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User:Contribution/Successive superparticular complementary pair: Difference between revisions

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Line 18: Line 18:
|+
|+
|-
|-
! colspan="3" | Tuning !! colspan="2" | Intervals !! colspan="2" | Mappings !! colspan="2" | Various optimizations (cent)
! colspan="3" | Tuning !! colspan="2" | Intervals !! colspan="2" | Mappings  
|-
|-
! Name
! Name
Line 27: Line 27:
! Steps (Equave, SSC pair)
! Steps (Equave, SSC pair)
! Errors (cent)
! Errors (cent)
! Pure Equave
! Dave Benson
|-
|-
| [[Alpha 3/1]]
| [[Alpha 3/1]]
Line 37: Line 35:
| 3\3<3/1>, 2\3<3/1>, 1\3<3/1>
| 3\3<3/1>, 2\3<3/1>, 1\3<3/1>
| 0, 67.970, -67.970
| 0, 67.970, -67.970
| 633.985000288462
| 629.130000247254
|-
|-
| [[Beta 3/1]]
| [[Beta 3/1]]
Line 45: Line 41:
| 5\5<3/1>, 3\5<3/1>, 2\5<3/1>
| 5\5<3/1>, 3\5<3/1>, 2\5<3/1>
| 0, -58.827, 58.827
| 0, -58.827, 58.827
| 380.391000173077
| 381.939079106782
|-
|-
| [[Gamma 3/1]]
| [[Gamma 3/1]]
Line 53: Line 47:
| 8\8<3/1>, 5\8<3/1>, 3\8<3/1>
| 8\8<3/1>, 5\8<3/1>, 3\8<3/1>
| 0, -11.278, 11.278
| 0, -11.278, 11.278
| 237.744375108173
| 237.974540913462
|-
|-
| [[Alpha 2/1]]
| [[Alpha 2/1]]
Line 63: Line 55:
| 5\5<2/1>, 3\5<2/1>, 2\5<2/1>
| 5\5<2/1>, 3\5<2/1>, 2\5<2/1>
| 0, 18.045, -18.045
| 0, 18.045, -18.045
| 240
| 239.525131601721
|-
|-
| [[Beta 2/1]]
| [[Beta 2/1]]
Line 71: Line 61:
| 7\7<2/1>, 4\7<2/1>, 3\7<2/1>
| 7\7<2/1>, 4\7<2/1>, 3\7<2/1>
| 0, -16.241, 16.241
| 0, -16.241, 16.241
| 171.428571428571
| 171.648040552235
|-
|-
| [[Gamma 2/1]]
| [[Gamma 2/1]]
Line 79: Line 67:
| 12\12<2/1>, 7\12<2/1>, 5\12<2/1>
| 12\12<2/1>, 7\12<2/1>, 5\12<2/1>
| 0, -1.955, 1.955
| 0, -1.955, 1.955
| 100
| 100.017935787756
|-
|-
| [[Alpha 5/3]]
| [[Alpha 5/3]]
Line 89: Line 75:
| 7\7<5/3>, 4\7<5/3>, 3\7<5/3>
| 7\7<5/3>, 4\7<5/3>, 3\7<5/3>
| 0, 7.303, -7.303
| 0, 7.303, -7.303
| 126.336958999921
| 126.238272015258
|-
|-
| [[Beta 5/3]]
| [[Beta 5/3]]
Line 97: Line 81:
| 9\9<5/3>, 5\9<5/3>, 4\9<5/3>
| 9\9<5/3>, 5\9<5/3>, 4\9<5/3>
| 0, -6.735, 6.735
| 0, -6.735, 6.735
| 98.2620792221608
| 98.3172808862904
|-
|-
| [[Gamma 5/3]]
| [[Gamma 5/3]]
Line 105: Line 87:
| 16\16<5/3>, 9\16<5/3>, 7\16<5/3>
| 16\16<5/3>, 9\16<5/3>, 7\16<5/3>
| 0, -0.593, 0.593
| 0, -0.593, 0.593
| 55.2724195624655
| 55.2754932571412
|-
|-
| [[Carlos Alpha|Alpha 3/2]]
| [[Carlos Alpha|Alpha 3/2]]
