Quindromeda family: Difference between revisions

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Created page with "The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the Pythagorean comma with a stack of five schismas, making it a member of the schismic-Pyth..."
 
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Line 24: Line 24:
[[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}}
{{Multival|legend=1| 5 -28 -70 -56 -125 -84 }}


[[POTE generator]]: ~200/189 = 99.555
[[POTE generator]]: ~200/189 = 99.555
Line 41: Line 41:
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
Line 54: Line 54:
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
Line 67: Line 67:
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
Line 80: Line 80:
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
Line 93: Line 93:
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
Line 106: Line 106:
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
Line 119: Line 119:
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
Line 134: Line 134:
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
Line 147: Line 147:
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
Line 160: Line 160:
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
Line 173: Line 173:
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
Line 186: Line 186:
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
Line 199: Line 199:
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
Line 212: Line 212:
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
Line 225: Line 225:
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
Line 238: Line 238:
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
Line 251: Line 251:
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
Line 264: Line 264:
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
Line 427: Line 427:
[[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 }}
{{Multival|legend=1| 5 -28 147 -56 219 420 }}
Line 442: Line 442:
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
Line 455: Line 455:
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
Line 468: Line 468:
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
Line 481: Line 481:
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
Line 496: Line 496:
[[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
Line 509: Line 509:
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
Line 522: Line 522:
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
Line 535: Line 535:
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
Line 548: Line 548:
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
Line 555: Line 555:


Badness: 0.025439
Badness: 0.025439
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Quindromeda family| ]] <!-- main article -->
[[Category:Rank 2]]

Revision as of 14:13, 21 November 2021

The quindromeda family tempers out [56 -28 -5⟩, equating the Pythagorean comma with a stack of five schismas, making it a member of the schismic-Pythagorean equivalence continuum.

Quindromeda

Subgroup: 2.3.5

Comma list: [56 -28 -5⟩

Mapping: [⟨1 2 0], ⟨0 -5 28]]

POTE generator: ~4428675/4194304 = 99.526

Template:Val list

Badness: 0.399849

Quintagar

See also: 28ed5 § Regular temperaments

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 garibaldi fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma.


Subgroup: 2.3.5.7

Comma list: 3136/3125, 33554432/33480783

Mapping: [⟨1 2 0 -3], ⟨0 -5 28 70]]

Wedgie: ⟨⟨ 5 -28 -70 -56 -125 -84 ]]

POTE generator: ~200/189 = 99.555

Template:Val list

Badness: 0.142897

Quintoneum

The name quintoneum is a play on the words "quintans" (Latin for "one fifth") and "cotoneum".

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3136/3125, 7168000/7144929

Mapping: [⟨1 2 0 -3 -5], ⟨0 -5 28 70 102]]

POTE generator: ~35/33 = 99.539

Vals: Template:Val list

Badness: 0.087157

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 3136/3125, 13720/13689

Mapping: [⟨1 2 0 -3 -5 -7], ⟨0 -5 28 70 102 129]]

POTE generator: ~35/33 = 99.541

Vals: Template:Val list

Badness: 0.052361

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 364/363, 441/440, 595/594, 3136/3125, 3757/3750

Mapping: [⟨1 2 0 -3 -5 -7 5], ⟨0 -5 28 70 102 129 -11]]

POTE generator: ~18/17 = 99.540

Vals: Template:Val list

Badness: 0.035653

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 364/363, 441/440, 476/475, 595/594, 1216/1215, 3757/3750

Mapping: [⟨1 2 0 -3 -5 -7 5 4], ⟨0 -5 28 70 102 129 -11 3]]

POTE generator: ~18/17 = 99.541

Vals: Template:Val list

Badness: 0.025782

Quintoneoid

Subgroup: 2.3.5.7.11.13

Comma list: 441/440, 1001/1000, 3136/3125, 59150/59049

Mapping: [⟨1 2 0 -3 -5 11], ⟨0 -5 28 70 102 -88]]

POTE generator: ~35/33 = 99.537

Vals: Template:Val list

Badness: 0.072826

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 441/440, 595/594, 1001/1000, 2601/2600, 3136/3125

Mapping: [⟨1 2 0 -3 -5 11 5], ⟨0 -5 28 70 102 -88 -11]]

POTE generator: ~18/17 = 99.537

Vals: Template:Val list

Badness: 0.042339

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 441/440, 476/475, 595/594, 1001/1000, 1216/1215, 2601/2600

Mapping: [⟨1 2 0 -3 -5 11 5 4], ⟨0 -5 28 70 102 -88 -11 3]]

