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Consider this second version for naming: "Alpha 2/1, Beta 2/1, Gamma 2/1, Alpha 7/5." Consistency and Clarity: The second version ("Alpha 2/1, Beta 2/1, Gamma 2/1, Alpha 7/5") places the descriptive name ("Alpha," "Beta," "Gamma") before the ratio. This makes it clear that "Alpha," "Beta," "Gamma," and so on are categories or types, while "2/1" and "7/5" are specific tunings or ratios within those categories. This ordering helps maintain a logical structure that is easier to follow.}}
Consider this second version for naming: "Alpha 2/1, Beta 2/1, Gamma 2/1, Alpha 7/5." Consistency and Clarity: The second version ("Alpha 2/1, Beta 2/1, Gamma 2/1, Alpha 7/5") places the descriptive name ("Alpha," "Beta," "Gamma") before the ratio. This makes it clear that "Alpha," "Beta," "Gamma," and so on are categories or types, while "2/1" and "7/5" are specific tunings or ratios within those categories. This ordering helps maintain a logical structure that is easier to follow.}}
{| class="wikitable"
{| class="wikitable"
|+
!
!
!1
!2
!3
!4
!5
!6
!7
!8
!9
|-
|-
| rowspan="9" |3/1
| Alpha 3/1
| rowspan="9" |2/1, 3/2
| 3ed3/1
| rowspan="3" |Alpha 3/1
| 1.892789
| rowspan="3" |3ed3/1
| 633.985000
| rowspan="3" |1.892789
| 1.907395926960071
| rowspan="3" |633.985000
| 629.130000247253548
| rowspan="3" |1.907395926960071
| 3/1, 2/1, 3/2
| rowspan="3" |629.130000247253548
| 3\3<3/1>, 2\3<3/1>, 1\3<3/1>
|3/1 mapping: 3\3<3/1>
| 0, 67.9700, -67.9700
|equal division error: 0.000
| -14.5650, 58.2600, -72.8250
|optimization error: -14.565
|-
|-
|2/1 mapping: 2\3<3/1>
| Beta 3/1
|equal division error: 67.970
| 5ed3/1
|optimization error: 58.260
| 3.154649
| 380.391000
| 3.141862316907629
| 381.939079106781893
| 3/1, 2/1, 3/2
| 5\5<3/1>, 3\5<3/1>, 2\5<3/1>
| 0, -58.8270, 58.8270
| 7.7404, -54.1828, 61.9232
|-
|-
|3/2 mapping: 1\3<3/1>
| Gamma 3/1
|equal division error: -67.970
| 8ed3/1
|optimization error: -72.825
| 5.047438
| 237.744375
| 5.042556213760587
| 237.974540913461853
| 3/1, 2/1, 3/2
| 8\8<3/1>, 5\8<3/1>, 3\8<3/1>
| 0, -11.2781, 11.2781
| 1.8413, -10.1273, 11.9686
|-
|-
| rowspan="3" |Beta 3/1
| Alpha 2/1
| rowspan="3" |5ed3/1
| 5ed2/1
| rowspan="3" |3.154649
| 5.000000
| rowspan="3" |380.391000
| 240.000000
| rowspan="3" |3.141862316907629
| 5.009912705090773
| rowspan="3" |381.939079106781893
| 239.525131601720722
|3/1 mapping: 5\5<3/1>
| 2/1, 3/2, 4/3
|equal division error: 0.000
| 5\5<2/1>, 3\5<2/1>, 2\5<2/1>
|optimization error: 7.740
| 0, 18.0450, -18.0450
| -2.3743, 16.6204, -18.9947
|-
|-
|2/1 mapping: 3\5<3/1>
| Beta 2/1
|equal division error: -58.827
| 7ed2/1
|optimization error: -54.183
| 7.000000
| 171.428571
| 6.991049802487100
| 171.648040552234965
| 2/1, 3/2, 4/3
| 7\7<2/1>, 4\7<2/1>, 3\7<2/1>
| 0, -16.2407, 16.2407
| 1.5363, -15.3628, 16.8991
|-
|-
|3/2 mapping: 2\5<3/1>
| Gamma 2/1
|equal division error: 58.827
| 12ed2/1
|optimization error: 61.923
| 12.000000
| 100.000000
| 11.997848091431052
| 100.017935787755848
| 2/1, 3/2, 4/3
| 12\12<2/1>, 7\12<2/1>, 5\12<2/1>
| 0, -1.9550, 1.9550
| 0.2152, -1.8295, 2.0447
|-
|-
| rowspan="3" |Gamma 3/1
| Alpha 5/3
| rowspan="3" |8ed3/1
| 7ed5/3
| rowspan="3" |5.047438
| 9.498408
| rowspan="3" |237.744375
| 126.336959
| rowspan="3" |5.042556213760587
| 9.505833538777849
| rowspan="3" |237.974540913461853
| 126.238272015257927
|3/1 mapping: 8\8<3/1>
| 5/3, 4/3, 5/4
|equal division error: 0.000
