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Marvel temperaments: Difference between revisions

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Badness: 0.057799
Badness: 0.057799
== Triton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 1029/1000
[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
[[POTE generator]]: ~7/5 = 568.865
{{Val list|legend=1| 2, 17d, 19, 78bd, 97bd }}
[[Badness]]: 0.059245
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 45/44, 56/55, 1029/1000
Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
POTE generator: ~7/5 = 569.144
Optimal GPV sequence: {{Val list| 2, 17d, 19, 59bde, 78bde, 97bde }}
Badness: 0.045675


== Tritonic ==
== Tritonic ==
Line 470: Line 440:


Badness: 0.045456
Badness: 0.045456
== Merman ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 2500000/2470629
[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}
[[POTE generator]]: ~7/5 = 585.585
{{Val list|legend=1| 41, 84, 125 }}
[[Badness]]: 0.055078
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 1344/1331
Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
POTE generator: ~7/5 = 585.606
Optimal GPV sequence: {{Val list| 41, 84, 125e }}
Badness: 0.036383
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 225/224, 364/363, 441/440
Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
POTE generator: ~7/5 = 585.657
Optimal GPV sequence: {{Val list| 41, 84, 125e, 209ef, 293ef }}
Badness: 0.027544
== Untriton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 125000000/121060821
[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
{{Multival|legend=1|9 -19 -20 -51 -57 7}}
[[POTE generator]]: ~7/5 = 588.641
{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
[[Badness]]: 0.143976
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 22000/21609
Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
POTE generator: ~7/5 = 588.626
Optimal GPV sequence: {{Val list| 51, 53 }}
Badness: 0.074295
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 1040/1029
Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
POTE generator: ~7/5 = 588.654
Optimal GPV sequence: {{Val list| 51f, 53 }}
Badness: 0.047441


== Septimin ==
== Septimin ==
Line 600: Line 484:
Badness: 0.023117
Badness: 0.023117


== Misneb ==
== Merman ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Misneb]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 4194304/4117715
[[Comma list]]: 225/224, 2500000/2470629


[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]


{{Multival|legend=1|15 -14 2 -57 -39 44}}
{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}


[[POTE generator]]: ~16/15 = 113.235
[[POTE generator]]: ~7/5 = 585.585


{{Val list|legend=1| 21, 32, 53 }}
{{Val list|legend=1| 41, 84, 125 }}


[[Badness]]: 0.140970
[[Badness]]: 0.055078


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 1310720/1294139
Comma list: 225/224, 441/440, 1344/1331


Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]


POTE generator: ~16/15 = 113.323
POTE generator: ~7/5 = 585.606


Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
Optimal GPV sequence: {{Val list| 41, 84, 125e }}


Badness: 0.085390
Badness: 0.036383


==== 13-limit ====
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 176/175, 640/637, 847/845
Comma list: 144/143, 225/224, 364/363, 441/440


Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]
Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]


POTE generator: ~16/15 = 113.323
POTE generator: ~7/5 = 585.657


Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
Optimal GPV sequence: {{Val list| 41, 84, 125e, 209ef, 293ef }}


Badness: 0.045569
Badness: 0.027544
 
=== Musneb ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 66550/64827
 
Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
 
POTE generator: ~16/15 = 113.142
 
Optimal GPV sequence: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
 
Badness: 0.087333


== Slender ==
== Slender ==
Line 699: Line 570:
Badness: 0.025913
Badness: 0.025913


== Marvolo ==
== Triton ==
Subgroup: 2.3.5.7
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
 
[[Comma list]]: 225/224, 156250000/155649627
 
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
 
{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
 
[[POTE generator]]: ~21/20 = 83.348
 
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
 
[[Badness]]: 0.083338
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 4000/3993
 
Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
 
POTE generator: ~21/20 = 83.340
 
Optimal GPV sequence: {{Val list| 29, 43, 72 }}
 
Badness: 0.028965
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 441/440
 
Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
 
POTE generator: ~21/20 = 83.330
 
Optimal GPV sequence: {{Val list| 29, 43, 72, 115f }}
 
Badness: 0.021470


== Enneaportent ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 40353607/40310784
[[Comma list]]: 225/224, 1029/1000


[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]


