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Aberschismic temperaments: Difference between revisions

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→Artoneutral: extend to the 23-limit
Cmloegcmluin (talk | contribs)
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5,173 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 52: Line 52:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.039
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.039


{{Val list|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}
{{Optimal ET sequence|legend=1| 29, 70, 99, 722bc, 821bc, 920bc, 1019bc, 1118bbcc, 1217bbcc, 1316bbccd }}


[[Badness]]: 0.094603
[[Badness]]: 0.094603
Line 72: Line 72:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.263
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.263


{{Val list|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 167d, 213d, 259cdd, 305bcdd }}


[[Badness]]: 0.096123
[[Badness]]: 0.096123
Line 85: Line 85:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.250


Optimal GPV sequence: {{Val list| 17c, 29, 46, 167de, 213de, 259cdde }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 167de, 213de, 259cdde }}


Badness: 0.038624
Badness: 0.038624
Line 98: Line 98:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.214


Optimal GPV sequence: {{Val list| 17c, 29, 46, 121def, 167def, 213deff }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 121def, 167def, 213deff }}


Badness: 0.024732
Badness: 0.024732
Line 111: Line 111:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.229


Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}
{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 121defg, 167defg, 213deffg }}


Badness: 0.017863
Badness: 0.017863
Line 124: Line 124:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.135


Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness: 0.017356
Badness: 0.017356
Line 137: Line 137:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.141


Optimal GPV sequence: {{Val list| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75dfgh, 121defgh }}


Badness: 0.014065
Badness: 0.014065
Line 150: Line 150:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.123


Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}
{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg, 121defghh }}


Badness: 0.019065
Badness: 0.019065
Line 163: Line 163:
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.114


Optimal GPV sequence: {{Val list| 17cgh, 29g, 46h, 75dfg, 121defghh }}
{{Optimal ET sequence|legend=1| 17cgh, 29g, 46h, 75dfg, 121defghh }}


Badness: 0.016067
Badness: 0.016067
Line 183: Line 183:
[[Optimal tuning]] ([[POTE]]): ~50/49 = 1\29, ~5/4 = 388.646
[[Optimal tuning]] ([[POTE]]): ~50/49 = 1\29, ~5/4 = 388.646


{{Val list|legend=1| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


[[Badness]]: 0.103734
[[Badness]]: 0.103734
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Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.460
Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.460


Optimal GPV sequence: {{Val list| 29, 58, 87, 145 }}
{{Optimal ET sequence|legend=1| 29, 58, 87, 145 }}


Badness: 0.034291
Badness: 0.034291
Line 209: Line 209:
Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.354
Optimal tuning (POTE): ~45/44 = 1\29, ~5/4 = 388.354


Optimal GPV sequence: {{Val list| 29, 58, 87, 145, 232, 377cef }}
{{Optimal ET sequence|legend=1| 29, 58, 87, 145, 232, 377cef }}


Badness: 0.018591
Badness: 0.018591
Line 222: Line 222:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 140.493
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~160/147 = 140.493


{{Val list|legend=1| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


[[Badness]]: 0.179475
[[Badness]]: 0.179475
Line 235: Line 235:
Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.489
Optimal tuning (POTE): ~2 = 1\1, ~88/81 = 140.489


Optimal GPV sequence: {{Val list| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


Badness: 0.058678
Badness: 0.058678
Line 248: Line 248:
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496


Optimal GPV sequence: {{Val list| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


Badness: 0.032481
Badness: 0.032481
Line 261: Line 261:
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.497
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.497


Optimal GPV sequence: {{Val list| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


Badness: 0.021112
Badness: 0.021112
Line 274: Line 274:
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496
Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 140.496


Optimal GPV sequence: {{Val list| 94, 111, 205 }}
{{Optimal ET sequence|legend=1| 94, 111, 205 }}


Badness: 0.017273
Badness: 0.017273
Line 289: Line 289:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 242.453
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~147/128 = 242.453


{{Val list|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}
{{Optimal ET sequence|legend=1| 94, 99, 292, 391, 881bd, 1272bcd }}


