Xenharmonic Wiki

Breedsmic temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Normalize mappings and generators
Xenllium (talk | contribs)
autopatrolled
4,516 edits
No edit summary
Line 12: Line 12:
* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Greenwoodmic temperaments #Greenwood|Greenwoodmic temperaments]]
* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Greenwoodmic temperaments #Greenwood|Greenwoodmic temperaments]]
* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]
* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]
* ''[[Quadrasruta]]'' (+2401/2400) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage|Magic family]]
* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage|Magic family]]
* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
Line 36: Line 36:
{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}
{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}


: mapping generators: ~2, ~49/40
: Mapping generators: ~2, ~49/40


{{Multival|legend=1| 2 25 13 35 15 -40 }}
{{Multival|legend=1| 2 25 13 35 15 -40 }}
Line 62: Line 62:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.521
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.521


{{Optimal ET sequence|legend=1| 17c, 41, 58, 99e }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99e }}


Badness: 0.023498
Badness: 0.023498
Line 75: Line 75:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.573
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.573


{{Optimal ET sequence|legend=1| 17c, 41, 58, 99ef, 157eff }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 41, 58, 99ef, 157eff }}


Badness: 0.019090
Badness: 0.019090
Line 86: Line 86:
Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}


: mapping generators: ~99/70, ~49/40
: Mapping generators: ~99/70, ~49/40


Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.505
Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.505


{{Optimal ET sequence|legend=1| 58, 140, 198 }}
Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198 }}


Badness: 0.042487
Badness: 0.042487
Line 103: Line 103:
Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.502
Optimal tuning (POTE): ~99/70 = 1\2, ~49/40 = 351.502


{{Optimal ET sequence|legend=1| 58, 140, 198, 536f }}
Optimal ET sequence: {{Optimal ET sequence| 58, 140, 198, 536f }}


Badness: 0.021188
Badness: 0.021188
Line 116: Line 116:
Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}


: mapping generators: ~2, ~243/220
: Mapping generators: ~2, ~243/220


Optimal tuning (POTE): ~2 = 1\1, ~243/220 = 175.7378
Optimal tuning (POTE): ~2 = 1\1, ~243/220 = 175.7378


{{Optimal ET sequence|legend=1| 41, 157, 198, 239, 676b, 915be }}
Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 239, 676b, 915be }}


Badness: 0.040170
Badness: 0.040170
Line 133: Line 133:
Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.7470
Optimal tuning (POTE): ~2 = 1\1, ~72/65 = 175.7470


{{Optimal ET sequence|legend=1| 41, 157, 198, 437f, 635bcff }}
Optimal ET sequence: {{Optimal ET sequence| 41, 157, 198, 437f, 635bcff }}


Badness: 0.031144
Badness: 0.031144
Line 148: Line 148:
{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}
{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}


: mapping generators: ~2, ~256/245
: Mapping generators: ~2, ~256/245


{{Multival|legend=1| 22 -5 3 -59 -57 21 }}
{{Multival|legend=1| 22 -5 3 -59 -57 21 }}
Line 167: Line 167:
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.227
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.227


{{Optimal ET sequence|legend=1| 31, 109e, 140e, 171, 202 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171, 202 }}


Badness: 0.035576
Badness: 0.035576
Line 180: Line 180:
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.203
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.203


{{Optimal ET sequence|legend=1| 31, 109e, 140e, 171 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171 }}


Badness: 0.036876
Badness: 0.036876
Line 193: Line 193:
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.201
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.201


{{Optimal ET sequence|legend=1| 31, 109eg, 140e, 171 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109eg, 140e, 171 }}


Badness: 0.027398
Badness: 0.027398
Line 206: Line 206:
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.173
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.173


{{Optimal ET sequence|legend=1| 31, 109, 140, 171e, 311e }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 171e, 311e }}


Badness: 0.030171
Badness: 0.030171
Line 219: Line 219:
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.158
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.158


{{Optimal ET sequence|legend=1| 31, 109, 140, 311e, 451ee }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 311e, 451ee }}


Badness: 0.028384
Badness: 0.028384
Line 232: Line 232:
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.162
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.162


{{Optimal ET sequence|legend=1| 31, 109g, 140, 311e, 451ee }}
Optimal ET sequence: {{Optimal ET sequence| 31, 109g, 140, 311e, 451ee }}