Line 115: Line 95:
| 9\9<3/2>, 5\9<3/2>, 4\9<3/2>
| 9\9<3/2>, 5\9<3/2>, 4\9<3/2>
| 0, 3.661, -3.661
| 0, 3.661, -3.661
| 77.9950000961542
| 77.9649895501219
|-
|-
| [[Carlos Beta|Beta 3/2]]
| [[Carlos Beta|Beta 3/2]]
Line 123: Line 101:
| 11\11<3/2>, 6\11<3/2>, 5\11<3/2>
| 11\11<3/2>, 6\11<3/2>, 5\11<3/2>
| 0, -3.429, 3.429
| 0, -3.429, 3.429
| 63.8140909877625
| 63.8329325698408
|-
|-
| [[Carlos Gamma|Gamma 3/2]]
| [[Carlos Gamma|Gamma 3/2]]
Line 131: Line 107:
| 20\20<3/2>, 11\20<3/2>, 9\20<3/2>
| 20\20<3/2>, 11\20<3/2>, 9\20<3/2>
| 0, -0.238, 0.238
| 0, -0.238, 0.238
| 35.0977500432694
| 35.0985422804417
|-
|-
| [[Alpha 7/5]]
| [[Alpha 7/5]]
Line 141: Line 115:
| 11\11<7/5>, 6\11<7/5>, 5\11<7/5>
| 11\11<7/5>, 6\11<7/5>, 5\11<7/5>
| 0, 2.093, -2.093
| 0, 2.093, -2.093
| 52.9556538731173
| 52.9441558718088
|-
|-
| [[Beta 7/5]]
| [[Beta 7/5]]
Line 149: Line 121:
| 13\13<7/5>, 7\13<7/5>, 6\13<7/5>
| 13\13<7/5>, 7\13<7/5>, 6\13<7/5>
| 0, -1.981, 1.981
| 0, -1.981, 1.981
| 44.8086302003300
| 44.8164289231577
|-
|-
| [[Gamma 7/5]]
| [[Gamma 7/5]]
Line 157: Line 127:
| 24\24<7/5>, 13\24<7/5>, 11\24<7/5>
| 24\24<7/5>, 13\24<7/5>, 11\24<7/5>
| 0, -0.114, 0.114
| 0, -0.114, 0.114
| 24.2713413585121
| 24.2716042900130
|-
|-
| [[Alpha 4/3]]
| [[Alpha 4/3]]
Line 167: Line 135:
| 13\13<4/3>, 7\13<4/3>, 6\13<4/3>
| 13\13<4/3>, 7\13<4/3>, 6\13<4/3>
| 0, 1.307, -1.307
| 0, 1.307, -1.307
| 38.3111537795856
| 38.3060074376432
|-
|-
| [[Beta 4/3]]
| [[Beta 4/3]]
Line 175: Line 141:
| 15\15<4/3>, 8\15<4/3>, 7\15<4/3>
| 15\15<4/3>, 8\15<4/3>, 7\15<4/3>
| 0, -1.247, 1.247
| 0, -1.247, 1.247
| 33.2029999423075
| 33.2066890135066
|-
|-
| [[Gamma 4/3]]
| [[Gamma 4/3]]
Line 183: Line 147:
| 28\28<4/3>, 15\28<4/3>, 13\28<4/3>
| 28\28<4/3>, 15\28<4/3>, 13\28<4/3>
| 0, -0.061, 0.061
| 0, -0.061, 0.061
| 17.7873213976647
| 17.7874251067289
|-
|-
| [[Alpha 9/7]]
| [[Alpha 9/7]]
Line 193: Line 155:
| 15\15<9/7>, 8\15<9/7>, 7\15<9/7>
| 15\15<9/7>, 8\15<9/7>, 7\15<9/7>
| 0, 0.871, -0.871
| 0, 0.871, -0.871
| 29.0056063507767
| 29.0030301458200
|-
|-
| [[Beta 9/7]]
| [[Beta 9/7]]
Line 201: Line 161:
| 17\17<9/7>, 9\17<9/7>, 8\17<9/7>
| 17\17<9/7>, 9\17<9/7>, 8\17<9/7>
| 0, -0.835, 0.835
| 0, -0.835, 0.835
| 25.5931820742147
| 25.5951070854196
|-
|-
| [[Gamma 9/7]]
| [[Gamma 9/7]]
Line 209: Line 167:
| 32\32<9/7>, 17\32<9/7>, 15\32<9/7>
| 32\32<9/7>, 17\32<9/7>, 15\32<9/7>
| 0, -0.036, 0.036
