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Quindromeda family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]].  
The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. It is also the temperament where the fourth ([[4/3]]) is identified by a stack of five generators, making it a member of [[Ploidacot/Omega-pentacot|omega-pentacot]] temperaments.  


== Quindromeda ==
== Quindromeda ==
Line 11: Line 11:
[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]
[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]


[[POTE generator]]: ~4428675/4194304 = 99.526
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.854¢, ~4428675/4194304 = 99.514¢
* [[CWE]]: ~2 = 1200.000¢, ~4428675/4194304 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 217, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 217, 422 }}


[[Badness]]: 0.399849
[[Badness]] (Sintel): 9.380


=== Subgroup temperament ===
=== Subgroup temperament ===
Line 32: Line 34:
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]


[[Tp tuning|POL2 generator]]: ~18/17 = 99.524
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.878¢, ~18/17 = 99.513¢
* [[CWE]]: ~2 = 1200.000¢, ~18/17 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0757 cents
[[Badness]] (Sintel): 0.768


==== 2.3.5.17.19 ====
==== 2.3.5.17.19 ====
Line 49: Line 53:
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]


[[Tp tuning|POL2 generator]]: ~18/17 = 99.524
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.852¢, ~18/17 = 99.512¢
* [[CWE]]: ~2 = 1200.000¢, ~18/17 = 99.523¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents
[[Badness]] (Sintel): 0.348
 
[[Badness]]: 0.007140


== Quintagar ==
== Quintagar ==
Line 66: Line 70:
[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]
[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]


[[POTE generator]]: ~200/189 = 99.555
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.824¢, ~200/189 = 99.540¢
* [[CWE]]: ~2 = 1200.000¢, ~200/189 = 99.553¢


{{Optimal ET sequence|legend=1| 12, 217, 229, 446, 675c }}
{{Optimal ET sequence|legend=1| 12, 217, 229, 446, 675c }}


[[Badness]]: 0.142897
[[Badness]] (Sintel): 3.616


=== Quintoneum ===
=== Quintoneum ===
Line 81: Line 87:
Mapping: [{{val| 1 2 0 -3 -5 }}, {{val| 0 -5 28 70 102 }}]
Mapping: [{{val| 1 2 0 -3 -5 }}, {{val| 0 -5 28 70 102 }}]


POTE generator: ~35/33 = 99.539
Optimal tunings:
* WE: ~2 = 1199.864¢, ~35/33 = 99.528¢
* 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: 0.087157
Badness (Sintel): 2.881


==== 13-limit ====
==== 13-limit ====
Line 94: Line 102:
Mapping: [{{val| 1 2 0 -3 -5 -7 }}, {{val| 0 -5 28 70 102 129 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 }}, {{val| 0 -5 28 70 102 129 }}]


POTE generator: ~35/33 = 99.541
Optimal tunings:
* WE: ~2 = 1199.855¢, ~35/33 = 99.529¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.540¢


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


Badness: 0.052361
Badness (Sintel): 2.164


===== 17-limit =====
===== 17-limit =====
Line 107: Line 117:
Mapping: [{{val| 1 2 0 -3 -5 -7 5 }}, {{val| 0 -5 28 70 102 129 -11 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 5 }}, {{val| 0 -5 28 70 102 129 -11 }}]


POTE generator: ~18/17 = 99.540
Optimal tunings:
* WE: ~2 = 1199.890¢, ~18/17 = 99.531¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.539¢


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


Badness: 0.035653
Badness (Sintel): 1.816


===== 19-limit =====
===== 19-limit =====
Line 120: Line 132:
Mapping: [{{val| 1 2 0 -3 -5 -7 5 4 }}, {{val| 0 -5 28 70 102 129 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -5 -7 5 4 }}, {{val| 0 -5 28 70 102 129 -11 3 }}]


POTE generator: ~18/17 = 99.541
Optimal tunings:
* WE: ~2 = 1199.859¢, ~18/17 = 99.529¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.540¢


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


Badness: 0.025782
Badness (Sintel): 1.569


==== Quintoneoid ====
==== Quintoneoid ====
Line 133: Line 147:
Mapping: [{{val| 1 2 0 -3 -5 11 }}, {{val| 0 -5 28 70 102 -88 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 }}, {{val| 0 -5 28 70 102 -88 }}]