Badness: 0.022416
Badness: 0.022416
Line 245: Line 245:
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.169
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.169


{{Optimal ET sequence|legend=1| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}


Badness: 0.056926
Badness: 0.056926
Line 258: Line 258:
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.168
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.168


{{Optimal ET sequence|legend=1| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}


Badness: 0.027474
Badness: 0.027474
Line 271: Line 271:
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169


{{Optimal ET sequence|legend=1| 140, 171, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


Badness: 0.018773
Badness: 0.018773
Line 284: Line 284:
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169


{{Optimal ET sequence|legend=1| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}


Badness: 0.017653
Badness: 0.017653
Line 297: Line 297:
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.168
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.168


{{Optimal ET sequence|legend=1| 140, 311, 762g, 1073g, 1384cfgg }}
Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfgg }}


Badness: 0.015123
Badness: 0.015123
Line 310: Line 310:
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.167
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.167


{{Optimal ET sequence|legend=1| 140, 311, 762g, 1073g, 1384cfggj }}
Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfggj }}


Badness: 0.012181
Badness: 0.012181
Line 323: Line 323:
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169


{{Optimal ET sequence|legend=1| 140, 171, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


Badness: 0.012311
Badness: 0.012311
Line 336: Line 336:
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.170
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.170


{{Optimal ET sequence|legend=1| 140, 171, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


Badness: 0.010949
Badness: 0.010949
Line 349: Line 349:
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169


{{Optimal ET sequence|legend=1| 140, 171, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


Badness: 0.009825
Badness: 0.009825
Line 360: Line 360:
Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}
Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}


: mapping generators: ~2, ~45/44
: Mapping generators: ~2, ~45/44


Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.596
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.596


{{Optimal ET sequence|legend=1| 31, 280, 311, 342 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 342 }}


Badness: 0.015633
Badness: 0.015633
Line 377: Line 377:
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.588
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.588


{{Optimal ET sequence|legend=1| 31, 280, 311, 964f, 1275f, 1586cff }}
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 964f, 1275f, 1586cff }}


Badness: 0.033573
Badness: 0.033573
Line 390: Line 390:
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.589
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.589


{{Optimal ET sequence|legend=1| 31, 280, 311, 653f, 964f }}
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 653f, 964f }}


Badness: 0.025298
Badness: 0.025298
Line 401: Line 401:
Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}
Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}


: mapping generators: ~99/70, ~256/245
: Mapping generators: ~99/70, ~256/245


Optimal tuning (POTE): ~99/70 = 1\2, ~256/245 = 77.193
Optimal tuning (POTE): ~99/70 = 1\2, ~256/245 = 77.193


{{Optimal ET sequence|legend=1| 62e, 140, 202, 342 }}
Optimal ET sequence: {{Optimal ET sequence| 62e, 140, 202, 342 }}


Badness: 0.025790
Badness: 0.025790
Line 420: Line 420:
{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}
{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}


: mapping generators: ~2, ~875/512
: Mapping generators: ~2, ~875/512


{{Multival|legend=1| 38 -3 8 -93 -94 27 }}
{{Multival|legend=1| 38 -3 8 -93 -94 27 }}
Line 439: Line 439:
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.111
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.111


{{Optimal ET sequence|legend=1| 31, 208, 239, 270 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 208, 239, 270 }}


Badness: 0.017540
Badness: 0.017540
Line 452: Line 452:
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.107
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.107


{{Optimal ET sequence|legend=1| 31, 239, 270, 571, 841, 1111 }}
Optimal ET sequence: {{Optimal ET sequence| 31, 239, 270, 571, 841, 1111 }}


Badness: 0.017921
Badness: 0.017921
Line 467: Line 467:
{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}
{{Mapping|legend=1| 10 0 47 36 | 0 2 -3 -1 }}


: mapping generators: ~15/14, ~8192/4725
: Mapping generators: ~15/14, ~8192/4725


{{Multival|legend=1| 20 -30 -10 -94 -72 61 }}
{{Multival|legend=1| 20 -30 -10 -94 -72 61 }}
Line 473: Line 473:
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)
[[Optimal tuning]] ([[POTE]]): ~15/14 = 1\10, ~8192/4725 = 951.099 (~16/15 = 111.099)


