Archytas clan: Difference between revisions

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Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]
Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]


{{EDOs|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}
{{Val list|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}


Badness: 0.0246
Badness: 0.0246
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Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]
Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]


{{EDOs|legend=1| 5, 10, 15, 25e, 40bef}}
{{Val list|legend=1| 5, 10, 15, 25e, 40bef}}


Badness: 0.0205
Badness: 0.0205
Line 62: Line 62:
Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]
Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]


{{EDOs|legend=1| 5e, 15 }}
{{Val list|legend=1| 5e, 15 }}


Badness: 0.0292
Badness: 0.0292
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Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]
Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]


{{EDOs|legend=1| 5e, 10e, 15 }}
{{Val list|legend=1| 5e, 10e, 15 }}


Badness: 0.0223
Badness: 0.0223
Line 84: Line 84:
Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]
Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]


{{EDOs|legend=1| 10 }}
{{Val list|legend=1| 10 }}


Badness: 0.0309
Badness: 0.0309
Line 99: Line 99:
Wedgie: {{wedgie| 1 9 -2 12 -6 -30 }}
Wedgie: {{wedgie| 1 9 -2 12 -6 -30 }}


{{EDOs|legend=1| 5, 17, 22, 27, 49 }}
{{Val list|legend=1| 5, 17, 22, 27, 49 }}


Badness: 0.0323
Badness: 0.0323
Line 110: Line 110:
Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]
Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]


{{EDOs|legend=1| 22, 27e, 49 }}
{{Val list|legend=1| 22, 27e, 49 }}


Badness: 0.0250
Badness: 0.0250
Line 121: Line 121:
Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]
Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]


{{EDOs|legend=1| 22, 27e, 49, 76bcde }}
{{Val list|legend=1| 22, 27e, 49, 76bcde }}


Badness: 0.0247
Badness: 0.0247
Line 132: Line 132:
Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]
Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]


{{EDOs|legend=1| 17, 22 }}
{{Val list|legend=1| 17, 22 }}


Badness: 0.0328
Badness: 0.0328
Line 143: Line 143:
Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]
Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]


{{EDOs|legend=1| 17, 22, 83cdf }}
{{Val list|legend=1| 17, 22, 83cdf }}


Badness: 0.0363
Badness: 0.0363
Line 149: Line 149:
= Beatles =
= Beatles =
== 5-limit ==
== 5-limit ==
Comma: 524288/492075
Comma list: 524288/492075


POTE generator: ~512/405 = 355.930
POTE generator: ~512/405 = 355.930


Map: [<1 1 5|,<0 2 -9|]
Mapping: [{{val| 1 1 5 }}, {{val| 0 2 -9 }}]


{{EDOs|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
{{Val list|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


Badness: 0.3585
Badness: 0.3585


== 7-limit ==
== 7-limit ==
Commas: 64/63, 686/675
Comma list: 64/63, 686/675


[[POTE generator]]: ~49/40 = 355.904
[[POTE generator]]: ~49/40 = 355.904


Map: [<1 1 5 4|,<0 2 -9 -4|]
Mapping: [{{val| 1 1 5 4 }}, {{val| 0 2 -9 -4 }}]


Wedgie: <<2 -9 -4 -19 -12 16||
Wedgie: {{wedgie| 2 -9 -4 -19 -12 16 }}


{{EDOs|legend=1| 10, 17c, 27, 64b, 91bcd, 118bcd }}
{{Val list|legend=1| 10, 17c, 27, 64b, 91bcd, 118bcd }}


Badness: 0.0459
Badness: 0.0459
Line 175: Line 175:


== 11-limit ==
== 11-limit ==
Commas: 64/63, 100/99, 686/675
Comma list: 64/63, 100/99, 686/675


POTE generator: ~49/40 = 356.140
POTE generator: ~49/40 = 356.140


Map: [<1 1 5 4 10|,<0 2 -9 -4 -22|]
Mapping: [{{val| 1 1 5 4 10 }}, {{val| 0 2 -9 -4 -22 }}]


{{EDOs|legend=1| 27e, 37, 64be, 91bcde }}
{{Val list|legend=1| 27e, 37, 64be, 91bcde }}


Badness: 0.0456
Badness: 0.0456


=== 13-limit ===
=== 13-limit ===
Commas: 64/63, 91/90, 100/99, 169/168
Comma list: 64/63, 91/90, 100/99, 169/168