| 7\7<5/3>, 4\7<5/3>, 3\7<5/3>
|optimization error: 1.841
| 0, 7.3028, -7.3028
| -0.6908, 6.9081, -7.5989
|-
|-
|2/1 mapping: 5\8<3/1>
| Beta 5/3
|equal division error: -11.278
| 9ed5/3
|optimization error: -10.127
| 12.212239
| 98.262079
| 12.205382300878206
| 98.317280886290400
| 5/3, 4/3, 5/4
| 9\9<5/3>, 5\9<5/3>, 4\9<5/3>
| 0, -6.7346, 6.7346
| 0.4968, -6.4586, 6.9554
|-
|-
|3/2 mapping: 3\8<3/1>
| Gamma 5/3
|equal division error: 11.278
| 16ed5/3
|optimization error: 11.969
| 21.710647
| 55.272420
| 21.709439921550910
| 55.275493257141231
| 5/3, 4/3, 5/4
| 16\16<5/3>, 9\16<5/3>, 7\16<5/3>
| 0, -0.5932, 0.5932
| 0.0492, -0.5656, 0.6147
|-
|-
| rowspan="9" |2/1
| Alpha 3/2
| rowspan="9" |3/2, 4/3
| 9ed3/2
| rowspan="3" |Alpha 2/1
| 15.385602
| rowspan="3" |5ed2/1
| 77.995000
| rowspan="3" |5.000000
| 15.391523899692793
| rowspan="3" |240.000000
| 77.964989550121895
| rowspan="3" |5.009912705090773
| 3/2, 5/4, 6/5
| rowspan="3" |239.525131601720722
| 9\9<3/2>, 5\9<3/2>, 4\9<3/2>
|2/1 mapping: 5\5<2/1>
| 0, 3.6613, -3.6613
|equal division error: 0.000
| -0.2701, 3.5112, -3.7813
|optimization error: -2.374
|-
|-
|3/2 mapping: 3\5<2/1>
| Beta 3/2
|equal division error: 18.045
| 11ed3/2
|optimization error: 16.620
| 18.804624
| 63.814091
| 18.799073639411081
| 63.832932569840843
| 3/2, 5/4, 6/5
| 11\11<3/2>, 6\11<3/2>, 5\11<3/2>
| 0, -3.4292, 3.4292
| 0.2073, -3.3161, 3.5234
|-
|-
|4/3 mapping: 2\5<2/1>
| Gamma 3/2
|equal division error: -18.045
| 20ed3/2
|optimization error: -18.995
| 34.190226
| 35.097750
| 34.189454092191388
| 35.098542280441702
| 3/2, 5/4, 6/5
| 20\20<3/2>, 11\20<3/2>, 9\20<3/2>
| 0, -0.2385, 0.2385
| 0.0158, -0.2297, 0.2456
|-
|-
| rowspan="3" |Beta 2/1
| Alpha 7/5
| rowspan="3" |7ed2/1
| 11ed7/5
| rowspan="3" |7.000000
| 22.660470
| rowspan="3" |171.428571
| 52.955654
| rowspan="3" |6.991049802487100
| 22.665391113336561
| rowspan="3" |171.648040552234965
| 52.944155871808760
|2/1 mapping: 7\7<2/1>
| 7/5, 6/5, 7/6
|equal division error: 0.000
| 11\11<7/5>, 6\11<7/5>, 5\11<7/5>
|optimization error: 1.536
| 0, 2.0926, -2.0926
| -0.1265, 2.0236, -2.1501
|-
|-
|3/2 mapping: 4\7<2/1>
| Beta 7/5
|equal division error: -16.241
| 13ed7/5
|optimization error: -15.363
| 26.780555
| 44.808630
| 26.775895108856630
| 44.816428923157735
| 7/5, 6/5, 7/6
| 13\13<7/5>, 7\13<7/5>, 6\13<7/5>
| 0, -1.9809, 1.9809
| 0.1014, -1.9263, 2.0277
|-
|-
|4/3 mapping: 3\7<2/1>
| Gamma 7/5
|equal division error: 16.241
| 24ed7/5
|optimization error: 16.899
| 49.441025
| 24.271341
| 49.440489621601243
| 24.271604290013001
| 7/5, 6/5, 7/6
| 24\24<7/5>, 13\24<7/5>, 11\24<7/5>
| 0, -0.1138, 0.1138
| 0.0063, -0.1104, 0.1167
|-
|-
| rowspan="3" |Gamma 2/1
| Alpha 4/3
| rowspan="3" |12ed2/1
| 13ed4/3
| rowspan="3" |12.000000
| 31.322471
| rowspan="3" |100.000000
| 38.311154
| rowspan="3" |11.997848091431052
| 31.326679032092577
| rowspan="3" |100.017935787755848
| 38.306007437643215
|2/1 mapping: 12\12<2/1>
| 4/3, 7/6, 8/7
|equal division error: 0.000
| 13\13<4/3>, 7\13<4/3>, 6\13<4/3>
|optimization error: 0.215
| 0, 1.3072, -1.3072
| -0.0669, 1.2711, -1.3380
|-
|-
|3/2 mapping: 7\12<2/1>
| Beta 4/3
|equal division error: -1.955
| 15ed4/3
|optimization error: -1.829
| 36.141313
| 33.203000
| 36.137297503882719
| 33.206689013506551
| 4/3, 7/6, 8/7
| 15\15<4/3>, 8\15<4/3>, 7\15<4/3>
| 0, -1.2469, 1.2469
| 0.0553, -1.2174, 1.2727
|-
|-
|4/3 mapping: 5\12<2/1>
| Gamma 4/3
|equal division error: 1.955
| 28ed4/3