{{Optimal ET sequence|legend=1| 10, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}
{{Optimal ET sequence|legend=1| 10, …, 120, 130, 270, 2020c, 2290c, 2560c, 2830bc, 3100bcc, 3370bcc, 3640bcc }}


[[Badness]]: 0.033902
[[Badness]]: 0.033902
Line 486: Line 486:
Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)
Optimal tuning (POTE): ~15/14 = 1\10, ~400/231 = 951.070 (~16/15 = 111.070)


{{Optimal ET sequence|legend=1| 10e, 130, 270, 670, 940, 1210, 2150c }}
Optimal ET sequence: {{Optimal ET sequence| 130, 270, 670, 940, 1210, 2150c }}


Badness: 0.018735
Badness: 0.018735
Line 499: Line 499:
Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)
Optimal tuning (POTE): ~15/14 = 1\10, ~26/15 = 951.083 (~16/15 = 111.083)


{{Optimal ET sequence|legend=1| 10e, 130, 270, 940, 1210f, 1480cf }}
Optimal ET sequence: {{Optimal ET sequence| 130, 270, 940, 1210f, 1480cf }}


Badness: 0.013475
Badness: 0.013475
Line 512: Line 512:
{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}
{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}


: mapping generators: ~2, ~189/160
: Mapping generators: ~2, ~189/160


{{Multival|legend=1| 6 41 22 51 18 -64 }}
{{Multival|legend=1| 6 41 22 51 18 -64 }}
Line 531: Line 531:
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 283.276
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 283.276


{{Optimal ET sequence|legend=1| 72, 161, 233, 305 }}
Optimal ET sequence: {{Optimal ET sequence| 72, 161, 233, 305 }}


Badness: 0.027959
Badness: 0.027959
Line 544: Line 544:
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 283.294
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 283.294


{{Optimal ET sequence|legend=1| 72, 161f, 233f }}
Optimal ET sequence: {{Optimal ET sequence| 72, 161f, 233f }}


Badness: 0.026942
Badness: 0.026942
Line 557: Line 557:
{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}
{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}


: mapping generators: ~2, ~2187/1372
: Mapping generators: ~2, ~2187/1372


{{Multival|legend=1| 14 59 33 61 13 -8 9 }}
{{Multival|legend=1| 14 59 33 61 13 -8 9 }}
Line 576: Line 576:
Optimal tuning (POTE): ~2 = 1\1, ~1372/1089 = 392.991
Optimal tuning (POTE): ~2 = 1\1, ~1372/1089 = 392.991


{{Optimal ET sequence|legend=1| 58, 113, 171 }}
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


Badness: 0.052358
Badness: 0.052358
Line 589: Line 589:
Optimal tuning (POTE): ~2 = 1\1, ~180/143 = 392.989
Optimal tuning (POTE): ~2 = 1\1, ~180/143 = 392.989


{{Optimal ET sequence|legend=1| 58, 113, 171 }}
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


Badness: 0.026974
Badness: 0.026974
Line 602: Line 602:
Optimal tuning (POTE): ~2 = 1\1, ~64/51 = 392.985
Optimal tuning (POTE): ~2 = 1\1, ~64/51 = 392.985


{{Optimal ET sequence|legend=1| 58, 113, 171 }}
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


Badness: 0.023205
Badness: 0.023205
Line 615: Line 615:
{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}
{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}


: mapping generators: ~2, ~42/25
: Mapping generators: ~2, ~42/25


{{Multival|legend=1| 34 29 23 -33 -59 -28 }}
{{Multival|legend=1| 34 29 23 -33 -59 -28 }}
Line 634: Line 634:
{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}
{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}


: mapping generators: ~2, ~6125/3888
: Mapping generators: ~2, ~6125/3888


{{Multival|legend=1| 42 47 34 -23 -64 -53 }}
{{Multival|legend=1| 42 47 34 -23 -64 -53 }}
Line 653: Line 653:
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.718
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.718


{{Optimal ET sequence|legend=1| 72, 167, 239, 311 }}
Optimal ET sequence: {{Optimal ET sequence| 72, 167, 239, 311 }}