POTE generator: ~16/13 = 356.229
POTE generator: ~16/13 = 356.229


Map: [<1 1 5 4 10 4|,<0 2 -9 -4 -22 -1|]
Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 -9 -4 -22 -1 }}]


{{EDOs|legend=1| 27e, 37, 64be }}
{{Val list|legend=1| 27e, 37, 64be }}


Badness: 0.0302
Badness: 0.0302


== Ringo ==
== Ringo ==
Commas: 56/55, 64/63, 540/539
Comma list: 56/55, 64/63, 540/539


POTE generator: ~11/9 = 355.419
POTE generator: ~11/9 = 355.419


Map: [<1 1 5 4 2|,<0 2 -9 -4 5|]
Mapping: [{{val| 1 1 5 4 2 }}, {{val| 0 2 -9 -4 5 }}]


{{EDOs|legend=1| 10, 17c, 27e }}
{{Val list|legend=1| 10, 17c, 27e }}


Badness: 0.0329
Badness: 0.0329


=== 13-limit ===
=== 13-limit ===
Commas: 56/55, 64/63, 78/77, 91/90
Comma list: 56/55, 64/63, 78/77, 91/90


POTE generator: ~11/9 = 355.456
POTE generator: ~11/9 = 355.456


Map: [<1 1 5 4 2 4|,<0 2 -9 -4 5 -1|]
Mapping: [{{val| 1 1 5 4 2 4 }}, {{val| 0 2 -9 -4 5 -1 }}]


{{EDOs|legend=1| 10, 17c, 27e }}
{{Val list|legend=1| 10, 17c, 27e }}


Badness: 0.0226
Badness: 0.0226
Line 221: Line 221:
{{see also|Schismatic family #Schism}}
{{see also|Schismatic family #Schism}}


Commas: 64/63, 360/343
Comma list: 64/63, 360/343


[[POTE generator]]: ~3/2 = 701.556
[[POTE generator]]: ~3/2 = 701.556


Map: [<1 0 15 6|, <0 1 -8 -2|]
Mapping: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]


Wedgie: <<1 -8 -2 -15 -6 18||
Wedgie: {{wedgie| 1 -8 -2 -15 -6 18 }}


{{EDOs|legend=1| 12, 41d, 53d }}
{{Val list|legend=1| 12, 41d, 53d }}


Badness: 0.0566
Badness: 0.0566


== 11-limit ==
== 11-limit ==
Commas: 45/44, 64/63, 99/98
Comma list: 45/44, 64/63, 99/98


POTE generator ~3/2 = 702.136
POTE generator ~3/2 = 702.136


Map: [<1 0 15 6 13|, <0 1 -8 -2 -6|]
Mapping: [{{val| 1 0 15 6 13 }}, {{val| 0 1 -8 -2 -6 }}]


{{EDOs|legend=1| 12, 29de, 41de }}
{{Val list|legend=1| 12, 29de, 41de }}


Badness: 0.0375
Badness: 0.0375
Line 246: Line 246:
= Passion =
= Passion =
== 5-limit ==
== 5-limit ==
Comma: 262144/253125
Comma list: 262144/253125


POTE generator: ~16/15 = 98.670
POTE generator: ~16/15 = 98.670


Map: [<1 2 2|, <0 -5 4|]
Mapping: [{{val| 1 2 2 }}, {{val| 0 -5 4 }}]


{{EDOs|legend=1| 11, 12, 49, 61, 73 }}
{{Val list|legend=1| 11, 12, 49, 61, 73 }}


Badness: 0.1686
Badness: 0.1686


=== Passive ===
=== Passive ===
Commas: 225/224, 256/245
Comma list: 225/224, 256/245


POTE generator: ~16/15 = 98.809
POTE generator: ~16/15 = 98.809


Map: [<1 2 2 3|, <0 -5 4 -2|]
Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]


{{EDOs|legend=1| 1, 11, 12, 49d }}
{{Val list|legend=1| 1, 11, 12, 49d }}


Badness: 0.0751
Badness: 0.0751


== 7-limit ==
== 7-limit ==
Commas: 64/63, 3125/3087
Comma list: 64/63, 3125/3087


[[POTE generator]]: ~16/15 = 98.153
[[POTE generator]]: ~16/15 = 98.153


Map: [<1 2 2 2|, <0 -5 4 10|]
Mapping: [{{val| 1 2 2 2 }}, {{val| 0 -5 4 10 }}]