POTE generator: ~35/33 = 99.537
Optimal tunings:
* WE: ~2 = 1199.901¢, ~35/33 = 99.529¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.537¢


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


Badness: 0.072826
Badness (Sintel): 3.009


===== 17-limit =====
===== 17-limit =====
Line 146: Line 162:
Mapping: [{{val| 1 2 0 -3 -5 11 5 }}, {{val| 0 -5 28 70 102 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 5 }}, {{val| 0 -5 28 70 102 -88 -11 }}]


POTE generator: ~18/17 = 99.537
Optimal tunings:
* WE: ~2 = 1199.912¢, ~18/17 = 99.530¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.537¢


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


Badness: 0.042339
Badness (Sintel): 2.157


===== 19-limit =====
===== 19-limit =====
Line 159: Line 177:
Mapping: [{{val| 1 2 0 -3 -5 11 5 4 }}, {{val| 0 -5 28 70 102 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -5 11 5 4 }}, {{val| 0 -5 28 70 102 -88 -11 3 }}]


POTE generator: ~18/17 = 99.537
Optimal tunings:
* WE: ~2 = 1199.889¢, ~18/17 = 99.528¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.537¢


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


Badness: 0.028983
Badness (Sintel): 1.763


=== Quinsandra ===
=== Quinsandra ===
Line 174: Line 194:
Mapping: [{{val| 1 2 0 -3 13 }}, {{val| 0 -5 28 70 -115 }}]
Mapping: [{{val| 1 2 0 -3 13 }}, {{val| 0 -5 28 70 -115 }}]


POTE generator: ~200/189 = 99.551
Optimal tunings:
* WE: ~2 = 1199.867¢, ~200/189 = 99.540¢
* 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: 0.109908
Badness (Sintel): 3.633


==== 13-limit ====
==== 13-limit ====
Line 187: Line 209:
Mapping: [{{val| 1 2 0 -3 13 11 }}, {{val| 0 -5 28 70 -115 -88 }}]
Mapping: [{{val| 1 2 0 -3 13 11 }}, {{val| 0 -5 28 70 -115 -88 }}]


POTE generator: ~55/52 = 99.548
Optimal tunings:
* WE: ~2 = 1199.922¢, ~55/52 = 99.541¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.799


==== 17-limit ====
==== 17-limit ====
Line 200: Line 224:
Mapping: [{{val| 1 2 0 -3 13 11 5 }}, {{val| 0 -5 28 70 -115 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 13 11 5 }}, {{val| 0 -5 28 70 -115 -88 -11 }}]


POTE generator: ~18/17 = 99.548
Optimal tunings:
* WE: ~2 = 1199.932¢, ~18/17 = 99.542¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.944


==== 19-limit ====
==== 19-limit ====
Line 213: Line 239:
Mapping: [{{val| 1 2 0 -3 13 11 5 4 }}, {{val| 0 -5 28 70 -115 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 13 11 5 4 }}, {{val| 0 -5 28 70 -115 -88 -11 3 }}]


POTE generator: ~18/17 = 99.547
Optimal tunings:
* WE: ~2 = 1199.907¢, ~18/17 = 99.540¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.621


=== Quinsandric ===
=== Quinsandric ===
Line 226: Line 254:
Mapping: [{{val| 1 2 0 -3 -6 }}, {{val| 0 -5 28 70 114 }}]
Mapping: [{{val| 1 2 0 -3 -6 }}, {{val| 0 -5 28 70 114 }}]


POTE generator: ~200/189 = 99.570
Optimal tunings:
* WE: ~2 = 1199.770¢, ~200/189 = 99.551¢
* 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: 0.093971
Badness (Sintel): 3.107


==== 13-limit ====
==== 13-limit ====
Line 239: Line 269:
Mapping: [{{val| 1 2 0 -3 -6 -8 }}, {{val| 0 -5 28 70 114 141 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 }}, {{val| 0 -5 28 70 114 141 }}]


