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No-fives subgroup temperaments: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 14: Line 14:
[[Tp tuning|POL2 generator]]: ~7/6 = 250.385
[[Tp tuning|POL2 generator]]: ~7/6 = 250.385


{{Val list|legend=1| 5, 14, 19, 24, 67d, 91d }}
{{Optimal ET sequence|legend=1| 5, 14, 19, 24, 67d, 91d }}


[[Tp tuning #T2 tuning|RMS error]]: 2.523 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.523 cents
Line 65: Line 65:
[[Tp tuning|POL2 generator]]: ~12/11 = 139.990
[[Tp tuning|POL2 generator]]: ~12/11 = 139.990


{{Val list|legend=1| 17, 43, 60d }}
{{Optimal ET sequence|legend=1| 17, 43, 60d }}


[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
Line 84: Line 84:
[[Tp tuning|POL2 generator]]: ~3/2 = 709.321
[[Tp tuning|POL2 generator]]: ~3/2 = 709.321


{{Val list|legend=1| 5, 12, 17, 22, 27, 137bd }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 27, 137bd }}


[[Tp tuning #T2 tuning|RMS error]]: 1.856 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.856 cents
Line 101: Line 101:
[[Tp tuning|POL2 generator]]: ~3/2 = 707.192
[[Tp tuning|POL2 generator]]: ~3/2 = 707.192


{{Val list|legend=1| 5, 12, 17, 39d, 56d }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 39d, 56d }}


[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
Line 118: Line 118:
[[Tp tuning|POL2 generator]]: ~3/2 = 706.137
[[Tp tuning|POL2 generator]]: ~3/2 = 706.137


{{Val list|legend=1| 5f, 12f, 17, 22, 39d, 56d }}
{{Optimal ET sequence|legend=1| 5f, 12f, 17, 22, 39d, 56d }}


[[Tp tuning #T2 tuning|RMS error]]: 2.095 cents
[[Tp tuning #T2 tuning|RMS error]]: 2.095 cents
Line 135: Line 135:
[[Tp tuning|POL2 generator]]: ~11/9 = 353.958
[[Tp tuning|POL2 generator]]: ~11/9 = 353.958


{{Val list|legend=1| 7, 10, 17, 44e, 61de, 78de }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de, 78de }}


[[Tp tuning #T2 tuning|RMS error]]: 1.968 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.968 cents
Line 152: Line 152:
[[Tp tuning|POL2 generator]]: ~11/9 = 353.775
[[Tp tuning|POL2 generator]]: ~11/9 = 353.775


{{Val list|legend=1| 7, 10, 17, 44e, 61de, 78de }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 44e, 61de, 78de }}


[[Tp tuning #T2 tuning|RMS error]]: 1.953 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.953 cents
Line 169: Line 169:
[[Tp tuning|POL2 generator]]: ~9/7 = 425.365
[[Tp tuning|POL2 generator]]: ~9/7 = 425.365


{{Val list|legend=1| 14, 17, 31, 48, 79, 189b, 268bd, 347bd }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79, 189b, 268bd, 347bd }}


[[Tp tuning #T2 tuning|RMS error]]: 1.149 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.149 cents
Line 188: Line 188:
[[Tp tuning|POL2 generator]]: ~9/7 = 425.244
[[Tp tuning|POL2 generator]]: ~9/7 = 425.244


{{Val list|legend=1| 14, 17, 31, 48, 79, 127, 206bde }}
{{Optimal ET sequence|legend=1| 14, 17, 31, 48, 79, 127, 206bde }}


[[Tp tuning #T2 tuning|RMS error]]: 1.099 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.099 cents
Line 205: Line 205:
[[Tp tuning|POL2 generator]]: ~9/7 = 424.457
[[Tp tuning|POL2 generator]]: ~9/7 = 424.457


{{Val list|legend=1| 17, 48f, 65ef, 82d, 147df }}
{{Optimal ET sequence|legend=1| 17, 48f, 65ef, 82d, 147df }}