|optimization error: 2.045
| 67.463784
| 17.787321
| 67.463390164664623
| 17.787425106728855
| 4/3, 7/6, 8/7
| 28\28<4/3>, 15\28<4/3>, 13\28<4/3>
| 0, -0.0611, 0.0611
| 0.0029, -0.0595, 0.0624
|-
|-
|
| Alpha 9/7
|
| 15ed9/7
| rowspan="3" |Alpha 5/3
| 41.371312
| rowspan="3" |7ed5/3
| 29.005606
| rowspan="3" |9.498408
| 41.374987163985893
| rowspan="3" |126.336959
| 29.003030145820039
| rowspan="3" |9.505833538777849
| 9/7, 8/7, 9/8
| rowspan="3" |126.238272015257927
| 15\15<9/7>, 8\15<9/7>, 7\15<9/7>
|5/3 mapping: 7\7<5/3>
| 0, 0.8708, -0.8708
|equal division error: 0.000
| -0.0386, 0.8501, -0.8888
|optimization error: -0.691
|-
|-
|
| Beta 9/7
|
| 17ed9/7
|4/3 mapping: 4\7<5/3>
| 46.887487
|equal division error: 7.303
| 25.593182
|optimization error: 6.908
| 46.883960906871343
| 25.595107085419638
| 9/7, 8/7, 9/8
| 17\17<9/7>, 9\17<9/7>, 8\17<9/7>
| 0, -0.8355, 0.8355
| 0.0327, -0.8181, 0.8509
|-
|-
|
| Gamma 9/7
|
| 32ed9/7
|5/4 mapping: 3\7<5/3>
| 88.258800
|equal division error: -7.303
| 13.596378
|optimization error: -7.599
| 88.258498580415662
| 13.596424359141285
| 9/7, 8/7, 9/8
| 32\32<9/7>, 17\32<9/7>, 15\32<9/7>
| 0, -0.0357, 0.0357
| 0.0015, -0.0349, 0.0364
|-
|-
|
| Alpha 5/4
|
| 17ed5/4
| rowspan="3" |Beta 5/3
| 52.806823
| rowspan="3" |9ed5/3
| 22.724336
| rowspan="3" |12.212239
| 52.810084374305705
| rowspan="3" |98.262079
| 22.722932830303330
| rowspan="3" |12.205382300878206
| 5/4, 9/8, 10/9
| rowspan="3" |98.317280886290400
| 17\17<5/4>, 9\17<5/4>, 8\17<5/4>
|5/3 mapping: 9\9<5/3>
| 0, 0.6090, -0.6090
|equal division error: 0.000
| -0.0239, 0.5964, -0.6202
|optimization error: 0.497
|-
|-
|
| Beta 5/4
|
| 19ed5/4
|4/3 mapping: 5\9<5/3>
| 59.019391
|equal division error: -6.735
| 20.332301
|optimization error: -6.459
| 59.016247125030467
| 20.333383745288099
| 5/4, 9/8, 10/9
| 19\19<5/4>, 10\19<5/4>, 9\19<5/4>
| 0, -0.5870, 0.5870
| 0.0206, -0.5762, 0.5967
|-
|-
|
| Gamma 5/4
|
| 36ed5/4
|5/4 mapping: 4\9<5/3>
| 111.826214
|equal division error: 6.735
| 10.730936
|optimization error: 6.955
| 111.825976049765954
| 10.730959320810789
| 5/4, 9/8, 10/9
| 36\36<5/4>, 19\36<5/4>, 17\36<5/4>
| 0, -0.0222, 0.0222
| 0.0008, -0.0218, 0.0226
|-
|-
|
| Alpha 11/9
|
| 19ed11/9
| rowspan="3" |Gamma 5/3
| 65.628897
| rowspan="3" |16ed5/3
| 18.284628
| rowspan="3" |21.710647
| 65.631828119476568
| rowspan="3" |55.272420
| 18.283811900157846
| rowspan="3" |21.709439921550910
| 11/9, 10/9, 11/10
| rowspan="3" |55.275493257141231
| 19\19<11/9>, 10\19<11/9>, 9\19<11/9>
|5/3 mapping: 16\16<5/3>
| 0, 0.4426, -0.4426
|equal division error: 0.000
| -0.0155, 0.4344, -0.4499
|optimization error: 0.049
|-
|-
|
| Beta 11/9
|
| 21ed11/9
|4/3 mapping: 9\16<5/3>
| 72.537202
|equal division error: -0.593
| 16.543235
|optimization error: -0.566
| 72.534366561494206
| 16.543881981552112
| 11/9, 10/9, 11/10
| 21\21<11/9>, 11\21<11/9>, 10\21<11/9>
| 0, -0.4281, 0.4281
| 0.0136, -0.4210, 0.4346
|-
|-
|
| Gamma 11/9
|
| 40ed11/9
|5/4 mapping: 7\16<5/3>
| 138.166099
|equal division error: 0.593
| 8.685199
|optimization error: 0.615
| 138.165906595462172
| 8.685210625176124
| 11/9, 10/9, 11/10
| 40\40<11/9>, 21\40<11/9>, 19\40<11/9>
| 0, -0.0145, 0.0145
| 0.0005, -0.0143, 0.0148
|-
|-
|
| Alpha 6/5
|
| 21ed6/5
| rowspan="3" |Alpha 3/2
| 79.837464
| rowspan="3" |9ed3/2
| 15.030537
| rowspan="3" |15.385602
| 79.840125772190183
| rowspan="3" |77.995000
| 15.030036443379233
| rowspan="3" |15.391523899692793
| 6/5, 11/10, 12/11
