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

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Contribution (talk | contribs)
3,302 edits
No edit summary
Line 14: Line 14:
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!1
!1
!2
!2
Line 24: Line 26:
!9
!9
|-
|-
| rowspan="9" |3/1
| rowspan="9" |2/1, 3/2
| rowspan="3" |Alpha 3/1
| rowspan="3" |Alpha 3/1
| rowspan="3" |3ed3/1
| rowspan="3" |3ed3/1
Line 78: Line 82:
|optimization error: 11.969
|optimization error: 11.969
|-
|-
| rowspan="9" |2/1
| rowspan="9" |3/2, 4/3
| rowspan="3" |Alpha 2/1
| rowspan="3" |Alpha 2/1
| rowspan="3" |5ed2/1
| rowspan="3" |5ed2/1
Line 132: Line 138:
|optimization error: 2.045
|optimization error: 2.045
|-
|-
|
|
| rowspan="3" |Alpha 5/3
| rowspan="3" |Alpha 5/3
| rowspan="3" |7ed5/3
| rowspan="3" |7ed5/3
Line 142: Line 150:
|optimization error: -0.691
|optimization error: -0.691
|-
|-
|
|
|4/3 mapping: 4\7<5/3>
|4/3 mapping: 4\7<5/3>
|equal division error: 7.303
|equal division error: 7.303
|optimization error: 6.908
|optimization error: 6.908
|-
|-
|
|
|5/4 mapping: 3\7<5/3>
|5/4 mapping: 3\7<5/3>
|equal division error: -7.303
|equal division error: -7.303
|optimization error: -7.599
|optimization error: -7.599
|-
|-
|
|
| rowspan="3" |Beta 5/3
| rowspan="3" |Beta 5/3
| rowspan="3" |9ed5/3
| rowspan="3" |9ed5/3
Line 160: Line 174:
|optimization error: 0.497
|optimization error: 0.497
|-
|-
|
|
|4/3 mapping: 5\9<5/3>
|4/3 mapping: 5\9<5/3>
|equal division error: -6.735
|equal division error: -6.735
|optimization error: -6.459
|optimization error: -6.459
|-
|-
|
|
|5/4 mapping: 4\9<5/3>
|5/4 mapping: 4\9<5/3>
|equal division error: 6.735
|equal division error: 6.735
|optimization error: 6.955
|optimization error: 6.955
|-
|-
|
|
| rowspan="3" |Gamma 5/3
| rowspan="3" |Gamma 5/3
| rowspan="3" |16ed5/3
| rowspan="3" |16ed5/3
Line 178: Line 198:
|optimization error: 0.049
|optimization error: 0.049
|-
|-
|
|
|4/3 mapping: 9\16<5/3>
|4/3 mapping: 9\16<5/3>
|equal division error: -0.593
|equal division error: -0.593
|optimization error: -0.566
|optimization error: -0.566
|-
|-
|
|
|5/4 mapping: 7\16<5/3>
|5/4 mapping: 7\16<5/3>
|equal division error: 0.593
|equal division error: 0.593
|optimization error: 0.615
|optimization error: 0.615
|-
|-
|
|
| rowspan="3" |Alpha 3/2
| rowspan="3" |Alpha 3/2
| rowspan="3" |9ed3/2
| rowspan="3" |9ed3/2
Line 196: Line 222:
|optimization error: -0.270
|optimization error: -0.270
|-
|-
|
|
|5/4 mapping: 5\9<3/2>
|5/4 mapping: 5\9<3/2>
|equal division error: 3.661
|equal division error: 3.661
|optimization error: 3.511
|optimization error: 3.511
|-
|-
|
|
|6/5 mapping: 4\9<3/2>
|6/5 mapping: 4\9<3/2>
|equal division error: -3.661
|equal division error: -3.661
|optimization error: -3.781
|optimization error: -3.781
|-
|-
|
|
| rowspan="3" |Beta 3/2
| rowspan="3" |Beta 3/2
| rowspan="3" |11ed3/2
| rowspan="3" |11ed3/2
Line 214: Line 246:
|optimization error: 0.207
|optimization error: 0.207
|-
|-
|
|
|5/4 mapping: 6\11<3/2>
|5/4 mapping: 6\11<3/2>
|equal division error: -3.429
|equal division error: -3.429
|optimization error: -3.316
|optimization error: -3.316
|-
|-
|
|
|6/5 mapping: 5\11<3/2>
|6/5 mapping: 5\11<3/2>
|equal division error: 3.429
|equal division error: 3.429
|optimization error: 3.523
|optimization error: 3.523
|-
|-
|
|
| rowspan="3" |Gamma 3/2
| rowspan="3" |Gamma 3/2
| rowspan="3" |20ed3/2
| rowspan="3" |20ed3/2
Line 232: Line 270:
|optimization error: 0.016
|optimization error: 0.016
|-
|-
|
|
|5/4 mapping: 11\20<3/2>
|5/4 mapping: 11\20<3/2>
|equal division error: -0.238
|equal division error: -0.238
|optimization error: -0.230
|optimization error: -0.230
|-
|-
|
|
|6/5 mapping: 9\20<3/2>
|6/5 mapping: 9\20<3/2>
|equal division error: 0.238
|equal division error: 0.238
|optimization error: 0.246
|optimization error: 0.246
|-
|-
|
|
| rowspan="3" |Alpha 7/5
| rowspan="3" |Alpha 7/5
| rowspan="3" |11ed7/5
| rowspan="3" |11ed7/5
Line 250: Line 294:
|optimization error: -0.126
|optimization error: -0.126
|-
|-
|
|
|6/5 mapping: 6\11<7/5>
|6/5 mapping: 6\11<7/5>
|equal division error: 2.093
|equal division error: 2.093
|optimization error: 2.024
|optimization error: 2.024
|-
|-
|
|
|7/6 mapping: 5\11<7/5>
|7/6 mapping: 5\11<7/5>
|equal division error: -2.093
|equal division error: -2.093
|optimization error: -2.150
|optimization error: -2.150
|-
|-
|
|
| rowspan="3" |Beta 7/5
| rowspan="3" |Beta 7/5
| rowspan="3" |13ed7/5
| rowspan="3" |13ed7/5
Line 268: Line 318:
|optimization error: 0.101
|optimization error: 0.101
|-
|-
|
|
|6/5 mapping: 7\13<7/5>
|6/5 mapping: 7\13<7/5>
|equal division error: -1.981
|equal division error: -1.981
|optimization error: -1.926
|optimization error: -1.926
|-
|-
|
|
|7/6 mapping: 6\13<7/5>
|7/6 mapping: 6\13<7/5>
|equal division error: 1.981
|equal division error: 1.981
|optimization error: 2.028
|optimization error: 2.028
|-
|-
|
|
| rowspan="3" |Gamma 7/5
| rowspan="3" |Gamma 7/5
| rowspan="3" |24ed7/5
| rowspan="3" |24ed7/5
Line 286: Line 342:
|optimization error: 0.006
|optimization error: 0.006
|-
|-
|
|
|6/5 mapping: 13\24<7/5>
|6/5 mapping: 13\24<7/5>
|equal division error: -0.114
|equal division error: -0.114
|optimization error: -0.110
|optimization error: -0.110
|-
|-
|
|
|7/6 mapping: 11\24<7/5>
|7/6 mapping: 11\24<7/5>
|equal division error: 0.114
|equal division error: 0.114
|optimization error: 0.117
|optimization error: 0.117
|-
|-
|
|
| rowspan="3" |Alpha 4/3
| rowspan="3" |Alpha 4/3
| rowspan="3" |13ed4/3
| rowspan="3" |13ed4/3
Line 304: Line 366:
|optimization error: -0.067
|optimization error: -0.067
|-
|-
|
|
|7/6 mapping: 7\13<4/3>
|7/6 mapping: 7\13<4/3>
|equal division error: 1.307
|equal division error: 1.307
|optimization error: 1.271
|optimization error: 1.271
|-
|-
|
|
|8/7 mapping: 6\13<4/3>
|8/7 mapping: 6\13<4/3>
|equal division error: -1.307
|equal division error: -1.307
|optimization error: -1.338
|optimization error: -1.338
|-
|-
|
|
| rowspan="3" |Beta 4/3
| rowspan="3" |Beta 4/3
| rowspan="3" |15ed4/3
| rowspan="3" |15ed4/3
Line 322: Line 390:
|optimization error: 0.055
|optimization error: 0.055
|-
|-
|
|
|7/6 mapping: 8\15<4/3>
|7/6 mapping: 8\15<4/3>
|equal division error: -1.247
|equal division error: -1.247
|optimization error: -1.217
|optimization error: -1.217
|-
|-
|
|
|8/7 mapping: 7\15<4/3>
|8/7 mapping: 7\15<4/3>
|equal division error: 1.247
|equal division error: 1.247
|optimization error: 1.273
|optimization error: 1.273
|-
|-
|
|
| rowspan="3" |Gamma 4/3
| rowspan="3" |Gamma 4/3
| rowspan="3" |28ed4/3
| rowspan="3" |28ed4/3
Line 340: Line 414:
|optimization error: 0.003
|optimization error: 0.003
|-
|-
|
|
|7/6 mapping: 15\28<4/3>
|7/6 mapping: 15\28<4/3>
|equal division error: -0.061
|equal division error: -0.061
|optimization error: -0.060
|optimization error: -0.060
|-
|-
|
|
|8/7 mapping: 13\28<4/3>
|8/7 mapping: 13\28<4/3>
|equal division error: 0.061
|equal division error: 0.061
|optimization error: 0.062
|optimization error: 0.062
|-
|-
|
|
| rowspan="3" |Alpha 9/7
| rowspan="3" |Alpha 9/7
| rowspan="3" |15ed9/7
| rowspan="3" |15ed9/7
Line 358: Line 438:
|optimization error: -0.039
|optimization error: -0.039
|-
|-
|
|
|8/7 mapping: 8\15<9/7>
|8/7 mapping: 8\15<9/7>
|equal division error: 0.871
|equal division error: 0.871
|optimization error: 0.850
|optimization error: 0.850
|-
|-
|
|
|9/8 mapping: 7\15<9/7>
|9/8 mapping: 7\15<9/7>
|equal division error: -0.871
|equal division error: -0.871
|optimization error: -0.889
|optimization error: -0.889
|-
|-
|
|
| rowspan="3" |Beta 9/7
| rowspan="3" |Beta 9/7
| rowspan="3" |17ed9/7
| rowspan="3" |17ed9/7
Line 376: Line 462:
|optimization error: 0.033
|optimization error: 0.033
|-
|-
|
|
|8/7 mapping: 9\17<9/7>
|8/7 mapping: 9\17<9/7>
|equal division error: -0.835
|equal division error: -0.835
|optimization error: -0.818
|optimization error: -0.818
|-
|-
|
|
|9/8 mapping: 8\17<9/7>
|9/8 mapping: 8\17<9/7>
|equal division error: 0.835
|equal division error: 0.835
|optimization error: 0.851
|optimization error: 0.851
|-
|-
|
|
| rowspan="3" |Gamma 9/7
| rowspan="3" |Gamma 9/7
| rowspan="3" |32ed9/7
| rowspan="3" |32ed9/7
Line 394: Line 486:
|optimization error: 0.001
|optimization error: 0.001
|-
|-
|
|
|8/7 mapping: 17\32<9/7>
|8/7 mapping: 17\32<9/7>
|equal division error: -0.036
|equal division error: -0.036
|optimization error: -0.035
|optimization error: -0.035
|-
|-
|
|
|9/8 mapping: 15\32<9/7>
|9/8 mapping: 15\32<9/7>
|equal division error: 0.036
|equal division error: 0.036
|optimization error: 0.036
|optimization error: 0.036
|-
|-
|
|
| rowspan="3" |Alpha 5/4
| rowspan="3" |Alpha 5/4
| rowspan="3" |17ed5/4
| rowspan="3" |17ed5/4
Line 412: Line 510:
|optimization error: -0.024
|optimization error: -0.024
|-
|-
|
|
|9/8 mapping: 9\17<5/4>
|9/8 mapping: 9\17<5/4>
|equal division error: 0.609
|equal division error: 0.609
|optimization error: 0.596
|optimization error: 0.596
|-
|-
|
|
|10/9 mapping: 8\17<5/4>
|10/9 mapping: 8\17<5/4>
|equal division error: -0.609
|equal division error: -0.609
|optimization error: -0.620
|optimization error: -0.620
|-
|-
|
|
| rowspan="3" |Beta 5/4
| rowspan="3" |Beta 5/4
| rowspan="3" |19ed5/4
| rowspan="3" |19ed5/4
Line 430: Line 534:
|optimization error: 0.021
|optimization error: 0.021
|-
|-
|
|
|9/8 mapping: 10\19<5/4>
|9/8 mapping: 10\19<5/4>
|equal division error: -0.587
|equal division error: -0.587
|optimization error: -0.576
|optimization error: -0.576
|-
|-
|
|
|10/9 mapping: 9\19<5/4>
|10/9 mapping: 9\19<5/4>
|equal division error: 0.587
|equal division error: 0.587
|optimization error: 0.597
|optimization error: 0.597
|-
|-
|
|
| rowspan="3" |Gamma 5/4
| rowspan="3" |Gamma 5/4
| rowspan="3" |36ed5/4
| rowspan="3" |36ed5/4
Line 448: Line 558:
|optimization error: 0.001
|optimization error: 0.001
|-
|-
|
|
|9/8 mapping: 19\36<5/4>
|9/8 mapping: 19\36<5/4>
|equal division error: -0.022
|equal division error: -0.022
|optimization error: -0.022
|optimization error: -0.022
|-
|-
|
|
|10/9 mapping: 17\36<5/4>
|10/9 mapping: 17\36<5/4>
|equal division error: 0.022
|equal division error: 0.022
|optimization error: 0.023
|optimization error: 0.023
|-
|-
|
|
| rowspan="3" |Alpha 11/9
| rowspan="3" |Alpha 11/9
| rowspan="3" |19ed11/9
| rowspan="3" |19ed11/9
Line 466: Line 582:
|optimization error: -0.016
|optimization error: -0.016
|-
|-
|
|
|10/9 mapping: 10\19<11/9>
|10/9 mapping: 10\19<11/9>
|equal division error: 0.443
|equal division error: 0.443
|optimization error: 0.434
|optimization error: 0.434
|-
|-
|
|
|11/10 mapping: 9\19<11/9>
|11/10 mapping: 9\19<11/9>
|equal division error: -0.443
|equal division error: -0.443
|optimization error: -0.450
|optimization error: -0.450
|-
|-
|
|
| rowspan="3" |Beta 11/9
| rowspan="3" |Beta 11/9
| rowspan="3" |21ed11/9
| rowspan="3" |21ed11/9
Line 484: Line 606:
|optimization error: 0.014
|optimization error: 0.014
|-
|-
|
|
|10/9 mapping: 11\21<11/9>
|10/9 mapping: 11\21<11/9>
|equal division error: -0.428
|equal division error: -0.428
|optimization error: -0.421
|optimization error: -0.421
|-
|-
|
|
|11/10 mapping: 10\21<11/9>
|11/10 mapping: 10\21<11/9>
|equal division error: 0.428
|equal division error: 0.428
|optimization error: 0.435
|optimization error: 0.435
|-
|-
|
|
| rowspan="3" |Gamma 11/9
| rowspan="3" |Gamma 11/9
| rowspan="3" |40ed11/9
| rowspan="3" |40ed11/9
Line 502: Line 630:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|10/9 mapping: 21\40<11/9>
|10/9 mapping: 21\40<11/9>
|equal division error: -0.015
|equal division error: -0.015
|optimization error: -0.014
|optimization error: -0.014
|-
|-
|
|
|11/10 mapping: 19\40<11/9>
|11/10 mapping: 19\40<11/9>
|equal division error: 0.015
|equal division error: 0.015
|optimization error: 0.015
|optimization error: 0.015
|-
|-
|
|
| rowspan="3" |Alpha 6/5
| rowspan="3" |Alpha 6/5
| rowspan="3" |21ed6/5
| rowspan="3" |21ed6/5
Line 520: Line 654:
|optimization error: -0.011
|optimization error: -0.011
|-
|-
|
|
|11/10 mapping: 11\21<6/5>
|11/10 mapping: 11\21<6/5>
|equal division error: 0.332
|equal division error: 0.332
|optimization error: 0.326
|optimization error: 0.326
|-
|-
|
|
|12/11 mapping: 10\21<6/5>
|12/11 mapping: 10\21<6/5>
|equal division error: -0.332
|equal division error: -0.332
|optimization error: -0.337
|optimization error: -0.337
|-
|-
|
|
| rowspan="3" |Beta 6/5
| rowspan="3" |Beta 6/5
| rowspan="3" |23ed6/5
| rowspan="3" |23ed6/5
Line 538: Line 678:
|optimization error: 0.009
|optimization error: 0.009
|-
|-
|
|
|11/10 mapping: 12\23<6/5>
|11/10 mapping: 12\23<6/5>
|equal division error: -0.322
|equal division error: -0.322
|optimization error: -0.317
|optimization error: -0.317
|-
|-
|
|
|12/11 mapping: 11\23<6/5>
|12/11 mapping: 11\23<6/5>
|equal division error: 0.322
|equal division error: 0.322
|optimization error: 0.326
|optimization error: 0.326
|-
|-
|
|
| rowspan="3" |Gamma 6/5
| rowspan="3" |Gamma 6/5
| rowspan="3" |44ed6/5
| rowspan="3" |44ed6/5
Line 556: Line 702:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|11/10 mapping: 23\44<6/5>
|11/10 mapping: 23\44<6/5>
|equal division error: -0.010
|equal division error: -0.010
|optimization error: -0.010
|optimization error: -0.010
|-
|-
|
|
