Xenharmonic Wiki

Marvel temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Sorting the links to families and clans by pergen
Update keys
Line 38: Line 38:


== Wizard ==
== Wizard ==
{{Main|Wizard}}
{{Main| Wizard }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 118098/117649
[[Comma list]]: 225/224, 118098/117649


[[Mapping]]: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}


Mapping generators: ~1225/864, ~245/216
: mapping generators: ~1225/864, ~245/216


[[POTE generator]]: ~5/4 = 383.256
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~5/4 = 383.256 (~245/216 = 216.744)


{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
Line 64: Line 64:
Comma list: 225/224, 385/384, 4000/3993
Comma list: 225/224, 385/384, 4000/3993


Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}


Mapping generators: ~99/70, ~25/22
Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.232 (~25/22 = 216.768)
 
POTE generator: ~5/4 = 383.232


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c }}
Line 81: Line 79:
Comma list: 225/224, 351/350, 364/363, 385/384
Comma list: 225/224, 351/350, 364/363, 385/384


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}


Mapping generators: ~99/70, ~25/22
Optimal tuning (POTE): ~55/39 = 1\2, ~5/4 = 383.389 (~25/22 = 216.711)
 
POTE generator: ~5/4 = 383.389


{{Optimal ET sequence|legend=1| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 122, 194df }}
Line 96: Line 92:
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374


Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


Mapping generators: ~17/12, ~17/15
Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.381 (~17/15 = 216.619)
 
POTE generator: ~5/4 = 383.381


{{Optimal ET sequence|legend=1| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 122g, 194dfg }}
Line 111: Line 105:
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


Mapping generators: ~17/12, ~17/15
Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.477 (~17/15 = 216.523)
 
POTE generator: ~5/4 = 383.477


{{Optimal ET sequence|legend=1| 22h, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=1| 22h, 50, 72, 122g, 194dfg }}
Line 126: Line 118:
Comma list: 225/224, 325/324, 385/384, 1573/1568
Comma list: 225/224, 325/324, 385/384, 1573/1568


Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
 
Mapping generators: ~99/70, ~25/22


POTE generator: ~5/4 = 383.170
Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.170 (~25/22 = 216.830)


{{Optimal ET sequence|legend=1| 72, 166, 238cf }}
{{Optimal ET sequence|legend=1| 72, 166, 238cf }}
Line 141: Line 131:
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384


Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
 
Mapping generators: ~17/12, ~17/15


POTE generator: ~5/4 = 383.175
Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.175 (~25/22 = 216.825)


{{Optimal ET sequence|legend=1| 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=1| 72, 166g, 238cfg }}
Line 156: Line 144:
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}


Mapping generators: ~17/12, ~17/15
Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.138 (~17/15 = 216.862)
 
POTE generator: ~5/4 = 383.138


{{Optimal ET sequence|legend=1| 72, 94, 166g }}
{{Optimal ET sequence|legend=1| 72, 94, 166g }}
Line 171: Line 157:
Comma list: 99/98, 176/175, 1331/1296
Comma list: 99/98, 176/175, 1331/1296


Mapping: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}


Mapping generators: ~77/54, ~55/48
Optimal tuning (POTE): ~77/54 = 1\2, ~5/4 = 383.124 (~55/48 = 216.876)
 
POTE generator: ~5/4 = 383.124


{{Optimal ET sequence|legend=1| 22, 50e, 72ee, 94ee }}
{{Optimal ET sequence|legend=1| 22, 50e, 72ee, 94ee }}
Line 184: Line 168:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 50421/50000
[[Comma list]]: 225/224, 50421/50000


[[Mapping]]: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}


{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}
{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}


[[POTE generator]]: ~7/5 = 580.286
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 580.286


{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
Line 203: Line 187:
Comma list: 121/120, 225/224, 441/440
Comma list: 121/120, 225/224, 441/440


Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}


POTE generator: ~7/5 = 580.267
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.267


{{Optimal ET sequence|legend=1| 29, 31, 60e }}
{{Optimal ET sequence|legend=1| 29, 31, 60e }}
Line 216: Line 200:
Comma list: 105/104, 121/120, 196/195, 275/273
Comma list: 105/104, 121/120, 196/195, 275/273


Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}


POTE generator: ~7/5 = 580.108
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.108


{{Optimal ET sequence|legend=1| 29, 31, 60e, 151cde }}
{{Optimal ET sequence|legend=1| 29, 31, 60e, 151cde }}
Line 229: Line 213:
Comma list: 225/224, 385/384, 27783/27500
Comma list: 225/224, 385/384, 27783/27500


Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}


POTE generator: ~7/5 = 580.389
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.389


{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}
{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}
Line 240: Line 224:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 84035/82944
[[Comma list]]: 225/224, 84035/82944


[[Mapping]]: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}


{{Multival|legend=1| 11 -6 10 -35 -15 40 }}
{{Multival|legend=1| 11 -6 10 -35 -15 40 }}


[[POTE generator]]: ~7/6 = 263.632
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 263.632


{{Optimal ET sequence|legend=1| 41, 91, 132d }}
{{Optimal ET sequence|legend=1| 41, 91, 132d }}
Line 259: Line 243:
Comma list: 225/224, 385/384, 2401/2376
Comma list: 225/224, 385/384, 2401/2376


Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}


POTE generator: ~7/6 = 263.634
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.634


{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
Line 272: Line 256:
Comma list: 105/104, 144/143, 196/195, 245/242
Comma list: 105/104, 144/143, 196/195, 245/242


Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}


POTE generator: ~7/6 = 263.700
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.700


{{Optimal ET sequence|legend=1| 41, 91 }}
{{Optimal ET sequence|legend=1| 41, 91 }}
Line 283: Line 267:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
: ''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, 2500000/2470629
[[Comma list]]: 225/224, 2500000/2470629


[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}


{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}
{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}


[[POTE generator]]: ~7/5 = 585.585
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.585


{{Optimal ET sequence|legend=1| 41, 84, 125 }}
{{Optimal ET sequence|legend=1| 41, 84, 125 }}
Line 302: Line 286:
Comma list: 225/224, 441/440, 1344/1331
Comma list: 225/224, 441/440, 1344/1331


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


POTE generator: ~7/5 = 585.606
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.606


{{Optimal ET sequence|legend=1| 41, 84, 125e }}
{{Optimal ET sequence|legend=1| 41, 84, 125e }}
Line 315: Line 299:
Comma list: 144/143, 225/224, 364/363, 441/440
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 }}]
Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}


POTE generator: ~7/5 = 585.657
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.657


{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}
{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}
Line 324: Line 308:


== Slender ==
== Slender ==
Slender (31&32) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma, this has a generator [[49/48]], 3 of which equal marvel's 16/15 - 15/14, and 10 generators is 5/4.
Slender (31 & 32) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma. This temperament has a generator of [[49/48]], 3 of which equal marvel's 16/15~15/14, and 10 generators is 5/4.


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 589824/588245
[[Comma list]]: 225/224, 589824/588245


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}


{{Multival|legend=1| 13 -10 6 -46 -27 42 }}
{{Multival|legend=1| 13 -10 6 -46 -27 42 }}


[[POTE generator]]: ~49/48 = 38.413
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/48 = 38.413


{{Optimal ET sequence|legend=1| 31, 94, 125 }}
{{Optimal ET sequence|legend=1| 31, 94, 125 }}
Line 345: Line 329:
Comma list: 225/224, 385/384, 1331/1323
Comma list: 225/224, 385/384, 1331/1323


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


POTE generator: ~49/48 = 38.387
Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.387


{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}
{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}
Line 358: Line 342:
Comma list: 225/224, 275/273, 385/384, 1331/1323
Comma list: 225/224, 275/273, 385/384, 1331/1323


Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


POTE generator: ~49/48 = 38.314
Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.314


{{Optimal ET sequence|legend=1| 31, 63, 94 }}
{{Optimal ET sequence|legend=1| 31, 63, 94 }}
Line 369: Line 353:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}


