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

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Line 18: Line 18:
|+
|+
|-
|-
! colspan="2" | Intervals !! colspan="3" | Tuning !! colspan="2" | Mapping !! colspan="2" | Various optimizations (cents)
! colspan="3" | Tuning !! colspan="2" | Intervals !! colspan="2" | Mapping !! colspan="2" | Various optimizations (cents)
|-
|-
! Equave
! Name
! SSCP
! Equal division
! Equal division
! Name
! Steps per octave
! Steps per octave
! Mappings (Equave, SSCP)
! Equave
! SSC pair
! Mappings (Equave, SSC pair)
! Errors (cent)
! Errors (cent)
! Pure Equave
! Pure Equave
! Dave Benson
! Dave Benson
|-
|-
| [[Alpha 3/1]]
| [[3edt|3ed3/1]]
| 1.89278926071437
| rowspan="3" | 3/1
| rowspan="3" | 3/1
| rowspan="3" | 2/1, 3/2
| rowspan="3" | 2/1, 3/2
| [[3edt|3ed3/1]]
| [[Alpha 3/1]]
| 1.89278926071437
| 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
Line 40: Line 40:
| 629.130000247254
| 629.130000247254
|-
|-
| [[Beta 3/1]]
| [[5edt|5ed3/1]]
| [[5edt|5ed3/1]]
| [[Beta 3/1]]
| 3.15464876785729
| 3.15464876785729
| 5\5<3/1>, 3\5<3/1>, 2\5<3/1>
| 5\5<3/1>, 3\5<3/1>, 2\5<3/1>
Line 48: Line 48:
| 381.939079106782
| 381.939079106782
|-
|-
| [[Gamma 3/1]]
| [[8edt|8ed3/1]]
| [[8edt|8ed3/1]]
| [[Gamma 3/1]]
| 5.04743802857166
| 5.04743802857166
| 8\8<3/1>, 5\8<3/1>, 3\8<3/1>
| 8\8<3/1>, 5\8<3/1>, 3\8<3/1>
Line 56: Line 56:
| 237.974540913462
| 237.974540913462
|-
|-
| [[Alpha 2/1]]
| [[5edo|5ed2/1]]
| 5.00000000000000
| rowspan="3" | 2/1
| rowspan="3" | 2/1
| rowspan="3" | 3/2, 4/3
| rowspan="3" | 3/2, 4/3
| [[5edo|5ed2/1]]
| [[Alpha 2/1]]
| 5.00000000000000
| 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
Line 66: Line 66:
| 239.525131601721
| 239.525131601721
|-
|-
| [[Beta 2/1]]
| [[7edo|7ed2/1]]
| [[7edo|7ed2/1]]
| [[Beta 2/1]]
| 7.00000000000000
| 7.00000000000000
| 7\7<2/1>, 4\7<2/1>, 3\7<2/1>
| 7\7<2/1>, 4\7<2/1>, 3\7<2/1>
Line 74: Line 74:
| 171.648040552235
| 171.648040552235
|-
|-
| [[Gamma 2/1]]
| [[12edo|12ed2/1]]
| [[12edo|12ed2/1]]
| [[Gamma 2/1]]
| 12.0000000000000
| 12.0000000000000
| 12\12<2/1>, 7\12<2/1>, 5\12<2/1>
| 12\12<2/1>, 7\12<2/1>, 5\12<2/1>
Line 82: Line 82:
| 100.017935787756
| 100.017935787756
|-
|-
| [[Alpha 5/3]]
| [[7ed5/3]]
| 9.49840814199707
| rowspan="3" | 5/3
| rowspan="3" | 5/3
| rowspan="3" | 4/3, 5/4
| rowspan="3" | 4/3, 5/4
| [[7ed5/3]]
| [[Alpha 5/3]]
| 9.49840814199707
| 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
Line 92: Line 92:
| 126.238272015258
| 126.238272015258
|-
|-
| [[Beta 5/3]]
| [[9ed5/3]]
| [[9ed5/3]]
| [[Beta 5/3]]
| 12.2122390397105
| 12.2122390397105
| 9\9<5/3>, 5\9<5/3>, 4\9<5/3>
| 9\9<5/3>, 5\9<5/3>, 4\9<5/3>
Line 100: Line 100:
| 98.3172808862904
| 98.3172808862904
|-
|-
| [[Gamma 5/3]]
| [[16ed5/3]]
| [[16ed5/3]]
| [[Gamma 5/3]]
| 21.7106471817076
| 21.7106471817076
| 16\16<5/3>, 9\16<5/3>, 7\16<5/3>
| 16\16<5/3>, 9\16<5/3>, 7\16<5/3>
Line 108: Line 108:
| 55.2754932571412
| 55.2754932571412