POTE generator: ~55/52 = 99.578
Optimal tunings:
* WE: ~2 = 1199.730¢, ~55/52 = 99.555¢
* CWE: ~2 = 1200.000¢, ~55/52 = 99.575¢


{{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 (Sintel): 2.715


===== 17-limit =====
===== 17-limit =====
Line 252: Line 284:
Mapping: [{{val| 1 2 0 -3 -6 -8 5 }}, {{val| 0 -5 28 70 114 141 -11 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 5 }}, {{val| 0 -5 28 70 114 141 -11 }}]


POTE generator: ~18/17 = 99.574
Optimal tunings:
* WE: ~2 = 1199.827¢, ~18/17 = 99.560¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.573¢


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


Badness: 0.046624
Badness (Sintel): 2.375


===== 19-limit =====
===== 19-limit =====
Line 265: Line 299:
Mapping: [{{val| 1 2 0 -3 -6 -8 5 4 }}, {{val| 0 -5 28 70 114 141 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -6 -8 5 4 }}, {{val| 0 -5 28 70 114 141 -11 3 }}]


POTE generator: ~18/17 = 99.575
Optimal tunings:
* WE: ~2 = 1199.804¢, ~18/17 = 99.559¢
* CWE: ~2 = 1200.000¢, ~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: 0.033145
Badness (Sintel): 2.016


==== Quinsandro ====
==== Quinsandro ====
Line 278: Line 314:
Mapping: [{{val| 1 2 0 -3 -6 11 }}, {{val| 0 -5 28 70 114 -88 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 }}, {{val| 0 -5 28 70 114 -88 }}]


Optimal tunings:
* WE: ~2 = 1200.032¢, ~200/189 = 99.559¢
* CWE: ~2 = 1200.000¢, ~200/189 = 99.556¢
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 (Sintel): 4.140


===== 17-limit =====
===== 17-limit =====
Line 291: Line 330:
Mapping: [{{val| 1 2 0 -3 -6 11 5 }}, {{val| 0 -5 28 70 114 -88 -11 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 5 }}, {{val| 0 -5 28 70 114 -88 -11 }}]


POTE generator: ~18/17 = 99.556
Optimal tunings:
* WE: ~2 = 1200.030¢, ~18/17 = 99.559¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.947


===== 19-limit =====
===== 19-limit =====
Line 304: Line 345:
Mapping: [{{val| 1 2 0 -3 -6 11 5 4 }}, {{val| 0 -5 28 70 114 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 -3 -6 11 5 4 }}, {{val| 0 -5 28 70 114 -88 -11 3 }}]


POTE generator: ~18/17 = 99.557
Optimal tunings:
* WE: ~2 = 1199.989¢, ~18/17 = 99.556¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.458


== 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 319: Line 362:
[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]
[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]


[[POTE generator]]: ~625/588 = 99.483
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.876¢, ~625/588 = 99.473¢
* [[CWE]]: ~2 = 1200.000¢, ~625/588 = 99.482¢


{{Optimal ET sequence|legend=1| 12, 169, 181, 193 }}
{{Optimal ET sequence|legend=1| 12, 169, 181, 193 }}


[[Badness]]: 0.155536
[[Badness]] (Sintel): 3.936


=== 11-limit ===
=== 11-limit ===
Line 332: Line 377:
Mapping: [{{val| 1 2 0 -2 -4 }}, {{val| 0 -5 28 58 90 }}]
Mapping: [{{val| 1 2 0 -2 -4 }}, {{val| 0 -5 28 58 90 }}]


POTE generator: ~35/33 = 99.472
Optimal tunings:
* WE: ~2 = 1199.906¢, ~35/33 = 99.464¢
* 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: 0.073158
Badness (Sintel): 2.419


==== 13-limit ====
==== 13-limit ====
Line 345: Line 392:
Mapping: [{{val| 1 2 0 -2 -4 10 }}, {{val| 0 -5 28 58 90 -76 }}]
Mapping: [{{val| 1 2 0 -2 -4 10 }}, {{val| 0 -5 28 58 90 -76 }}]


POTE generator: ~35/33 = 99.468
Optimal tunings:
* WE: ~2 = 1199.958¢, ~35/33 = 99.465¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.592