{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}


[[POTE generator]]: ~7/5 = 568.865
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 568.865


{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
Line 388: Line 372:
Comma list: 45/44, 56/55, 1029/1000
Comma list: 45/44, 56/55, 1029/1000


Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


POTE generator: ~7/5 = 569.144
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 569.144


{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}
Line 397: Line 381:


== Submajor ==
== Submajor ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 69198046875/68719476736
[[Comma list]]: 69198046875/68719476736


[[Mapping]]: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]
{{Mapping|legend=1| 1 4 -1 | 0 -8 11 }}


[[POTE generator]]: ~10125/8192 = 362.321
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10125/8192 = 362.321


{{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
{{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
Line 410: Line 394:


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 51200/50421
[[Comma list]]: 225/224, 51200/50421


[[Mapping]]: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
{{Mapping|legend=1| 1 4 -1 1 | 0 -8 11 6 }}


{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}
{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}


[[POTE generator]]: ~49/40 = 362.255
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 362.255


{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
Line 429: Line 413:
Comma list: 225/224, 385/384, 6655/6561
Comma list: 225/224, 385/384, 6655/6561


Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}


POTE generator: ~27/22 = 362.101
Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 362.101


{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cde }}
{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cde }}
Line 442: Line 426:
Comma list: 169/168, 225/224, 275/273, 385/384
Comma list: 169/168, 225/224, 275/273, 385/384


Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}


POTE generator: ~16/13 = 362.105
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.105


{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cdef }}
{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cdef }}
Line 455: Line 439:
Comma list: 99/98, 176/175, 51200/50421
Comma list: 99/98, 176/175, 51200/50421


POTE generator: ~49/40 = 362.418
Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}


Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 362.418
 
POTE generator: ~49/40 = 362.418


{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
Line 470: Line 452:
Comma list: 99/98, 169/168, 176/175, 640/637
Comma list: 99/98, 169/168, 176/175, 640/637


POTE generator: ~16/13 = 362.402
Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}
 
Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]


POTE generator: ~16/13 = 362.402
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.402


{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
Line 481: Line 461:


== Marvolo ==
== Marvolo ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}


{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}


[[POTE generator]]: ~21/20 = 83.348
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 83.348


{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
Line 500: Line 480:
Comma list: 225/224, 441/440, 4000/3993
Comma list: 225/224, 441/440, 4000/3993


Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


POTE generator: ~21/20 = 83.340
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.340


{{Optimal ET sequence|legend=1| 29, 43, 72 }}
{{Optimal ET sequence|legend=1| 29, 43, 72 }}
Line 513: Line 493:
Comma list: 169/168, 225/224, 364/363, 441/440
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 }}]
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


POTE generator: ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}
Line 526: Line 506:
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440


Mapping: [{{val| 1 2 1 1 2 3 2 }}, {{val| 0 -6 19 26 21 10 30 }}]
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


POTE generator: ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
Line 537: Line 517:
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440


Mapping: [{{val| 1 2 1 1 2 3 2 3 }}, {{val| 0 -6 19 26 21 10 30 18 }}]
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


POTE generator: ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}


== Enneaportent ==
== Enneaportent ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


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


{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
{{Multival|legend=1| 18 -9 18 -56 -22 67 }}


[[POTE generator]]: ~5/4 = 383.165
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~5/4 = 383.165


{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
Line 563: Line 543:
Comma list: 225/224, 385/384, 12005/11979
Comma list: 225/224, 385/384, 12005/11979


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


POTE generator: ~5/4 = 383.146
Optimal tuning (POTE): ~121/112 = 1\9, ~5/4 = 383.146


{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}
Line 576: Line 556:
Comma list: 169/168, 225/224, 364/363, 1716/1715
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 }}]
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


POTE generator: ~5/4 = 383.047
Optimal tuning (POTE): ~14/13 = 1\9, ~5/4 = 383.047


{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}
Line 587: Line 567:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Gracecordial]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Gracecordial]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 781250000/771895089
[[Comma list]]: 225/224, 781250000/771895089


[[Mapping]]: [{{val| 1 0 34 63 }}, {{val| 0 1 -20 -38 }}]
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}