|-
|-
| [[Carlos Alpha|Alpha 3/2]]
| [[9edf|9ed3/2]]
| 15.3856016221631
| rowspan="3" | 3/2
| rowspan="3" | 3/2
| rowspan="3" | 5/4, 6/5
| rowspan="3" | 5/4, 6/5
| [[9edf|9ed3/2]]
| [[Carlos Alpha|Alpha 3/2]]
| 15.3856016221631
| 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
Line 118: Line 118:
| 77.9649895501219
| 77.9649895501219
|-
|-
| [[Carlos Beta|Beta 3/2]]
| [[11edf|11ed3/2]]
| [[11edf|11ed3/2]]
| [[Carlos Beta|Beta 3/2]]
| 18.8046242048660
| 18.8046242048660
| 11\11<3/2>, 6\11<3/2>, 5\11<3/2>
| 11\11<3/2>, 6\11<3/2>, 5\11<3/2>
Line 126: Line 126:
| 63.8329325698408
| 63.8329325698408
|-
|-
| [[Carlos Gamma|Gamma 3/2]]
| [[20edf|20ed3/2]]
| [[20edf|20ed3/2]]
| [[Carlos Gamma|Gamma 3/2]]
| 34.1902258270291
| 34.1902258270291
| 20\20<3/2>, 11\20<3/2>, 9\20<3/2>
| 20\20<3/2>, 11\20<3/2>, 9\20<3/2>
Line 134: Line 134:
| 35.0985422804417
| 35.0985422804417
|-
|-
| [[Alpha 7/5]]
| [[11ed7/5]]
| 22.6604698881676
| rowspan="3" | 7/5
| rowspan="3" | 7/5
| rowspan="3" | 6/5, 7/6
| rowspan="3" | 6/5, 7/6
| [[11ed7/5]]
| [[Alpha 7/5]]
| 22.6604698881676
| 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
Line 144: Line 144:
| 52.9441558718088
| 52.9441558718088
|-
|-
| [[Beta 7/5]]
| [[13ed7/5]]
| [[13ed7/5]]
| [[Beta 7/5]]
| 26.7805553223799
| 26.7805553223799
| 13\13<7/5>, 7\13<7/5>, 6\13<7/5>
| 13\13<7/5>, 7\13<7/5>, 6\13<7/5>
Line 152: Line 152:
| 44.8164289231577
| 44.8164289231577
|-
|-
| [[Gamma 7/5]]
| [[24ed7/5]]
| [[24ed7/5]]
| [[Gamma 7/5]]
| 49.4410252105475
| 49.4410252105475
| 24\24<7/5>, 13\24<7/5>, 11\24<7/5>
| 24\24<7/5>, 13\24<7/5>, 11\24<7/5>
Line 160: Line 160:
| 24.2716042900130
| 24.2716042900130
|-
|-
| [[Alpha 4/3]]
| [[13ed4/3]]
| 31.3224709154917
| rowspan="3" | 4/3
| rowspan="3" | 4/3
| rowspan="3" | 7/6, 8/7
| rowspan="3" | 7/6, 8/7
| [[13ed4/3]]
| [[Alpha 4/3]]
| 31.3224709154917
| 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
Line 170: Line 170:
| 38.3060074376432
| 38.3060074376432
|-
|-
| [[Beta 4/3]]
| [[15ed4/3]]
| [[15ed4/3]]
| [[Beta 4/3]]
| 36.1413125947981
| 36.1413125947981
| 15\15<4/3>, 8\15<4/3>, 7\15<4/3>
| 15\15<4/3>, 8\15<4/3>, 7\15<4/3>
Line 178: Line 178:
| 33.2066890135066
| 33.2066890135066
|-
|-
| [[Gamma 4/3]]
| [[28ed4/3]]
| [[28ed4/3]]
| [[Gamma 4/3]]
| 67.4637835102899
| 67.4637835102899
| 28\28<4/3>, 15\28<4/3>, 13\28<4/3>
| 28\28<4/3>, 15\28<4/3>, 13\28<4/3>
Line 186: Line 186:
| 17.7874251067289
| 17.7874251067289
|-
|-
| [[Alpha 9/7]]
| [[15ed9/7]]
| 41.3713123417559
| rowspan="3" | 9/7
| rowspan="3" | 9/7
| rowspan="3" | 8/7, 9/8
| rowspan="3" | 8/7, 9/8
| [[15ed9/7]]
| [[Alpha 9/7]]
| 41.3713123417559
| 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
Line 196: Line 196:
| 29.0030301458200
| 29.0030301458200
|-
|-
| [[Beta 9/7]]
| [[17ed9/7]]
| [[17ed9/7]]
| [[Beta 9/7]]
| 46.8874873206567
| 46.8874873206567
| 17\17<9/7>, 9\17<9/7>, 8\17<9/7>
| 17\17<9/7>, 9\17<9/7>, 8\17<9/7>
Line 204: Line 204:
| 25.5951070854196