{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}


[[POTE generator]]: ~5/4 = 383.165
[[POTE generator]]: ~7/5 = 568.865


{{Val list|legend=1| 9, 63, 72, 495bcd }}
{{Val list|legend=1| 2, 17d, 19, 78bd, 97bd }}


[[Badness]]: 0.093679
[[Badness]]: 0.059245


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 12005/11979
Comma list: 45/44, 56/55, 1029/1000


Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]


POTE generator: ~5/4 = 383.146
POTE generator: ~7/5 = 569.144


Optimal GPV sequence: {{Val list| 9, 63, 72, 423cd, 495bcd }}
Optimal GPV sequence: {{Val list| 2, 17d, 19, 59bde, 78bde, 97bde }}


Badness: 0.030426
Badness: 0.045675
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 1716/1715
 
Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
 
POTE generator: ~5/4 = 383.047
 
Optimal GPV sequence: {{Val list| 9, 63, 72, 279cf }}
 
Badness: 0.022322


== Submajor ==
== Submajor ==
Line 865: Line 684:
Badness: 0.029680
Badness: 0.029680


== Alphorn ==
== Marvolo ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 5764801/5668704
[[Comma list]]: 225/224, 156250000/155649627


[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]


{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}


[[POTE generator]]: ~48/35 = 556.221
[[POTE generator]]: ~21/20 = 83.348


{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}


[[Badness]]: 0.129258
[[Badness]]: 0.083338


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 12250/11979
Comma list: 225/224, 441/440, 4000/3993


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]


POTE generator: ~11/8 = 556.144
POTE generator: ~21/20 = 83.340


Optimal GPV sequence: {{Val list| 28d, 41, 315cde }}
Optimal GPV sequence: {{Val list| 29, 43, 72 }}


Badness: 0.073459
Badness: 0.028965


== Tertiosec ==
=== 13-limit ===
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7
Comma list: 169/168, 225/224, 364/363, 441/440


[[Comma list]]: 225/224, 14495514624/13841287201
Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]


[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
POTE generator: ~21/20 = 83.330


{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
Optimal GPV sequence: {{Val list| 29, 43, 72, 115f }}


[[POTE generator]]: ~15/14 = 112.283
Badness: 0.021470


{{Val list|legend=1| 21, 54, 75, 96, 171d }}
== Enneaportent ==
Subgroup: 2.3.5.7


[[Badness]]: 0.431636
[[Comma list]]: 225/224, 40353607/40310784


=== 11-limit ===
[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
Subgroup: 2.3.5.7.11


Comma list: 225/224, 3840/3773, 12005/11979
{{Multival|legend=1| 18 -9 18 -56 -22 67 }}


Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
[[POTE generator]]: ~5/4 = 383.165


POTE generator: ~15/14 = 112.171
{{Val list|legend=1| 9, 63, 72, 495bcd }}


Optimal GPV sequence: {{Val list| 21, 54, 75e }}
[[Badness]]: 0.093679


Badness: 0.173485
=== 11-limit ===
Subgroup: 2.3.5.7.11


== Gwazy ==
Comma list: 225/224, 385/384, 12005/11979
{{see also|Very high accuracy temperaments #Kwazy}}


Subgroup: 2.3.5.7
Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]


[[Comma list]]: 225/224, 5971968/5764801
POTE generator: ~5/4 = 383.146


[[Mapping]]: [{{val| 2 1 6 4 }}, {{val| 0 8 -5 6 }}]
Optimal GPV sequence: {{Val list| 9, 63, 72, 423cd, 495bcd }}


{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
Badness: 0.030426


[[POTE generator]]: ~35/32 = 162.658
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


{{Val list|legend=1| 22, 74, 96, 118d }}
Comma list: 169/168, 225/224, 364/363, 1716/1715


[[Badness]]: 0.178826
Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]


=== 11-limit ===
POTE generator: ~5/4 = 383.047
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 65536/65219
Optimal GPV sequence: {{Val list| 9, 63, 72, 279cf }}


Mapping: [{{val| 2 1 6 4 8 }}, {{val| 0 8 -5 6 -4 }}]
Badness: 0.022322
 
POTE generator: ~11/10 = 162.592
 
Optimal GPV sequence: {{Val list| 22, 74, 96, 118d }}
 
Badness: 0.068410


== Gracecordial ==
== Gracecordial ==
Line 1,112: Line 925:


