No-threes subgroup temperaments: Difference between revisions
m Text replacement - "Subgroup-val mapping: {{mapping| " to "{{Mapping|legend=2| " |
|||
| (3 intermediate revisions by the same user not shown) | |||
| Line 28: | Line 28: | ||
[[Comma list]]: [[2100875/2097152]] | [[Comma list]]: [[2100875/2097152]] | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 3 | 0 5 -3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 2 3 | 0 0 5 -3 }} | ||
: mapping generators: ~2, ~256/245 | : mapping generators: ~2, ~256/245 | ||
| Line 52: | Line 52: | ||
[[Comma list]]: 128/125 | [[Comma list]]: 128/125 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 7 0 | 0 0 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 3 0 7 0 | 0 0 0 1 }} | ||
: mapping generators: ~5/4, ~7 | : mapping generators: ~5/4, ~7 | ||
| Line 72: | Line 72: | ||
Comma list: 56/55, 128/125 | Comma list: 56/55, 128/125 | ||
{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }} | |||
{{Mapping|legend=4| 3 0 7 0 2 | 0 0 0 1 1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 91: | Line 91: | ||
[[Comma list]]: 78125/76832 | [[Comma list]]: 78125/76832 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 4 | 0 -4 -7 }} | ||
: mapping generators: ~2, ~28/25 | : mapping generators: ~2, ~28/25 | ||
| Line 109: | Line 109: | ||
Comma list: 245/242, 625/616 | Comma list: 245/242, 625/616 | ||
{{Mapping|legend=2| 1 3 4 5 | 0 -4 -7 -9 }} | |||
: mapping generators: ~2, ~28/25 | : mapping generators: ~2, ~28/25 | ||
| Line 130: | Line 130: | ||
[[Comma list]]: 1071875/1048576 | [[Comma list]]: 1071875/1048576 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 5 | 0 3 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 1 5 | 0 0 3 -5 }} | ||
: mapping generators: ~2, ~175/128 | : mapping generators: ~2, ~175/128 | ||
| Line 154: | Line 154: | ||
[[Comma list]]: 40960000/40353607 | [[Comma list]]: 40960000/40353607 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -4 0 | 0 9 4 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 -4 0 | 0 0 9 4 }} | ||
: mapping generators: ~2, ~80/49 | : mapping generators: ~2, ~80/49 | ||
| Line 174: | Line 174: | ||
Comma list: 640/637, 10985/10976 | Comma list: 640/637, 10985/10976 | ||
{{Mapping|legend=2| 1 -4 0 3 | 0 9 4 1 }} | |||
{{Mapping|legend=4| 1 0 -4 0 0 3 | 0 0 9 4 0 1 }} | |||
: mapping generators: ~2, ~13/8 | : mapping generators: ~2, ~13/8 | ||
| Line 196: | Line 196: | ||
Comma list: 170/169, 640/637, 5525/5488 | Comma list: 170/169, 640/637, 5525/5488 | ||
{{Mapping|legend=2| 1 -4 0 3 9 | 0 9 4 1 -7 }} | |||
{{Mapping|legend=4| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 215: | Line 215: | ||
Comma list: 8589934592/8544921875, 30691800524/30517578125 | Comma list: 8589934592/8544921875, 30691800524/30517578125 | ||
{{Mapping|legend=2| 1 1 20 -49 | 0 3 -39 119 }} | |||
: mapping generators: ~2, ~5120/3773 | : mapping generators: ~2, ~5120/3773 | ||
| Line 231: | Line 231: | ||
Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125 | Comma list: 1001/1000, 34420736/34328125, 5670699008/5661858125 | ||
{{Mapping|legend=2| 1 1 20 -49 35 | 0 3 -39 119 -71 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 246: | Line 246: | ||
Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251 | Comma list: 1001/1000, 32768/32725, 147968/147875, 537824/537251 | ||
{{Mapping|legend=2| 1 1 20 -49 35 42 | 0 3 -39 119 -71 -86 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 261: | Line 261: | ||
Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875 | Comma list: 1001/1000, 2128/2125, 3328/3325, 16807/16796, 147968/147875 | ||
{{Mapping|legend=2| 1 1 20 -49 35 42 21 | 0 3 -39 119 -71 -86 -38 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 280: | Line 280: | ||
