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Quindromeda family: Difference between revisions

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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]].  
{{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]].  


== Quindromeda ==
== Quindromeda ==
The name ''quindromeda'' comes from "quintans" (Latin for "one fifth") and "[[Wikipedia:Andromeda|Andromeda]]", because the generator is 1/5 of the [[Schismatic family #Garibaldi|andromeda]] fourth (~4/3, about 497.6 cents).
Subgroup: 2.3.5
Subgroup: 2.3.5


[[Comma list]]: {{monzo| 56 -28 -5 }}
[[Comma]]: {{monzo| 56 -28 -5 }} = 72057594037927936/71489976421753125


[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]
[[Mapping]]: [{{val| 1 2 0 }}, {{val| 0 -5 28 }}]
Line 10: Line 13:
[[POTE generator]]: ~4428675/4194304 = 99.526
[[POTE generator]]: ~4428675/4194304 = 99.526


{{Val list|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]]: 0.399849


== Quintagar ==
=== Subgroup temperament ===
{{See also| 28ed5 #Regular temperaments }}
 
The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the [[1216/1215|password comma]] (1216/1215), [[1445/1444|aureusma]] (1445/1444), and [[6144/6137|langwisma]] (6144/6137). An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]].
 
==== 2.3.5.17 ====
Subgroup: 2.3.5.17
 
[[Comma list]]: 24576/24565, 295936/295245
 
[[Gencom]]: [2 18/17; 24576/24565 295936/295245]
 
[[Gencom|Gencom mapping]]: [{{val| 1 2 0 0 0 0 5 }}, {{val| 0 -5 28 0 0 0 -11 }}]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 0 5 }}, {{val| 0 -5 28 -11 }}]
 
[[Tp tuning|POL2 generator]]: ~18/17 = 99.524
 
{{Optimal ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0757 cents
 
==== 2.3.5.17.19 ====
Subgroup: 2.3.5.17.19
 
[[Comma list]]: 1216/1215, 1445/1444, 6144/6137
 
[[Gencom]]: [2 18/17; 1216/1215 1445/1444 6144/6137]
 
[[Gencom|Gencom mapping]]: [{{val| 1 2 0 0 0 0 5 4 }}, {{val| 0 -5 28 0 0 0 -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 ET sequence|legend=1| 12, 169, 181, 193, 205, 422 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents


The ''quintagar'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quintasandra'' (217&229, equating 385/384 with 400/399), and ''quintasandroid'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quintasandra'' (217&229), ''quintasandroid'' (12f&229), and ''quintasand'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma.
[[Badness]]: 0.007140


== Quintagar ==
The ''quintagar'' temperament (12&217) tempers out the [[3136/3125|hemimean comma]] (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, [[256/255]] (the difference between 16/15 and 17/16), [[289/288]] (between 17/16 and 18/17), [[324/323]] (between 18/17 and 19/18), [[361/360]] (between 19/18 and 20/19), and [[400/399]] (between 20/19 and 21/20) are equated together, and [[476/475]] (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out [[441/440]]), ''quinsandra'' (217&229, equating [[385/384]] with 400/399), and ''quinsandric'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quinsandra'' (217&229), ''quinsandric'' (12f&229), and ''quinsandro'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents).


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 24: Line 64:
[[Comma list]]: 3136/3125, 33554432/33480783
[[Comma list]]: 3136/3125, 33554432/33480783


[[Mapping]]: [{{val|1 2 0 -3}}, {{val|0 -5 28 70}}]
[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}]
 
{{Multival|legend=1|5 -28 -70 -56 -125 -84}}


[[POTE generator]]: ~200/189 = 99.555
[[POTE generator]]: ~200/189 = 99.555


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


[[Badness]]: 0.142897
[[Badness]]: 0.142897


=== Quintoneum ===
=== Quintoneum ===
The name ''quintoneum'' is a play on the words "quintans" (Latin for "one fifth") and "[[Hemimage temperaments #Cotoneum|cotoneum]]".
The name ''quintoneum'' is a play on the words "quintans" and "[[Hemimage temperaments #Cotoneum|cotoneum]]".