| rowspan="3" |77.964989550121895
| 21\21<6/5>, 11\21<6/5>, 10\21<6/5>
|3/2 mapping: 9\9<3/2>
| 0, 0.3317, -0.3317
|equal division error: 0.000
| -0.0105, 0.3262, -0.3367
|optimization error: -0.270
|-
|-
|
| Beta 6/5
|
| 23ed6/5
|5/4 mapping: 5\9<3/2>
| 87.441032
|equal division error: 3.661
| 13.723534
|optimization error: 3.511
| 87.438449973495273
| 13.723939529620542
| 6/5, 11/10, 12/11
| 23\23<6/5>, 12\23<6/5>, 11\23<6/5>
| 0, -0.3218, 0.3218
| 0.0093, -0.3170, 0.3263
|-
|-
|
| Gamma 6/5
|
| 44ed6/5
|6/5 mapping: 4\9<3/2>
| 167.278497
|equal division error: -3.661
| 7.173666
|optimization error: -3.781
| 167.278337553931523
| 7.173672440480304
| 6/5, 11/10, 12/11
| 44\44<6/5>, 23\44<6/5>, 21\44<6/5>
| 0, -0.0099, 0.0099
| 0.0003, -0.0098, 0.0101
|-
|-
|
| Alpha 13/11
|
| 23ed13/11
| rowspan="3" |Beta 3/2
| 95.432477
| rowspan="3" |11ed3/2
| 12.574336
| rowspan="3" |18.804624
| 95.434914550823771
| rowspan="3" |63.814091
| 12.574014506618971
| rowspan="3" |18.799073639411081
| 13/11, 12/11, 13/12
| rowspan="3" |63.832932569840843
| 23\23<13/11>, 12\23<13/11>, 11\23<13/11>
|3/2 mapping: 11\11<3/2>
| 0, 0.2550, -0.2550
|equal division error: 0.000
| -0.0074, 0.2511, -0.2585
|optimization error: 0.207
|-
|-
|
| Beta 13/11
|
| 25ed13/11
|5/4 mapping: 6\11<3/2>
| 103.730954
|equal division error: -3.429
| 11.568389
|optimization error: -3.316
| 103.728582924336770
| 11.568653173208022
| 13/11, 12/11, 13/12
| 25\25<13/11>, 13\25<13/11>, 12\25<13/11>
| 0, -0.2480, 0.2480
| 0.0066, -0.2446, 0.2512
|-
|-
|
| Gamma 13/11
|
| 48ed13/11
|6/5 mapping: 5\11<3/2>
| 199.163431
|equal division error: 3.429
| 6.025202
|optimization error: 3.523
| 199.163297261207502
| 6.025206534044126
| 13/11, 12/11, 13/12
| 48\48<13/11>, 25\48<13/11>, 23\48<13/11>
| 0, -0.0070, 0.0070
| 0.0002, -0.0069, 0.0071
|-
|-
|
| Alpha 7/6
|
| 25ed7/6
| rowspan="3" |Gamma 3/2
| 112.413903
| rowspan="3" |20ed3/2
| 10.674836
| rowspan="3" |34.190226
| 112.416150402630623
| rowspan="3" |35.097750
| 10.674622780642016
| rowspan="3" |34.189454092191388
| 7/6, 13/12, 14/13
| rowspan="3" |35.098542280441702
| 25\25<7/6>, 13\25<7/6>, 12\25<7/6>
|3/2 mapping: 20\20<3/2>
| 0, 0.2002, -0.2002
|equal division error: 0.000
| -0.0053, 0.1974, -0.2028
|optimization error: 0.016
|-
|-
|
| Beta 7/6
|
| 27ed7/6
|5/4 mapping: 11\20<3/2>
| 121.407015
|equal division error: -0.238
| 9.884108
|optimization error: -0.230
| 121.404823766036118
| 9.884286000962910
| 7/6, 13/12, 14/13
| 27\27<7/6>, 14\27<7/6>, 13\27<7/6>
| 0, -0.1952, 0.1952
| 0.0048, -0.1927, 0.1975
|-
|-
|
| Gamma 7/6
|
| 52ed7/6
|6/5 mapping: 9\20<3/2>
| 233.820917
|equal division error: 0.238
| 5.132133
|optimization error: 0.246
| 233.820803527976982
| 5.132135301452842
| 7/6, 13/12, 14/13
| 52\52<7/6>, 27\52<7/6>, 25\52<7/6>
| 0, -0.0051, 0.0051
| 0.0001, -0.0050, 0.0051
|-
|-
|
| Alpha 15/13
|
| 27ed15/13
| rowspan="3" |Alpha 7/5
| 130.781716
| rowspan="3" |11ed7/5
| 9.175595
| rowspan="3" |22.660470
| 130.783801507844919
| rowspan="3" |52.955654
| 9.175448229557843
| rowspan="3" |22.665391113336561
| 15/13, 14/13, 15/14
| rowspan="3" |52.944155871808760
| 27\27<15/13>, 14\27<15/13>, 13\27<15/13>
|7/5 mapping: 11\11<7/5>
| 0, 0.1601, -0.1601
|equal division error: 0.000
| -0.0040, 0.1580, -0.1620
|optimization error: -0.126
|-
|-
|
| Beta 15/13
|
| 29ed15/13
|6/5 mapping: 6\11<7/5>
| 140.469250
|equal division error: 2.093
| 8.542795
|optimization error: 2.024
| 140.467213664559518