|12/11 mapping: 21\44<6/5>
|12/11 mapping: 21\44<6/5>
|equal division error: 0.010
|equal division error: 0.010
|optimization error: 0.010
|optimization error: 0.010
|-
|-
|
|
| rowspan="3" |Alpha 13/11
| rowspan="3" |Alpha 13/11
| rowspan="3" |23ed13/11
| rowspan="3" |23ed13/11
Line 574: Line 726:
|optimization error: -0.007
|optimization error: -0.007
|-
|-
|
|
|12/11 mapping: 12\23<13/11>
|12/11 mapping: 12\23<13/11>
|equal division error: 0.255
|equal division error: 0.255
|optimization error: 0.251
|optimization error: 0.251
|-
|-
|
|
|13/12 mapping: 11\23<13/11>
|13/12 mapping: 11\23<13/11>
|equal division error: -0.255
|equal division error: -0.255
|optimization error: -0.259
|optimization error: -0.259
|-
|-
|
|
| rowspan="3" |Beta 13/11
| rowspan="3" |Beta 13/11
| rowspan="3" |25ed13/11
| rowspan="3" |25ed13/11
Line 592: Line 750:
|optimization error: 0.007
|optimization error: 0.007
|-
|-
|
|
|12/11 mapping: 13\25<13/11>
|12/11 mapping: 13\25<13/11>
|equal division error: -0.248
|equal division error: -0.248
|optimization error: -0.245
|optimization error: -0.245
|-
|-
|
|
|13/12 mapping: 12\25<13/11>
|13/12 mapping: 12\25<13/11>
|equal division error: 0.248
|equal division error: 0.248
|optimization error: 0.251
|optimization error: 0.251
|-
|-
|
|
| rowspan="3" |Gamma 13/11
| rowspan="3" |Gamma 13/11
| rowspan="3" |48ed13/11
| rowspan="3" |48ed13/11
Line 610: Line 774:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|12/11 mapping: 25\48<13/11>
|12/11 mapping: 25\48<13/11>
|equal division error: -0.007
|equal division error: -0.007
|optimization error: -0.007
|optimization error: -0.007
|-
|-
|
|
|13/12 mapping: 23\48<13/11>
|13/12 mapping: 23\48<13/11>
|equal division error: 0.007
|equal division error: 0.007
|optimization error: 0.007
|optimization error: 0.007
|-
|-
|
|
| rowspan="3" |Alpha 7/6
| rowspan="3" |Alpha 7/6
| rowspan="3" |25ed7/6
| rowspan="3" |25ed7/6
Line 628: Line 798:
|optimization error: -0.005
|optimization error: -0.005
|-
|-
|
|
|13/12 mapping: 13\25<7/6>
|13/12 mapping: 13\25<7/6>
|equal division error: 0.200
|equal division error: 0.200
|optimization error: 0.197
|optimization error: 0.197
|-
|-
|
|
|14/13 mapping: 12\25<7/6>
|14/13 mapping: 12\25<7/6>
|equal division error: -0.200
|equal division error: -0.200
|optimization error: -0.203
|optimization error: -0.203
|-
|-
|
|
| rowspan="3" |Beta 7/6
| rowspan="3" |Beta 7/6
| rowspan="3" |27ed7/6
| rowspan="3" |27ed7/6
Line 646: Line 822:
|optimization error: 0.005
|optimization error: 0.005
|-
|-
|
|
|13/12 mapping: 14\27<7/6>
|13/12 mapping: 14\27<7/6>
|equal division error: -0.195
|equal division error: -0.195
|optimization error: -0.193
|optimization error: -0.193
|-
|-
|
|
|14/13 mapping: 13\27<7/6>
|14/13 mapping: 13\27<7/6>
|equal division error: 0.195
|equal division error: 0.195
|optimization error: 0.197
|optimization error: 0.197
|-
|-
|
|
| rowspan="3" |Gamma 7/6
| rowspan="3" |Gamma 7/6
| rowspan="3" |52ed7/6
| rowspan="3" |52ed7/6
Line 664: Line 846:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|13/12 mapping: 27\52<7/6>
|13/12 mapping: 27\52<7/6>
|equal division error: -0.005
|equal division error: -0.005
|optimization error: -0.005
|optimization error: -0.005
|-
|-
|
|
|14/13 mapping: 25\52<7/6>
|14/13 mapping: 25\52<7/6>
|equal division error: 0.005
|equal division error: 0.005
|optimization error: 0.005
|optimization error: 0.005
|-
|-
|
|
| rowspan="3" |Alpha 15/13
| rowspan="3" |Alpha 15/13
| rowspan="3" |27ed15/13
| rowspan="3" |27ed15/13
Line 682: Line 870:
|optimization error: -0.004
|optimization error: -0.004
|-
|-
|
|
|14/13 mapping: 14\27<15/13>
|14/13 mapping: 14\27<15/13>
|equal division error: 0.160
|equal division error: 0.160
|optimization error: 0.158
|optimization error: 0.158
|-
|-
|
|
|15/14 mapping: 13\27<15/13>
|15/14 mapping: 13\27<15/13>
|equal division error: -0.160
|equal division error: -0.160
|optimization error: -0.162
|optimization error: -0.162
|-
|-
|
|
| rowspan="3" |Beta 15/13
| rowspan="3" |Beta 15/13
| rowspan="3" |29ed15/13
| rowspan="3" |29ed15/13
Line 700: Line 894:
|optimization error: 0.004
|optimization error: 0.004
|-
|-
|
|
|14/13 mapping: 15\29<15/13>
|14/13 mapping: 15\29<15/13>
|equal division error: -0.156
|equal division error: -0.156
|optimization error: -0.154
|optimization error: -0.154
|-
|-
|
|
|15/14 mapping: 14\29<15/13>
|15/14 mapping: 14\29<15/13>
|equal division error: 0.156
|equal division error: 0.156
|optimization error: 0.158
|optimization error: 0.158
|-
|-
|
|
| rowspan="3" |Gamma 15/13
| rowspan="3" |Gamma 15/13
| rowspan="3" |56ed15/13
| rowspan="3" |56ed15/13
Line 718: Line 918:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|14/13 mapping: 29\56<15/13>
|14/13 mapping: 29\56<15/13>
|equal division error: -0.004
|equal division error: -0.004
|optimization error: -0.004
|optimization error: -0.004
|-
|-
|
|
|15/14 mapping: 27\56<15/13>
|15/14 mapping: 27\56<15/13>
|equal division error: 0.004
|equal division error: 0.004
|optimization error: 0.004
|optimization error: 0.004
|-
|-
|
|
| rowspan="3" |Alpha 8/7
| rowspan="3" |Alpha 8/7
| rowspan="3" |29ed8/7
| rowspan="3" |29ed8/7
Line 736: Line 942:
|optimization error: -0.003
|optimization error: -0.003
|-
|-
|
|
|15/14 mapping: 15\29<8/7>
|15/14 mapping: 15\29<8/7>
|equal division error: 0.130
|equal division error: 0.130
|optimization error: 0.128
|optimization error: 0.128
|-
|-
|
|
|16/15 mapping: 14\29<8/7>
|16/15 mapping: 14\29<8/7>
|equal division error: -0.130
|equal division error: -0.130
|optimization error: -0.131
|optimization error: -0.131
|-
|-
|
|
| rowspan="3" |Beta 8/7
| rowspan="3" |Beta 8/7
| rowspan="3" |31ed8/7
| rowspan="3" |31ed8/7
Line 754: Line 966:
|optimization error: 0.003
|optimization error: 0.003
|-
|-
|
|
|15/14 mapping: 16\31<8/7>
|15/14 mapping: 16\31<8/7>
|equal division error: -0.127
|equal division error: -0.127
|optimization error: -0.126
|optimization error: -0.126
|-
|-
|
|
|16/15 mapping: 15\31<8/7>
|16/15 mapping: 15\31<8/7>
|equal division error: 0.127
|equal division error: 0.127
|optimization error: 0.128
|optimization error: 0.128
|-
|-
|
|
| rowspan="3" |Gamma 8/7
| rowspan="3" |Gamma 8/7
| rowspan="3" |60ed8/7
| rowspan="3" |60ed8/7
Line 772: Line 990:
|optimization error: 0.000
|optimization error: 0.000
|-
|-
|
|
|15/14 mapping: 31\60<8/7>
|15/14 mapping: 31\60<8/7>
|equal division error: -0.003
|equal division error: -0.003
|optimization error: -0.003
|optimization error: -0.003
|-
|-
|
|
|16/15 mapping: 29\60<8/7>
|16/15 mapping: 29\60<8/7>
|equal division error: 0.003
|equal division error: 0.003