Wedgie: <<5 -4 -10 -18 -30 -12||
Mapping generators: 2, 16/15


Generators: 2, 16/15
Wedgie: {{wedgie| 5 -4 -10 -18 -30 -12 }}


{{EDOs|legend=1| 12, 37, 49, 110bcd }}
{{Val list|legend=1| 12, 37, 49, 110bcd }}


Badness: 0.0623
Badness: 0.0623


== 11-limit ==
== 11-limit ==
Commas: 64/63, 100/99, 1375/1372
Comma list: 64/63, 100/99, 1375/1372


POTE generator: ~16/15 = 98.019
POTE generator: ~16/15 = 98.019


Map: [<1 2 2 2 2|, <0 -5 4 10 18|]
Mapping: [{{val| 1 2 2 2 2 }}, {{val| 0 -5 4 10 18 }}]


{{EDOs|legend=1| 12, 37, 49 }}
{{Val list|legend=1| 12, 37, 49 }}


Badness: 0.0408
Badness: 0.0408


== 13-limit ==
== 13-limit ==
Commas: 64/63, 100/99, 196/195, 275/273
Comma list: 64/63, 100/99, 196/195, 275/273


POTE generator: ~16/15 = 97.910
POTE generator: ~16/15 = 97.910


Map: [<1 2 2 2 2 2|, <0 -5 4 10 18 21|]
Mapping: [{{val| 1 2 2 2 2 2 }}, {{val| 0 -5 4 10 18 21 }}]


{{EDOs|legend=1| 12f, 37, 49f }}
{{Val list|legend=1| 12f, 37, 49f }}


Badness: 0.0309
Badness: 0.0309
Line 306: Line 306:
= Fervor =
= Fervor =
== 5-limit ==
== 5-limit ==
Comma: 67108864/61509375
Comma list: 67108864/61509375


POTE generator: ~64/45 = 577.705
POTE generator: ~64/45 = 577.705


Map: [<1 4 -2|, <0 -5 9|]
Mapping: [{{val| 1 4 -2 }}, {{val| 0 -5 9 }}]


{{EDOs|legend=1| 25, 27 }}
{{Val list|legend=1| 25, 27 }}


Badness: 0.8526
Badness: 0.8526


== 7-limit ==
== 7-limit ==
Commas: 64/63, 9604/9375
Comma list: 64/63, 9604/9375


POTE generator: ~7/5 = 577.777
POTE generator: ~7/5 = 577.777


Map: [<1 4 -2 -2|, <0 -5 9 10|]
Mapping: [{{val| 1 4 -2 -2 }}, {{val| 0 -5 9 10 }}]


Wedgie: <<5 -9 -10 -26 -30 2||
Wedgie: {{wedgie| 5 -9 -10 -26 -30 2 }}


{{EDOs|legend=1| 25, 27 }}
{{Val list|legend=1| 25, 27 }}


Badness: 0.1085
Badness: 0.1085


== 11-limit ==
== 11-limit ==
Commas: 56/55, 64/63, 1350/1331
Comma list: 56/55, 64/63, 1350/1331


POTE generator: ~7/5 = 577.850
POTE generator: ~7/5 = 577.850


Map: [<1 4 -2 -2 3|, <0 -5 9 10 1|]
Mapping: [{{val| 1 4 -2 -2 3 }}, {{val| 0 -5 9 10 1 }}]


{{EDOs|legend=1| 25e, 27e }}
{{Val list|legend=1| 25e, 27e }}


Badness: 0.0521
Badness: 0.0521


== 13-limit ==
== 13-limit ==
Commas: 56/55, 64/63, 78/77, 507/500
Comma list: 56/55, 64/63, 78/77, 507/500


POTE generator: ~7/5 = 578.060
POTE generator: ~7/5 = 578.060


Map: [<1 4 -2 -2 3 -4|, <0 -5 9 10 1 16|]
Mapping: [{{val| 1 4 -2 -2 3 -4 }}, {{val| 0 -5 9 10 1 16 }}]


{{EDOs|legend=1| 27e }}
{{Val list|legend=1| 27e }}


Badness: 0.0397
Badness: 0.0397


= Quasisuper =
= Quasisuper =
Commas: 64/63, 2430/2401
Comma list: 64/63, 2430/2401


[[POTE_tuning|POTE generator]]: 708.328
[[POTE generator]]: 708.328


Map: [<1 0 23 6|, <0 1 -13 -2|]
Mapping: [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2 }}]


Wedgie: <<1 -13 -2 -23 -2 -6 32||
Wedgie: {{wedgie| 1 -13 -2 -23 -2 -6 32 }}


{{EDOs|legend=1| 22, 61 }}
{{Val list|legend=1| 22, 61 }}


Badness: 0.0638
Badness: 0.0638
Line 367: Line 367:
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).


