Marvel temperaments: Difference between revisions
→Decic: added nice range and strict range Tags: Mobile edit Mobile web edit |
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== 5-limit == | == 5-limit == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 31: | Line 20: | ||
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}] | [[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}] | ||
{{Multival|legend=1| 4 -3 -14 }} | |||
[[POTE generator]]: ~16/15 = 125.7549 | |||
{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }} | {{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }} | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 56: | Line 34: | ||
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}] | [[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}] | ||
{{Multival|legend=1| 4 -3 2 -14 -8 13 }} | |||
[[POTE generator]]: ~15/14 = 125.608 | |||
{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }} | {{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }} | ||
=== Negra === | === Negra === | ||
This is the 2.3.5.7.13 extension of negri. | This is the 2.3.5.7.13 extension of negri. | ||
Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.13 | ||
| Line 81: | Line 47: | ||
[[Comma list]]: 49/48, 65/64, 91/90 | [[Comma list]]: 49/48, 65/64, 91/90 | ||
[[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}] | [[Sval]] [[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}] | ||
Gencom mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}] | |||
Gencom | [[Gencom]]: [2 14/13; 49/48 65/64 91/90] | ||
POTE generator: ~14/13 = 125.567 | |||
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }} | {{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }} | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 109: | Line 64: | ||
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}] | Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}] | ||
POTE generator: ~15/14 = 126.474 | |||
{{Val list|legend=1| 9, 10, 19 }} | {{Val list|legend=1| 9, 10, 19 }} | ||
Badness: 0.0262 | |||
</div></div> | </div></div> | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 133: | Line 79: | ||
Comma list: 45/44, 49/48, 56/55, 78/77 | Comma list: 45/44, 49/48, 56/55, 78/77 | ||
[ | Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}] | ||
POTE generator: ~14/13 = 126.431 | |||
{{Val list|legend=1| 9, 10, 19 }} | {{Val list|legend=1| 9, 10, 19 }} | ||
== Negril == | == Negril == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 159: | Line 92: | ||
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}] | Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}] | ||
POTE generator: ~15/14 = 124.767 | |||
{{Val list|legend=1| 19, 29, 48d, 77cdd }} | {{Val list|legend=1| 19, 29, 48d, 77cdd }} | ||
Badness: 0.0387 | Badness: 0.0387 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 184: | Line 106: | ||
Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}] | Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}] | ||
POTE generator: ~14/13 = 124.716 | |||
{{Val list|legend=1| 19, 29, 48df, 77cddf }} | {{Val list|legend=1| 19, 29, 48df, 77cddf }} | ||
Badness: 0.0244 | Badness: 0.0244 | ||
== Negric == | == Negric == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 209: | Line 120: | ||
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}] | Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}] | ||
POTE generator: ~15/14 = 127.039 | |||
{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }} | {{Val list|legend=1| 9, 19e, 47…, 66…, 85… }} | ||
Badness: 0.0306 | Badness: 0.0306 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 234: | Line 134: | ||
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}] | Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}] | ||
POTE generator: ~14/13 = 127.039 | |||
{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }} | {{Val list|legend=1| 9, 19e, 47…, 66…, 85… }} | ||
Badness: 0.0202 | Badness: 0.0202 | ||
== Negroni == | == Negroni == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 259: | Line 148: | ||
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}] | Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}] | ||
POTE generator: ~15/14 = 124.539 | |||
{{Val list|legend=1| 10, 19e, 29, 77cddee }} | {{Val list|legend=1| 10, 19e, 29, 77cddee }} | ||
Badness: 0.0353 | Badness: 0.0353 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 284: | Line 162: | ||
Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}] | Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}] | ||
POTE generator: ~14/13 = 124.545 | |||
{{Val list|legend=1| 10, 19e, 29, 77cddeef }} | {{Val list|legend=1| 10, 19e, 29, 77cddeef }} | ||
Badness: 0.0216 | Badness: 0.0216 | ||
== Wilsec == | == Wilsec == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 309: | Line 176: | ||
Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}] | Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}] | ||