Revision as of 20:30, 4 September 2024

Todo: Finish the article and move it

When the article is finished and the table explained, move it to the main root

For each pair of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math]​ and [math]\displaystyle{ {s2}/{s3} }[/math], there exists a ratio [math]\displaystyle{ {a}/{b} }[/math] such that [math]\displaystyle{ {s1}/{s2} }[/math]​ and [math]\displaystyle{ {s2}/{s3} }[/math]​ are [math]\displaystyle{ {a}/{b} }[/math] complementary; it is observed that [math]\displaystyle{ a−b=1 }[/math] or [math]\displaystyle{ a−b=2 }[/math]. In other words, for each ratio [math]\displaystyle{ a/b }[/math] where [math]\displaystyle{ a−b=1 }[/math] or [math]\displaystyle{ a−b=2 }[/math], there exists a pair of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math]​ and [math]\displaystyle{ {s2}/{s3} }[/math] that are [math]\displaystyle{ {a}/{b} }[/math] complementary.

Bellow is a table that show for equal divisions of [math]\displaystyle{ a/b }[/math] the cent error in the mapping of superparticular ratios [math]\displaystyle{ {s1}/{s2} }[/math]​ and [math]\displaystyle{ {s2}/{s3} }[/math] that are [math]\displaystyle{ a/b }[/math] complementary.

We can observe a converging sequence and pattern for low errors: 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; then 15, 17, 32; then 17, 19, 36; then 19, 21, 40; then 21, 23, 44; etc. --

Todo: Table

Explain the table.

Todo: Pattern

Clarify the observed pattern and create a descriptive name for it, such as the "Alpha-Beta-Gamma pattern" or the "Alpha-Beta-Gamma class" when referring to the group of scales. Assign distinct names to each scale within this class. For instance, 5edo might be called "2/1 Alpha", 7edo could be "2/1 Beta", and 12edo could be "2/1 Gamma". Additionally, compute the Dave Benson optimization for each scale as an alternative tuning. Note: 23edo with stretched octave is "7/5 Alpha". 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.