| 8.542918797162452
| 15/13, 14/13, 15/14
| 29\29<15/13>, 15\29<15/13>, 14\29<15/13>
| 0, -0.1563, 0.1563
| 0.0036, -0.1545, 0.1581
|-
|-
|
| Gamma 15/13
|
| 56ed15/13
|7/6 mapping: 5\11<7/5>
| 271.250966
|equal division error: -2.093
| 4.423947
|optimization error: -2.150
| 271.250868008139347
| 4.423948976871078
| 15/13, 14/13, 15/14
| 56\56<15/13>, 29\56<15/13>, 27\56<15/13>
| 0, -0.0038, 0.0038
| 0.0001, -0.0037, 0.0038
|-
|-
|
| Alpha 8/7
|
| 29ed8/7
| rowspan="3" |Beta 7/5
| 150.535899
| rowspan="3" |13ed7/5
| 7.971520
| rowspan="3" |26.780555
| 150.537844310638475
| rowspan="3" |44.808630
| 7.971417456488689
| rowspan="3" |26.775895108856630
| 8/7, 15/14, 16/15
| rowspan="3" |44.816428923157735
| 29\29<8/7>, 15\29<8/7>, 14\29<8/7>
|7/5 mapping: 13\13<7/5>
| 0, 0.1300, -0.1300
|equal division error: 0.000
| -0.0030, 0.1285, -0.1314
|optimization error: 0.101
|-
|-
|
| Beta 8/7
|
| 31ed8/7
|6/5 mapping: 7\13<7/5>
| 160.917685
|equal division error: -1.981
| 7.457229
|optimization error: -1.926
| 160.915782495277457
|-
| 7.457316997698579
|
| 8/7, 15/14, 16/15
|
| 31\31<8/7>, 16\31<8/7>, 15\31<8/7>
|7/6 mapping: 6\13<7/5>
| 0, -0.1271, 0.1271
|equal division error: 1.981
| 0.0027, -0.1257, 0.1285
|optimization error: 2.028
|-
|
|
| rowspan="3" |Gamma 7/5
| rowspan="3" |24ed7/5
| rowspan="3" |49.441025
| rowspan="3" |24.271341
| rowspan="3" |49.440489621601243
| rowspan="3" |24.271604290013001
|7/5 mapping: 24\24<7/5>
|equal division error: 0.000
|optimization error: 0.006
|-
|
|
|6/5 mapping: 13\24<7/5>
|equal division error: -0.114
|optimization error: -0.110
|-
|
|
|7/6 mapping: 11\24<7/5>
|equal division error: 0.114
|optimization error: 0.117
|-
|
|
| rowspan="3" |Alpha 4/3
| rowspan="3" |13ed4/3
| rowspan="3" |31.322471
| rowspan="3" |38.311154
| rowspan="3" |31.326679032092577
| rowspan="3" |38.306007437643215
|4/3 mapping: 13\13<4/3>
|equal division error: 0.000
|optimization error: -0.067
|-
|
|
|7/6 mapping: 7\13<4/3>
|equal division error: 1.307
|optimization error: 1.271
|-
|
|
|8/7 mapping: 6\13<4/3>
|equal division error: -1.307
|optimization error: -1.338
|-
|
|
| rowspan="3" |Beta 4/3
| rowspan="3" |15ed4/3
| rowspan="3" |36.141313
| rowspan="3" |33.203000
| rowspan="3" |36.137297503882719
| rowspan="3" |33.206689013506551
|4/3 mapping: 15\15<4/3>
|equal division error: 0.000
|optimization error: 0.055
|-
|
|
|7/6 mapping: 8\15<4/3>
|equal division error: -1.247
|optimization error: -1.217
|-
|
|
|8/7 mapping: 7\15<4/3>
|equal division error: 1.247
|optimization error: 1.273
|-
|
|
| rowspan="3" |Gamma 4/3
| rowspan="3" |28ed4/3
| rowspan="3" |67.463784
| rowspan="3" |17.787321
| rowspan="3" |67.463390164664623
| rowspan="3" |17.787425106728855
|4/3 mapping: 28\28<4/3>
|equal division error: 0.000
|optimization error: 0.003
|-
|
|
|7/6 mapping: 15\28<4/3>
|equal division error: -0.061
|optimization error: -0.060
|-
|
|
|8/7 mapping: 13\28<4/3>
|equal division error: 0.061
|optimization error: 0.062
|-
|
|
| rowspan="3" |Alpha 9/7
| rowspan="3" |15ed9/7
| rowspan="3" |41.371312
| rowspan="3" |29.005606
| rowspan="3" |41.374987163985893
| rowspan="3" |29.003030145820039
|9/7 mapping: 15\15<9/7>
|equal division error: 0.000
|optimization error: -0.039
|-
|
|
|8/7 mapping: 8\15<9/7>
|equal division error: 0.871
|optimization error: 0.850
|-
|
|
|9/8 mapping: 7\15<9/7>
|equal division error: -0.871
|optimization error: -0.889
|-
|
|
| rowspan="3" |Beta 9/7
| rowspan="3" |17ed9/7
