Xenharmonic Wiki

Jubilismic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
→Overview to extensions: expand and improve linking
m Update the keys
Line 2: Line 2:


== Jubilic ==
== Jubilic ==
The head of this clan, jubilic, is generated by an approximate [[5/4]]. That and a semioctave gives [[7/4]].  
The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave gives ~[[7/4]].  


[[Subgroup]]: 2.5.7
[[Subgroup]]: 2.5.7
Line 14: Line 14:
[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]


[[Optimal tuning]] ([[POTE]]) ~5/4 = 380.840
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.840


{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
{{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
Line 37: Line 37:
{{Main| Lemba }}
{{Main| Lemba }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 525/512
[[Comma list]]: 50/49, 525/512
Line 45: Line 45:
Mapping generators: ~7/5, ~8/7
Mapping generators: ~7/5, ~8/7


[[POTE generator]]: ~8/7 = 232.089
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089


{{Val list|legend=1| 10, 16, 26, 62c }}
{{Val list|legend=1| 10, 16, 26, 62c }}
Line 58: Line 58:
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]


POTE generator: ~8/7 = 230.974
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974


Optimal GPV sequence: {{Val list| 10, 16, 26 }}
Optimal GPV sequence: {{Val list| 10, 16, 26 }}
Line 71: Line 71:
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]


POTE generator: ~8/7 = 230.966
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966


Optimal GPV sequence: {{Val list| 10, 16, 26 }}
Optimal GPV sequence: {{Val list| 10, 16, 26 }}
Line 79: Line 79:
== Diminished ==
== Diminished ==
<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
{{see also|Dimipent family #Diminished}}
{{See also| Dimipent family #Diminished }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 50/49
[[Comma list]]: 36/35, 50/49
Line 89: Line 89:
Mapping generators: ~6/5, ~3
Mapping generators: ~6/5, ~3


[[POTE generator]]: ~3/2 = 699.523
[[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~3/2 = 699.523


{{Val list|legend=1| 4, 8d, 12 }}
{{Val list|legend=1| 4, 8d, 12 }}
Line 104: Line 104:
Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]
Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]


Mapping generators: ~6/5, ~3
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109
 
POTE generator: ~3/2 = 709.109


Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
Line 121: Line 119:
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]
Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]


Mapping generators: ~6/5, ~3
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773
 
POTE generator: ~3/2 = 713.773


Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}
Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}
Line 138: Line 134:
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]
Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]


Mapping generators: ~6/5, ~3
Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881
 
POTE generator: ~3/2 = 689.881


Optimal GPV sequence: {{Val list| 12, 28, 40de }}
Optimal GPV sequence: {{Val list| 12, 28, 40de }}
Line 157: Line 151:
Mapping generators: ~6/5, ~11/7
Mapping generators: ~6/5, ~11/7


POTE generator: ~12/11 = 101.679
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679


Optimal GPV sequence: {{Val list| 8bce, 12 }}
Optimal GPV sequence: {{Val list| 8bce, 12 }}
Line 170: Line 164:
Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}]
Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}]


POTE generator: ~12/11 = 102.299
Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299


Optimal GPV sequence: {{Val list| 8bcef, 12f }}
Optimal GPV sequence: {{Val list| 8bcef, 12f }}
Line 177: Line 171:


== Doublewide ==
== Doublewide ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 875/864
[[Comma list]]: 50/49, 875/864
Line 183: Line 177:
[[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]
[[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]


[[POTE generator]]: ~6/5 = 325.719
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719


{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}
{{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}
Line 196: Line 190:
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]


POTE generator: ~6/5 = 325.545
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545


Optimal GPV sequence: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}
Optimal GPV sequence: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}
Line 209: Line 203:
Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]
Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]


POTE generator: ~6/5 = 327.038
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038


Optimal GPV sequence: {{Val list| 4e, 18e, 22 }}
Optimal GPV sequence: {{Val list| 4e, 18e, 22 }}
Line 222: Line 216:
Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]


POTE generator: ~6/5 = 327.841
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841


Optimal GPV sequence: {{Val list| 4ef, 18e, 22, 84bddf }}
Optimal GPV sequence: {{Val list| 4ef, 18e, 22, 84bddf }}
Line 235: Line 229:
Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]
Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]


POTE generator: ~6/5 = 323.427
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427


Optimal GPV sequence: {{Val list| 22e, 26 }}
Optimal GPV sequence: {{Val list| 22e, 26 }}
Line 248: Line 242:
Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]


POTE generator: ~6/5 = 323.396
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396


Optimal GPV sequence: {{Val list| 22ef, 26 }}
Optimal GPV sequence: {{Val list| 22ef, 26 }}
Line 257: Line 251:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 8505/8192
[[Comma list]]: 50/49, 8505/8192
Line 265: Line 259:
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}


[[POTE generator]]: ~45/32 = 553.721
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~45/32 = 553.721


{{Val list|legend=1| 2, 24c, 26 }}
{{Val list|legend=1| 2, 24c, 26 }}
Line 278: Line 272:
Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]


POTE generator: ~11/8 = 553.882
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882


Optimal GPV sequence: {{Val list| 2, 24c, 26 }}
Optimal GPV sequence: {{Val list| 2, 24c, 26 }}
Line 291: Line 285:
Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]


POTE generator: ~11/8 = 553.892
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892


Optimal GPV sequence: {{Val list| 2f, 24cf, 26 }}
Optimal GPV sequence: {{Val list| 2f, 24cf, 26 }}
Line 298: Line 292:


== Crepuscular ==
== Crepuscular ==
{{see also| Fifive family #Crepuscular }}
{{See also| Fifive family #Crepuscular }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 4375/4374
[[Comma list]]: 50/49, 4375/4374


[[Mapping]]: [{{val|2 2 3 4}}, {{val|0 5 7 7}}]
[[Mapping]]: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]


{{Multival|legend=1|10 14 14 -1 -6 -7}}
{{Multival|legend=1|10 14 14 -1 -6 -7}}


[[POTE generator]]: ~27/25 = 140.349
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349


{{Val list|legend=1| 8d, 26, 34d, 60d }}
{{Val list|legend=1| 8d, 26, 34d, 60d }}
Line 319: Line 313:
Comma list: 50/49, 99/98, 864/847
Comma list: 50/49, 99/98, 864/847


Mapping: [{{val|2 2 3 4 6}}, {{val|0 5 7 7 4}}]
Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]


POTE generator: ~12/11 = 140.587
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587


Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
Line 332: Line 326:
Comma list: 50/49, 78/77, 99/98, 144/143
Comma list: 50/49, 78/77, 99/98, 144/143


Mapping: [{{val|2 2 3 4 6 6}}, {{val|0 5 7 7 4 6}}]
Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]


POTE generator: ~12/11 = 140.554
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554


Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
Line 343: Line 337:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 2240/2187
[[Comma list]]: 50/49, 2240/2187
Line 351: Line 345:
{{Multival|legend=1| 4 14 14 13 11 -7 }}
{{Multival|legend=1| 4 14 14 13 11 -7 }}


[[POTE generator]]: ~81/80 = 54.699
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~81/80 = 54.699


{{Val list|legend=1| 20cd, 22 }}
{{Val list|legend=1| 20cd, 22 }}
Line 364: Line 358:
Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]


POTE generator: ~81/80 = 55.184
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184


Optimal GPV sequence: {{Val list| 20cde, 22 }}
Optimal GPV sequence: {{Val list| 20cde, 22 }}
Line 377: Line 371:
Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]


POTE generator: ~81/80 = 54.435
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435


Optimal GPV sequence: {{Val list| 22 }}
Optimal GPV sequence: {{Val list| 22 }}
Line 384: Line 378:


== Bipyth ==
== Bipyth ==
{{see also| Archytas clan #Superpyth }}
{{See also| Archytas clan #Superpyth }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 20480/19683
[[Comma list]]: 50/49, 20480/19683
Line 394: Line 388:
{{Multival|legend=1| 2 18 18 24 23 -9 }}
{{Multival|legend=1| 2 18 18 24 23 -9 }}


[[POTE generator]]: ~3/2 = 709.437
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 709.437


{{Val list|legend=1| 10cd, 12cd, 22 }}
{{Val list|legend=1| 10cd, 12cd, 22 }}
Line 407: Line 401:
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]


POTE generator: ~3/2 = 709.310
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310


Optimal GPV sequence: {{Val list| 10cd, 12cde, 22 }}
Optimal GPV sequence: {{Val list| 10cd, 12cde, 22 }}
Line 414: Line 408:


== Sedecic ==
== Sedecic ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 50/49, 546875/524288
[[Comma list]]: 50/49, 546875/524288
Line 422: Line 416:
{{Multival|legend=1| 16 0 0 -37 -45 0 }}
{{Multival|legend=1| 16 0 0 -37 -45 0 }}


[[POTE generator]]: ~3/2 = 700.554
[[Optimal tuning]] ([[POTE]]): ~128/125 = 1\16, ~3/2 = 700.554


{{Val list|legend=1| 16, 32, 48 }}
{{Val list|legend=1| 16, 32, 48 }}
Line 435: Line 429:
Mapping: [{{val| 16 0 37 45 30 }}, {{val| 0 1 0 0 1 }}]
Mapping: [{{val| 16 0 37 45 30 }}, {{val| 0 1 0 0 1 }}]


POTE generator: ~3/2 = 700.331
Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331


Optimal GPV sequence: {{Val list| 16, 32, 48 }}
Optimal GPV sequence: {{Val list| 16, 32, 48 }}
Line 442: Line 436:


== Duodecim ==
== Duodecim ==
{{see also| Compton family #Duodecim }}
{{See also| Compton family #Duodecim }}


Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 36/35, 50/49, 64/63
[[Comma list]]: 36/35, 50/49, 64/63
Line 450: Line 444:
[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]


[[POTE generator]]: ~11/8 = 565.023
[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023


{{Val list|legend=1| 12, 24d, 36d }}
{{Val list|legend=1| 12, 24d, 36d }}
Line 457: Line 451:


== Vigintiduo ==
== Vigintiduo ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 50/49, 64/63, 245/243
[[Comma list]]: 50/49, 64/63, 245/243
Line 463: Line 457:
[[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
[[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]


[[POTE generator]]: ~11/8 = 557.563
[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\22, ~11/8 = 557.563


{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}
{{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}
Line 470: Line 464:


== Vigin ==
== Vigin ==
Subgroup: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


[[Comma list]]: 50/49, 55/54, 64/63, 99/98
[[Comma list]]: 50/49, 55/54, 64/63, 99/98
Line 476: Line 470:
[[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
[[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]


[[POTE generator]]: ~13/8 = 844.624
[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\22, ~13/8 = 844.624


{{Val list|legend=1| 22, 44 }}
{{Val list|legend=1| 22, 44 }}
Retrieved from "https://en.xen.wiki/w/Jubilismic_clan"