Commas: 64/63, 99/98, 121/120
Comma list: 64/63, 99/98, 121/120


POTE generator: ~3/2 = 708.205
POTE generator: ~3/2 = 708.205


Map: [<1 2 -3 2 1|, <0 -1 13 2 6|]
Mapping: [{{val| 1 2 -3 2 1 }}, {{val| 0 -1 13 2 6 }}]


{{EDOs|legend=1| 17c, 22, 27c, 39d, 61d }}
{{Val list|legend=1| 17c, 22, 27c, 39d, 61d }}


Badness: 0.0322
Badness: 0.0322


=== 13-limit ===
=== 13-limit ===
Commas: 64/63, 78/77, 91/90, 121/120
Comma list: 64/63, 78/77, 91/90, 121/120


POTE generator: ~3/2 = 708.004
POTE generator: ~3/2 = 708.004


Map: [<1 0 23 6 13 18|, <0 1 -13 -2 -6 -9|]
Mapping: [{{val| 1 0 23 6 13 18 }}, {{val| 0 1 -13 -2 -6 -9 }}]


{{EDOs|legend=1| 17c, 22, 39d, 61df, 100bcdf }}
{{Val list|legend=1| 17c, 22, 39d, 61df, 100bcdf }}


Badness: 0.0302
Badness: 0.0302


== Quasisoup ==
== Quasisoup ==
Commas: 55/54, 64/63, 2430/2401
Comma list: 55/54, 64/63, 2430/2401


POTE generator: ~3/2 = 709.021
POTE generator: ~3/2 = 709.021


Map: [<1 0 23 6 -22|, <0 1 -13 -2 16|]
Mapping: [{{val| 1 0 23 6 -22 }}, {{val| 0 1 -13 -2 16 }}]


{{EDOs|legend=1| 22 }}
{{Val list|legend=1| 22 }}


Badness: 0.0835
Badness: 0.0835
Line 401: Line 401:
= Progress =
= Progress =
== 5-limit ==
== 5-limit ==
Comma: 32768/30375
Comma list: 32768/30375


POTE generator: ~64/45 = 561.264
POTE generator: ~64/45 = 561.264


Map: [<1 0 5|, <0 3 -5|]
Mapping: [{{val| 1 0 5 }}, {{val| 0 3 -5 }}]


{{EDOs|legend=1| 4, 13, 15, 32c, 47bc, 62bc }}
{{Val list|legend=1| 4, 13, 15, 32c, 47bc, 62bc }}


Badness: 0.2461
Badness: 0.2461


== 7-limit ==
== 7-limit ==
Commas: 64/63, 392/375
Comma list: 64/63, 392/375


POTE generator: ~7/5 = 562.122
POTE generator: ~7/5 = 562.122


Map: [<1 0 5 6|, <0 3 -5 -6|]
Mapping: [{{val| 1 0 5 6 }}, {{val| 0 3 -5 -6 }}]


Wedgie: <<3 -5 -6 -15 -18 0||
Wedgie: {{wedgie| 3 -5 -6 -15 -18 0 }}


{{EDOs|legend=1| 13, 15, 32c, 79bcc, 111bcc }}
{{Val list|legend=1| 13, 15, 32c, 79bcc, 111bcc }}


Badness: 0.0664
Badness: 0.0664


== 11-limit ==
== 11-limit ==
Commas: 56/55, 64/63, 77/75
Comma list: 56/55, 64/63, 77/75


POTE generator: ~7/5 = 562.085
POTE generator: ~7/5 = 562.085


Map: [<1 0 5 6 4|, <0 3 -5 -6 -1|]
Mapping: [{{val| 1 0 5 6 4 }}, {{val| 0 3 -5 -6 -1 }}]


{{EDOs|legend=1| 13, 15, 32c, 47bc, 79bcce }}
{{Val list|legend=1| 13, 15, 32c, 47bc, 79bcce }}