Badness: 0.022926
Badness: 0.022926
Line 666: Line 666:
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.716
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.716


{{Optimal ET sequence|legend=1| 72, 239f, 311, 694, 1005c }}
Optimal ET sequence: {{Optimal ET sequence| 72, 239f, 311, 694, 1005c }}


Badness: 0.020888
Badness: 0.020888
Line 679: Line 679:
{{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}
{{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}


: mapping generators: ~2, ~49/40
: Mapping generators: ~2, ~49/40


{{Multival|legend=1| 2 -57 -28 -95 -50 95 }}
{{Multival|legend=1| 2 -57 -28 -95 -50 95 }}
Line 685: Line 685:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 351.113
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 351.113


{{Optimal ET sequence|legend=1| 41, …, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}


[[Badness]]: 0.041878
[[Badness]]: 0.041878
Line 698: Line 698:
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.115
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.115


{{Optimal ET sequence|legend=1| 41, 188, 229, 270, 581, 851, 1121, 1972 }}
Optimal ET sequence: {{Optimal ET sequence| 41, 147ce, 188, 229, 270, 581, 851, 1121, 1972 }}


Badness: 0.019461
Badness: 0.019461
Line 711: Line 711:
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117


{{Optimal ET sequence|legend=1| 41, 229, 270, 581, 851, 2283b }}
Optimal ET sequence: {{Optimal ET sequence| 41, 147cef, 188f, 229, 270, 581, 851, 2283b, 3134b }}


Badness: 0.013830
Badness: 0.013830
==== Neoneut ====
'''Neonewt''' is a remarkable subgroup extension with a prime harmonic of 19.
Subgroup: 2.3.5.7.11.13.19
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117
Optimal ET sequence: {{Optimal ET sequence| 41, 147cefh, 188f, 229, 270, 581, 851, 3134b, 3985b, 4836bb }}


== Septidiasemi ==
== Septidiasemi ==
Line 726: Line 739:
{{Mapping|legend=1| 1 25 -31 -8 | 0 -26 37 12 }}
{{Mapping|legend=1| 1 25 -31 -8 | 0 -26 37 12 }}


: mapping generators: ~2, ~28/15
: Mapping generators: ~2, ~28/15


{{Multival|legend=1| 26 -37 -12 -119 -92 76 }}
{{Multival|legend=1| 26 -37 -12 -119 -92 76 }}
Line 747: Line 760:
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.279
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.279


{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 332 }}
Optimal ET sequence: {{Optimal ET sequence| 10, 151, 161, 171, 332 }}


Badness: 0.090687
Badness: 0.090687
Line 760: Line 773:
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281


{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 332, 835eeff }}
Optimal ET sequence: {{Optimal ET sequence| 10, 151, 161, 171, 332, 835eeff }}


Badness: 0.045773
Badness: 0.045773
Line 773: Line 786:
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281
Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281


{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 332, 503ef, 835eeff }}
Optimal ET sequence: {{Optimal ET sequence|l 10, 151, 161, 171, 332, 503ef, 835eeff }}


Badness: 0.027322
Badness: 0.027322
Line 786: Line 799:
{{Mapping|legend=1| 1 31 34 26 | 0 -52 -56 -41 }}
{{Mapping|legend=1| 1 31 34 26 | 0 -52 -56 -41 }}


: mapping generators: ~2, ~1296/875
: Mapping generators: ~2, ~1296/875


{{Multival|legend=1| 52 56 41 -32 -81 -62 }}
{{Multival|legend=1| 52 56 41 -32 -81 -62 }}
Line 805: Line 818:
{{Mapping|legend=1| 1 19 0 6 | 0 -60 8 -11 }}
{{Mapping|legend=1| 1 19 0 6 | 0 -60 8 -11 }}


: mapping generators: ~2, ~57344/46875
: Mapping generators: ~2, ~57344/46875


{{Multival|legend=1| 60 -8 11 -152 -151 48 }}
{{Multival|legend=1| 60 -8 11 -152 -151 48 }}
Line 824: Line 837:
{{Mapping|legend=1| 1 13 33 21 | 0 -32 -86 -51 }}
{{Mapping|legend=1| 1 13 33 21 | 0 -32 -86 -51 }}