1 2 3 4 5 6 7 8 9
3/1 2/1, 3/2 Alpha 3/1 3ed3/1 1.892789 633.985000 1.907395926960071 629.130000247253548 3/1 mapping: 3\3<3/1> equal division error: 0.000 optimization error: -14.565
2/1 mapping: 2\3<3/1> equal division error: 67.970 optimization error: 58.260
3/2 mapping: 1\3<3/1> equal division error: -67.970 optimization error: -72.825
Beta 3/1 5ed3/1 3.154649 380.391000 3.141862316907629 381.939079106781893 3/1 mapping: 5\5<3/1> equal division error: 0.000 optimization error: 7.740
2/1 mapping: 3\5<3/1> equal division error: -58.827 optimization error: -54.183
3/2 mapping: 2\5<3/1> equal division error: 58.827 optimization error: 61.923
Gamma 3/1 8ed3/1 5.047438 237.744375 5.042556213760587 237.974540913461853 3/1 mapping: 8\8<3/1> equal division error: 0.000 optimization error: 1.841
2/1 mapping: 5\8<3/1> equal division error: -11.278 optimization error: -10.127
3/2 mapping: 3\8<3/1> equal division error: 11.278 optimization error: 11.969
2/1 3/2, 4/3 Alpha 2/1 5ed2/1 5.000000 240.000000 5.009912705090773 239.525131601720722 2/1 mapping: 5\5<2/1> equal division error: 0.000 optimization error: -2.374
3/2 mapping: 3\5<2/1> equal division error: 18.045 optimization error: 16.620
4/3 mapping: 2\5<2/1> equal division error: -18.045 optimization error: -18.995
Beta 2/1 7ed2/1 7.000000 171.428571 6.991049802487100 171.648040552234965 2/1 mapping: 7\7<2/1> equal division error: 0.000 optimization error: 1.536
3/2 mapping: 4\7<2/1> equal division error: -16.241 optimization error: -15.363
4/3 mapping: 3\7<2/1> equal division error: 16.241 optimization error: 16.899
Gamma 2/1 12ed2/1 12.000000 100.000000 11.997848091431052 100.017935787755848 2/1 mapping: 12\12<2/1> equal division error: 0.000 optimization error: 0.215
3/2 mapping: 7\12<2/1> equal division error: -1.955 optimization error: -1.829
4/3 mapping: 5\12<2/1> equal division error: 1.955 optimization error: 2.045
Alpha 5/3 7ed5/3 9.498408 126.336959 9.505833538777849 126.238272015257927 5/3 mapping: 7\7<5/3> equal division error: 0.000 optimization error: -0.691
4/3 mapping: 4\7<5/3> equal division error: 7.303 optimization error: 6.908
5/4 mapping: 3\7<5/3> equal division error: -7.303 optimization error: -7.599
Beta 5/3 9ed5/3 12.212239 98.262079 12.205382300878206 98.317280886290400 5/3 mapping: 9\9<5/3> equal division error: 0.000 optimization error: 0.497
4/3 mapping: 5\9<5/3> equal division error: -6.735 optimization error: -6.459
5/4 mapping: 4\9<5/3> equal division error: 6.735 optimization error: 6.955
Gamma 5/3 16ed5/3 21.710647 55.272420 21.709439921550910 55.275493257141231 5/3 mapping: 16\16<5/3> equal division error: 0.000 optimization error: 0.049
4/3 mapping: 9\16<5/3> equal division error: -0.593 optimization error: -0.566
5/4 mapping: 7\16<5/3> equal division error: 0.593 optimization error: 0.615
Alpha 3/2 9ed3/2 15.385602 77.995000 15.391523899692793 77.964989550121895 3/2 mapping: 9\9<3/2> equal division error: 0.000 optimization error: -0.270
5/4 mapping: 5\9<3/2> equal division error: 3.661 optimization error: 3.511
6/5 mapping: 4\9<3/2> equal division error: -3.661 optimization error: -3.781
Beta 3/2 11ed3/2 18.804624 63.814091 18.799073639411081 63.832932569840843 3/2 mapping: 11\11<3/2> equal division error: 0.000 optimization error: 0.207
5/4 mapping: 6\11<3/2> equal division error: -3.429 optimization error: -3.316
6/5 mapping: 5\11<3/2> equal division error: 3.429 optimization error: 3.523
Gamma 3/2 20ed3/2 34.190226 35.097750 34.189454092191388 35.098542280441702 3/2 mapping: 20\20<3/2> equal division error: 0.000 optimization error: 0.016
5/4 mapping: 11\20<3/2> equal division error: -0.238 optimization error: -0.230
6/5 mapping: 9\20<3/2> equal division error: 0.238 optimization error: 0.246
Alpha 7/5 11ed7/5 22.660470 52.955654 22.665391113336561 52.944155871808760 7/5 mapping: 11\11<7/5> equal division error: 0.000 optimization error: -0.126
6/5 mapping: 6\11<7/5> equal division error: 2.093 optimization error: 2.024
7/6 mapping: 5\11<7/5> equal division error: -2.093 optimization error: -2.150
Beta 7/5 13ed7/5 26.780555 44.808630 26.775895108856630 44.816428923157735 7/5 mapping: 13\13<7/5> equal division error: 0.000 optimization error: 0.101
6/5 mapping: 7\13<7/5> equal division error: -1.981 optimization error: -1.926
7/6 mapping: 6\13<7/5> equal division error: 1.981 optimization error: 2.028
Gamma 7/5 24ed7/5 49.441025 24.271341 49.440489621601243 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
Alpha 4/3 13ed4/3 31.322471 38.311154 31.326679032092577 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
Beta 4/3 15ed4/3 36.141313 33.203000 36.137297503882719 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
Gamma 4/3 28ed4/3 67.463784 17.787321 67.463390164664623 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
Alpha 9/7 15ed9/7 41.371312 29.005606 41.374987163985893 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
Beta 9/7 17ed9/7 46.887487 25.593182 46.883960906871343 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
Gamma 9/7 32ed9/7 88.258800 13.596378 88.258498580415662 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
Alpha 5/4 17ed5/4 52.806823 22.724336 52.810084374305705 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
Beta 5/4 19ed5/4 59.019391 20.332301 59.016247125030467 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
Gamma 5/4 36ed5/4 111.826214 10.730936 111.825976049765954 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
Alpha 11/9 19ed11/9 65.628897 18.284628 65.631828119476568 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
Beta 11/9 21ed11/9 72.537202 16.543235 72.534366561494206 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
Gamma 11/9 40ed11/9 138.166099 8.685199 138.165906595462172 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
Alpha 6/5 21ed6/5 79.837464 15.030537 79.840125772190183 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
Beta 6/5 23ed6/5 87.441032 13.723534 87.438449973495273 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
Gamma 6/5 44ed6/5 167.278497 7.173666 167.278337553931523 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
Alpha 13/11 23ed13/11 95.432477 12.574336 95.434914550823771 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
Beta 13/11 25ed13/11 103.730954 11.568389 103.728582924336770 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
Gamma 13/11 48ed13/11 199.163431 6.025202 199.163297261207502 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
Alpha 7/6 25ed7/6 112.413903 10.674836 112.416150402630623 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
Beta 7/6 27ed7/6 121.407015 9.884108 121.404823766036118 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
Gamma 7/6 52ed7/6 233.820917 5.132133 233.820803527976982 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
Alpha 15/13 27ed15/13 130.781716 9.175595 130.783801507844919 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
Beta 15/13 29ed15/13 140.469250 8.542795 140.467213664559518 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
Gamma 15/13 56ed15/13 271.250966 4.423947 271.250868008139347 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
Alpha 8/7 29ed8/7 150.535899 7.971520 150.537844310638475 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
Beta 8/7 31ed8/7 160.917685 7.457229 160.915782495277457 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
Gamma 8/7 60ed8/7 311.453584 3.852902 311.453498588281532 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
Todo: Temperaments

Compute the temperaments associated to each Alpha-Beta-Gamma scales.

