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Jubilismic clan: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Update keys and +descriptions for lemba and astrology
Line 8: Line 8:
[[Comma list]]: 50/49
[[Comma list]]: 50/49


[[Sval]] [[mapping]]: [{{val| 2 0 1 }}, {{val| 0 1 1 }}]
{{Mapping|legend=2| 2 0 1 | 0 1 1 }}


Sval mapping generators: ~7/5, ~5
: sval mapping generators: ~7/5, ~5


[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
[[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
Line 36: Line 36:
== Lemba ==
== Lemba ==
{{Main| Lemba }}
{{Main| Lemba }}
Lemba tempers out 1029/1024, the gamelisma, and a stack of three ~8/7 generators gives an approximate perfect fifth.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 41: Line 43:
[[Comma list]]: 50/49, 525/512
[[Comma list]]: 50/49, 525/512


[[Mapping]]: [{{val| 2 2 5 6 }}, {{val| 0 3 -1 -1 }}]
{{Mapping|legend=1| 2 2 5 6 | 0 3 -1 -1 }}


Mapping generators: ~7/5, ~8/7
: mapping generators: ~7/5, ~8/7


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089
Line 56: Line 58:
Comma list: 45/44, 50/49, 385/384
Comma list: 45/44, 50/49, 385/384


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


Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
Line 69: Line 71:
Comma list: 45/44, 50/49, 65/64, 78/77
Comma list: 45/44, 50/49, 65/64, 78/77


Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
Mapping: {{mapping| 2 2 5 6 5 7 | 0 3 -1 -1 5 1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
Line 78: Line 80:


== Astrology ==
== Astrology ==
{{See also| Magic family }}
Astrology tempers out 3125/3072, the magic comma, and a stack of five ~5/4 generators gives an approximate harmonic 3.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 84: Line 86:
[[Comma list]]: 50/49, 3125/3072
[[Comma list]]: 50/49, 3125/3072


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


Mapping geenerators: ~7/5, ~5/4
: mapping geenerators: ~7/5, ~5/4


{{Multival|legend=1| 10 2 2 -20 -25 -1 }}
{{Multival|legend=1| 10 2 2 -20 -25 -1 }}
Line 101: Line 103:
Comma list: 50/49, 121/120, 176/175
Comma list: 50/49, 121/120, 176/175


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


Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530
Line 114: Line 116:
Comma list: 50/49, 65/64, 78/77, 121/120
Comma list: 50/49, 65/64, 78/77, 121/120


Mapping: [{{val| 2 0 4 5 5 8 }}, {{val| 0 5 1 1 3 -1 }}]
Mapping: {{mapping| 2 0 4 5 5 8 | 0 5 1 1 3 -1 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787
Line 130: Line 132:
Comma list: 50/49, 66/65, 105/104, 121/120
Comma list: 50/49, 66/65, 105/104, 121/120


Mapping: [{{val| 2 0 4 5 5 3 }}, {{val| 0 5 1 1 3 7 }}]
Mapping: {{mapping| 2 0 4 5 5 3 | 0 5 1 1 3 7 }}


POTE generator: ~5/4 = 379.837
Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.837


{{Optimal ET sequence|legend=1| 16, 22f, 38 }}
{{Optimal ET sequence|legend=1| 16, 22f, 38 }}
Line 143: Line 145:
[[Comma list]]: 50/49, 875/864
[[Comma list]]: 50/49, 875/864


[[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]
{{Mapping|legend=1| 2 1 3 4 | 0 4 3 3 }}


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
Line 156: Line 158:
Comma list: 50/49, 99/98, 875/864
Comma list: 50/49, 99/98, 875/864


Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
Mapping: {{mapping| 2 1 3 4 8 | 0 4 3 3 -2 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
Line 169: Line 171:
Comma list: 50/49, 55/54, 176/175
Comma list: 50/49, 55/54, 176/175


Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]
Mapping: {{mapping| 2 1 3 4 2 | 0 4 3 3 9 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
Line 182: Line 184:
Comma list: 50/49, 55/54, 65/63, 176/175
Comma list: 50/49, 55/54, 65/63, 176/175


Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
Mapping: {{mapping| 2 1 3 4 2 3 | 0 4 3 3 9 8 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
Line 195: Line 197:
Comma list: 45/44, 50/49, 875/864
Comma list: 45/44, 50/49, 875/864