: mapping generators: ~2, ~2800/2187
: Mapping generators: ~2, ~2800/2187


{{Multival|legend=1| 32 86 51 62 -9 -123 }}
{{Multival|legend=1| 32 86 51 62 -9 -123 }}
Line 841: Line 854:
{{Mapping|legend=1| 1 5 1 3 | 0 -18 7 -1 }}
{{Mapping|legend=1| 1 5 1 3 | 0 -18 7 -1 }}


: mapping generators: ~2, ~8/7
: Mapping generators: ~2, ~8/7


{{Multival|legend=1| 18 -7 1 -53 -49 22 }}
{{Multival|legend=1| 18 -7 1 -53 -49 22 }}
Line 860: Line 873:
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.500
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.500


{{Optimal ET sequence|legend=1| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}
Optimal ET sequence: {{Optimal ET sequence| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}


Badness: 0.059260
Badness: 0.059260
Line 873: Line 886:
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.493
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.493


{{Optimal ET sequence|legend=1| 21, 37, 58, 153bcef, 211bccdeeff }}
Optimal ET sequence: {{Optimal ET sequence| 21, 37, 58, 153bcef, 211bccdeeff }}


Badness: 0.032205
Badness: 0.032205
Line 884: Line 897:
{{Mapping|legend=1| 1 19 8 10 | 0 -46 -15 -19 }}
{{Mapping|legend=1| 1 19 8 10 | 0 -46 -15 -19 }}


: mapping generators: ~2, ~125/96
: Mapping generators: ~2, ~125/96


{{Multival|legend=1| 46 15 19 -83 -99 2 }}
{{Multival|legend=1| 46 15 19 -83 -99 2 }}
Line 903: Line 916:
Optimal tuning (POTE): ~2 = 1\1, ~100/77 = 454.318
Optimal tuning (POTE): ~2 = 1\1, ~100/77 = 454.318


{{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243e }}
Optimal ET sequence: {{Optimal ET sequence| 37, 66b, 103, 140, 243e }}


Badness: 0.056514
Badness: 0.056514
Line 916: Line 929:
Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 454.316
Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 454.316


{{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243e }}
Optimal ET sequence: {{Optimal ET sequence| 37, 66b, 103, 140, 243e }}


Badness: 0.027429
Badness: 0.027429
Line 929: Line 942:
{{Mapping|legend=1| 1 5 9 7 | 0 -22 -43 -27 }}
{{Mapping|legend=1| 1 5 9 7 | 0 -22 -43 -27 }}


: mapping generators: ~2, ~10/9
: Mapping generators: ~2, ~10/9


{{Multival|legend=1| 22 43 27 17 -19 -58 }}
{{Multival|legend=1| 22 43 27 17 -19 -58 }}
Line 948: Line 961:
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.345
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.345


{{Optimal ET sequence|legend=1| 58, 103, 161, 425b, 586b, 747bc }}
Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586b, 747bc }}


Badness: 0.039962
Badness: 0.039962
Line 961: Line 974:
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.347
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.347


{{Optimal ET sequence|legend=1| 58, 103, 161, 425b, 586bf }}
Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586bf }}


Badness: 0.021849
Badness: 0.021849
Line 974: Line 987:
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.348
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.348


{{Optimal ET sequence|legend=1| 58, 103, 161, 425b, 586bf }}
Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586bf }}


Badness: 0.020295
Badness: 0.020295
Line 987: Line 1,000:
{{Mapping|legend=1| 1 13 17 13 | 0 -28 -36 -25 }}
{{Mapping|legend=1| 1 13 17 13 | 0 -28 -36 -25 }}


: mapping generators: ~2, ~250/189
: Mapping generators: ~2, ~250/189


{{Multival|legend=1| 28 36 25 -8 -39 -43 }}
{{Multival|legend=1| 28 36 25 -8 -39 -43 }}
Line 1,006: Line 1,019:
Optimal tuning (POTE): ~2 = 1\1, ~250/189 = 489.252
Optimal tuning (POTE): ~2 = 1\1, ~250/189 = 489.252


{{Optimal ET sequence|legend=1| 103, 130, 233, 363, 493e, 856be }}
Optimal ET sequence: {{Optimal ET sequence| 103, 130, 233, 363, 493e, 856be }}