POTE generator: ~18/17 = 99.537

Vals: Template:Val list

Badness: 0.028983

Quintasandra

The name quintasandra is a play on the words "quintans" and "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

Comma list: 3136/3125, 19712/19683, 41503/41472

Mapping: [⟨1 2 0 -3 13], ⟨0 -5 28 70 -115]]

POTE generator: ~200/189 = 99.551

Vals: Template:Val list

Badness: 0.109908

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3136/3125, 4096/4095, 19712/19683

Mapping: [⟨1 2 0 -3 13 11], ⟨0 -5 28 70 -115 -88]]

POTE generator: ~55/52 = 99.548

Vals: Template:Val list

Badness: 0.067730

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 936/935, 1156/1155, 1377/1375, 3136/3125, 4096/4095

Mapping: [⟨1 2 0 -3 13 11 5], ⟨0 -5 28 70 -115 -88 -11]]

POTE generator: ~18/17 = 99.548

Vals: Template:Val list

Badness: 0.038153

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 476/475, 936/935, 1156/1155, 1216/1215, 1377/1375, 1729/1728

Mapping: [⟨1 2 0 -3 13 11 5 4], ⟨0 -5 28 70 -115 -88 -11 3]]

POTE generator: ~18/17 = 99.547

Vals: Template:Val list

Badness: 0.026654

Quintasandroid

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 2 0 -3 -6], ⟨0 -5 28 70 114]]

POTE generator: ~200/189 = 99.570

Vals: Template:Val list

Badness: 0.093971

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 2080/2079, 3136/3125, 10648/10647

Mapping: [⟨1 2 0 -3 -6 -8], ⟨0 -5 28 70 114 141]]

POTE generator: ~55/52 = 99.578

Vals: Template:Val list

Badness: 0.065701

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 442/441, 561/560, 3136/3125, 7744/7735

Mapping: [⟨1 2 0 -3 -6 -8 5], ⟨0 -5 28 70 114 141 -11]]

POTE generator: ~18/17 = 99.574

Vals: Template:Val list

Badness: 0.046624

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 351/350, 442/441, 476/475, 561/560, 627/625, 6144/6137

Mapping: [⟨1 2 0 -3 -6 -8 5 4], ⟨0 -5 28 70 114 141 -11 3]]

POTE generator: ~18/17 = 99.575

Vals: Template:Val list

Badness: 0.033145

Quintasand

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 2 0 -3 -6 11], ⟨0 -5 28 70 114 -88]]

POTE generator: ~200/189 = 99.556

Vals: Template:Val list

Badness: 0.100195

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 561/560, 715/714, 1701/1700, 3136/3125, 4096/4095

Mapping: [⟨1 2 0 -3 -6 11 5], ⟨0 -5 28 70 114 -88 -11]]

POTE generator: ~18/17 = 99.556

Vals: Template:Val list

Badness: 0.057851

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 286/285, 476/475, 561/560, 627/625, 1216/1215, 1729/1728

Mapping: [⟨1 2 0 -3 -6 11 5 4], ⟨0 -5 28 70 114 -88 -11 3]]

POTE generator: ~18/17 = 99.557

Vals: Template:Val list

Badness: 0.040410

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 kwai fourth (~4/3, about 497.4 cents).


Subgroup: 2.3.5.7

Comma list: 5120/5103, 9765625/9680832

Mapping: [⟨1 2 0 -2], ⟨0 -5 28 58]]

Wedgie: ⟨⟨ 5 -28 -58 -56 -106 -56 ]]

POTE generator: ~625/588 = 99.483

Template:Val list

Badness: 0.155536

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 4375/4356, 5120/5103

Mapping: [⟨1 2 0 -2 -4], ⟨0 -5 28 58 90]]

POTE generator: ~35/33 = 99.472

Vals: Template:Val list

Badness: 0.073158

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 1375/1372, 1575/1573, 4096/4095

Mapping: [⟨1 2 0 -2 -4 10], ⟨0 -5 28 58 90 -76]]

POTE generator: ~35/33 = 99.468

Vals: Template:Val list

Badness: 0.062737

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 325/324, 375/374, 595/594, 1275/1274, 4096/4095

Mapping: [⟨1 2 0 -2 -4 10 5], ⟨0 -5 28 58 90 -76 -11]]

POTE generator: ~18/17 = 99.469

Vals: Template:Val list

Badness: 0.037855

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 325/324, 375/374, 400/399, 595/594, 1216/1215, 1275/1274

Mapping: [⟨1 2 0 -2 -4 10 5 4], ⟨0 -5 28 58 90 -76 -11 3]]

POTE generator: ~18/17 = 99.469

Vals: Template:Val list

Badness: 0.025861

Quinkwai

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 847/845, 1375/1372, 4375/4356

