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Fractional-octave temperaments: Difference between revisions

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m Added to category “lists of temperaments”
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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 99: Line 99:
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9420
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9420


{{Val list|legend=1| 176, 660, 836, 1848, 2684, 4532, 19976, 24508, 29040, 33572 }}
{{Optimal ET sequence|legend=1| 176, 660, 836, 1848, 2684, 4532, 19976, 24508, 29040, 33572 }}


[[Badness]]: 0.111
[[Badness]]: 0.111
Line 143: Line 143:
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9379
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9379


{{Val list|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5992, 8064, 26264, 34328b, 42392b }}
{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5992, 8064, 26264, 34328b, 42392b }}


[[Badness]]: 4.70
[[Badness]]: 4.70
Line 156: Line 156:
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9433
[[Optimal tuning]] ([[CTE]]): ~3/2 = 701.9433


{{Val list|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5768, 7616, 17080, 24696cd }}
{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 2072, 5768, 7616, 17080, 24696cd }}


[[Badness]]: 0.227
[[Badness]]: 0.227
Line 169: Line 169:
Optimal tuning (CTE): ~3/2 = 701.9431
Optimal tuning (CTE): ~3/2 = 701.9431


Optimal GPV sequence: {{Val list| 224, 1176, 1400, 1624, 1848, 3920, 5768, 7616, 21000cd, 28616cd }}
{{Optimal ET sequence|legend=1| 224, 1176, 1400, 1624, 1848, 3920, 5768, 7616, 21000cd, 28616cd }}


Badness: 0.0345
Badness: 0.0345
Line 227: Line 227:
[[Optimal tuning]] ([[POTE]]): ~7/4 = 969.1359
[[Optimal tuning]] ([[POTE]]): ~7/4 = 969.1359


{{Val list|legend=1| 65, 130 }}
{{Optimal ET sequence|legend=1| 65, 130 }}


[[Badness]]: 0.169778
[[Badness]]: 0.169778
Line 240: Line 240:
Optimal tuning (POTE): ~7/4 = 969.5715
Optimal tuning (POTE): ~7/4 = 969.5715


Optimal GPV sequence: {{Val list| 65d, 130 }}
{{Optimal ET sequence|legend=1| 65d, 130 }}


Badness: 0.059966
Badness: 0.059966
Line 253: Line 253:
Optimal tuning (POTE): ~7/4 = 969.9612
Optimal tuning (POTE): ~7/4 = 969.9612


Optimal GPV sequence: {{Val list| 65d, 130 }}
{{Optimal ET sequence|legend=1| 65d, 130 }}


Badness: 0.036267
Badness: 0.036267
Line 270: Line 270:
Optimal tuning (CTE): ~3/2 = 702.0195
Optimal tuning (CTE): ~3/2 = 702.0195


Optimal GPV sequence: {{Val list| 364, 819e, 1183, 1547 }}
{{Optimal ET sequence|legend=1| 364, 819e, 1183, 1547 }}


Badness: 0.0777
Badness: 0.0777
Line 283: Line 283:
Optimal tuning (CTE): ~3/2 = 702.0269
Optimal tuning (CTE): ~3/2 = 702.0269


Optimal GPV sequence: {{Val list| 364, 1183, 1547, 1911 }}
{{Optimal ET sequence|legend=1| 364, 1183, 1547, 1911 }}


Badness: 0.0582
Badness: 0.0582
Line 327: Line 327:
[[Optimal tuning]] ([[POTE]]): ~7/4 = 968.7235
[[Optimal tuning]] ([[POTE]]): ~7/4 = 968.7235


{{Val list|legend=1| 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b }}
{{Optimal ET sequence|legend=1| 118, 236, 354, 472, 2242, 2714b, 3186b, 3658b }}


[[Badness]]: 0.145166
[[Badness]]: 0.145166
Line 340: Line 340:
Optimal tuning (POTE): ~7/4 = 968.5117
Optimal tuning (POTE): ~7/4 = 968.5117


Optimal GPV sequence: {{Val list| 118, 354, 472 }}
{{Optimal ET sequence|legend=1| 118, 354, 472 }}


Badness: 0.049316
Badness: 0.049316
Line 357: Line 357:
Optimal tuning (CTE): ~202752/153125 = 484.4837
Optimal tuning (CTE): ~202752/153125 = 484.4837


Optimal GPV sequence: {{val list| 354, 944e, 1298 }}
{{Optimal ET sequence|legend=1| 354, 944e, 1298 }}


Badness: 0.357
Badness: 0.357
Line 370: Line 370:
Optimal tuning (CTE): ~8125/6144 = 484.4867
Optimal tuning (CTE): ~8125/6144 = 484.4867


Optimal GPV sequence: {{val list| 354, 944e, 1298 }}
{{Optimal ET sequence|legend=1| 354, 944e, 1298 }}


Badness: 0.122
Badness: 0.122
Line 389: Line 389:
[[Optimal tuning]] ([[CTE]]): ~1953125/1354752 = 634.0068
[[Optimal tuning]] ([[CTE]]): ~1953125/1354752 = 634.0068


{{Val list|legend=1| 354, 2360, 2714, 3068, 3442, 3776, 7198cd, 10974bccdd }}
{{Optimal ET sequence|legend=1| 354, 2360, 2714, 3068, 3442, 3776, 7198cd, 10974bccdd }}


[[Badness]]: 2.66
[[Badness]]: 2.66
Line 402: Line 402:
Optimal tuning (CTE): ~1953125/1354752 = 634.0085
Optimal tuning (CTE): ~1953125/1354752 = 634.0085


Optimal GPV sequence: {{Val list| 354, 3068e, 3442, 3776, 11682ccdde }}
{{Optimal ET sequence|legend=1| 354, 3068e, 3442, 3776, 11682ccdde }}


Badness: 0.568
Badness: 0.568
Line 417: Line 417:
Optimal tuning (CTE): ~1124864/779625 = 634.0087
Optimal tuning (CTE): ~1124864/779625 = 634.0087


Optimal GPV sequence: {{Val list| 354, 3068e, 3422, 3776 }}
{{Optimal ET sequence|legend=1| 354, 3068e, 3422, 3776 }}


Badness: 0.172
Badness: 0.172
Line 432: Line 432:
Optimal tuning (CTE): ~238/165 = 634.0080
Optimal tuning (CTE): ~238/165 = 634.0080


Optimal GPV sequence: {{Val list| 354, 3068e, 3422, 3776 }}
{{Optimal ET sequence|legend=1| 354, 3068e, 3422, 3776 }}


Badness: 0.105
Badness: 0.105
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