[[Tp tuning #T2 tuning|RMS error]]: 1.769 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.769 cents
Line 222: Line 222:
[[Tp tuning|POL2 generator]]: ~9/7 = 424.702
[[Tp tuning|POL2 generator]]: ~9/7 = 424.702


{{Val list|legend=1| 14, 17, 31 }}
{{Optimal ET sequence|legend=1| 14, 17, 31 }}


[[Tp tuning #T2 tuning|RMS error]]: 1.290 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.290 cents
Line 239: Line 239:
[[Tp tuning|POL2 generator]]: ~3/2 = 696.544
[[Tp tuning|POL2 generator]]: ~3/2 = 696.544


{{Val list|legend=1| 12, 19, 31, 112b, 143b, 174b }}
{{Optimal ET sequence|legend=1| 12, 19, 31, 112b, 143b, 174b }}


[[Tp tuning #T2 tuning|RMS error]]: 1.226 cents
[[Tp tuning #T2 tuning|RMS error]]: 1.226 cents
Line 260: Line 260:
[[Tp tuning|POL2 generator]]: ~3/2 = 704.721 cents
[[Tp tuning|POL2 generator]]: ~3/2 = 704.721 cents


{{Val list|legend=1| 17, 46, 63 }}
{{Optimal ET sequence|legend=1| 17, 46, 63 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.6202 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6202 cents
Line 279: Line 279:
[[Tp tuning|POL2 generator]]: ~3/2 = 704.753 cents
[[Tp tuning|POL2 generator]]: ~3/2 = 704.753 cents


{{Val list|legend=1| 17, 46, 63 }}
{{Optimal ET sequence|legend=1| 17, 46, 63 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.6047 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6047 cents
Line 296: Line 296:
[[Tp tuning|POL2 generator]]: ~3/2 = 704.745 cents
[[Tp tuning|POL2 generator]]: ~3/2 = 704.745 cents


{{Val list|legend=1| 17, 46, 63 }}
{{Optimal ET sequence|legend=1| 17, 46, 63 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.7541 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7541 cents
Line 313: Line 313:
[[Tp tuning|POL2 generator]]: ~3/2 = 704.729 cents
[[Tp tuning|POL2 generator]]: ~3/2 = 704.729 cents


{{Val list|legend=1| 17, 46, 63 }}
{{Optimal ET sequence|legend=1| 17, 46, 63 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.6265 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6265 cents
Line 330: Line 330:
[[Tp tuning|POL2 generator]]: ~3/2 = 704.729 cents
[[Tp tuning|POL2 generator]]: ~3/2 = 704.729 cents


{{Val list|legend=1| 17, 46, 63 }}
{{Optimal ET sequence|legend=1| 17, 46, 63 }}


; Music
; Music
Line 355: Line 355:
[[Tp tuning|POL2 generator]]: ~81/56 = 633.525
[[Tp tuning|POL2 generator]]: ~81/56 = 633.525


{{Val list|legend=1| 17, 36, 89, 125, 161, 358, 519b }}
{{Optimal ET sequence|legend=1| 17, 36, 89, 125, 161, 358, 519b }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents
Line 372: Line 372:
[[Tp tuning|POL2 generator]]: ~8/7 = 233.688
[[Tp tuning|POL2 generator]]: ~8/7 = 233.688


{{Val list|legend=1| 5, 21, 26, 31, 36, 77, 113, 190 }}
{{Optimal ET sequence|legend=1| 5, 21, 26, 31, 36, 77, 113, 190 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
Line 387: Line 387:
[[Tp tuning|POL2 generator]]: ~8/7 = 233.6044
[[Tp tuning|POL2 generator]]: ~8/7 = 233.6044