Coincidence?

As a coincidence (?), all Alpha scales are (s1 + s2)ED(a / b), all Beta scales are (s2 + s3)ED(a / b), and all Gamma scales are (s1 + s2 + s2 + s3)ED(a / b).

Error (abs, ¢) on successive superparticular complementary pair in equal divisions
#ed3/1 2/1, 3/2 error #ed2/1 3/2, 4/3 error #ed5/3 4/3, 5/4 error #ed3/2 5/4, 6/5 error #ed7/5 6/5, 7/6 error #ed4/3 7/6, 8/7 error #ed9/7 8/7, 9/8 error #ed5/4 9/8, 10/9 error #ed11/9 10/9, 11/10 error #ed6/5 11/10, 12/11 error
1ed3/1 701.96 1ed2/1 498.04 1ed5/3 386.31 1ed3/2 315.64 1ed7/5 266.87 1ed4/3 231.17 1ed9/7 203.91 1ed5/4 182.40 1ed11/9 165.00 1ed6/5 150.64
2ed3/1 249.02 2ed2/1 101.96 2ed5/3 55.87 2ed3/2 35.34 2ed7/5 24.39 2ed4/3 17.85 2ed9/7 13.63 2ed5/4 10.75 2ed11/9 8.70 2ed6/5 7.18
3ed3/1 67.97 3ed2/1 98.04 3ed5/3 91.53 3ed3/2 81.66 3ed7/5 72.70 3ed4/3 65.16 3ed9/7 58.88 3ed5/4 53.63 3ed11/9 49.20 3ed6/5 45.42
4ed3/1 226.47 4ed2/1 101.96 4ed5/3 55.87 4ed3/2 35.34 4ed7/5 24.39 4ed4/3 17.85 4ed9/7 13.63 4ed5/4 10.75 4ed11/9 8.70 4ed6/5 7.18
5ed3/1 58.83 5ed2/1 18.04 5ed5/3 32.57 5ed3/2 34.86 5ed7/5 33.87 5ed4/3 31.96 5ed9/7 29.88 5ed5/4 27.88 5ed11/9 26.04 5ed6/5 24.38
6ed3/1 67.97 6ed2/1 98.04 6ed5/3 55.87 6ed3/2 35.34 6ed7/5 24.39 6ed4/3 17.85 6ed9/7 13.63 6ed5/4 10.75 6ed11/9 8.70 6ed6/5 7.18
7ed3/1 113.17 7ed2/1 16.24 7ed5/3 7.30 7ed3/2 14.80 7ed7/5 17.22 7ed4/3 17.73 7ed9/7 17.45 7ed5/4 16.84 7ed11/9 16.12 7ed6/5 15.36
8ed3/1 11.28 8ed2/1 48.04 8ed5/3 54.68 8ed3/2 35.34 8ed7/5 24.39 8ed4/3 17.85 8ed9/7 13.63 8ed5/4 10.75 8ed11/9 8.70 8ed6/5 7.18
9ed3/1 67.97 9ed2/1 35.29 9ed5/3 6.73 9ed3/2 3.66 9ed7/5 7.98 9ed4/3 9.82 9ed9/7 10.54 9ed5/4 10.71 9ed11/9 10.60 9ed6/5 10.35
10ed3/1 58.83 10ed2/1 18.04 10ed5/3 32.57 10ed3/2 34.86 10ed7/5 24.39 10ed4/3 17.85 10ed9/7 13.63 10ed5/4 10.75 10ed11/9 8.70 10ed6/5 7.18
11ed3/1 10.34 11ed2/1 47.41 11ed5/3 15.67 11ed3/2 3.43 11ed7/5 2.09 11ed4/3 4.79 11ed9/7 6.14 11ed5/4 6.81 11ed11/9 7.09 11ed6/5 7.16
12ed3/1 67.97 12ed2/1 1.96 12ed5/3 17.83 12ed3/2 23.16 12ed7/5 24.16 12ed4/3 17.85 12ed9/7 13.63 12ed5/4 10.75 12ed11/9 8.70 12ed6/5 7.18
13ed3/1 29.57 13ed2/1 36.51 13ed5/3 21.85 13ed3/2 8.34 13ed7/5 1.98 13ed4/3 1.31 13ed9/7 3.10 13ed5/4 4.11 13ed11/9 4.66 13ed6/5 4.96
14ed3/1 22.69 14ed2/1 16.24 14ed5/3 7.30 14ed3/2 14.80 14ed7/5 17.22 14ed4/3 17.73 14ed9/7 13.63 14ed5/4 10.75 14ed11/9 8.70 14ed6/5 7.18
15ed3/1 58.83 15ed2/1 18.04 15ed5/3 26.39 15ed3/2 11.94 15ed7/5 4.97 15ed4/3 1.25 15ed9/7 0.87 15ed5/4 2.12 15ed11/9 2.88 15ed6/5 3.34
16ed3/1 11.28 16ed2/1 26.96 16ed5/3 0.59 16ed3/2 8.54 16ed7/5 12.02 16ed4/3 13.28 16ed9/7 13.56 16ed5/4 10.75 16ed11/9 8.70 16ed6/5 7.18
17ed3/1 30.68 17ed2/1 3.93 17ed5/3 22.17 17ed3/2 14.69 17ed7/5 7.25 17ed4/3 3.20 17ed9/7 0.84 17ed5/4 0.61 17ed11/9 1.52 17ed6/5 2.10
18ed3/1 37.69 18ed2/1 31.38 18ed5/3 6.73 18ed3/2 3.66 18ed7/5 7.98 18ed4/3 9.82 18ed9/7 10.54 18ed5/4 10.71 18ed11/9 8.70 18ed6/5 7.18
19ed3/1 1.23 19ed2/1 7.22 19ed5/3 13.95 19ed3/2 16.86 19ed7/5 9.06 19ed4/3 4.74 19ed9/7 2.18 19ed5/4 0.59 19ed11/9 0.44 19ed6/5 1.12
20ed3/1 36.27 20ed2/1 18.04 20ed5/3 11.65 20ed3/2 0.24 20ed7/5 4.74 20ed4/3 7.05 20ed9/7 8.12 20ed5/4 8.56 20ed11/9 8.67 20ed6/5 7.18
21ed3/1 22.60 21ed2/1 16.24 21ed5/3 7.30 21ed3/2 14.80 21ed7/5 10.52 21ed4/3 5.99 21ed9/7 3.27 21ed5/4 1.56 21ed11/9 0.43 21ed6/5 0.33
22ed3/1 10.34 22ed2/1 7.14 22ed5/3 15.67 22ed3/2 3.43 22ed7/5 2.09 22ed4/3 4.79 22ed9/7 6.14 22ed5/4 6.81 22ed11/9 7.09 22ed6/5 7.16
