} | ||
: mapping generators: ~2, ~512/297 | : mapping generators: ~2, ~512/297 | ||
| Line 945: | Line 945: | ||
[[Comma list]]: 729/704 | [[Comma list]]: 729/704 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -6 | 0 1 6 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 963: | Line 963: | ||
Comma list: 144/143, 729/704 | Comma list: 144/143, 729/704 | ||
{{Mapping|legend=2| 1 0 -6 10 | 0 1 6 -4 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 978: | Line 978: | ||
Comma list: 363/361, 729/704 | Comma list: 363/361, 729/704 | ||
{{Mapping|legend=2| 1 0 -6 -6 | 0 2 12 13 }} | |||
: mapping generators: ~2, ~19/11 | : mapping generators: ~2, ~19/11 | ||
| Line 994: | Line 994: | ||
[[Comma list]]: 4096/3993 | [[Comma list]]: 4096/3993 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 4 | 0 3 -1 }} | ||
: mapping generators: ~2, ~16/11 | : mapping generators: ~2, ~16/11 | ||
| Line 1,016: | Line 1,016: | ||
Comma list: 512/507, 1352/1331 | Comma list: 512/507, 1352/1331 | ||
{{Mapping|legend=2| 1 -3 5 6 | 0 6 -2 -3 }} | |||
: mapping generators: ~2, ~22/13 | : mapping generators: ~2, ~22/13 | ||
| Line 1,034: | Line 1,034: | ||
[[Comma list]]: 10554638336/10460353203 | [[Comma list]]: 10554638336/10460353203 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 0 | 0 5 21 }} | ||
: mapping generators: ~2, ~88/81 | : mapping generators: ~2, ~88/81 | ||
| Line 1,052: | Line 1,052: | ||
Comma list: 352/351, 531674/531441 | Comma list: 352/351, 531674/531441 | ||
{{Mapping|legend=2| 1 1 0 3 | 0 5 21 6 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,069: | Line 1,069: | ||
[[Comma list]]: 19487171/19131876 | [[Comma list]]: 19487171/19131876 | ||
{{Mapping|legend= | {{Mapping|legend=3| 7 0 2 | 0 1 2 }} | ||
: mapping generators: ~1458/1331, ~3 | : mapping generators: ~1458/1331, ~3 | ||
| Line 1,088: | Line 1,088: | ||
[[Comma list]]: 2197/2187 | [[Comma list]]: 2197/2187 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 | 0 3 7 }} | ||
: mapping generators: ~2, ~13/9 | : mapping generators: ~2, ~13/9 | ||
| Line 1,108: | Line 1,108: | ||
[[Comma list]]: 27/26 | [[Comma list]]: 27/26 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 1 3 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 1,148: | Line 1,148: | ||
[[Comma list]]: 1053/1024 | [[Comma list]]: 1053/1024 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 10 | 0 1 -4 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 1,168: | Line 1,168: | ||
[[Comma list]]: 816293376/815730721 | [[Comma list]]: 816293376/815730721 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -5 -7 | 0 8 13 }} | ||
: mapping generators: ~2, ~3888/2197 | : mapping generators: ~2, ~3888/2197 | ||
| Line 1,186: | Line 1,186: | ||
Comma list: 3888/3887, 12168/12167 | Comma list: 3888/3887, 12168/12167 | ||
{{Mapping|legend=2| 1 -5 -7 -7 | 0 8 13 14 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 1,209: | Line 1,209: | ||
[[Comma list]]: 373248/371293 | [[Comma list]]: 373248/371293 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 3 | 0 5 6 }} | ||
: mapping generators: ~2, ~13/12 | : mapping generators: ~2, ~13/12 | ||
| Line 1,224: | Line 1,224: | ||
== Temperaments with a higher-limit gene == | == Temperaments with a higher-limit gene == | ||
=== Semitonic === | === Semitonic === | ||
Note that [[34edo]] and [[46edo]] also support this temperament but do not appear in the optimal ET sequence due to their sharp fifths, but they are on opposite sides of the just-17's tuning such that 34 + 46 = [[80edo]] is effectively a pure [[consistent circle]] of 80 [[17/16]]'s; all of these are good tunings for the related temperament [[srutal]] in 2.3.5.17 (sometimes called [[srutal archagall]] to distinguish it from diaschismic, which prefers tunings with a more just fifth), but the accuracy of primes 7, 11 and 13 varies depending on the tuning; especially, 34edo's 7 is extremely sharp and its 11 not much better. | |||
[[Subgroup]]: 2.3.17 | [[Subgroup]]: 2.3.17 | ||
[[Comma list]]: [[289/288]] | [[Comma list]]: [[289/288]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 5 | 0 1 1 }} | ||
: mapping generators: ~17/12, ~3 | : mapping generators: ~17/12, ~3 | ||
| Line 1,248: | Line 1,250: | ||
[[Comma list]]: 513/512 | [[Comma list]]: 513/512 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 9 | 0 1 -3 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 1,268: | Line 1,270: | ||
[[Comma list]]: 6912/6859 | [[Comma list]]: 6912/6859 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 8 | 0 1 1 }} | ||
: mapping generators: ~24/19, ~3 | : mapping generators: ~24/19, ~3 | ||
| Line 1,288: | Line 1,290: | ||
[[Comma list]]: 2187/2116 | [[Comma list]]: 2187/2116 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 2 7 }} | ||
: mapping generators: ~2, ~46/27 | : mapping generators: ~2, ~46/27 | ||
| Line 1,306: | Line 1,308: | ||
[[Comma list]]: 24576/24389 | [[Comma list]]: 24576/24389 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 5 | 0 -3 -1 }} | ||
: mapping generators: ~2, ~32/29 | : mapping generators: ~2, ~32/29 | ||
| Line 1,326: | Line 1,328: | ||
[[Comma list]]: 17249876309/17179869184 | [[Comma list]]: 17249876309/17179869184 | ||
{{Mapping|legend= | {{Mapping|legend=3| 7 0 34 | 0 1 0 }} | ||
: mapping generators: ~32/29, ~3 | : mapping generators: ~32/29, ~3 | ||
| Line 1,346: | Line 1,348: | ||
[[Comma list]]: 4107/4096 | [[Comma list]]: 4107/4096 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 | 0 2 -1 }} | ||
: mapping generators: ~2, ~64/37 | : mapping generators: ~2, ~64/37 | ||
| Line 1,364: | Line 1,366: | ||
[[Comma list]]: 81/74 | [[Comma list]]: 81/74 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 1 4 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 1,384: | Line 1,386: | ||
[[Comma list]]: 82/81 | [[Comma list]]: 82/81 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -1 | 0 1 4 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||