===== 17-limit =====
===== 17-limit =====
Line 358: Line 407:
Mapping: [{{val| 1 2 0 -2 -4 10 5 }}, {{val| 0 -5 28 58 90 -76 -11 }}]
Mapping: [{{val| 1 2 0 -2 -4 10 5 }}, {{val| 0 -5 28 58 90 -76 -11 }}]


POTE generator: ~18/17 = 99.469
Optimal tunings:
* WE: ~2 = 1199.929¢, ~18/17 = 99.463¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.928


===== 19-limit =====
===== 19-limit =====
Line 371: Line 422:
Mapping: [{{val| 1 2 0 -2 -4 10 5 4 }}, {{val| 0 -5 28 58 90 -76 -11 3 }}]
Mapping: [{{val| 1 2 0 -2 -4 10 5 4 }}, {{val| 0 -5 28 58 90 -76 -11 3 }}]


POTE generator: ~18/17 = 99.469
Optimal tunings:
* WE: ~2 = 1199.910¢, ~18/17 = 99.462¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.573


==== Quinkwai ====
==== Quinkwai ====
Line 384: Line 437:
Mapping: [{{val| 1 2 0 -2 -4 -5 }}, {{val| 0 -5 28 58 90 105 }}]
Mapping: [{{val| 1 2 0 -2 -4 -5 }}, {{val| 0 -5 28 58 90 105 }}]


POTE generator: ~35/33 = 99.456
Optimal tunings:
* WE: ~2 = 1199.964¢, ~35/33 = 99.453¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.455¢


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


Badness: 0.061873
Badness (Sintel): 2.557


===== 17-limit =====
===== 17-limit =====
Line 397: Line 452:
Mapping: [{{val| 1 2 0 -2 -4 -5 5 }}, {{val| 0 -5 28 58 90 105 -11 }}]
Mapping: [{{val| 1 2 0 -2 -4 -5 5 }}, {{val| 0 -5 28 58 90 105 -11 }}]


POTE generator: ~18/17 = 99.458
Optimal tunings:
* WE: ~2 = 1199.901¢, ~18/17 = 99.450¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.216


===== 19-limit =====
===== 19-limit =====
Line 410: Line 467:
Mapping: [{{val| 1 2 0 -2 -4 -5 5 4 }}, {{val| 0 -5 28 58 90 105 -11 3 }}]
Mapping: [{{val| 1 2 0 -2 -4 -5 5 4 }}, {{val| 0 -5 28 58 90 105 -11 3 }}]


POTE generator: ~18/17 = 99.459
Optimal tunings:
* WE: ~2 = 1199.879¢, ~18/17 = 99.449¢
* CWE: ~2 = 1200.000¢, ~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: 0.031313
Badness (Sintel): 1.905


==== Quintakwoid ====
==== Quintakwoid ====
Line 423: Line 482:
Mapping: [{{val| 1 2 0 -2 -4 -6 }}, {{val| 0 -5 28 58 90 117 }}]
Mapping: [{{val| 1 2 0 -2 -4 -6 }}, {{val| 0 -5 28 58 90 117 }}]


POTE generator: ~35/33 = 99.484
Optimal tunings:
* WE: ~2 = 1199.844¢, ~35/33 = 99.471¢
* CWE: ~2 = 1200.000¢, ~35/33 = 99.483¢


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


Badness: 0.057357
Badness (Sintel): 2.370


===== 17-limit =====
===== 17-limit =====
Line 436: Line 497:
Mapping: [{{val| 1 2 0 -2 -4 -6 5 }}, {{val| 0 -5 28 58 90 117 -11 }}]
Mapping: [{{val| 1 2 0 -2 -4 -6 5 }}, {{val| 0 -5 28 58 90 117 -11 }}]


POTE generator: ~18/17 = 99.484
Optimal tunings:
* WE: ~2 = 1199.838¢, ~18/17 = 99.471¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.483¢


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


Badness: 0.039289
Badness (Sintel): 2.002


===== 19-limit =====
===== 19-limit =====
Line 449: Line 512:
Mapping: [{{val| 1 2 0 -2 -4 -6 5 4 }}, {{val| 0 -5 28 58 90 117 -11 3 }}]
Mapping: [{{val| 1 2 0 -2 -4 -6 5 4 }}, {{val| 0 -5 28 58 90 117 -11 3 }}]