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 41: Line 79:
Comma list: 441/440, 3136/3125, 7168000/7144929
Comma list: 441/440, 3136/3125, 7168000/7144929


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
POTE generator: ~35/33 = 99.539


Vals: {{Val list| 12, 205d, 217 }}
{{Optimal ET sequence|legend=1| 12, 205d, 217 }}


Badness: 0.087157
Badness: 0.087157
Line 54: Line 92:
Comma list: 364/363, 441/440, 3136/3125, 13720/13689
Comma list: 364/363, 441/440, 3136/3125, 13720/13689


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
POTE generator: ~35/33 = 99.541


Vals: {{Val list| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}


Badness: 0.052361
Badness: 0.052361
Line 67: Line 105:
Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750
Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750


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
POTE generator: ~18/17 = 99.540


Vals: {{Val list| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}


Badness: 0.035653
Badness: 0.035653
Line 80: Line 118:
Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750
Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750


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
POTE generator: ~18/17 = 99.541


Vals: {{Val list| 12f, 205df, 217 }}
{{Optimal ET sequence|legend=1| 12f, 205df, 217 }}


Badness: 0.025782
Badness: 0.025782
Line 93: Line 131:
Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049
Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049


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
POTE generator: ~35/33 = 99.537


Vals: {{Val list| 12, 205d, 217 }}
{{Optimal ET sequence|legend=1| 12, 205d, 217 }}


Badness: 0.072826
Badness: 0.072826
Line 106: Line 144:
Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125
Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125


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
POTE generator: ~18/17 = 99.537


Vals: {{Val list| 12, 205d, 217 }}
{{Optimal ET sequence|legend=1| 12, 205d, 217 }}


Badness: 0.042339
Badness: 0.042339
Line 119: Line 157:
Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600
Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600


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
POTE generator: ~18/17 = 99.537


Vals: {{Val list| 12, 205d, 217 }}
{{Optimal ET sequence|legend=1| 12, 205d, 217 }}


Badness: 0.028983
Badness: 0.028983


=== Quintasandra ===
=== Quinsandra ===
The name ''quintasandra'' is a play on the words "quintans" and "[[Schismatic family #Garibaldi|cassandra]]". This temperament tempers out 19712/19683 and 41503/41472 in the 2.3.7.11 subgroup as the cassandra temperament, but with the hemimean comma rather than the [[schisma]] tempered out.
The name ''quinsandra'' is a play on the words "quintans" and "[[Schismatic family #Garibaldi|cassandra]]". This temperament tempers out 19712/19683 and 41503/41472 in the 2.3.7.11 subgroup as the cassandra temperament, but with the hemimean comma rather than the [[schisma]] tempered out.


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 134: Line 172:
Comma list: 3136/3125, 19712/19683, 41503/41472
Comma list: 3136/3125, 19712/19683, 41503/41472


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
POTE generator: ~200/189 = 99.551


Vals: {{Val list| 12e, 217, 446 }}
{{Optimal ET sequence|legend=1| 12e, 217, 446 }}


Badness: 0.109908
Badness: 0.109908
Line 147: Line 185:
Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683
Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683


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
POTE generator: ~55/52 = 99.548


Vals: {{Val list| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=1| 12e, 217, 446, 663c }}


Badness: 0.067730
Badness: 0.067730
Line 160: Line 198:
Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095
Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095


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
POTE generator: ~18/17 = 99.548


Vals: {{Val list| 12e, 217, 446, 663c }}
{{Optimal ET sequence|legend=1| 12e, 217, 446, 663c }}


Badness: 0.038153
Badness: 0.038153
Line 173: Line 211:
Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728
Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728


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
POTE generator: ~18/17 = 99.547


Vals: {{Val list| 12e, 217, 446, 663ch }}
{{Optimal ET sequence|legend=1| 12e, 217, 446, 663ch }}


Badness: 0.026654
Badness: 0.026654


=== Quintasandroid ===
=== Quinsandric ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3136/3125, 8019/8000, 15488/15435
Comma list: 3136/3125, 8019/8000, 15488/15435


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
POTE generator: ~200/189 = 99.570


Vals: {{Val list| 12, 217e, 229, 470cd, 699cd }}
{{Optimal ET sequence|legend=1| 12, 217e, 229, 470cd, 699cd }}


Badness: 0.093971
Badness: 0.093971
Line 199: Line 237:
Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647
Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647


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
POTE generator: ~55/52 = 99.578


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


Badness: 0.065701
Badness: 0.065701
Line 212: Line 250:
Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735
Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735


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
POTE generator: ~18/17 = 99.574


Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=1| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.046624
Badness: 0.046624
Line 225: Line 263:
Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137
Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137


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
POTE generator: ~18/17 = 99.575


Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}
{{Optimal ET sequence|legend=1| 12f, 217ef, 229, 241, 470cd }}


Badness: 0.033145
Badness: 0.033145


==== Quintasand ====
==== Quinsandro ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455
Comma list: 1573/1568, 3136/3125, 4096/4095, 4459/4455