POTE generator: ~11/8 = 537.186 | |||
{{Val list|legend=1| 9, 20, 29, 38d, 67cdde }} | {{Val list|legend=1| 9, 20, 29, 38d, 67cdde }} | ||
Badness: 0.0419 | Badness: 0.0419 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 334: | Line 190: | ||
Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}] | Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}] | ||
POTE generator: ~11/8 = 537.208 | |||
{{Val list|legend=1| 9, 20, 29, 38df, 67cddef }} | {{Val list|legend=1| 9, 20, 29, 38df, 67cddef }} | ||
Badness: 0.0252 | Badness: 0.0252 | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 359: | Line 204: | ||
Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}] | Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}] | ||
POTE generator: ~11/8 = 537.230 | |||
{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }} | {{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }} | ||
Badness: 0.0218 | Badness: 0.0218 | ||
=== 19-limit === | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 384: | Line 218: | ||
Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}] | Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}] | ||
POTE generator: ~11/8 = 537.214 | |||
{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }} | {{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }} | ||
Badness: 0.0168 | Badness: 0.0168 | ||
= Passive = | = Passive = | ||
{{see also | Archytas clan #Passion }} | {{see also | Archytas clan #Passion }} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 256/245 | |||
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}] | |||
[[POTE generator]]: ~16/15 = 98.809 | |||
{{Val list|legend=1| 12, 49dd }} | {{Val list|legend=1| 12, 49dd }} | ||
Badness: 0.0751 | [[Badness]]: 0.0751 | ||
= Wizard = | = 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]]: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}] | ||
Mapping generators: ~1225/864, ~245/216 | Mapping generators: ~1225/864, ~245/216 | ||
[[POTE generator]]: ~5/4 = 383.256 | |||
{{Multival|legend=1| 12 -2 20 -31 -2 52 }} | |||
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }} | {{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }} | ||
Badness: 0.0408 | [[Badness]]: 0.0408 | ||
Scales: [[wizard22]] | |||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 471: | Line 271: | ||
Mapping generators: ~99/70, ~25/22 | Mapping generators: ~99/70, ~25/22 | ||
POTE generator: ~5/4 = 383.232 | |||
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }} | {{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }} | ||
| Line 476: | Line 278: | ||
Badness: 0.0185 | Badness: 0.0185 | ||
Scales: [[wizard22]] | |||
=== Lizard === | === Lizard === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 499: | Line 289: | ||
Mapping generators: ~99/70, ~25/22 | Mapping generators: ~99/70, ~25/22 | ||
POTE generator: ~5/4 = 383.389 | |||
{{Val list|legend=1| 22, 50, 72, 122, 194df }} | {{Val list|legend=1| 22, 50, 72, 122, 194df }} | ||
Badness: 0.0218 | Badness: 0.0218 | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 527: | Line 305: | ||
Mapping generators: ~17/12, ~17/15 | Mapping generators: ~17/12, ~17/15 | ||
POTE generator: ~5/4 = 383.381 | |||
{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }} | {{Val list|legend=1| 22, 50, 72, 122g, 194dfg }} | ||
| Line 535: | Line 315: | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 555: | Line 323: | ||
Mapping generators: ~17/12, ~17/15 | Mapping generators: ~17/12, ~17/15 | ||
POTE generator: ~5/4 = 383.477 | |||
{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }} | {{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }} | ||
| Line 563: | Line 333: | ||
=== Gizzard === | === Gizzard === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 583: | Line 341: | ||
Mapping generators: ~99/70, ~25/22 | Mapping generators: ~99/70, ~25/22 | ||
POTE generator: ~5/4 = 383.170 | |||
{{Val list|legend=1| 72, 166, 238cf }} | {{Val list|legend=1| 72, 166, 238cf }} | ||
| Line 591: | Line 351: | ||
==== 17-limit ==== | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 611: | Line 359: | ||
Mapping generators: ~17/12, ~17/15 | Mapping generators: ~17/12, ~17/15 | ||
POTE generator: ~5/4 = 383.175 | |||
{{Val list|legend=1| 72, 166g, 238cfg }} | {{Val list|legend=1| 72, 166g, 238cfg }} | ||
| Line 619: | Line 369: | ||
==== 19-limit ==== | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 639: | Line 377: | ||
Mapping generators: ~17/12, ~17/15 | Mapping generators: ~17/12, ~17/15 | ||
POTE generator: ~5/4 = 383.138 | |||
{{Val list|legend=1| 72, 94, 166g }} | {{Val list|legend=1| 72, 94, 166g }} | ||
Badness: 0.0148 | Badness: 0.0148 | ||
== Mage == | == Mage == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 667: | Line 393: | ||
Mapping generators: ~77/54, ~55/48 | Mapping generators: ~77/54, ~55/48 | ||
POTE generator: ~5/4 = 383.124 | |||
{{Val list|legend=1| 22, 50e, 72ee, 94ee }} | {{Val list|legend=1| 22, 50e, 72ee, 94ee }} | ||