| rowspan="3" |46.887487
| rowspan="3" |25.593182
| rowspan="3" |46.883960906871343
| rowspan="3" |25.595107085419638
|9/7 mapping: 17\17<9/7>
|equal division error: 0.000
|optimization error: 0.033
|-
|
|
|8/7 mapping: 9\17<9/7>
|equal division error: -0.835
|optimization error: -0.818
|-
|
|
|9/8 mapping: 8\17<9/7>
|equal division error: 0.835
|optimization error: 0.851
|-
|
|
| rowspan="3" |Gamma 9/7
| rowspan="3" |32ed9/7
| rowspan="3" |88.258800
| rowspan="3" |13.596378
| rowspan="3" |88.258498580415662
| rowspan="3" |13.596424359141285
|9/7 mapping: 32\32<9/7>
|equal division error: 0.000
|optimization error: 0.001
|-
|
|
|8/7 mapping: 17\32<9/7>
|equal division error: -0.036
|optimization error: -0.035
|-
|
|
|9/8 mapping: 15\32<9/7>
|equal division error: 0.036
|optimization error: 0.036
|-
|
|
| rowspan="3" |Alpha 5/4
| rowspan="3" |17ed5/4
| rowspan="3" |52.806823
| rowspan="3" |22.724336
| rowspan="3" |52.810084374305705
| rowspan="3" |22.722932830303330
|5/4 mapping: 17\17<5/4>
|equal division error: 0.000
|optimization error: -0.024
|-
|
|
|9/8 mapping: 9\17<5/4>
|equal division error: 0.609
|optimization error: 0.596
|-
|
|
|10/9 mapping: 8\17<5/4>
|equal division error: -0.609
|optimization error: -0.620
|-
|
|
| rowspan="3" |Beta 5/4
| rowspan="3" |19ed5/4
| rowspan="3" |59.019391
| rowspan="3" |20.332301
| rowspan="3" |59.016247125030467
| rowspan="3" |20.333383745288099
|5/4 mapping: 19\19<5/4>
|equal division error: 0.000
|optimization error: 0.021
|-
|
|
|9/8 mapping: 10\19<5/4>
|equal division error: -0.587
|optimization error: -0.576
|-
|
|
|10/9 mapping: 9\19<5/4>
|equal division error: 0.587
|optimization error: 0.597
|-
|
|
| rowspan="3" |Gamma 5/4
| rowspan="3" |36ed5/4
| rowspan="3" |111.826214
| rowspan="3" |10.730936
| rowspan="3" |111.825976049765954
| rowspan="3" |10.730959320810789
|5/4 mapping: 36\36<5/4>
|equal division error: 0.000
|optimization error: 0.001
|-
|
|
|9/8 mapping: 19\36<5/4>
|equal division error: -0.022
|optimization error: -0.022
|-
|
|
|10/9 mapping: 17\36<5/4>
|equal division error: 0.022
|optimization error: 0.023
|-
|
|
| rowspan="3" |Alpha 11/9
| rowspan="3" |19ed11/9
| rowspan="3" |65.628897
| rowspan="3" |18.284628
| rowspan="3" |65.631828119476568
| rowspan="3" |18.283811900157846
|11/9 mapping: 19\19<11/9>
|equal division error: 0.000
|optimization error: -0.016
|-
|
|
|10/9 mapping: 10\19<11/9>
|equal division error: 0.443
|optimization error: 0.434
|-
|
|
|11/10 mapping: 9\19<11/9>
|equal division error: -0.443
|optimization error: -0.450
|-
|
|
| rowspan="3" |Beta 11/9
| rowspan="3" |21ed11/9
| rowspan="3" |72.537202
| rowspan="3" |16.543235
| rowspan="3" |72.534366561494206
| rowspan="3" |16.543881981552112
|11/9 mapping: 21\21<11/9>
|equal division error: 0.000
|optimization error: 0.014
|-
|
|
|10/9 mapping: 11\21<11/9>
|equal division error: -0.428
|optimization error: -0.421
|-
|
|
|11/10 mapping: 10\21<11/9>
|equal division error: 0.428
|optimization error: 0.435
|-
|
|
| rowspan="3" |Gamma 11/9
| rowspan="3" |40ed11/9
| rowspan="3" |138.166099
| rowspan="3" |8.685199
| rowspan="3" |138.165906595462172
| rowspan="3" |8.685210625176124
|11/9 mapping: 40\40<11/9>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|10/9 mapping: 21\40<11/9>
|equal division error: -0.015
|optimization error: -0.014
|-
|
|
|11/10 mapping: 19\40<11/9>
|equal division error: 0.015
|optimization error: 0.015
|-
|
|
| rowspan="3" |Alpha 6/5