23ed3/1 40.41 23ed2/1 23.69 23ed5/3 1.81 23ed3/2 10.44 23ed7/5 11.72 23ed4/3 7.02 23ed9/7 4.17 23ed5/4 2.36 23ed11/9 1.15 23ed6/5 0.32
24ed3/1 11.28 24ed2/1 1.96 24ed5/3 17.83 24ed3/2 6.09 24ed7/5 0.11 24ed4/3 2.90 24ed9/7 4.50 24ed5/4 5.34 24ed11/9 5.78 24ed6/5 5.97
25ed3/1 17.25 25ed2/1 18.04 25ed5/3 2.80 25ed3/2 6.78 25ed7/5 10.57 25ed4/3 7.89 25ed9/7 4.93 25ed5/4 3.03 25ed11/9 1.75 25ed6/5 0.87
26ed3/1 29.57 26ed2/1 9.65 26ed5/3 12.16 26ed3/2 8.34 26ed7/5 1.98 26ed4/3 1.31 26ed9/7 3.10 26ed5/4 4.11 26ed11/9 4.66 26ed6/5 4.96
27ed3/1 2.47 27ed2/1 9.16 27ed5/3 6.73 27ed3/2 3.66 27ed7/5 7.98 27ed4/3 8.63 27ed9/7 5.57 27ed5/4 3.60 27ed11/9 2.27 27ed6/5 1.34
28ed3/1 22.69 28ed2/1 16.24 28ed5/3 7.30 28ed3/2 10.27 28ed7/5 3.58 28ed4/3 0.06 28ed9/7 1.91 28ed5/4 3.04 28ed11/9 3.71 28ed6/5 4.09
29ed3/1 19.48 29ed2/1 1.49 29ed5/3 10.12 29ed3/2 0.97 29ed7/5 5.74 29ed4/3 7.91 29ed9/7 6.13 29ed5/4 4.09 29ed11/9 2.71 29ed6/5 1.74
30ed3/1 4.57 30ed2/1 18.04 30ed5/3 3.09 30ed3/2 11.46 30ed7/5 4.97 30ed4/3 1.25 30ed9/7 0.87 30ed5/4 2.12 30ed11/9 2.88 30ed6/5 3.34
31ed3/1 27.07 31ed2/1 5.18 31ed5/3 13.07 31ed3/2 1.37 31ed7/5 3.80 31ed4/3 6.25 31ed9/7 6.61 31ed5/4 4.52 31ed11/9 3.10 31ed6/5 2.09
32ed3/1 11.28 32ed2/1 10.54 32ed5/3 0.59 32ed3/2 8.54 32ed7/5 6.18 32ed4/3 2.28 32ed9/7 0.04 32ed5/4 1.32 32ed11/9 2.16 32ed6/5 2.68
33ed3/1 10.34 33ed2/1 11.05 33ed5/3 11.13 33ed3/2 3.43 33ed7/5 2.09 33ed4/3 4.79 33ed9/7 6.14 33ed5/4 4.90 33ed11/9 3.44 33ed6/5 2.40
34ed3/1 25.26 34ed2/1 3.93 34ed5/3 3.84 34ed3/2 5.96 34ed7/5 7.25 34ed4/3 3.20 34ed9/7 0.84 34ed5/4 0.61 34ed11/9 1.52 34ed6/5 2.10
35ed3/1 4.49 35ed2/1 16.24 35ed5/3 7.30 35ed3/2 5.25 35ed7/5 0.58 35ed4/3 3.50 35ed9/7 5.01 35ed5/4 5.23 35ed11/9 3.74 35ed6/5 2.67
36ed3/1 15.14 36ed2/1 1.96 36ed5/3 6.73 36ed3/2 3.66 36ed7/5 7.98 36ed4/3 4.01 36ed9/7 1.55 36ed5/4 0.02 36ed11/9 0.95 36ed6/5 1.58
37ed3/1 17.70 37ed2/1 11.56 37ed5/3 3.89 37ed3/2 6.88 37ed7/5 0.77 37ed4/3 2.34 37ed9/7 4.01 37ed5/4 4.91 37ed11/9 4.01 37ed6/5 2.92
38ed3/1 1.23 38ed2/1 7.22 38ed5/3 9.32 38ed3/2 1.61 38ed7/5 6.27 38ed4/3 4.74 38ed9/7 2.18 38ed5/4 0.59 38ed11/9 0.44 38ed6/5 1.12
39ed3/1 19.20 39ed2/1 5.74 39ed5/3 0.82 39ed3/2 8.34 39ed7/5 1.98 39ed4/3 1.31 39ed9/7 3.10 39ed5/4 4.11 39ed11/9 4.25 39ed6/5 3.14
40ed3/1 11.28 40ed2/1 11.96 40ed5/3 10.46 40ed3/2 0.24 40ed7/5 4.74 40ed4/3 5.40 40ed9/7 2.75 40ed5/4 1.10 40ed11/9 0.01 40ed6/5 0.71
41ed3/1 6.12 41ed2/1 0.48 41ed5/3 1.94 41ed3/2 7.47 41ed7/5 3.07 41ed4/3 0.37 41ed9/7 2.29 41ed5/4 3.38 41ed11/9 4.01 41ed6/5 3.33
42ed3/1 22.60 42ed2/1 12.33 42ed5/3 7.30 42ed3/2 1.91 42ed7/5 3.35 42ed4/3 5.87 42ed9/7 3.27 42ed5/4 1.56 42ed11/9 0.43 42ed6/5 0.33
43ed3/1 5.75 43ed2/1 4.28 43ed5/3 4.45 43ed3/2 5.48 43ed7/5 4.06 43ed4/3 0.47 43ed9/7 1.55 43ed5/4 2.72 43ed11/9 3.42 43ed6/5 3.51
44ed3/1 10.34 44ed2/1 7.14 44ed5/3 4.43 44ed3/2 3.43 44ed7/5 2.09 44ed4/3 4.79 44ed9/7 3.74 44ed5/4 1.97 44ed11/9 0.80 44ed6/5 0.01
45ed3/1 16.56 45ed2/1 8.62 45ed5/3 6.73 45ed3/2 3.66 45ed7/5 4.97 45ed4/3 1.25 45ed9/7 0.87 45ed5/4 2.12 45ed11/9 2.88 45ed6/5 3.34
46ed3/1 0.94 46ed2/1 2.39 46ed5/3 1.81 46ed3/2 4.82 46ed7/5 0.94 46ed4/3 3.81 46ed9/7 4.17 46ed5/4 2.36 46ed11/9 1.15 46ed6/5 0.32
47ed3/1 14.01 47ed2/1 12.59 47ed5/3 8.83 47ed3/2 2.00 47ed7/5 5.79 47ed4/3 1.95 47ed9/7 0.25 47ed5/4 1.58 47ed11/9 2.39 47ed6/5 2.89
48ed3/1 11.28 48ed2/1 1.96 48ed5/3 0.59 48ed3/2 6.09 48ed7/5 0.11 48ed4/3 2.90 48ed9/7 4.50 48ed5/4 2.70 48ed11/9 1.46 48ed6/5 0.61