Badness: 0.027559
Badness: 0.027559
== Alphorn ==
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 5764801/5668704
[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
[[POTE generator]]: ~48/35 = 556.221
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
[[Badness]]: 0.129258
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 12250/11979
Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
POTE generator: ~11/8 = 556.144
Optimal GPV sequence: {{Val list| 28d, 41, 315cde }}
Badness: 0.073459
== Misneb ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Misneb]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 4194304/4117715
[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
{{Multival|legend=1|15 -14 2 -57 -39 44}}
[[POTE generator]]: ~16/15 = 113.235
{{Val list|legend=1| 21, 32, 53 }}
[[Badness]]: 0.140970
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 1310720/1294139
Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
POTE generator: ~16/15 = 113.323
Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
Badness: 0.085390
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 640/637, 847/845
Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]
POTE generator: ~16/15 = 113.323
Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
Badness: 0.045569
=== Musneb ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 66550/64827
Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
POTE generator: ~16/15 = 113.142
Optimal GPV sequence: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
Badness: 0.087333
== Untriton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 125000000/121060821
[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
{{Multival|legend=1|9 -19 -20 -51 -57 7}}
[[POTE generator]]: ~7/5 = 588.641
{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
[[Badness]]: 0.143976
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 22000/21609
Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
POTE generator: ~7/5 = 588.626
Optimal GPV sequence: {{Val list| 51, 53 }}
Badness: 0.074295
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 1040/1029
Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
POTE generator: ~7/5 = 588.654
Optimal GPV sequence: {{Val list| 51f, 53 }}
Badness: 0.047441
== Quintannic ==
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 9805926501/9765625000
[[Mapping]]: [{{val| 1 1 5 7 }}, {{val| 0 5 -23 -36 }}]
{{Multival|legend=1| 5 -23 -36 -48 -71 -19 }}
[[POTE generator]]: ~10000/9261 = 139.838
{{Val list|legend=1| 43, 60, 103, 266bcd, 369bcd }}
[[Badness]]: 0.150565
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 441/440, 43923/43750
Mapping: [{{val| 1 1 5 7 8 }}, {{val| 0 5 -23 -36 -39 }}]
POTE generator: ~320/297 = 139.827
Optimal GPV sequence: {{Val list| 43, 60e, 103 }}
Badness: 0.052590
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
Mapping: [{{val| 1 1 5 7 8 3 }}, {{val| 0 5 -23 -36 -39 6 }}]
POTE generator: ~13/12 = 139.812
Optimal GPV sequence: {{Val list| 43, 60e, 103 }}
Badness: 0.032730
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
Mapping: [{{val| 1 1 5 7 8 3 7 }}, {{val| 0 5 -23 -36 -39 6 -25 }}]
POTE generator: ~13/12 = 139.815
Optimal GPV sequence: {{Val list| 43, 60e, 103 }}
Badness: 0.023038
== Gwazy ==
{{see also|Very high accuracy temperaments #Kwazy}}
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 5971968/5764801
[[Mapping]]: [{{val| 2 1 6 4 }}, {{val| 0 8 -5 6 }}]
{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
[[POTE generator]]: ~35/32 = 162.658
{{Val list|legend=1| 22, 74, 96, 118d }}
[[Badness]]: 0.178826
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 65536/65219
Mapping: [{{val| 2 1 6 4 8 }}, {{val| 0 8 -5 6 -4 }}]
POTE generator: ~11/10 = 162.592
Optimal GPV sequence: {{Val list| 22, 74, 96, 118d }}
Badness: 0.068410
== Tertiosec ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 14495514624/13841287201
[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
[[POTE generator]]: ~15/14 = 112.283
{{Val list|legend=1| 21, 54, 75, 96, 171d }}
[[Badness]]: 0.431636
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 3840/3773, 12005/11979
Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
POTE generator: ~15/14 = 112.171
Optimal GPV sequence: {{Val list| 21, 54, 75e }}
Badness: 0.173485


[[Category:Temperament collections]]
[[Category:Temperament collections]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"