Xenharmonic Wiki

Quindromeda family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,014 edits
No edit summary
Tags: Mobile edit Mobile web edit
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,014 edits
No edit summary
Tags: Mobile edit Mobile web edit
Line 91: Line 91:
* CWE: ~2 = 1200.000¢, ~35/33 = 99.538¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.538¢


{{Optimal ET sequence|legend=1| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness (Sintel): 2.881
Badness (Sintel): 2.881
Line 104: Line 104:
POTE generator: ~35/33 = 99.541
POTE generator: ~35/33 = 99.541


{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.052361
Badness: 0.052361
Line 117: Line 117:
POTE generator: ~18/17 = 99.540
POTE generator: ~18/17 = 99.540


{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.035653
Badness: 0.035653
Line 130: Line 130:
POTE generator: ~18/17 = 99.541
POTE generator: ~18/17 = 99.541


{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=0| 12f, 205df, 217 }}


Badness: 0.025782
Badness: 0.025782
Line 143: Line 143:
POTE generator: ~35/33 = 99.537
POTE generator: ~35/33 = 99.537


{{Optimal ET sequence|legend=1| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.072826
Badness: 0.072826
Line 156: Line 156:
POTE generator: ~18/17 = 99.537
POTE generator: ~18/17 = 99.537


{{Optimal ET sequence|legend=1| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.042339
Badness: 0.042339
Line 169: Line 169:
POTE generator: ~18/17 = 99.537
POTE generator: ~18/17 = 99.537


{{Optimal ET sequence|legend=1| 12, 205d, 217 }}
{{Optimal ET sequence|legend=0| 12, 205d, 217 }}


Badness: 0.028983
Badness: 0.028983
Line 186: Line 186:
* CWE: ~2 = 1200.000¢, ~200/189 = 99.551¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.551¢


{{Optimal ET sequence|legend=1| 12e, 217, 446 }}
{{Optimal ET sequence|legend=0| 12e, 217, 446 }}


Badness (Sintel): 3.633
Badness (Sintel): 3.633
Line 199: Line 199:
POTE generator: ~55/52 = 99.548
POTE generator: ~55/52 = 99.548


{{Optimal ET sequence|legend=1| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}


Badness: 0.067730
Badness: 0.067730
Line 212: Line 212:
POTE generator: ~18/17 = 99.548
POTE generator: ~18/17 = 99.548


{{Optimal ET sequence|legend=1| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663c }}


Badness: 0.038153
Badness: 0.038153
Line 225: Line 225:
POTE generator: ~18/17 = 99.547
POTE generator: ~18/17 = 99.547


{{Optimal ET sequence|legend=1| 12e, 217, 446, 663ch }}
{{Optimal ET sequence|legend=0| 12e, 217, 446, 663ch }}


Badness: 0.026654
Badness: 0.026654
Line 240: Line 240:
* CWE: ~2 = 1200.000¢, ~200/189 = 99.568¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.568¢


{{Optimal ET sequence|legend=1| 12, 217e, 229, 470cd, 699cd }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 470cd, 699cd }}


Badness (Sintel): 3.107
Badness (Sintel): 3.107
Line 253: Line 253:
POTE generator: ~55/52 = 99.578
POTE generator: ~55/52 = 99.578


{{Optimal ET sequence|legend=1| 12f, 217ef, 229, 241, 470cd, 711ccd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd, 711ccd }}


Badness: 0.065701
Badness: 0.065701
Line 266: Line 266:
POTE generator: ~18/17 = 99.574
POTE generator: ~18/17 = 99.574


{{Optimal ET sequence|legend=1| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.046624
Badness: 0.046624
Line 279: Line 279:
POTE generator: ~18/17 = 99.575
POTE generator: ~18/17 = 99.575


{{Optimal ET sequence|legend=1| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=0| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.033145
Badness: 0.033145
Line 292: Line 292:
POTE generator: ~200/189 = 99.556
POTE generator: ~200/189 = 99.556