{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}
{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}


[[POTE generator]]: ~3/2 = 700.824
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.824


{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
Line 606: Line 586:
Comma list: 225/224, 385/384, 236328125/234365481
Comma list: 225/224, 385/384, 236328125/234365481


Mapping: [{{val| 1 0 34 63 -90 }}, {{val| 0 1 -20 -38 59 }}]
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


POTE generator: ~3/2 = 700.834
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.834


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}
Line 619: Line 599:
Comma list: 225/224, 325/324, 385/384, 831875/830466
Comma list: 225/224, 325/324, 385/384, 831875/830466


Mapping: [{{val| 1 0 34 63 -90 -66 }}, {{val| 0 1 -20 -38 59 44 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


POTE generator: ~3/2 = 700.841
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.841


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 632: Line 612:
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


Mapping: [{{val| 1 0 34 63 -90 -66 -7 }}, {{val| 0 1 -20 -38 59 44 7 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


POTE generator: ~3/2 = 700.841
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.841


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 645: Line 625:
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 }}, {{val| 0 1 -20 -38 59 44 7 -3 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


POTE generator: ~3/2 = 700.842
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.842


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 658: Line 638:
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


POTE generator: ~3/2 = 700.843
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.843


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}
Line 671: Line 651:
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


POTE generator: ~3/2 = 700.842
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.842


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}
Line 684: Line 664:
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 53 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


POTE generator: ~3/2 = 700.838
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.838


{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}
Line 697: Line 677:
Comma list: 225/224, 441/440, 109375/107811
Comma list: 225/224, 441/440, 109375/107811


Mapping: [{{val| 1 0 34 63 89 }}, {{val| 0 1 -20 -38 -54 }}]
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


POTE generator: ~3/2 = 700.885
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.885


{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}
{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}
Line 710: Line 690:
Comma list: 225/224, 364/363, 441/440, 6125/6084
Comma list: 225/224, 364/363, 441/440, 6125/6084


Mapping: [{{val| 1 0 34 63 89 113 }}, {{val| 0 1 -20 -38 -54 -69 }}]
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


POTE generator: ~3/2 = 700.890
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.890


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 723: Line 703:
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


Mapping: [{{val| 1 0 34 63 89 113 -7 }}, {{val| 0 1 -20 -38 -54 -69 7 }}]
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


POTE generator: ~3/2 = 700.870
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.870


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 736: Line 716:
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663


Mapping: [{{val| 1 0 34 63 89 113 -7 9 }}, {{val| 0 1 -20 -38 -54 -69 7 -3 }}]
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


POTE generator: ~3/2 = 700.866
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.866


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 745: Line 725:


== Alphorn ==
== Alphorn ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}


{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
{{Multival|legend=1| 16 -5 22 -45 -10 65 }}


[[POTE generator]]: ~48/35 = 556.221
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 556.221


{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
Line 764: Line 744:
Comma list: 225/224, 385/384, 12250/11979
Comma list: 225/224, 385/384, 12250/11979


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}


POTE generator: ~11/8 = 556.144
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 556.144


{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}
{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}
Line 775: Line 755:
: ''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 #Misneb]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}


{{Multival|legend=1|15 -14 2 -57 -39 44}}
{{Multival|legend=1| 15 -14 2 -57 -39 44 }}


[[POTE generator]]: ~16/15 = 113.235
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 113.235


{{Optimal ET sequence|legend=1| 21, 32, 53 }}
{{Optimal ET sequence|legend=1| 21, 32, 53 }}
Line 794: Line 774:
Comma list: 99/98, 176/175, 1310720/1294139
Comma list: 99/98, 176/175, 1310720/1294139


Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}


POTE generator: ~16/15 = 113.323
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.323


{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
Line 807: Line 787:
Comma list: 99/98, 176/175, 640/637, 847/845
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}}]
Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}


POTE generator: ~16/15 = 113.323
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.323


{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
Line 820: Line 800:
Comma list: 225/224, 385/384, 66550/64827
Comma list: 225/224, 385/384, 66550/64827


Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


POTE generator: ~16/15 = 113.142
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.142


{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}
{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}
Line 831: Line 811:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 125000000/121060821
[[Comma list]]: 225/224, 125000000/121060821


[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}


{{Multival|legend=1|9 -19 -20 -51 -57 7}}
{{Multival|legend=1| 9 -19 -20 -51 -57 7 }}


[[POTE generator]]: ~7/5 = 588.641
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 588.641


{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
Line 850: Line 830:
Comma list: 121/120, 225/224, 22000/21609
Comma list: 121/120, 225/224, 22000/21609


Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}


POTE generator: ~7/5 = 588.626
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 588.626


{{Optimal ET sequence|legend=1| 51, 53 }}
{{Optimal ET sequence|legend=1| 51, 53 }}
Line 863: Line 843:
Comma list: 121/120, 225/224, 275/273, 1040/1029
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}}]
Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}


POTE generator: ~7/5 = 588.654
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 588.654


{{Optimal ET sequence|legend=1| 51f, 53 }}
{{Optimal ET sequence|legend=1| 51f, 53 }}
Line 872: Line 852:


== Quintannic ==
== Quintannic ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 9805926501/9765625000
[[Comma list]]: 225/224, 9805926501/9765625000


[[Mapping]]: [{{val| 1 1 5 7 }}, {{val| 0 5 -23 -36 }}]
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}


{{Multival|legend=1| 5 -23 -36 -48 -71 -19 }}
{{Multival|legend=1| 5 -23 -36 -48 -71 -19 }}


[[POTE generator]]: ~10000/9261 = 139.838
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10000/9261 = 139.838


{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
Line 891: Line 871:
Comma list: 225/224, 441/440, 43923/43750
Comma list: 225/224, 441/440, 43923/43750


Mapping: [{{val| 1 1 5 7 8 }}, {{val| 0 5 -23 -36 -39 }}]
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


POTE generator: ~320/297 = 139.827
Optimal tuning (POTE): ~2 = 1\1, ~320/297 = 139.827


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 904: Line 884:
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
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 }}]
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


POTE generator: ~13/12 = 139.812
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.812


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 917: Line 897:
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
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 }}]
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


POTE generator: ~13/12 = 139.815
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.815


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 926: Line 906:


== Gwazy ==
== Gwazy ==
{{see also|Very high accuracy temperaments #Kwazy}}
{{See also| Very high accuracy temperaments #Kwazy }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 5971968/5764801
[[Comma list]]: 225/224, 5971968/5764801


[[Mapping]]: [{{val| 2 1 6 4 }}, {{val| 0 8 -5 6 }}]
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}


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


[[POTE generator]]: ~35/32 = 162.658
[[Optimal tuning]] ([[POTE]]): 1\2, ~35/32 = 162.658


{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
Line 947: Line 927:
Comma list: 99/98, 176/175, 65536/65219
Comma list: 99/98, 176/175, 65536/65219


Mapping: [{{val| 2 1 6 4 8 }}, {{val| 0 8 -5 6 -4 }}]
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


POTE generator: ~11/10 = 162.592
Optimal tuning (POTE): 1\2, ~11/10 = 162.592


{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
Line 958: Line 938:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 14495514624/13841287201
[[Comma list]]: 225/224, 14495514624/13841287201


[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}


{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
{{Multival|legend=1| 24 -21 6 -89 -58 73 }}


[[POTE generator]]: ~15/14 = 112.283
[[Optimal tuning]] ([[POTE]]): 1\3, ~15/14 = 112.283


{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
Line 977: Line 957:
Comma list: 225/224, 3840/3773, 12005/11979
Comma list: 225/224, 3840/3773, 12005/11979


Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}


POTE generator: ~15/14 = 112.171
Optimal tuning (POTE): 1\3, ~15/14 = 112.171


{{Optimal ET sequence|legend=1| 21, 54, 75e }}
{{Optimal ET sequence|legend=1| 21, 54, 75e }}
Line 986: Line 966:


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Marvel]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"