[[Comma list]]: {{monzo| 1426 -596 -15 }} | [[Comma list]]: {{monzo| 1426 -596 -15 }} | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -4 254 | 0 15 -596 }} | ||
: mapping generators: ~2, ~{{monzo| -380 159 4 }} | : mapping generators: ~2, ~{{monzo| -380 159 4 }} | ||
| Line 303: | Line 303: | ||
[[Comma list]]: 5021863/5000000 | [[Comma list]]: 5021863/5000000 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -2 3 | 0 1 1 1 | 0 0 4 -3 }} | ||
: mapping generators: ~2, ~5, ~77/50 | : mapping generators: ~2, ~5, ~77/50 | ||
| Line 321: | Line 321: | ||
Comma list: 847/845, 1001/1000 | Comma list: 847/845, 1001/1000 | ||
{{Mapping|legend=2| 1 0 -2 3 2 | 0 1 1 1 1 | 0 0 4 -3 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 336: | Line 336: | ||
Comma list: 170/169, 221/220, 847/845 | Comma list: 170/169, 221/220, 847/845 | ||
{{Mapping|legend=2| 1 0 -2 3 2 3 | 0 1 1 1 1 1 | 0 0 4 -3 -1 -2 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 359: | Line 359: | ||
[[Comma list]]: 15625/15488 | [[Comma list]]: 15625/15488 | ||
{{Mapping|legend= | {{Mapping|legend=3| 2 0 -7 | 0 1 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 2 0 4 0 5 | 0 0 1 0 3 }} | ||
: mapping generators: ~125/88, ~5/4 | : mapping generators: ~125/88, ~5/4 | ||
| Line 379: | Line 379: | ||
[[Comma list]]: 33275/32768 | [[Comma list]]: 33275/32768 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 5 | 0 3 -2 }} | ||
: mapping generators, ~2, ~55/32 | : mapping generators, ~2, ~55/32 | ||
| Line 399: | Line 399: | ||
[[Comma list]]: 1331/1280 | [[Comma list]]: 1331/1280 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 3 | 0 3 1 }} | ||
: mapping generators: ~2, ~11/8 | : mapping generators: ~2, ~11/8 | ||
| Line 421: | Line 421: | ||
[[Comma list]]: 34375/32768 | [[Comma list]]: 34375/32768 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 15 | 0 1 -5 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 15 | 0 0 1 0 -5 }} | ||
: mapping generators: ~2, ~5 | : mapping generators: ~2, ~5 | ||
| Line 441: | Line 441: | ||
Comma list: 65/64, 6875/6656 | Comma list: 65/64, 6875/6656 | ||
{{Mapping|legend=2| 1 0 15 6 | 0 1 -5 -1 }} | |||
{{Mapping|legend=4| 1 0 0 0 15 6 | 0 0 1 0 -5 -1 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 458: | Line 458: | ||
Comma list: 65/64, 170/169, 221/220 | Comma list: 65/64, 170/169, 221/220 | ||
{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }} | |||
{{Mapping|legend=4| 1 0 0 0 15 6 11 | 0 0 1 0 -5 -1 -3 }} | |||
Optimal tunings: | Optimal tunings: | ||
| Line 475: | Line 475: | ||
[[Comma list]]: 26/25 | [[Comma list]]: 26/25 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 3 | 0 1 2 }} | ||
: mapping generators, ~2, ~5/4 | : mapping generators, ~2, ~5/4 | ||
| Line 493: | Line 493: | ||
[[Comma list]]: 64000000/62748517 | [[Comma list]]: 64000000/62748517 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 -2 0 | 0 7 6 }} | ||
: mapping generators, ~2, ~20/13 | : mapping generators, ~2, ~20/13 | ||
| Line 523: | Line 523: | ||
[[Comma list]]: 5767168/5764801 | [[Comma list]]: 5767168/5764801 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 -19 | 0 1 8 }} | ||
: mapping generators: ~2, ~7 | : mapping generators: ~2, ~7 | ||
| Line 543: | Line 543: | ||
[[Comma list]]: 1372/1331 | [[Comma list]]: 1372/1331 | ||
{{Mapping|legend= | {{Mapping|legend=3| 3 0 2 | 0 1 1 }} | ||
: mapping generators: ~14/11, ~7 | : mapping generators: ~14/11, ~7 | ||
| Line 565: | Line 565: | ||
[[Comma list]]: 343/338, 847/832 | [[Comma list]]: 343/338, 847/832 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 3 1 | 0 4 1 6 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 1 3 1 | 0 0 0 4 1 6 }} | ||
: mapping generators: ~2, ~11/8 | : mapping generators: ~2, ~11/8 | ||
| Line 587: | Line 587: | ||