| 25.5951070854196
|-
|-
| [[Gamma 9/7]]
| [[32ed9/7]]
| [[32ed9/7]]
| [[Gamma 9/7]]
| 88.2587996624126
| 88.2587996624126
| 32\32<9/7>, 17\32<9/7>, 15\32<9/7>
| 32\32<9/7>, 17\32<9/7>, 15\32<9/7>
Line 212: Line 212:
| 13.5964243591413
| 13.5964243591413
|-
|-
| [[Alpha 5/4]]
| [[17ed5/4]]
| 52.8068232315916
| rowspan="3" | 5/4
| rowspan="3" | 5/4
| rowspan="3" | 9/8, 10/9
| rowspan="3" | 9/8, 10/9
| [[17ed5/4]]
| [[Alpha 5/4]]
| 52.8068232315916
| 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
Line 222: Line 222:
| 22.7229328303033
| 22.7229328303033
|-
|-
| [[Beta 5/4]]
| [[19ed5/4]]
| [[19ed5/4]]
| [[Beta 5/4]]
| 59.0193906706024
| 59.0193906706024
| 19\19<5/4>, 10\19<5/4>, 9\19<5/4>
| 19\19<5/4>, 10\19<5/4>, 9\19<5/4>
Line 230: Line 230:
| 20.3333837452881
| 20.3333837452881
|-
|-
| [[Gamma 5/4]]
| [[36ed5/4]]
| [[36ed5/4]]
| [[Gamma 5/4]]
| 111.826213902194
| 111.826213902194
| 36\36<5/4>, 19\36<5/4>, 17\36<5/4>
| 36\36<5/4>, 19\36<5/4>, 17\36<5/4>
Line 238: Line 238:
| 10.7309593208108
| 10.7309593208108
|-
|-
| [[Alpha 11/9]]
| [[19ed11/9]]
| 65.6288971357202
| rowspan="3" | 11/9
| rowspan="3" | 11/9
| rowspan="3" | 10/9, 11/10
| rowspan="3" | 10/9, 11/10
| [[19ed11/9]]
| [[Alpha 11/9]]
| 65.6288971357202
| 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
Line 248: Line 248:
| 18.2838119001578
| 18.2838119001578
|-
|-
| [[Beta 11/9]]
| [[21ed11/9]]
| [[21ed11/9]]
| [[Beta 11/9]]
| 72.5372020973750
| 72.5372020973750
| 21\21<11/9>, 11\21<11/9>, 10\21<11/9>
| 21\21<11/9>, 11\21<11/9>, 10\21<11/9>
Line 256: Line 256:
| 16.5438819815521
| 16.5438819815521
|-
|-
| [[Gamma 11/9]]
| [[40ed11/9]]
| [[40ed11/9]]
| [[Gamma 11/9]]
| 138.166099233095
| 138.166099233095
| 40\40<11/9>, 21\40<11/9>, 19\40<11/9>
| 40\40<11/9>, 21\40<11/9>, 19\40<11/9>
Line 264: Line 264:
| 8.68521062517612
| 8.68521062517612
|-
|-
| [[Alpha 6/5]]
| [[21ed6/5]]
| 79.8374643554025
| rowspan="3" | 6/5
| rowspan="3" | 6/5
| rowspan="3" | 11/10, 12/11
| rowspan="3" | 11/10, 12/11
| [[21ed6/5]]
| [[Alpha 6/5]]
| 79.8374643554025
| 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
Line 274: Line 274:
| 15.0300364433792
| 15.0300364433792
|-
|-
| [[Beta 6/5]]
| [[23ed6/5]]
| [[23ed6/5]]
| [[Beta 6/5]]
| 87.4410323892504
| 87.4410323892504
| 23\23<6/5>, 12\23<6/5>, 11\23<6/5>
| 23\23<6/5>, 12\23<6/5>, 11\23<6/5>
Line 282: Line 282:
| 13.7239395296205
| 13.7239395296205
|-
|-
| [[Gamma 6/5]]
| [[44ed6/5]]
| [[44ed6/5]]
| [[Gamma 6/5]]
| 167.278496744653
| 167.278496744653
| 44\44<6/5>, 23\44<6/5>, 21\44<6/5>
| 44\44<6/5>, 23\44<6/5>, 21\44<6/5>
Line 290: Line 290:
| 7.17367244048030
| 7.17367244048030
|-
|-
| [[Alpha 13/11]]
| [[23ed13/11]]
| 95.4324773621886
| rowspan="3" | 13/11
| rowspan="3" | 13/11
| rowspan="3" | 12/11, 13/12
| rowspan="3" | 12/11, 13/12
| [[23ed13/11]]
| [[Alpha 13/11]]
| 95.4324773621886
| 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
Line 300: Line 300:
| 12.5740145066190
| 12.5740145066190
|-
|-