Badness: 0.0578 | Badness: 0.0578 | ||
= Triton = | = Triton = | ||
| Line 678: | Line 404: | ||
: ''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 | |||
[[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| 19, 78bd, 97bd }} | {{Val list|legend=1| 19, 78bd, 97bd }} | ||
Badness: 0.0592 | [[Badness]]: 0.0592 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 723: | Line 425: | ||
Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}] | Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}] | ||
POTE generator: ~7/5 = 569.144 | |||
{{Val list|legend=1| 19, 59bde, 78bde, 97bde }} | {{Val list|legend=1| 19, 59bde, 78bde, 97bde }} | ||
Badness: 0.0457 | Badness: 0.0457 | ||
= Tritonic = | = Tritonic = | ||
| Line 734: | Line 436: | ||
: ''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 | |||
[[Comma list]]: 225/224, 50421/50000 | |||
[[Mapping]]: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}] | |||
{{Multival|legend=1| 5 -11 -12 -29 -33 3 }} | |||
[[POTE generator]]: ~7/5 = 580.286 | |||
{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }} | {{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }} | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 777: | Line 455: | ||
Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}] | Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}] | ||
POTE generator: ~7/5 = 580.267 | |||
{{Val list|legend=1| 29, 31, 60e }} | {{Val list|legend=1| 29, 31, 60e }} | ||
Badness: 0.0237 | Badness: 0.0237 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 803: | Line 469: | ||
Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}] | Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}] | ||
POTE generator: ~7/5 = 580.108 | |||
{{Val list|legend=1| 29, 31, 60e, 151cde }} | {{Val list|legend=1| 29, 31, 60e, 151cde }} | ||
Badness: 0.0230 | Badness: 0.0230 | ||
== Tritoni == | == Tritoni == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 829: | Line 483: | ||
Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}] | Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}] | ||
POTE generator: ~7/5 = 580.389 | |||
{{Val list|legend=1| 31, 91, 122, 153d }} | {{Val list|legend=1| 31, 91, 122, 153d }} | ||
Badness: 0.0455 | Badness: 0.0455 | ||
= Merman = | = Merman = | ||
| Line 840: | Line 494: | ||
: ''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 | |||
[[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 }} | {{Val list|legend=1| 41, 84, 125 }} | ||
Badness: 0.0551 | [[Badness]]: 0.0551 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 885: | Line 515: | ||
Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}] | Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}] | ||
POTE generator: ~7/5 = 585.606 | |||
{{Val list|legend=1| 41, 84, 125e }} | {{Val list|legend=1| 41, 84, 125e }} | ||
Badness: 0.0364 | Badness: 0.0364 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 911: | Line 529: | ||
Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}] | Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}] | ||
POTE generator: ~7/5 = 585.657 | |||
{{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }} | {{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }} | ||
Badness: 0.0275 | Badness: 0.0275 | ||
= Septimin = | = Septimin = | ||
| Line 922: | Line 540: | ||
: ''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 | |||
[[Comma list]]: 225/224, 84035/82944 | |||
[[Mapping]]: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}] | |||
{{Multival|legend=1| 11 -6 10 -35 -15 40 }} | |||
[[POTE generator]]: ~7/6 = 263.632 | |||
{{Val list|legend=1| 41, 91, 132 }} | {{Val list|legend=1| 41, 91, 132 }} | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 965: | Line 559: | ||
Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}] | Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}] | ||
POTE generator: ~7/6 = 263.634 | |||
{{Val list|legend=1| 41, 91, 223cdef }} | {{Val list|legend=1| 41, 91, 223cdef }} | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 989: | Line 571: | ||
Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}] | Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}] | ||
POTE generator: ~7/6 = 263.700 | |||
{{Val list|legend=1| 41, 91 }} | {{Val list|legend=1| 41, 91 }} | ||
= Slender = | = Slender = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 589824/588245 | |||
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}] | |||
{{Multival|legend=1| 13 -10 6 -46 -27 42 }} | |||
[[POTE generator]]: ~49/48 = 38.413 | |||
{{Val list|legend=1| 31, 94, 125 }} | {{Val list|legend=1| 31, 94, 125 }} | ||
Badness: 0.0569 | [[Badness]]: 0.0569 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,041: | Line 599: | ||
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}] | Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}] | ||
POTE generator: ~49/48 = 38.387 | |||
{{Val list|legend=1| 31, 63, 94, 125 }} | {{Val list|legend=1| 31, 63, 94, 125 }} | ||