{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.100195
Badness: 0.100195
Line 305: Line 305:
POTE generator: ~18/17 = 99.556
POTE generator: ~18/17 = 99.556


{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.057851
Badness: 0.057851
Line 318: Line 318:
POTE generator: ~18/17 = 99.557
POTE generator: ~18/17 = 99.557


{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceefh }}
{{Optimal ET sequence|legend=0| 12, 217e, 229, 446e, 675ceefh }}


Badness: 0.040410
Badness: 0.040410


== Quintakwai ==
== Quintakwai ==
The ''quintakwai'' temperament (12&193) tempers out the [[5120/5103|hemifamity comma]] (5120/5103) and the compass comma (9765625/9680832) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, [[225/224]] (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).
The ''quintakwai'' temperament (12&193) tempers out the [[5120/5103|hemifamity comma]] (5120/5103) and the [[compass comma]] (9765625/9680832) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, [[225/224]] (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 350: Line 350:
* CWE: ~2 = 1200.000¢, ~35/33 = 99.470¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.470¢


{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce }}
{{Optimal ET sequence|legend=0| 12, 181, 193, 374, 567ce }}


Badness (Sintel): 2.419
Badness (Sintel): 2.419
Line 363: Line 363:
POTE generator: ~35/33 = 99.468
POTE generator: ~35/33 = 99.468


{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce, 941bce }}
{{Optimal ET sequence|legend=0| 12, 181, 193, 374, 567ce, 941bce }}


Badness: 0.062737
Badness: 0.062737
Line 376: Line 376:
POTE generator: ~18/17 = 99.469
POTE generator: ~18/17 = 99.469


{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce, 941bceg }}
{{Optimal ET sequence|legend=0| 12, 181, 193, 374, 567ce, 941bceg }}


Badness: 0.037855
Badness: 0.037855
Line 389: Line 389:
POTE generator: ~18/17 = 99.469
POTE generator: ~18/17 = 99.469


{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh }}
{{Optimal ET sequence|legend=0| 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh }}


Badness: 0.025861
Badness: 0.025861
Line 402: Line 402:
POTE generator: ~35/33 = 99.456
POTE generator: ~35/33 = 99.456


{{Optimal ET sequence|legend=1| 12f, 169e, 181 }}
{{Optimal ET sequence|legend=0| 12f, 169e, 181 }}


Badness: 0.061873
Badness: 0.061873
Line 415: Line 415:
POTE generator: ~18/17 = 99.458
POTE generator: ~18/17 = 99.458


{{Optimal ET sequence|legend=1| 12f, 169e, 181, 374ff, 555cff }}
{{Optimal ET sequence|legend=0| 12f, 169e, 181, 374ff, 555cff }}


Badness: 0.043506
Badness: 0.043506
Line 428: Line 428:
POTE generator: ~18/17 = 99.459
POTE generator: ~18/17 = 99.459


{{Optimal ET sequence|legend=1| 12f, 169e, 181, 374ff, 555cff }}
{{Optimal ET sequence|legend=0| 12f, 169e, 181, 374ff, 555cff }}


Badness: 0.031313
Badness: 0.031313
Line 441: Line 441:
POTE generator: ~35/33 = 99.484
POTE generator: ~35/33 = 99.484


{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=0| 12f, 181f, 193 }}


Badness: 0.057357
Badness: 0.057357
Line 454: Line 454:
POTE generator: ~18/17 = 99.484
POTE generator: ~18/17 = 99.484


{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=0| 12f, 181f, 193 }}


Badness: 0.039289
Badness: 0.039289
Line 467: Line 467:
POTE generator: ~18/17 = 99.485
POTE generator: ~18/17 = 99.485


{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=0| 12f, 181f, 193 }}


Badness: 0.028101
Badness: 0.028101
Line 499: Line 499:
* CWE: ~2 = 1200.000¢, ~17325/16384 = 99.529¢
* CWE: ~2 = 1200.000¢, ~17325/16384 = 99.529¢


{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061e }}
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061e }}