Mapping: [⟨1 2 0 -2 -4 -5], ⟨0 -5 28 58 90 105]]

POTE generator: ~35/33 = 99.456

Vals: Template:Val list

Badness: 0.061873

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 352/351, 375/374, 595/594, 833/832, 1375/1372

Mapping: [⟨1 2 0 -2 -4 -5 5], ⟨0 -5 28 58 90 105 -11]]

POTE generator: ~18/17 = 99.458

Vals: Template:Val list

Badness: 0.043506

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 352/351, 375/374, 400/399, 495/494, 595/594, 1375/1372

Mapping: [⟨1 2 0 -2 -4 -5 5 4], ⟨0 -5 28 58 90 105 -11 3]]

POTE generator: ~18/17 = 99.459

Vals: Template:Val list

Badness: 0.031313

Quintakwoid

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 625/624, 1375/1372, 5120/5103

Mapping: [⟨1 2 0 -2 -4 -6], ⟨0 -5 28 58 90 117]]

POTE generator: ~35/33 = 99.484

Vals: Template:Val list

Badness: 0.057357

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 364/363, 375/374, 442/441, 595/594, 5120/5103

Mapping: [⟨1 2 0 -2 -4 -6 5], ⟨0 -5 28 58 90 117 -11]]

POTE generator: ~18/17 = 99.484

Vals: Template:Val list

Badness: 0.039289

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215

Mapping: [⟨1 2 0 -2 -4 -6 5 4], ⟨0 -5 28 58 90 117 -11 3]]

POTE generator: ~18/17 = 99.485

Vals: Template:Val list

Badness: 0.028101

Quindro

The quindro temperament (205&217) is an extension of the quindromeda temperament which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).

Subgroup: 2.3.5.7

Comma list: 4375/4374, 72057594037927936/71489976421753125

Mapping: [⟨1 2 0 15], ⟨0 -5 28 -147]]

Wedgie: ⟨⟨ 5 -28 147 -56 219 420 ]]

POTE generator: ~4428675/4194304 = 99.529

Template:Val list

Badness: 0.316850

11-limit

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 5632/5625, 25165824/25109315

Mapping: [⟨1 2 0 15 -5], ⟨0 -5 28 -147 102]]

POTE generator: ~17325/16384 = 99.529

Vals: Template:Val list

Badness: 0.085219

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4375/4374, 5632/5625, 20480/20449

Mapping: [⟨1 2 0 15 -5 11], ⟨0 -5 28 -147 102 -88]]

POTE generator: ~4096/3861 = 99.529

Vals: Template:Val list

Badness: 0.039203

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 1156/1155, 2080/2079, 2431/2430, 4375/4374, 5632/5625

Mapping: [⟨1 2 0 15 -5 11 5], ⟨0 -5 28 -147 102 -88 -11]]

POTE generator: ~18/17 = 99.529

Vals: Template:Val list

Badness: 0.024110

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1156/1155, 1216/1215, 1445/1444, 2080/2079, 2376/2375, 2431/2430

Mapping: [⟨1 2 0 15 -5 11 5 4], ⟨0 -5 28 -147 102 -88 -11 3]]

POTE generator: ~18/17 = 99.529

Vals: Template:Val list

Badness: 0.016764

Semiquindromeda

The semiquindromeda temperament (410&422) is an extension of the quindromeda temperament with a half-octave period.

Subgroup: 2.3.5.7

Comma list: 102760448/102515625, 1220703125/1219784832

Mapping: [⟨2 4 0 -5], ⟨0 -5 28 64]]

POTE generator: ~1323/1250 = 99.521

Template:Val list

Badness: 0.233140

11-limit

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 9801/9800, 85937500/85766121

Mapping: [⟨2 4 0 -5 -10], ⟨0 -5 28 64 102]]

POTE generator: ~1323/1250 = 99.525

Vals: Template:Val list

Badness: 0.093926

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466

Mapping: [⟨2 4 0 -5 -10 -13], ⟨0 -5 28 64 102 123]]

POTE generator: ~1323/1250 = 99.523

Vals: Template:Val list

Badness: 0.053361

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876

Mapping: [⟨2 4 0 -5 -10 -13 10], ⟨0 -5 28 64 102 123 -11]]

POTE generator: ~18/17 = 99.522

Vals: Template:Val list

Badness: 0.034659

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499

Mapping: [⟨2 4 0 -5 -10 -13 10 8], ⟨0 -5 28 64 102 123 -11 3]]

POTE generator: ~18/17 = 99.523

Vals: Template:Val list

Badness: 0.025439

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