Badness: 0.0310
Badness: 0.0310


=== 13-limit ===
=== 13-limit ===
Commas: 56/55, 64/63, 66/65, 77/75
Comma list: 56/55, 64/63, 66/65, 77/75


POTE generator: ~7/5 = 562.365
POTE generator: ~7/5 = 562.365


Map: [<1 0 5 6 4 0|, <0 3 -5 -6 -1 7|]
Mapping: [{{val| 1 0 5 6 4 0 }}, {{val| 0 3 -5 -6 -1 7 }}]


{{EDOs|legend=1| 15, 17c, 32cf }}
{{Val list|legend=1| 15, 17c, 32cf }}


Badness: 0.0262
Badness: 0.0262


=== Progressive ===
=== Progressive ===
Commas: 26/25, 56/55, 64/63, 77/75
Comma list: 26/25, 56/55, 64/63, 77/75


POTE generator: ~7/5 = 563.239
POTE generator: ~7/5 = 563.239


Map: [<1 0 5 6 4 9|, <0 3 -5 -6 -1 -10|]
Mapping: [{{val| 1 0 5 6 4 9 }}, {{val| 0 3 -5 -6 -1 -10 }}]


{{EDOs|legend=1| 15f, 17c, 32c, 49c }}
{{Val list|legend=1| 15f, 17c, 32c, 49c }}


Badness: 0.0327
Badness: 0.0327
Line 459: Line 459:
= Sixix =
= Sixix =
== 5-limit ==
== 5-limit ==
Comma: 3125/2916
Comma list: 3125/2916


POTE generator: ~6/5 = 338.365
POTE generator: ~6/5 = 338.365


Map: [<1 3 4|, <0 -5 -6|]
Mapping: [{{val| 1 3 4 }}, {{val| 0 -5 -6 }}]


EDOs: {{EDOs| 7, 25, 32 }}
{{Val list|legend=1| 7, 25, 32 }}


Badness: 0.1531
Badness: 0.1531


== 7-limit ==
== 7-limit ==
Commas: 3125/2916, 64/63
Comma list: 3125/2916, 64/63


POTE generator: ~6/5 = 337.4419
POTE generator: ~6/5 = 337.4419


Map: [<1 3 4 0 |, <0 -5 -6 10|]
Mapping: [{{val| 1 3 4 0 }}, {{val| 0 -5 -6 10 }}]
 
EDOs: {{EDOs| 7, 25, 32 }}


{{Val list|legend=1| 7, 25, 32 }}


[[Category:Theory]]
[[Category:Theory]]

Revision as of 10:05, 13 February 2021

The archytas clan tempers out the Archytas comma, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to 81/80 in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of 22edo.

Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.

Discussed under subgroup temperaments is the 2.3.7 archy. Under their respective 5-limit families are mother, dominant, augene, porcupine, pajara, modus, and immunized. The rest are considered below.

Blacksmith

5-limit (blackwood)

blacksmith10.jpg
Lattice of blacksmith

Comma list: 256/243

POTE generator: ~5/4 = 399.594

Mapping: [⟨5 8 0], ⟨0 0 1]]

Template:Val list

Badness: 0.0638

7-limit

Comma list: 28/27, 49/48

POTE generator: ~5/4 = 392.767

Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]

Wedgie: ⟨⟨0 5 0 8 0 -14]]

Template:Val list

Badness: 0.0256

11-limit

Comma list: 28/27, 49/48, 55/54

POTE generator: ~5/4 = 394.948

Mapping: [⟨5 8 0 14 29], ⟨0 0 1 0 -1]]

Template:Val list

Badness: 0.0246

13-limit

Comma list: 28/27, 40/39, 49/48, 55/54

POTE generator: ~5/4 = 391.0367

Mapping: [⟨5 8 0 14 29 7], ⟨0 0 1 0 -1 1]]

Template:Val list

Badness: 0.0205

Farrier

Comma list: 28/27, 49/48, 77/75

POTE generator: ~5/4 = 398.070

Mapping: [⟨5 8 0 14 -6], ⟨0 0 1 0 2]]

Template:Val list

Badness: 0.0292

13-limit

Comma list: 28/27, 40/39, 49/48, 66/65

POTE generator: ~5/4 = 396.812

Mapping: [⟨5 8 0 14 -6 7], ⟨0 0 1 0 2 1]]