POTE generator: ~18/17 = 99.485
Optimal tunings:
* WE: ~2 = 1199.826¢, ~18/17 = 99.470¢
* CWE: ~2 = 1200.000¢, ~18/17 = 99.484¢


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


Badness: 0.028101
Badness (Sintel): 1.709


== Quindro ==
== Quindro ==
Line 464: Line 529:
[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]
[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]


[[POTE generator]]: ~4428675/4194304 = 99.529
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.843¢, ~4428675/4194304 = 99.516¢
* [[CWE]]: ~2 = 1200.000¢, ~4428675/4194304 = 99.529¢


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


[[Badness]]: 0.316850
[[Badness]] (Sintel): 8.019


=== 11-limit ===
=== 11-limit ===
Line 477: Line 544:
Mapping: [{{val| 1 2 0 15 -5 }}, {{val| 0 -5 28 -147 102 }}]
Mapping: [{{val| 1 2 0 15 -5 }}, {{val| 0 -5 28 -147 102 }}]


POTE generator: ~17325/16384 = 99.529
Optimal tunings:
* WE: ~2 = 1199.839¢, ~17325/16384 = 99.515¢
* 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: 0.085219
Badness (Sintel): 2.817


=== 13-limit ===
=== 13-limit ===
Line 490: Line 559:
Mapping: [{{val| 1 2 0 15 -5 11 }}, {{val| 0 -5 28 -147 102 -88 }}]
Mapping: [{{val| 1 2 0 15 -5 11 }}, {{val| 0 -5 28 -147 102 -88 }}]


POTE generator: ~4096/3861 = 99.529
Optimal tunings:
* WE: ~2 = 1199.825¢, ~143/135 = 99.514¢
* CWE: ~2 = 1200.000¢, ~143/135 = 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 (Sintel): 1.620


=== 17-limit ===
=== 17-limit ===
Line 503: Line 574:
Mapping: [{{val| 1 2 0 15 -5 11 5 }}, {{val| 0 -5 28 -147 102 -88 -11 }}]
Mapping: [{{val| 1 2 0 15 -5 11 5 }}, {{val| 0 -5 28 -147 102 -88 -11 }}]


POTE generator: ~18/17 = 99.529
Optimal tunings:
* WE: ~2 = 1199.843¢, ~18/17 = 99.516¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.228


=== 19-limit ===
=== 19-limit ===
Line 516: Line 589:
Mapping: [{{val| 1 2 0 15 -5 11 5 4 }}, {{val| 0 -5 28 -147 102 -88 -11 3 }}]
Mapping: [{{val| 1 2 0 15 -5 11 5 4 }}, {{val| 0 -5 28 -147 102 -88 -11 3 }}]


POTE generator: ~18/17 = 99.529
Optimal tunings:
* WE: ~2 = 1199.830¢, ~18/17 = 99.515¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.020


== 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 529: Line 606:
[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]
[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]


[[POTE generator]]: ~36/35 = 49.756
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.925¢, ~36/35 = 49.753¢
* [[CWE]]: ~2 = 1200.000¢, ~36/35 = 49.757¢


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


[[Badness]]: 0.244589
[[Badness]] (Sintel): 6.190


=== 11-limit ===
=== 11-limit ===
Line 542: Line 621:
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]


POTE generator: ~36/35 = 49.757
Optimal tunings:
* WE: ~2 = 1199.834¢, ~36/35 = 49.750¢
* 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: 0.093130
Badness (Sintel): 3.079


=== 13-limit ===
=== 13-limit ===
Line 555: Line 636:
Mapping: [{{val|1 2 0 6 4 2}}, {{val|0 -10 56 -77 -13 41}}]
Mapping: [{{val|1 2 0 6 4 2}}, {{val|0 -10 56 -77 -13 41}}]


POTE generator: ~36/35 = 49.759
Optimal tunings:
* WE: ~2 = 1199.885¢, ~36/35 = 49.754¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 2.013