| 0, -0.036, 0.036
| 13.5963779769266
| 13.5964243591413
|-
|-
| [[Alpha 5/4]]
| [[Alpha 5/4]]
Line 219: Line 175:
| 17\17<5/4>, 9\17<5/4>, 8\17<5/4>
| 17\17<5/4>, 9\17<5/4>, 8\17<5/4>
| 0, 0.609, -0.609
| 0, 0.609, -0.609
| 22.7243361096962
| 22.7229328303033
|-
|-
| [[Beta 5/4]]
| [[Beta 5/4]]
Line 227: Line 181:
| 19\19<5/4>, 10\19<5/4>, 9\19<5/4>
| 19\19<5/4>, 10\19<5/4>, 9\19<5/4>
| 0, -0.587, 0.587
| 0, -0.587, 0.587
| 20.3323007297281
| 20.3333837452881
|-
|-
| [[Gamma 5/4]]
| [[Gamma 5/4]]
Line 235: Line 187:
| 36\36<5/4>, 19\36<5/4>, 17\36<5/4>
| 36\36<5/4>, 19\36<5/4>, 17\36<5/4>
| 0, -0.022, 0.022
| 0, -0.022, 0.022
| 10.7309364962454
| 10.7309593208108
|-
|-
| [[Alpha 11/9]]
| [[Alpha 11/9]]
Line 245: Line 195:
| 19\19<11/9>, 10\19<11/9>, 9\19<11/9>
| 19\19<11/9>, 10\19<11/9>, 9\19<11/9>
| 0, 0.443, -0.443
| 0, 0.443, -0.443
| 18.2846284544201
| 18.2838119001578
|-
|-
| [[Beta 11/9]]
| [[Beta 11/9]]
Line 253: Line 201:
| 21\21<11/9>, 11\21<11/9>, 10\21<11/9>
| 21\21<11/9>, 11\21<11/9>, 10\21<11/9>
| 0, -0.428, 0.428
| 0, -0.428, 0.428
| 16.5432352682849
| 16.5438819815521
|-
|-
| [[Gamma 11/9]]
| [[Gamma 11/9]]
Line 261: Line 207:
| 40\40<11/9>, 21\40<11/9>, 19\40<11/9>
| 40\40<11/9>, 21\40<11/9>, 19\40<11/9>
| 0, -0.015, 0.015
| 0, -0.015, 0.015
| 8.68519851584955
| 8.68521062517612
|-
|-
| [[Alpha 6/5]]
| [[Alpha 6/5]]
Line 271: Line 215:
| 21\21<6/5>, 11\21<6/5>, 10\21<6/5>
| 21\21<6/5>, 11\21<6/5>, 10\21<6/5>
| 0, 0.332, -0.332
| 0, 0.332, -0.332
| 15.0305374762168
| 15.0300364433792
|-
|-
| [[Beta 6/5]]
| [[Beta 6/5]]
Line 279: Line 221:
| 23\23<6/5>, 12\23<6/5>, 11\23<6/5>
| 23\23<6/5>, 12\23<6/5>, 11\23<6/5>
| 0, -0.322, 0.322
| 0, -0.322, 0.322
| 13.7235342174153
| 13.7239395296205
|-
|-
| [[Gamma 6/5]]
| [[Gamma 6/5]]
Line 287: Line 227:
| 44\44<6/5>, 23\44<6/5>, 21\44<6/5>
| 44\44<6/5>, 23\44<6/5>, 21\44<6/5>
| 0, -0.010, 0.010
| 0, -0.010, 0.010
| 7.17366561364892
| 7.17367244048030
|-
|-
| [[Alpha 13/11]]
| [[Alpha 13/11]]
Line 297: Line 235:
| 23\23<13/11>, 12\23<13/11>, 11\23<13/11>
| 23\23<13/11>, 12\23<13/11>, 11\23<13/11>
| 0, 0.255, -0.255
| 0, 0.255, -0.255
| 12.5743356262850
| 12.5740145066190
|-
|-
| [[Beta 13/11]]
| [[Beta 13/11]]
Line 305: Line 241:
| 25\25<13/11>, 13\25<13/11>, 12\25<13/11>
| 25\25<13/11>, 13\25<13/11>, 12\25<13/11>
| 0, -0.248, 0.248
| 0, -0.248, 0.248
| 11.5683887761822
| 11.5686531732080
|-
|-