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 }}]


POTE generator: ~200/189 = 99.556
POTE generator: ~200/189 = 99.556


Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.100195
Badness: 0.100195
Line 251: Line 289:
Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095
Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095


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
POTE generator: ~18/17 = 99.556


Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}
{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceef }}


Badness: 0.057851
Badness: 0.057851
Line 264: Line 302:
Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728
Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728


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
POTE generator: ~18/17 = 99.557


Vals: {{Val list| 12, 217e, 229, 446e, 675ceefh }}
{{Optimal ET sequence|legend=1| 12, 217e, 229, 446e, 675ceefh }}


Badness: 0.040410
Badness: 0.040410


== Quintakwai ==
== Quintakwai ==
The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) 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 281: Line 318:


[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]
[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}]
{{Multival|legend=1| 5 -28 -58 -56 -106 -56 }}


[[POTE generator]]: ~625/588 = 99.483
[[POTE generator]]: ~625/588 = 99.483


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


[[Badness]]: 0.155536
[[Badness]]: 0.155536
Line 299: Line 334:
POTE generator: ~35/33 = 99.472
POTE generator: ~35/33 = 99.472


Vals: {{Val list| 12, 181, 193, 374, 567ce }}
{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce }}


Badness: 0.073158
Badness: 0.073158
Line 312: Line 347:
POTE generator: ~35/33 = 99.468
POTE generator: ~35/33 = 99.468


Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bce }}
{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce, 941bce }}


Badness: 0.062737
Badness: 0.062737
Line 325: Line 360:
POTE generator: ~18/17 = 99.469
POTE generator: ~18/17 = 99.469


Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bceg }}
{{Optimal ET sequence|legend=1| 12, 181, 193, 374, 567ce, 941bceg }}


Badness: 0.037855
Badness: 0.037855
Line 338: Line 373:
POTE generator: ~18/17 = 99.469
POTE generator: ~18/17 = 99.469


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


Badness: 0.025861
Badness: 0.025861
Line 351: Line 386:
POTE generator: ~35/33 = 99.456
POTE generator: ~35/33 = 99.456


Vals: {{Val list| 12f, 169e, 181 }}
{{Optimal ET sequence|legend=1| 12f, 169e, 181 }}


Badness: 0.061873
Badness: 0.061873
Line 364: Line 399:
POTE generator: ~18/17 = 99.458
POTE generator: ~18/17 = 99.458


Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}
{{Optimal ET sequence|legend=1| 12f, 169e, 181, 374ff, 555cff }}


Badness: 0.043506
Badness: 0.043506
Line 377: Line 412:
POTE generator: ~18/17 = 99.459
POTE generator: ~18/17 = 99.459


Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}
{{Optimal ET sequence|legend=1| 12f, 169e, 181, 374ff, 555cff }}


Badness: 0.031313
Badness: 0.031313
Line 390: Line 425:
POTE generator: ~35/33 = 99.484
POTE generator: ~35/33 = 99.484


Vals: {{Val list| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}


Badness: 0.057357
Badness: 0.057357
Line 403: Line 438:
POTE generator: ~18/17 = 99.484
POTE generator: ~18/17 = 99.484


Vals: {{Val list| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}


Badness: 0.039289
Badness: 0.039289
Line 416: Line 451:
POTE generator: ~18/17 = 99.485
POTE generator: ~18/17 = 99.485


Vals: {{Val list| 12f, 181f, 193 }}
{{Optimal ET sequence|legend=1| 12f, 181f, 193 }}


Badness: 0.028101
Badness: 0.028101


== Quindro ==
== Quindro ==
The ''quindro'' temperament (205&217) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).  
The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the [[4375/4374|ragisma]] (4375/4374), the [[5632/5625|vishdel comma]] (5632/5625), and the [[2080/2079|ibnsinma]] (2080/2079).  