| rowspan="3" |21ed6/5
| rowspan="3" |79.837464
| rowspan="3" |15.030537
| rowspan="3" |79.840125772190183
| rowspan="3" |15.030036443379233
|6/5 mapping: 21\21<6/5>
|equal division error: 0.000
|optimization error: -0.011
|-
|
|
|11/10 mapping: 11\21<6/5>
|equal division error: 0.332
|optimization error: 0.326
|-
|
|
|12/11 mapping: 10\21<6/5>
|equal division error: -0.332
|optimization error: -0.337
|-
|
|
| rowspan="3" |Beta 6/5
| rowspan="3" |23ed6/5
| rowspan="3" |87.441032
| rowspan="3" |13.723534
| rowspan="3" |87.438449973495273
| rowspan="3" |13.723939529620542
|6/5 mapping: 23\23<6/5>
|equal division error: 0.000
|optimization error: 0.009
|-
|
|
|11/10 mapping: 12\23<6/5>
|equal division error: -0.322
|optimization error: -0.317
|-
|
|
|12/11 mapping: 11\23<6/5>
|equal division error: 0.322
|optimization error: 0.326
|-
|
|
| rowspan="3" |Gamma 6/5
| rowspan="3" |44ed6/5
| rowspan="3" |167.278497
| rowspan="3" |7.173666
| rowspan="3" |167.278337553931523
| rowspan="3" |7.173672440480304
|6/5 mapping: 44\44<6/5>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|11/10 mapping: 23\44<6/5>
|equal division error: -0.010
|optimization error: -0.010
|-
|
|
|12/11 mapping: 21\44<6/5>
|equal division error: 0.010
|optimization error: 0.010
|-
|
|
| rowspan="3" |Alpha 13/11
| rowspan="3" |23ed13/11
| rowspan="3" |95.432477
| rowspan="3" |12.574336
| rowspan="3" |95.434914550823771
| rowspan="3" |12.574014506618971
|13/11 mapping: 23\23<13/11>
|equal division error: 0.000
|optimization error: -0.007
|-
|
|
|12/11 mapping: 12\23<13/11>
|equal division error: 0.255
|optimization error: 0.251
|-
|
|
|13/12 mapping: 11\23<13/11>
|equal division error: -0.255
|optimization error: -0.259
|-
|
|
| rowspan="3" |Beta 13/11
| rowspan="3" |25ed13/11
| rowspan="3" |103.730954
| rowspan="3" |11.568389
| rowspan="3" |103.728582924336770
| rowspan="3" |11.568653173208022
|13/11 mapping: 25\25<13/11>
|equal division error: 0.000
|optimization error: 0.007
|-
|
|
|12/11 mapping: 13\25<13/11>
|equal division error: -0.248
|optimization error: -0.245
|-
|
|
|13/12 mapping: 12\25<13/11>
|equal division error: 0.248
|optimization error: 0.251
|-
|
|
| rowspan="3" |Gamma 13/11
| rowspan="3" |48ed13/11
| rowspan="3" |199.163431
| rowspan="3" |6.025202
| rowspan="3" |199.163297261207502
| rowspan="3" |6.025206534044126
|13/11 mapping: 48\48<13/11>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|12/11 mapping: 25\48<13/11>
|equal division error: -0.007
|optimization error: -0.007
|-
|
|
|13/12 mapping: 23\48<13/11>
|equal division error: 0.007
|optimization error: 0.007
|-
|
|
| rowspan="3" |Alpha 7/6
| rowspan="3" |25ed7/6
| rowspan="3" |112.413903
| rowspan="3" |10.674836
| rowspan="3" |112.416150402630623
| rowspan="3" |10.674622780642016
|7/6 mapping: 25\25<7/6>
|equal division error: 0.000
|optimization error: -0.005
|-
|
|
|13/12 mapping: 13\25<7/6>
|equal division error: 0.200
|optimization error: 0.197
|-
|
|
|14/13 mapping: 12\25<7/6>
|equal division error: -0.200
|optimization error: -0.203
|-
|
|
| rowspan="3" |Beta 7/6
| rowspan="3" |27ed7/6
| rowspan="3" |121.407015
| rowspan="3" |9.884108
| rowspan="3" |121.404823766036118
| rowspan="3" |9.884286000962910
|7/6 mapping: 27\27<7/6>
|equal division error: 0.000
|optimization error: 0.005
|-
|
|
|13/12 mapping: 14\27<7/6>
|equal division error: -0.195
|optimization error: -0.193
|-
|
|
|14/13 mapping: 13\27<7/6>
|equal division error: 0.195