{{Val list|legend=1| 10, 26, 36, 154…, 190…, 226…, 262… }}
{{Optimal ET sequence|legend=1| 10, 26, 36, 154…, 190…, 226…, 262… }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5452 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5452 cents
Line 402: Line 402:
[[Tp tuning|POL2 generator]]: ~8/7 = 233.6155
[[Tp tuning|POL2 generator]]: ~8/7 = 233.6155


{{Val list|legend=1| 10, 26, 36, 154…, 190…, 226… }}
{{Optimal ET sequence|legend=1| 10, 26, 36, 154…, 190…, 226… }}


[[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents
Line 419: Line 419:
[[Tp tuning|POL2 generator]]: ~2187/1792 = 351.485
[[Tp tuning|POL2 generator]]: ~2187/1792 = 351.485


{{Val list|legend=1| 7, 17, 41, 58, 99 }}
{{Optimal ET sequence|legend=1| 7, 17, 41, 58, 99 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents
Line 438: Line 438:
[[Tp tuning|POL2 generator]]: ~11/9 = 351.535
[[Tp tuning|POL2 generator]]: ~11/9 = 351.535


{{Val list|legend=1| 7, 17, 41, 58, 99e }}
{{Optimal ET sequence|legend=1| 7, 17, 41, 58, 99e }}


[[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents
Line 455: Line 455:
[[Tp tuning|POL2 generator]]: ~11/9 = 351.691
[[Tp tuning|POL2 generator]]: ~11/9 = 351.691


{{Val list|legend=1| 7, 10, 17, 24, 41, 58 }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 58 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents
Line 472: Line 472:
[[Tp tuning|POL2 generator]]: ~99/98 = 17.6258
[[Tp tuning|POL2 generator]]: ~99/98 = 17.6258


{{Val list|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}
{{Optimal ET sequence|legend=1| 54, 63, 72, 135, 342, 477, 1089, 1566 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.0383 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.0383 cents
Line 491: Line 491:
[[Tp tuning|POL2 tuning]]: ~3 = 1903.834, ~7 = 3369.872
[[Tp tuning|POL2 tuning]]: ~3 = 1903.834, ~7 = 3369.872


{{Val list|legend=1| 17, 36, 41, 58, 63, 104 }}
{{Optimal ET sequence|legend=1| 17, 36, 41, 58, 63, 104 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.4149 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.4149 cents
Line 510: Line 510:
[[Tp tuning|POL2 tuning]]: ~3 = 1903.856, ~7 = 3369.907
[[Tp tuning|POL2 tuning]]: ~3 = 1903.856, ~7 = 3369.907


{{Val list|legend=1| 17, 41, 46, 58, 87, 104 }}
{{Optimal ET sequence|legend=1| 17, 41, 46, 58, 87, 104 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
Line 529: Line 529:
[[Tp tuning|POL2 generator]]: ~11/9 = 350.525
[[Tp tuning|POL2 generator]]: ~11/9 = 350.525


{{Val list|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
Line 551: Line 551:
[[Tp tuning|POL2 generator]]: ~11/9 = 351.488
[[Tp tuning|POL2 generator]]: ~11/9 = 351.488


{{Val list|legend=1| 7, 10, 17, 24, 41 }}
{{Optimal ET sequence|legend=1| 7, 10, 17, 24, 41 }}


[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents
Line 568: Line 568:
[[Tp tuning|POL2 generator]]: ~4/3 = 494.509
[[Tp tuning|POL2 generator]]: ~4/3 = 494.509


{{Val list|legend=1| 5, 12, 17 }}
{{Optimal ET sequence|legend=1| 5, 12, 17 }}


=== 2.3.7.41 subgroup ===
=== 2.3.7.41 subgroup ===
Line 583: Line 583:
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029


[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 49 }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}


=== 2.3.7.11.41 subgroup ===
=== 2.3.7.11.41 subgroup ===
Line 598: Line 598:
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454


[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 39d }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }}


== Magi ==
== Magi ==
Retrieved from "https://en.xen.wiki/w/No-fives_subgroup_temperaments"