Template:Val list

Badness: 0.0223

Ferrum

Comma list: 28/27, 35/33, 49/48

POTE generator: ~5/4 = 374.763

Mapping: [⟨5 8 0 14 6], ⟨0 0 1 0 1]]

Template:Val list

Badness: 0.0309

Superpyth

Main article: Superpyth

Comma list: 64/63, 245/243

POTE generator: ~3/2 = 710.291

Mapping: [⟨1 0 -12 6], ⟨0 1 9 -2]]

Wedgie: ⟨⟨1 9 -2 12 -6 -30]]

Template:Val list

Badness: 0.0323

11-limit

Comma list: 64/63, 100/99, 245/243

POTE generator: ~3/2 = 710.175

Mapping: [⟨1 0 -12 6 -22], ⟨0 1 9 -2 16]]

Template:Val list

Badness: 0.0250

13-limit

Comma list: 64/63, 78/77, 91/90, 100/99

POTE generator: ~3/2 = 710.479

Mapping: [⟨1 0 -12 6 -22 -17], ⟨0 1 9 -2 16 13]]

Template:Val list

Badness: 0.0247

Suprapyth

Comma list: 55/54, 64/63, 99/98

POTE generator: ~3/2 = 709.495

Mapping: [⟨1 0 -12 6 13], ⟨0 1 9 -2 -6]]

Template:Val list

Badness: 0.0328

13-limit

Comma list: 55/54, 64/63, 65/63, 99/98

POTE generator: ~3/2 = 708.703

Mapping: [⟨1 0 -12 6 13 18], ⟨0 1 9 -2 -6 -9]]

Template:Val list

Badness: 0.0363

Beatles

5-limit

Comma list: 524288/492075

POTE generator: ~512/405 = 355.930

Mapping: [⟨1 1 5], ⟨0 2 -9]]

Template:Val list

Badness: 0.3585

7-limit

Comma list: 64/63, 686/675

POTE generator: ~49/40 = 355.904

Mapping: [⟨1 1 5 4], ⟨0 2 -9 -4]]

Wedgie: ⟨⟨2 -9 -4 -19 -12 16]]

Template:Val list

Badness: 0.0459

Music: Beatles Improv by Herman Miller

11-limit

Comma list: 64/63, 100/99, 686/675

POTE generator: ~49/40 = 356.140

Mapping: [⟨1 1 5 4 10], ⟨0 2 -9 -4 -22]]

Template:Val list

Badness: 0.0456

13-limit

Comma list: 64/63, 91/90, 100/99, 169/168

POTE generator: ~16/13 = 356.229

Mapping: [⟨1 1 5 4 10 4], ⟨0 2 -9 -4 -22 -1]]

Template:Val list

Badness: 0.0302

Ringo

Comma list: 56/55, 64/63, 540/539

POTE generator: ~11/9 = 355.419

Mapping: [⟨1 1 5 4 2], ⟨0 2 -9 -4 5]]

Template:Val list

Badness: 0.0329

13-limit

Comma list: 56/55, 64/63, 78/77, 91/90

POTE generator: ~11/9 = 355.456

Mapping: [⟨1 1 5 4 2 4], ⟨0 2 -9 -4 5 -1]]

Template:Val list

Badness: 0.0226

Schism

See also: Schismatic family § Schism

Comma list: 64/63, 360/343

POTE generator: ~3/2 = 701.556

Mapping: [⟨1 0 15 6], ⟨0 1 -8 -2]]

Wedgie: ⟨⟨1 -8 -2 -15 -6 18]]

Template:Val list

Badness: 0.0566

11-limit

Comma list: 45/44, 64/63, 99/98

POTE generator ~3/2 = 702.136

Mapping: [⟨1 0 15 6 13], ⟨0 1 -8 -2 -6]]

Template:Val list

Badness: 0.0375

Passion

5-limit

Comma list: 262144/253125

POTE generator: ~16/15 = 98.670

Mapping: [⟨1 2 2], ⟨0 -5 4]]

Template:Val list

Badness: 0.1686

Passive

Comma list: 225/224, 256/245

POTE generator: ~16/15 = 98.809

Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]

Template:Val list

Badness: 0.0751

7-limit

Comma list: 64/63, 3125/3087

POTE generator: ~16/15 = 98.153

Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]