Badness: 0.02534 | Badness: 0.02534 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,067: | Line 613: | ||
Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}] | Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}] | ||
POTE generator: ~49/48 = 38.314 | |||
{{Val list|legend=1| 31, 63, 94 }} | {{Val list|legend=1| 31, 63, 94 }} | ||
Badness: 0.02591 | Badness: 0.02591 | ||
= Marvo = | = Marvo = | ||
{{see also| Gravity family }} | {{see also| Gravity family }} | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,095: | Line 629: | ||
Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}] | Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}] | ||
{{Multival|legend=1| 6 17 46 13 56 59 }} | |||
POTE generator: ~27/20 = 516.694 | |||
{{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }} | {{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }} | ||
Badness: 0.0976 | Badness: 0.0976 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,122: | Line 644: | ||
Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}] | Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}] | ||
POTE generator: ~27/20 = 516.699 | |||
{{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }} | {{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }} | ||
Badness: 0.0317 | Badness: 0.0317 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,148: | Line 658: | ||
Mapping: [{{val| 1 5 12 29 12 39 }}, {{val| 0 -6 -17 -46 -15 -62 }}] | Mapping: [{{val| 1 5 12 29 12 39 }}, {{val| 0 -6 -17 -46 -15 -62 }}] | ||
POTE generator: ~27/20 = 516.730 | |||
{{Val list|legend=1| 65d, 72, 137, 209, 281f, 490bcf }} | {{Val list|legend=1| 65d, 72, 137, 209, 281f, 490bcf }} | ||
Badness: 0.0269 | Badness: 0.0269 | ||
= Marvolo = | = Marvolo = | ||
Subgroup: 2.3.5.7 | |||
[[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 }} | {{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }} | ||
Badness: 0.0833 | [[Badness]]: 0.0833 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,202: | Line 688: | ||
Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}] | Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}] | ||
POTE generator: ~21/20 = 83.340 | |||
{{Val list|legend=1| 29, 43, 72 }} | {{Val list|legend=1| 29, 43, 72 }} | ||
| Line 1,210: | Line 698: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,228: | Line 704: | ||
Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}] | Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}] | ||
POTE generator: ~21/20 = 83.330 | |||
{{Val list|legend=1| 29, 43, 72, 115f }} | {{Val list|legend=1| 29, 43, 72, 115f }} | ||
| Line 1,238: | Line 716: | ||
== 5-limit (mabila) == | == 5-limit (mabila) == | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 268435456/263671875 | |||
[[Mapping]]: [{{val| 1 6 1 }}, {{val| 0 -10 3 }}] | |||
[[POTE generator]]: ~512/375 = 529.6849 | |||
{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }} | {{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }} | ||
Badness: 0.2325 | [[Badness]]: 0.2325 | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 17496/16807 | |||
[[Mapping]]: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}] | |||
{{Multival|legend=1| 10 -3 14 -28 -6 41 }} | |||
[[POTE generator]]: ~48/35 = 529.979 | |||
{{Val list|legend=1| 9, 25d, 34d, 43, 77d }} | {{Val list|legend=1| 9, 25d, 34d, 43, 77d }} | ||
Badness: 0.1096 | [[Badness]]: 0.1096 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,309: | Line 751: | ||
Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}] | Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}] | ||
POTE generator: ~15/11 = 529.974 | |||
{{Val list|legend=1| 9, 34d, 43, 77de }} | {{Val list|legend=1| 9, 34d, 43, 77de }} | ||
Badness: 0.0426 | Badness: 0.0426 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,335: | Line 765: | ||
Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}] | Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}] | ||
POTE generator: ~15/11 = 529.951 | |||
{{Val list|legend=1| 9, 34d, 43, 77de }} | {{Val list|legend=1| 9, 34d, 43, 77de }} | ||
Badness: 0.0258 | Badness: 0.0258 | ||
= Enneaportent = | = Enneaportent = | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 40353607/40310784 | |||
[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}] | |||
{{Multival|legend=1| 18 -9 18 -56 -22 67 }} | |||
[[POTE generator]]: ~5/4 = 383.165 | |||
{{Val list|legend=1| 63, 72, 495bcd }} | {{Val list|legend=1| 63, 72, 495bcd }} | ||
Badness: 0.0937 | [[Badness]]: 0.0937 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,389: | Line 795: | ||
Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}] | Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}] | ||
POTE generator: ~5/4 = 383.146 | |||
{{Val list|legend=1| 63, 72, 423cd, 495bcd }} | {{Val list|legend=1| 63, 72, 423cd, 495bcd }} | ||
| Line 1,397: | Line 805: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,415: | Line 811: | ||
Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}] | Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}] | ||
POTE generator: ~5/4 = 383.047 | |||
{{Val list|legend=1| 63, 72, 279cf }} | {{Val list|legend=1| 63, 72, 279cf }} | ||
| Line 1,425: | Line 823: | ||
== 5-limit == | == 5-limit == | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 69198046875/68719476736 | |||
[[Mapping]]: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}] | |||
[[POTE generator]]: ~10125/8192 = 362.321 | |||
{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}} | {{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}} | ||
Badness: 0.1302 | [[Badness]]: 0.1302 | ||
== 7-limit == | == 7-limit == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 225/224, 51200/50421 | |||
[[Mapping]]: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}] | |||
{{Multival|legend=1| 8 -11 -6 -36 -32 17 }} | |||
[[POTE generator]]: ~49/40 = 362.255 | |||
{{Val list|legend=1| 10, 33, 43, 53 }} | {{Val list|legend=1| 10, 33, 43, 53 }} | ||
Badness: 0.0605 | [[Badness]]: 0.0605 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,496: | Line 858: | ||
Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}] | Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}] | ||
POTE generator: ~27/22 = 362.101 | |||
{{Val list|legend=1| 53, 116, 169de, 285cde }} | {{Val list|legend=1| 53, 116, 169de, 285cde }} | ||
Badness: 0.0506 | Badness: 0.0506 | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,522: | Line 872: | ||
Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}] | Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}] | ||
POTE generator: ~16/13 = 362.105 | |||
{{Val list|legend=1| 53, 116, 169de, 285cdef }} | {{Val list|legend=1| 53, 116, 169de, 285cdef }} | ||
| Line 1,530: | Line 882: | ||
== Interpental == | == Interpental == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,550: | Line 890: | ||
Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}] | Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}] | ||
POTE generator: ~49/40 = 362.418 | |||
{{Val list|legend=1| 43, 53, 96, 149d }} | {{Val list|legend=1| 43, 53, 96, 149d }} | ||
| Line 1,558: | Line 900: | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,578: | Line 908: | ||
Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 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 | |||
{{Val list|legend=1| 43, 53, 96, 149d }} | {{Val list|legend=1| 43, 53, 96, 149d }} | ||
| Line 1,586: | Line 918: | ||
= Alphorn = | = 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 }} | {{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }} | ||
Badness: 0.1293 | [[Badness]]: 0.1293 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,630: | Line 940: | ||
Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}] | Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}] | ||
POTE generator: ~11/8 = 556.144 | |||
{{Val list|legend=1| 28d, 41, 315cde }} | {{Val list|legend=1| 28d, 41, 315cde }} | ||
Badness: 0.0735 | Badness: 0.0735 | ||
= Decic = | = Decic = | ||
The ''decic'' temperament (10&50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order. | The ''decic'' temperament (10&50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,662: | Line 959: | ||
{{Multival|legend=1| 10 -10 0 -39 -28 28 }} | {{Multival|legend=1| 10 -10 0 -39 -28 28 }} | ||
[[POTE generator]]: ~3/2 = 698.696 | |||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
| Line 1,671: | Line 970: | ||
[[Badness]]: 0.089135 | [[Badness]]: 0.089135 | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,696: | Line 981: | ||
Mapping generators: ~15/14, ~3 | Mapping generators: ~15/14, ~3 | ||
POTE generator: ~3/2 = 696.791 | |||
Tuning ranges: | |||
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* nice range: ~3/2 = [689.363, 702.512] | * nice range: ~3/2 = [689.363, 702.512] | ||
| Line 1,704: | Line 991: | ||
Badness: 0.063900 | Badness: 0.063900 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,728: | Line 1,002: | ||
Mapping generators: ~14/13, ~3 | Mapping generators: ~14/13, ~3 | ||
POTE generator: ~3/2 = 696.993 | |||
Tuning ranges: | |||
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* nice range: ~3/2 = [689.363, 702.512] | * nice range: ~3/2 = [689.363, 702.512] | ||
| Line 1,736: | Line 1,012: | ||
Badness: 0.036880 | Badness: 0.036880 | ||
== 17-limit == | == 17-limit == | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 1,760: | Line 1,023: | ||
Mapping generators: ~14/13, ~3 | Mapping generators: ~14/13, ~3 | ||
POTE generator: ~3/2 = 697.085 | |||
Tuning ranges: | |||
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | * valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60) | ||
* nice range: ~3/2 = [689.363, 704.955] | * nice range: ~3/2 = [689.363, 704.955] | ||
| Line 1,768: | Line 1,033: | ||
Badness: 0.025064 | Badness: 0.025064 | ||
[[Category:Theory]] | [[Category:Theory]] | ||