| [[Beta 13/11]]
| [[25ed13/11]]
| [[25ed13/11]]
| [[Beta 13/11]]
| 103.730953654553
| 103.730953654553
| 25\25<13/11>, 13\25<13/11>, 12\25<13/11>
| 25\25<13/11>, 13\25<13/11>, 12\25<13/11>
Line 308: Line 308:
| 11.5686531732080
| 11.5686531732080
|-
|-
| [[Gamma 13/11]]
| [[48ed13/11]]
| [[48ed13/11]]
| [[Gamma 13/11]]
| 199.163431016741
| 199.163431016741
| 48\48<13/11>, 25\48<13/11>, 23\48<13/11>
| 48\48<13/11>, 25\48<13/11>, 23\48<13/11>
Line 316: Line 316:
| 6.02520653404413
| 6.02520653404413
|-
|-
| [[Alpha 7/6]]
| [[25ed7/6]]
| 112.413902640048
| rowspan="3" | 7/6
| rowspan="3" | 7/6
| rowspan="3" | 13/12, 14/13
| rowspan="3" | 13/12, 14/13
| [[25ed7/6]]
| [[Alpha 7/6]]
| 112.413902640048
| 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
Line 326: Line 326:
| 10.6746227806420
| 10.6746227806420
|-
|-
| [[Beta 7/6]]
| [[27ed7/6]]
| [[27ed7/6]]
| [[Beta 7/6]]
| 121.407014851252
| 121.407014851252
| 27\27<7/6>, 14\27<7/6>, 13\27<7/6>
| 27\27<7/6>, 14\27<7/6>, 13\27<7/6>
Line 334: Line 334:
| 9.88428600096291
| 9.88428600096291
|-
|-
| [[Gamma 7/6]]
| [[52ed7/6]]
| [[52ed7/6]]
| [[Gamma 7/6]]
| 233.820917491300
| 233.820917491300
| 52\52<7/6>, 27\52<7/6>, 25\52<7/6>
| 52\52<7/6>, 27\52<7/6>, 25\52<7/6>
Line 342: Line 342:
| 5.13213530145284
| 5.13213530145284
|-
|-
| [[Alpha 15/13]]
| [[27ed15/13]]
| 130.781715879411
| rowspan="3" | 15/13
| rowspan="3" | 15/13
| rowspan="3" | 14/13, 15/14
| rowspan="3" | 14/13, 15/14
| [[27ed15/13]]
| [[Alpha 15/13]]
| 130.781715879411
| 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
Line 352: Line 352:
| 9.17544822955784
| 9.17544822955784
|-
|-
| [[Beta 15/13]]
| [[29ed15/13]]
| [[29ed15/13]]
| [[Beta 15/13]]
| 140.469250388997
| 140.469250388997
| 29\29<15/13>, 15\29<15/13>, 14\29<15/13>
| 29\29<15/13>, 15\29<15/13>, 14\29<15/13>
Line 360: Line 360:
| 8.54291879716245
| 8.54291879716245
|-
|-
| [[Gamma 15/13]]
| [[56ed15/13]]
| [[56ed15/13]]
| [[Gamma 15/13]]
| 271.250966268408
| 271.250966268408
| 56\56<15/13>, 29\56<15/13>, 27\56<15/13>
| 56\56<15/13>, 29\56<15/13>, 27\56<15/13>
Line 368: Line 368:
| 4.42394897687108
| 4.42394897687108
|-
|-
| [[Alpha 8/7]]
| [[29ed8/7]]
| 150.535899020849
| rowspan="3" | 8/7
| rowspan="3" | 8/7
| rowspan="3" | 15/14, 16/15
| rowspan="3" | 15/14, 16/15
| [[29ed8/7]]
| [[Alpha 8/7]]
| 150.535899020849
| 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
Line 378: Line 378:
| 7.97141745648869
| 7.97141745648869
|-
|-
| [[Beta 8/7]]
| [[31ed8/7]]
| [[31ed8/7]]
| [[Beta 8/7]]
| 160.917685160217
| 160.917685160217
| 31\31<8/7>, 16\31<8/7>, 15\31<8/7>
| 31\31<8/7>, 16\31<8/7>, 15\31<8/7>
Line 386: Line 386:
| 7.45731699769858
| 7.45731699769858
|-
|-
| [[Gamma 8/7]]
| [[60ed8/7]]
| [[60ed8/7]]
| [[Gamma 8/7]]
| 311.453584181066
| 311.453584181066
| 60\60<8/7>, 31\60<8/7>, 29\60<8/7>
| 60\60<8/7>, 31\60<8/7>, 29\60<8/7>
Retrieved from "https://en.xen.wiki/w/User:Contribution/Successive_superparticular_complementary_pair"