Badness: 0.036785
Badness: 0.036785
Line 1,019: Line 1,032:
Optimal tuning (POTE): ~2 = 1\1, ~65/49 = 489.256
Optimal tuning (POTE): ~2 = 1\1, ~65/49 = 489.256


{{Optimal ET sequence|legend=1| 103, 130, 233, 363 }}
Optimal ET sequence: {{Optimal ET sequence| 103, 130, 233, 363 }}


Badness: 0.021694
Badness: 0.021694
Line 1,030: Line 1,043:
{{Mapping|legend=1| 1 17 9 10 | 0 -30 -13 -14 }}
{{Mapping|legend=1| 1 17 9 10 | 0 -30 -13 -14 }}


: mappping generators: ~2, ~10/7
: Mappping generators: ~2, ~10/7


{{Multival|legend=1| 30 13 14 -49 -62 -4 }}
{{Multival|legend=1| 30 13 14 -49 -62 -4 }}
Line 1,049: Line 1,062:
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387


{{Optimal ET sequence|legend=1| 35, 37, 72, 109, 181, 253 }}
Optimal ET sequence: {{Optimal ET sequence| 35, 37, 72, 109, 181, 253 }}


Badness: 0.032225
Badness: 0.032225
Line 1,062: Line 1,075:
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387


{{Optimal ET sequence|legend=1| 37, 72, 109, 181f }}
Optimal ET sequence: {{Optimal ET sequence| 37, 72, 109, 181f }}


Badness: 0.028683
Badness: 0.028683
Line 1,075: Line 1,088:
{{Mapping|legend=1| 1 1 9 6 | 0 2 -23 -11 }}
{{Mapping|legend=1| 1 1 9 6 | 0 2 -23 -11 }}


: mapping generators: ~2, ~49/40
: Mapping generators: ~2, ~49/40


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 348.603
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 348.603
Line 1,092: Line 1,105:
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.639
Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.639


{{Optimal ET sequence|legend=1| 31, 86ce, 117ce, 148bce }}
Optimal ET sequence: {{Optimal ET sequence| 31, 86ce, 117ce, 148bce }}


Badness: 0.046181
Badness: 0.046181
Line 1,105: Line 1,118:
{{Mapping|legend=1| 1 43 -74 -25 | 0 -70 129 47 }}
{{Mapping|legend=1| 1 43 -74 -25 | 0 -70 129 47 }}


: mapping generators: ~2, ~675/448
: Mapping generators: ~2, ~675/448


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~675/448 = 709.9719
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~675/448 = 709.9719
Line 1,111: Line 1,124:
{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}
{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}


[[Badness]]: 0.202
[[Badness]]: 0.202249


=== 11-limit ===
=== 11-limit ===
Line 1,122: Line 1,135:
Optimal tuning (CTE): ~2 = 1\1, ~675/448 = 709.9720
Optimal tuning (CTE): ~2 = 1\1, ~675/448 = 709.9720


{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 1795 }}
Optimal ET sequence: {{Optimal ET sequence| 120, 191, 311, 742, 1053, 1795 }}


Badness: 0.0523
Badness: 0.052308


=== 13-limit ===
=== 13-limit ===
Line 1,135: Line 1,148:
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9723
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9723


{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 1795f }}
Optimal ET sequence: {{Optimal ET sequence| 120, 191, 311, 742, 1053, 1795f }}


Badness: 0.0325
Badness: 0.032503


=== 17-limit ===
=== 17-limit ===
Line 1,148: Line 1,161:
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722


{{Optimal ET sequence|legend=1| 120g, 191g, 311, 431, 742, 1795f }}
Optimal ET sequence: {{Optimal ET sequence| 120g, 191g, 311, 431, 742, 1795f }}


Badness: 0.0325
Badness: 0.020995


=== 19-limit ===
=== 19-limit ===
Line 1,161: Line 1,174:
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722
Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722


{{Optimal ET sequence|legend=1| 120g, 191g, 311, 431, 742, 1795f }}
Optimal ET sequence: {{Optimal ET sequence| 120g, 191g, 311, 431, 742, 1795f }}


Badness: 0.0138
Badness: 0.013771


[[Category:Temperament collections]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Breedsmic_temperaments"