| [[Gamma 13/11]]
| [[Gamma 13/11]]
Line 313: Line 247:
| 48\48<13/11>, 25\48<13/11>, 23\48<13/11>
| 48\48<13/11>, 25\48<13/11>, 23\48<13/11>
| 0, -0.007, 0.007
| 0, -0.007, 0.007
| 6.02520248759487
| 6.02520653404413
|-
|-
| [[Alpha 7/6]]
| [[Alpha 7/6]]
Line 323: Line 255:
| 25\25<7/6>, 13\25<7/6>, 12\25<7/6>
| 25\25<7/6>, 13\25<7/6>, 12\25<7/6>
| 0, 0.200, -0.200
| 0, 0.200, -0.200
| 10.6748362241495
| 10.6746227806420
|-
|-
| [[Beta 7/6]]
| [[Beta 7/6]]
Line 331: Line 261:
| 27\27<7/6>, 14\27<7/6>, 13\27<7/6>
| 27\27<7/6>, 14\27<7/6>, 13\27<7/6>
| 0, -0.195, 0.195
| 0, -0.195, 0.195
| 9.88410761495324
| 9.88428600096291
|-
|-
| [[Gamma 7/6]]
| [[Gamma 7/6]]
Line 339: Line 267:
| 52\52<7/6>, 27\52<7/6>, 25\52<7/6>
| 52\52<7/6>, 27\52<7/6>, 25\52<7/6>
| 0, -0.005, 0.005
| 0, -0.005, 0.005
| 5.13213280007188
| 5.13213530145284
|-
|-
| [[Alpha 15/13]]
| [[Alpha 15/13]]
Line 349: Line 275:
| 27\27<15/13>, 14\27<15/13>, 13\27<15/13>
| 27\27<15/13>, 14\27<15/13>, 13\27<15/13>
| 0, 0.160, -0.160
| 0, 0.160, -0.160
| 9.17559455410784
| 9.17544822955784
|-
|-
| [[Beta 15/13]]
| [[Beta 15/13]]
Line 357: Line 281:
| 29\29<15/13>, 15\29<15/13>, 14\29<15/13>
| 29\29<15/13>, 15\29<15/13>, 14\29<15/13>
| 0, -0.156, 0.156
| 0, -0.156, 0.156
| 8.54279492968661
| 8.54291879716245
|-
|-
| [[Gamma 15/13]]
| [[Gamma 15/13]]
Line 365: Line 287:
| 56\56<15/13>, 29\56<15/13>, 27\56<15/13>
| 56\56<15/13>, 29\56<15/13>, 27\56<15/13>
| 0, -0.004, 0.004
| 0, -0.004, 0.004
| 4.42394737430199
| 4.42394897687108
|-
|-
| [[Alpha 8/7]]
| [[Alpha 8/7]]
Line 375: Line 295:
| 29\29<8/7>, 15\29<8/7>, 14\29<8/7>
| 29\29<8/7>, 15\29<8/7>, 14\29<8/7>
| 0, 0.130, -0.130
| 0, 0.130, -0.130
| 7.97152046658190
| 7.97141745648869
|-
|-
| [[Beta 8/7]]
| [[Beta 8/7]]
Line 383: Line 301:
| 31\31<8/7>, 16\31<8/7>, 15\31<8/7>
| 31\31<8/7>, 16\31<8/7>, 15\31<8/7>
| 0, -0.127, 0.127
| 0, -0.127, 0.127
| 7.45722882357662
| 7.45731699769858
|-
|-
| [[Gamma 8/7]]
| [[Gamma 8/7]]
Line 391: Line 307:
| 60\60<8/7>, 31\60<8/7>, 29\60<8/7>
| 60\60<8/7>, 31\60<8/7>, 29\60<8/7>
| 0, -0.003, 0.003
| 0, -0.003, 0.003
| 3.85290155884792
| 3.85290261769161
|}
|}
{{todo|Temperaments|inline=1|comment=Compute the temperaments associated to each Alpha-Beta-Gamma scales.}}
{{todo|Temperaments|inline=1|comment=Compute the temperaments associated to each Alpha-Beta-Gamma scales.}}
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