Mapping generators: 2, 16/15

Wedgie: ⟨⟨5 -4 -10 -18 -30 -12]]

Template:Val list

Badness: 0.0623

11-limit

Comma list: 64/63, 100/99, 1375/1372

POTE generator: ~16/15 = 98.019

Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]

Template:Val list

Badness: 0.0408

13-limit

Comma list: 64/63, 100/99, 196/195, 275/273

POTE generator: ~16/15 = 97.910

Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]

Template:Val list

Badness: 0.0309

Fervor

5-limit

Comma list: 67108864/61509375

POTE generator: ~64/45 = 577.705

Mapping: [⟨1 4 -2], ⟨0 -5 9]]

Template:Val list

Badness: 0.8526

7-limit

Comma list: 64/63, 9604/9375

POTE generator: ~7/5 = 577.777

Mapping: [⟨1 4 -2 -2], ⟨0 -5 9 10]]

Wedgie: ⟨⟨5 -9 -10 -26 -30 2]]

Template:Val list

Badness: 0.1085

11-limit

Comma list: 56/55, 64/63, 1350/1331

POTE generator: ~7/5 = 577.850

Mapping: [⟨1 4 -2 -2 3], ⟨0 -5 9 10 1]]

Template:Val list

Badness: 0.0521

13-limit

Comma list: 56/55, 64/63, 78/77, 507/500

POTE generator: ~7/5 = 578.060

Mapping: [⟨1 4 -2 -2 3 -4], ⟨0 -5 9 10 1 16]]

Template:Val list

Badness: 0.0397

Quasisuper

Comma list: 64/63, 2430/2401

POTE generator: 708.328

Mapping: [⟨1 0 23 6], ⟨0 1 -13 -2]]

Wedgie: ⟨⟨1 -13 -2 -23 -2 -6 32]]

Template:Val list

Badness: 0.0638

Quasisupra

Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament supra, with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).

Comma list: 64/63, 99/98, 121/120

POTE generator: ~3/2 = 708.205

Mapping: [⟨1 2 -3 2 1], ⟨0 -1 13 2 6]]

Template:Val list

Badness: 0.0322

13-limit

Comma list: 64/63, 78/77, 91/90, 121/120

POTE generator: ~3/2 = 708.004

Mapping: [⟨1 0 23 6 13 18], ⟨0 1 -13 -2 -6 -9]]

Template:Val list

Badness: 0.0302

Quasisoup

Comma list: 55/54, 64/63, 2430/2401

POTE generator: ~3/2 = 709.021

Mapping: [⟨1 0 23 6 -22], ⟨0 1 -13 -2 16]]

Template:Val list

Badness: 0.0835

Progress

5-limit

Comma list: 32768/30375

POTE generator: ~64/45 = 561.264

Mapping: [⟨1 0 5], ⟨0 3 -5]]

Template:Val list

Badness: 0.2461

7-limit

Comma list: 64/63, 392/375

POTE generator: ~7/5 = 562.122

Mapping: [⟨1 0 5 6], ⟨0 3 -5 -6]]

Wedgie: ⟨⟨3 -5 -6 -15 -18 0]]

Template:Val list

Badness: 0.0664

11-limit

Comma list: 56/55, 64/63, 77/75

POTE generator: ~7/5 = 562.085

Mapping: [⟨1 0 5 6 4], ⟨0 3 -5 -6 -1]]

Template:Val list

Badness: 0.0310

13-limit

Comma list: 56/55, 64/63, 66/65, 77/75

POTE generator: ~7/5 = 562.365

Mapping: [⟨1 0 5 6 4 0], ⟨0 3 -5 -6 -1 7]]

Template:Val list

Badness: 0.0262

Progressive

Comma list: 26/25, 56/55, 64/63, 77/75

POTE generator: ~7/5 = 563.239

Mapping: [⟨1 0 5 6 4 9], ⟨0 3 -5 -6 -1 -10]]

Template:Val list

Badness: 0.0327

Sixix

5-limit

Comma list: 3125/2916

POTE generator: ~6/5 = 338.365

Mapping: [⟨1 3 4], ⟨0 -5 -6]]

Template:Val list

Badness: 0.1531

7-limit

Comma list: 3125/2916, 64/63

POTE generator: ~6/5 = 337.4419

Mapping: [⟨1 3 4 0], ⟨0 -5 -6 10]]

Template:Val list

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