=== 17-limit ===
=== 17-limit ===
Line 568: Line 651:
Mapping: [{{val|1 2 0 6 4 2 5}}, {{val|0 -10 56 -77 -13 41 -22}}]
Mapping: [{{val|1 2 0 6 4 2 5}}, {{val|0 -10 56 -77 -13 41 -22}}]


POTE generator: ~34/33 = 49.759
Optimal tunings:
* WE: ~2 = 1199.889¢, ~34/33 = 49.754¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.434


=== 19-limit ===
=== 19-limit ===
Line 581: Line 666:
Mapping: [{{val|1 2 0 6 4 2 5 4}}, {{val|0 -10 56 -77 -13 41 -22 6}}]
Mapping: [{{val|1 2 0 6 4 2 5 4}}, {{val|0 -10 56 -77 -13 41 -22 6}}]


POTE generator: ~34/33 = 49.759
Optimal tunings:
* WE: ~2 = 1199.872¢, ~34/33 = 49.754¢
* CWE: ~2 = 1200.000¢, ~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 (Sintel): 1.178


== Semiquindromeda ==
== Semiquindromeda ==
Line 595: Line 682:


[[Mapping]]: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]
[[Mapping]]: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]
: Mapping generators: ~10125/7168, ~1323/1250


[[POTE generator]]: ~1323/1250 = 99.521
[[Optimal tuning]]s:
* [[WE]]: ~10125/7168 = 599.929¢, ~1323/1250 = 99.509¢
* [[CWE]]: ~10125/7168 = 600.000¢, ~1323/1250 = 99.519¢


{{Optimal ET sequence|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}
{{Optimal ET sequence|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}


[[Badness]]: 0.233140
[[Badness]] (Sintel): 5.900


=== 11-limit ===
=== 11-limit ===
Line 609: Line 699:
Mapping: [{{val| 2 4 0 -5 -10 }}, {{val| 0 -5 28 64 102 }}]
Mapping: [{{val| 2 4 0 -5 -10 }}, {{val| 0 -5 28 64 102 }}]


POTE generator: ~1323/1250 = 99.525
Optimal tunings:
* WE: ~99/70 = 599.922¢, ~1323/1250 = 99.512¢
* 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: 0.093926
Badness (Sintel): 3.105


=== 13-limit ===
=== 13-limit ===
Line 622: Line 714:
Mapping: [{{val| 2 4 0 -5 -10 -13 }}, {{val| 0 -5 28 64 102 123 }}]
Mapping: [{{val| 2 4 0 -5 -10 -13 }}, {{val| 0 -5 28 64 102 123 }}]


POTE generator: ~1323/1250 = 99.523
Optimal tunings:
* WE: ~99/70 = 599.927¢, ~1323/1250 = 99.511¢
* CWE: ~99/70 = 600.000¢, ~1323/1250 = 99.522¢


{{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 (Sintel): 2.205


=== 17-limit ===
=== 17-limit ===
Line 635: Line 729:
Mapping: [{{val| 2 4 0 -5 -10 -13 10 }}, {{val| 0 -5 28 64 102 123 -11 }}]
Mapping: [{{val| 2 4 0 -5 -10 -13 10 }}, {{val| 0 -5 28 64 102 123 -11 }}]


POTE generator: ~18/17 = 99.522
Optimal tunings:
* WE: ~99/70 = 599.938¢, ~18/17 = 99.512¢
* CWE: ~99/70 = 600.000¢, ~18/17 = 99.521¢


{{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 (Sintel): 1.766


=== 19-limit ===
=== 19-limit ===
Line 648: Line 744:
Mapping: [{{val| 2 4 0 -5 -10 -13 10 8 }}, {{val| 0 -5 28 64 102 123 -11 3 }}]
Mapping: [{{val| 2 4 0 -5 -10 -13 10 8 }}, {{val| 0 -5 28 64 102 123 -11 3 }}]


POTE generator: ~18/17 = 99.523
Optimal tunings:
* WE: ~99/70 = 599.925¢, ~18/17 = 99.511¢
* CWE: ~99/70 = 600.000¢, ~18/17 = 99.522¢


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


Badness: 0.025439
Badness (Sintel): 1.547


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Quindromeda family| ]] <!-- main article -->
[[Category:Quindromeda family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Quindromeda_family"