[[Badness]]: 0.053760
[[Badness]]: 0.053760
Line 302: Line 302:
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4511
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4511


Optimal GPV sequence: {{Val list| 94, 198, 292, 490 }}
{{Optimal ET sequence|legend=1| 94, 198, 292, 490 }}


Badness: 0.064160
Badness: 0.064160
Line 315: Line 315:
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4448
Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 242.4448


Optimal GPV sequence: {{Val list| 94, 198, 490f }}
{{Optimal ET sequence|legend=1| 94, 198, 490f }}


Badness: 0.034834
Badness: 0.034834
Line 332: Line 332:
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1728/1225 = 588.582
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1728/1225 = 588.582


{{Val list|legend=1| 53, 157, 210 }}
{{Optimal ET sequence|legend=1| 53, 157, 210 }}


[[Badness]]: 0.131191
[[Badness]]: 0.131191
Line 345: Line 345:
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.545


Optimal GPV sequence: {{Val list| 53, 104c, 157 }}
{{Optimal ET sequence|legend=1| 53, 104c, 157 }}


Badness: 0.084782
Badness: 0.084782
Line 358: Line 358:
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544
Optimal tuning (POTE): ~2 = 1\1, ~108/77 = 588.544


Optimal GPV sequence: {{Val list| 53, 104c, 157 }}
{{Optimal ET sequence|legend=1| 53, 104c, 157 }}


Badness: 0.042321
Badness: 0.042321
Line 373: Line 373:
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~64/63 = 25.719
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~64/63 = 25.719


{{Val list|legend=1| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


[[Badness]]: 0.084538
[[Badness]]: 0.084538
Line 386: Line 386:
Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693
Optimal tuning (POTE): ~99/70 = 1\2, ~64/63 = 25.693


Optimal GPV sequence: {{Val list| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


Badness: 0.039555
Badness: 0.039555
Line 399: Line 399:
Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697
Optimal tuning (POTE): ~99/70 = 1\2, ~66/65 = 25.697


Optimal GPV sequence: {{Val list| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


Badness: 0.024824
Badness: 0.024824
Line 412: Line 412:
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.701


Optimal GPV sequence: {{Val list| 46, 94, 140 }}
{{Optimal ET sequence|legend=1| 46, 94, 140 }}


Badness: 0.016591
Badness: 0.016591
Line 425: Line 425:
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.660


Optimal GPV sequence: {{Val list| 46, 94, 140h, 234eh }}
{{Optimal ET sequence|legend=1| 46, 94, 140h, 234eh }}


Badness: 0.018170
Badness: 0.018170
Line 438: Line 438:
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661
Optimal tuning (POTE): ~17/12 = 1\2, ~66/65 = 25.661


Optimal GPV sequence: {{Val list| 46, 94, 140h, 234ehi }}
{{Optimal ET sequence|legend=1| 46, 94, 140h, 234ehi }}


Badness: 0.014033
Badness: 0.014033
Line 455: Line 455:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~105/64 = 855.2452
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~105/64 = 855.2452


{{Val list|legend=1| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


[[Badness]]: 0.157
[[Badness]]: 0.157
Line 468: Line 468:
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2397


Optimal GPV sequence: {{Val list| 87, 181 }}
{{Optimal ET sequence|legend=1| 87, 181 }}


Badness: 0.0459
Badness: 0.0459
Line 481: Line 481:
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2369


Optimal GPV sequence: {{Val list| 87, 181 }}
{{Optimal ET sequence|legend=1| 87, 181 }}


Badness: 0.0263
Badness: 0.0263
Line 494: Line 494:
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2495


Optimal GPV sequence: {{Val list| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


Badness: 0.0227
Badness: 0.0227
Line 507: Line 507:
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2534


Optimal GPV sequence: {{Val list| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


Badness: 0.0196
Badness: 0.0196
Line 520: Line 520:
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576
Optimal tuning (CTE): ~2 = 1\1, ~18/11 = 855.2576


Optimal GPV sequence: {{Val list| 87, 94, 181 }}
{{Optimal ET sequence|legend=1| 87, 94, 181 }}


Badness: 0.0163
Badness: 0.0163
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