[[Comma list]]: 214358881/210827008 | [[Comma list]]: 214358881/210827008 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 | 0 8 7 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 1 | 0 0 0 8 7 }} | ||
: mapping generators: ~2, ~14/11 | : mapping generators: ~2, ~14/11 | ||
| Line 607: | Line 607: | ||
Comma list: 1573/1568, 15488/15379 | Comma list: 1573/1568, 15488/15379 | ||
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }} | |||
Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }} | Gencom mapping: {{mapping|| 1 0 0 0 1 3 | 0 0 0 8 7 2 }} | ||
| Line 626: | Line 626: | ||
[[Comma list]]: 28672/28561 | [[Comma list]]: 28672/28561 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 3 | 0 4 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 0 3 | 0 0 0 4 0 1 }} | ||
: mapping generators: ~2, ~13 | : mapping generators: ~2, ~13 | ||
| Line 646: | Line 646: | ||
[[Comma list]]: 4913/4802 | [[Comma list]]: 4913/4802 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 2 3 | 0 3 4 }} | ||
: mapping generators, ~2, ~17/14 | : mapping generators, ~2, ~17/14 | ||
| Line 664: | Line 664: | ||
[[Comma list]]: 2024782584832/2015993900449 | [[Comma list]]: 2024782584832/2015993900449 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 1 | 0 10 11 }} | ||
: mapping generators, ~2, ~17/14 | : mapping generators, ~2, ~17/14 | ||
| Line 682: | Line 682: | ||
[[Comma list]]: 1048576/1042139 | [[Comma list]]: 1048576/1042139 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 | 0 3 -1 }}] | ||
: mapping generators, ~2, ~64/53 | : mapping generators, ~2, ~64/53 | ||
| Line 704: | Line 704: | ||
[[Comma list]]: 1352/1331 | [[Comma list]]: 1352/1331 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 3 3 | 0 2 3 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 3 3 | 0 0 0 0 2 3 }} | ||
: mapping generators, ~2, ~13/11 | : mapping generators, ~2, ~13/11 | ||
| Line 727: | Line 727: | ||
[[Comma list]]: 265837/262144 | [[Comma list]]: 265837/262144 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 6 | 0 3 -2 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }} | ||
: mapping generators, ~2, ~143/128 | : mapping generators, ~2, ~143/128 | ||
| Line 751: | Line 751: | ||
[[Comma list]]: 29282/28561 | [[Comma list]]: 29282/28561 | ||
{{Mapping|legend= | {{Mapping|legend=3| 4 0 1 | 0 1 1 }} | ||
{{Mapping|legend= | {{Mapping|legend=5| 4 0 0 0 12 13 | 0 0 0 0 1 1 }} | ||
: mapping generators, ~13/11, ~11 | : mapping generators, ~13/11, ~11 | ||
| Line 773: | Line 773: | ||
[[Comma list]]: 209/208, 2057/2048, 83521/83486 | [[Comma list]]: 209/208, 2057/2048, 83521/83486 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 8 9 11 | 0 4 -7 -8 -11 }} | ||
: mapping generators: ~2, ~26/17 | : mapping generators: ~2, ~26/17 | ||
| Line 791: | Line 791: | ||
[[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432 | [[Comma list]]: 2432/2431, 7086244/7054567, 33698267/33554432 | ||
{{Mapping|legend= | {{Mapping|legend=3| 33 0 8 249 26 | 0 1 1 -1 1 }} | ||
: mapping generators: ~247/242, ~11 | : mapping generators: ~247/242, ~11 | ||
| Line 811: | Line 811: | ||
[[Comma list]]: 1874161/1874048 | [[Comma list]]: 1874161/1874048 | ||
{{Mapping|legend= | {{Mapping|legend=3| 4 0 7 | 0 1 1 }} | ||
: mapping generators: ~44/37, ~11 | : mapping generators: ~44/37, ~11 | ||
| Line 829: | Line 829: | ||
[[Comma list]]: 47525504/47045881 | [[Comma list]]: 47525504/47045881 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 2 | 0 6 5 }} | ||
: mapping generators: ~2, ~26/19 | : mapping generators: ~2, ~26/19 | ||
| Line 847: | Line 847: | ||
[[Comma list]]: 209/208, 2057/2048 | [[Comma list]]: 209/208, 2057/2048 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 11 4 | 0 1 0 -2 -1 | 0 0 1 0 1 }} | ||
: mapping generators: ~2, ~11, ~13 | : mapping generators: ~2, ~11, ~13 | ||