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 427: Line 462:
[[Comma list]]: 4375/4374, 72057594037927936/71489976421753125
[[Comma list]]: 4375/4374, 72057594037927936/71489976421753125


[[Mapping]]: [{{val|1 2 0 15}}, {{val|0 -5 28 -147}}]
[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}]
 
{{Multival|legend=1| 5 -28 147 -56 219 420 }}


[[POTE generator]]: ~4428675/4194304 = 99.529
[[POTE generator]]: ~4428675/4194304 = 99.529


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


[[Badness]]: 0.316850
[[Badness]]: 0.316850
Line 442: Line 475:
Comma list: 4375/4374, 5632/5625, 25165824/25109315
Comma list: 4375/4374, 5632/5625, 25165824/25109315


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
POTE generator: ~17325/16384 = 99.529


Vals: {{Val list| 205, 217, 422, 639, 1061e }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061e }}


Badness: 0.085219
Badness: 0.085219
Line 455: Line 488:
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449
Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449


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
POTE generator: ~4096/3861 = 99.529


Vals: {{Val list| 205, 217, 422, 639, 1061ef }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061ef }}


Badness: 0.039203
Badness: 0.039203
Line 468: Line 501:
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625
Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625


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
POTE generator: ~18/17 = 99.529


Vals: {{Val list| 205, 217, 422, 639, 1061ef }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639, 1061ef }}


Badness: 0.024110
Badness: 0.024110
Line 481: Line 514:
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430
Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430


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
POTE generator: ~18/17 = 99.529


Vals: {{Val list| 205, 217, 422, 639h, 1061efh }}
{{Optimal ET sequence|legend=1| 205, 217, 422, 639h, 1061efh }}


Badness: 0.016764
Badness: 0.016764
== Hemiquindromeda ==
Subgroup: 2.3.5.7
[[Comma list]]: 4802000/4782969, 67108864/66976875
[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}]
[[POTE generator]]: ~36/35 = 49.756
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410 }}
[[Badness]]: 0.244589
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 14700/14641, 16384/16335, 19712/19683
Mapping: [{{val|1 2 0 6 4}}, {{val|0 -10 56 -77 -13}}]
POTE generator: ~36/35 = 49.757
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e }}
Badness: 0.093130
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 676/675, 4096/4095, 19712/19683
Mapping: [{{val|1 2 0 6 4 2}}, {{val|0 -10 56 -77 -13 41}}]
POTE generator: ~36/35 = 49.759
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e, 627e }}
Badness: 0.048715
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 595/594, 676/675, 1156/1155, 4096/4095
Mapping: [{{val|1 2 0 6 4 2 5}}, {{val|0 -10 56 -77 -13 41 -22}}]
POTE generator: ~34/33 = 49.759
{{Optimal ET sequence|legend=1| 24, 169d, 193, 217, 410e, 627e }}
Badness: 0.028155
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 364/363, 595/594, 676/675, 1156/1155, 1216/1215, 1729/1728
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 ET sequence|legend=1| 24, 169d, 193, 217, 410e }}
Badness: 0.019364


== Semiquindromeda ==
== Semiquindromeda ==
The ''semiquindromeda'' temperament (410&422) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] with a half-octave period.
The ''semiquindromeda'' temperament (410&422) is an extension of the ''quindromeda'' temperament with a half-octave period.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 496: Line 594:
[[Comma list]]: 102760448/102515625, 1220703125/1219784832
[[Comma list]]: 102760448/102515625, 1220703125/1219784832


[[Mapping]]: [{{val|2 4 0 -5}}, {{val|0 -5 28 64}}]
[[Mapping]]: [{{val| 2 4 0 -5 }}, {{val| 0 -5 28 64 }}]


[[POTE generator]]: ~1323/1250 = 99.521
[[POTE generator]]: ~1323/1250 = 99.521


{{Val list|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]]: 0.233140
Line 509: Line 607:
Comma list: 5632/5625, 9801/9800, 85937500/85766121
Comma list: 5632/5625, 9801/9800, 85937500/85766121


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
POTE generator: ~1323/1250 = 99.525


Vals: {{Val list| 12, 410, 422 }}
{{Optimal ET sequence|legend=1| 12, 410, 422 }}


Badness: 0.093926
Badness: 0.093926
Line 522: Line 620:
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466


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
POTE generator: ~1323/1250 = 99.523


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


Badness: 0.053361
Badness: 0.053361
Line 535: Line 633:
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876


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
POTE generator: ~18/17 = 99.522


Vals: {{Val list| 12f, 410, 422, 832, 1254df, 1676bdff }}
{{Optimal ET sequence|legend=1| 12f, 410, 422, 832, 1254df, 1676bdff }}


Badness: 0.034659
Badness: 0.034659
Line 548: Line 646:
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499


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
POTE generator: ~18/17 = 99.523


Vals: {{Val list| 12f, 410, 422, 1254dfhh, 1676bdffhh }}
{{Optimal ET sequence|legend=1| 12f, 410, 422, 1254dfhh, 1676bdffhh }}


Badness: 0.025439
Badness: 0.025439
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Quindromeda family| ]] <!-- main article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Quindromeda_family"