|optimization error: 0.197
|-
|
|
| rowspan="3" |Gamma 7/6
| rowspan="3" |52ed7/6
| rowspan="3" |233.820917
| rowspan="3" |5.132133
| rowspan="3" |233.820803527976982
| rowspan="3" |5.132135301452842
|7/6 mapping: 52\52<7/6>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|13/12 mapping: 27\52<7/6>
|equal division error: -0.005
|optimization error: -0.005
|-
|
|
|14/13 mapping: 25\52<7/6>
|equal division error: 0.005
|optimization error: 0.005
|-
|
|
| rowspan="3" |Alpha 15/13
| rowspan="3" |27ed15/13
| rowspan="3" |130.781716
| rowspan="3" |9.175595
| rowspan="3" |130.783801507844919
| rowspan="3" |9.175448229557843
|15/13 mapping: 27\27<15/13>
|equal division error: 0.000
|optimization error: -0.004
|-
|
|
|14/13 mapping: 14\27<15/13>
|equal division error: 0.160
|optimization error: 0.158
|-
|
|
|15/14 mapping: 13\27<15/13>
|equal division error: -0.160
|optimization error: -0.162
|-
|
|
| rowspan="3" |Beta 15/13
| rowspan="3" |29ed15/13
| rowspan="3" |140.469250
| rowspan="3" |8.542795
| rowspan="3" |140.467213664559518
| rowspan="3" |8.542918797162452
|15/13 mapping: 29\29<15/13>
|equal division error: 0.000
|optimization error: 0.004
|-
|
|
|14/13 mapping: 15\29<15/13>
|equal division error: -0.156
|optimization error: -0.154
|-
|
|
|15/14 mapping: 14\29<15/13>
|equal division error: 0.156
|optimization error: 0.158
|-
|
|
| rowspan="3" |Gamma 15/13
| rowspan="3" |56ed15/13
| rowspan="3" |271.250966
| rowspan="3" |4.423947
| rowspan="3" |271.250868008139347
| rowspan="3" |4.423948976871078
|15/13 mapping: 56\56<15/13>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|14/13 mapping: 29\56<15/13>
|equal division error: -0.004
|optimization error: -0.004
|-
|
|
|15/14 mapping: 27\56<15/13>
|equal division error: 0.004
|optimization error: 0.004
|-
|
|
| rowspan="3" |Alpha 8/7
| rowspan="3" |29ed8/7
| rowspan="3" |150.535899
| rowspan="3" |7.971520
| rowspan="3" |150.537844310638475
| rowspan="3" |7.971417456488689
|8/7 mapping: 29\29<8/7>
|equal division error: 0.000
|optimization error: -0.003
|-
|
|
|15/14 mapping: 15\29<8/7>
|equal division error: 0.130
|optimization error: 0.128
|-
|
|
|16/15 mapping: 14\29<8/7>
|equal division error: -0.130
|optimization error: -0.131
|-
|
|
| rowspan="3" |Beta 8/7
| rowspan="3" |31ed8/7
| rowspan="3" |160.917685
| rowspan="3" |7.457229
| rowspan="3" |160.915782495277457
| rowspan="3" |7.457316997698579
|8/7 mapping: 31\31<8/7>
|equal division error: 0.000
|optimization error: 0.003
|-
|
|
|15/14 mapping: 16\31<8/7>
|equal division error: -0.127
|optimization error: -0.126
|-
|
|
|16/15 mapping: 15\31<8/7>
|equal division error: 0.127
|optimization error: 0.128
|-
|
|
| rowspan="3" |Gamma 8/7
| rowspan="3" |60ed8/7
| rowspan="3" |311.453584
| rowspan="3" |3.852902
| rowspan="3" |311.453498588281532
| rowspan="3" |3.852902617691610
|8/7 mapping: 60\60<8/7>
|equal division error: 0.000
|optimization error: 0.000
|-
|
|
|15/14 mapping: 31\60<8/7>
|equal division error: -0.003
|optimization error: -0.003
|-
|
|
|16/15 mapping: 29\60<8/7>
|equal division error: 0.003
|optimization error: 0.003
|-
|-
| Gamma 8/7
| 60ed8/7
| 311.453584
| 3.852902
| 311.453498588281532
| 3.852902617691610
| 8/7, 15/14, 16/15
| 60\60<8/7>, 31\60<8/7>, 29\60<8/7>
| 0, -0.0029, 0.0029
| 0.0001, -0.0028, 0.0029
|}
|}
{{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.}}
Retrieved from "https://en.xen.wiki/w/User:Contribution/Successive_superparticular_complementary_pair"