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


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
Line 208: Line 210:
Comma list: 45/44, 50/49, 78/77, 325/324
Comma list: 45/44, 50/49, 78/77, 325/324


Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
Mapping: {{mapping| 2 1 3 4 1 2 | 0 4 3 3 11 10 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
Line 223: Line 225:
[[Comma list]]: 50/49, 8505/8192
[[Comma list]]: 50/49, 8505/8192


[[Mapping]]: [{{val| 2 1 10 11 }}, {{val| 0 2 -5 -5 }}]
{{Mapping|legend=1| 2 1 10 11 | 0 2 -5 -5 }}


{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
{{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
Line 238: Line 240:
Comma list: 45/44, 50/49, 1344/1331
Comma list: 45/44, 50/49, 1344/1331


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


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
Line 251: Line 253:
Comma list: 45/44, 50/49, 78/77, 1053/1024
Comma list: 45/44, 50/49, 78/77, 1053/1024


Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
Mapping: {{mapping| 2 1 10 11 8 16 | 0 2 -5 -5 -1 -8 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
Line 266: Line 268:
[[Comma list]]: 50/49, 4375/4374
[[Comma list]]: 50/49, 4375/4374


[[Mapping]]: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]
{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}


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


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
Line 281: Line 283:
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: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
Line 294: Line 296:
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: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
Line 309: Line 311:
[[Comma list]]: 50/49, 2240/2187
[[Comma list]]: 50/49, 2240/2187


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


{{Multival|legend=1| 4 14 14 13 11 -7 }}
{{Multival|legend=1| 4 14 14 13 11 -7 }}
Line 324: Line 326:
Comma list: 50/49, 99/98, 2662/2625
Comma list: 50/49, 99/98, 2662/2625


Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
Mapping: {{mapping| 2 1 -3 -2 -4 | 0 2 7 7 10 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
Line 337: Line 339:
Comma list: 50/49, 65/63, 99/98, 968/945
Comma list: 50/49, 65/63, 99/98, 968/945


Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
Mapping: {{mapping| 2 1 -3 -2 -4 3 | 0 2 7 7 10 4 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
Line 352: Line 354:
[[Comma list]]: 50/49, 20480/19683
[[Comma list]]: 50/49, 20480/19683


[[Mapping]]: [{{val| 2 0 -24 -23 }}, {{val| 0 1 9 9 }}]
{{Mapping|legend=1| 2 0 -24 -23 | 0 1 9 9 }}


{{Multival|legend=1| 2 18 18 24 23 -9 }}
{{Multival|legend=1| 2 18 18 24 23 -9 }}
Line 367: Line 369:
Comma list: 50/49, 121/120, 896/891
Comma list: 50/49, 121/120, 896/891


Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
Mapping: {{mapping| 2 0 -24 -23 -9 | 0 1 9 9 5 }}


Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
Line 380: Line 382:
[[Comma list]]: 50/49, 546875/524288
[[Comma list]]: 50/49, 546875/524288


[[Mapping]]: [{{val| 16 0 37 45 }}, {{val| 0 1 0 0 }}]
{{Mapping|legend=1| 16 0 37 45 | 0 1 0 0 }}


{{Multival|legend=1| 16 0 0 -37 -45 0 }}
{{Multival|legend=1| 16 0 0 -37 -45 0 }}
Line 395: Line 397:
Comma list: 50/49, 385/384, 1331/1323
Comma list: 50/49, 385/384, 1331/1323


Mapping: [{{val| 16 0 37 45 30 }}, {{val| 0 1 0 0 1 }}]
Mapping: {{mapping| 16 0 37 45 30 | 0 1 0 0 1 }}


Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
Line 410: Line 412:
[[Comma list]]: 36/35, 50/49, 64/63
[[Comma list]]: 36/35, 50/49, 64/63


[[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 12 19 28 34 0 | 0 0 0 0 1 }}


[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
Line 423: Line 425:
[[Comma list]]: 50/49, 64/63, 245/243
[[Comma list]]: 50/49, 64/63, 245/243


[[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
{{Mapping|legend=1| 22 35 51 62 0 | 0 0 0 0 1 }}


[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\22, ~11/8 = 557.563
[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\22, ~11/8 = 557.563
Line 436: Line 438:
[[Comma list]]: 50/49, 55/54, 64/63, 99/98
[[Comma list]]: 50/49, 55/54, 64/63, 99/98


[[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
{{Mapping|legend=1| 22 35 51 62 76 0 | 0 0 0 0 0 1 }}


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