Badness (Sintel): 2.817
Badness (Sintel): 2.817
Line 512: Line 512:
POTE generator: ~4096/3861 = 99.529
POTE generator: ~4096/3861 = 99.529


{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061ef }}
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061ef }}


Badness: 0.039203
Badness: 0.039203
Line 525: Line 525:
POTE generator: ~18/17 = 99.529
POTE generator: ~18/17 = 99.529


{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061ef }}
{{Optimal ET sequence|legend=0| 205, 217, 422, 639, 1061ef }}


Badness: 0.024110
Badness: 0.024110
Line 538: Line 538:
POTE generator: ~18/17 = 99.529
POTE generator: ~18/17 = 99.529


{{Optimal ET sequence|legend=1| 205, 217, 422, 639h, 1061efh }}
{{Optimal ET sequence|legend=0| 205, 217, 422, 639h, 1061efh }}


Badness: 0.016764
Badness: 0.016764


== Hemiquindromeda ==
== Hemiquindromeda ==
The ''hemiquindromeda'' temperament (193&217) splits the fourth in ten, and tempers out the [[canousma]] (4802000/4782969) and the decovulture comma (67108864/66976875) in the 7-limit.
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 568: Line 570:
* CWE: ~2 = 1200.000¢, ~36/35 = 49.757¢
* CWE: ~2 = 1200.000¢, ~36/35 = 49.757¢


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e }}
{{Optimal ET sequence|legend=0| 24, 169d, 193, 217, 410e }}


Badness (Sintel): 3.079
Badness (Sintel): 3.079
Line 581: Line 583:
POTE generator: ~36/35 = 49.759
POTE generator: ~36/35 = 49.759


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e, 627e }}
{{Optimal ET sequence|legend=0| 24, 169d, 193, 217, 410e, 627e }}


Badness: 0.048715
Badness: 0.048715
Line 594: Line 596:
POTE generator: ~34/33 = 49.759
POTE generator: ~34/33 = 49.759


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e, 627e }}
{{Optimal ET sequence|legend=0| 24, 169d, 193, 217, 410e, 627e }}


Badness: 0.028155
Badness: 0.028155
Line 607: Line 609:
POTE generator: ~34/33 = 49.759
POTE generator: ~34/33 = 49.759


{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e }}
{{Optimal ET sequence|legend=0| 24, 169d, 193, 217, 410e }}


Badness: 0.019364
Badness: 0.019364
Line 640: Line 642:
* CWE: ~99/70 = 600.000¢, ~1323/1250 = 99.523¢
* CWE: ~99/70 = 600.000¢, ~1323/1250 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 410, 422 }}
{{Optimal ET sequence|legend=0| 12, 410, 422 }}


Badness (Sintel): 3.105
Badness (Sintel): 3.105
Line 653: Line 655:
POTE generator: ~1323/1250 = 99.523
POTE generator: ~1323/1250 = 99.523


{{Optimal ET sequence|legend=1| 12f, 410, 422, 1254df, 1676bdff, 2098bcddff }}
{{Optimal ET sequence|legend=0| 12f, 410, 422, 1254df, 1676bdff, 2098bcddff }}


Badness: 0.053361
Badness: 0.053361
Line 666: Line 668:
POTE generator: ~18/17 = 99.522
POTE generator: ~18/17 = 99.522


{{Optimal ET sequence|legend=1| 12f, 410, 422, 832, 1254df, 1676bdff }}
{{Optimal ET sequence|legend=0| 12f, 410, 422, 832, 1254df, 1676bdff }}


Badness: 0.034659
Badness: 0.034659
Line 679: Line 681:
POTE generator: ~18/17 = 99.523
POTE generator: ~18/17 = 99.523


{{Optimal ET sequence|legend=1| 12f, 410, 422, 1254dfhh, 1676bdffhh }}
{{Optimal ET sequence|legend=0| 12f, 410, 422, 1254dfhh, 1676bdffhh }}


Badness: 0.025439
Badness: 0.025439
Retrieved from "https://en.xen.wiki/w/Quindromeda_family"