49ed3/1 3.28 49ed2/1 8.25 49ed5/3 7.30 49ed3/2 0.48 49ed7/5 5.33 49ed4/3 2.60 49ed9/7 0.31 49ed5/4 1.07 49ed11/9 1.94 49ed6/5 2.48
50ed3/1 17.25 50ed2/1 5.96 50ed5/3 2.80 50ed3/2 6.78 50ed7/5 1.08 50ed4/3 2.07 50ed9/7 3.77 50ed5/4 3.03 50ed11/9 1.75 50ed6/5 0.87
51ed3/1 6.62 51ed2/1 3.93 51ed5/3 4.83 51ed3/2 0.93 51ed7/5 4.17 51ed4/3 3.20 51ed9/7 0.84 51ed5/4 0.61 51ed11/9 1.52 51ed6/5 2.10
52ed3/1 7.01 52ed2/1 9.65 52ed5/3 4.84 52ed3/2 5.16 52ed7/5 1.98 52ed4/3 1.31 52ed9/7 3.10 52ed5/4 3.32 52ed11/9 2.02 52ed6/5 1.11
53ed3/1 15.76 53ed2/1 0.07 53ed5/3 2.54 53ed3/2 2.23 53ed7/5 3.09 53ed4/3 3.75 53ed9/7 1.32 53ed5/4 0.18 53ed11/9 1.13 53ed6/5 1.75
54ed3/1 2.47 54ed2/1 9.16 54ed5/3 6.73 54ed3/2 3.66 54ed7/5 2.81 54ed4/3 0.60 54ed9/7 2.48 54ed5/4 3.55 54ed11/9 2.27 54ed6/5 1.34
55ed3/1 10.34 55ed2/1 3.77 55ed5/3 0.41 55ed3/2 3.43 55ed7/5 2.09 55ed4/3 4.27 55ed9/7 1.77 55ed5/4 0.22 55ed11/9 0.78 55ed6/5 1.42
56ed3/1 11.28 56ed2/1 5.19 56ed5/3 7.30 56ed3/2 2.27 56ed7/5 3.58 56ed4/3 0.06 56ed9/7 1.91 56ed5/4 3.04 56ed11/9 2.50 56ed6/5 1.55
57ed3/1 1.23 57ed2/1 7.22 57ed5/3 1.56 57ed3/2 4.55 57ed7/5 1.16 57ed4/3 4.00 57ed9/7 2.18 57ed5/4 0.59 57ed11/9 0.44 57ed6/5 1.12
58ed3/1 13.32 58ed2/1 1.49 58ed5/3 5.12 58ed3/2 0.97 58ed7/5 4.30 58ed4/3 0.67 58ed9/7 1.37 58ed5/4 2.57 58ed11/9 2.71 58ed6/5 1.74
59ed3/1 7.25 59ed2/1 9.91 59ed5/3 3.40 59ed3/2 5.59 59ed7/5 0.30 59ed4/3 3.26 59ed9/7 2.57 59ed5/4 0.93 59ed11/9 0.13 59ed6/5 0.84
60ed3/1 4.57 60ed2/1 1.96 60ed5/3 3.09 60ed3/2 0.24 60ed7/5 4.74 60ed4/3 1.25 60ed9/7 0.87 60ed5/4 2.12 60ed11/9 2.88 60ed6/5 1.92
61ed3/1 15.18 61ed2/1 6.24 61ed5/3 5.12 61ed3/2 4.94 61ed7/5 0.51 61ed4/3 2.56 61ed9/7 2.93 61ed5/4 1.25 61ed11/9 0.16 61ed6/5 0.58
62ed3/1 3.61 62ed2/1 5.18 62ed5/3 1.19 62ed3/2 1.37 62ed7/5 3.80 62ed4/3 1.78 62ed9/7 0.40 62ed5/4 1.71 62ed11/9 2.51 62ed6/5 2.09
63ed3/1 7.59 63ed2/1 2.81 63ed5/3 6.73 63ed3/2 3.66 63ed7/5 1.27 63ed4/3 1.92 63ed9/7 3.27 63ed5/4 1.56 63ed11/9 0.43 63ed6/5 0.33
64ed3/1 11.28 64ed2/1 8.21 64ed5/3 0.59 64ed3/2 2.43 64ed7/5 2.92 64ed4/3 2.28 64ed9/7 0.04 64ed5/4 1.32 64ed11/9 2.16 64ed6/5 2.25
65ed3/1 0.31 65ed2/1 0.42 65ed5/3 5.36 65ed3/2 2.46 65ed7/5 1.98 65ed4/3 1.31 65ed9/7 3.10 65ed5/4 1.84 65ed11/9 0.68 65ed6/5 0.10
66ed3/1 10.34 66ed2/1 7.14 66ed5/3 2.27 66ed3/2 3.43 66ed7/5 2.09 66ed4/3 2.76 66ed9/7 0.45 66ed5/4 0.95 66ed11/9 1.83 66ed6/5 2.38
67ed3/1 7.73 67ed2/1 3.45 67ed5/3 3.53 67ed3/2 1.33 67ed7/5 2.65 67ed4/3 0.74 67ed9/7 2.60 67ed5/4 2.10 67ed11/9 0.92 67ed6/5 0.12
68ed3/1 2.71 68ed2/1 3.93 68ed5/3 3.84 68ed3/2 4.37 68ed7/5 1.31 68ed4/3 3.20 68ed9/7 0.84 68ed5/4 0.61 68ed11/9 1.52 68ed6/5 2.10
69ed3/1 12.84 69ed2/1 6.30 69ed5/3 1.81 69ed3/2 0.27 69ed7/5 3.28 69ed4/3 0.20 69ed9/7 2.13 69ed5/4 2.36 69ed11/9 1.15 69ed6/5 0.32
70ed3/1 4.49 70ed2/1 0.90 70ed5/3 5.33 70ed3/2 4.78 70ed7/5 0.58 70ed4/3 3.50 70ed9/7 1.20 70ed5/4 0.28 70ed11/9 1.23 70ed6/5 1.83
71ed3/1 5.46 71ed2/1 7.90 71ed5/3 0.19 71ed3/2 0.73 71ed7/5 3.87 71ed4/3 0.31 71ed9/7 1.69 71ed5/4 2.59 71ed11/9 1.36 71ed6/5 0.52
72ed3/1 11.28 72ed2/1 1.96 72ed5/3 5.55 72ed3/2 3.66 72ed7/5 0.11 72ed4/3 2.90 72ed9/7 1.55 72ed5/4 0.02 72ed11/9 0.95 72ed6/5 1.58
73ed3/1 1.51 73ed2/1 4.89 73ed5/3 1.35 73ed3/2 1.68 73ed7/5 3.54 73ed4/3 0.79 73ed9/7 1.27 73ed5/4 2.48 73ed11/9 1.56 73ed6/5 0.70
74ed3/1 8.00 74ed2/1 4.66 74ed5/3 3.89 74ed3/2 2.61 74ed7/5 0.77 74ed4/3 2.34 74ed9/7 1.87 74ed5/4 0.31 74ed11/9 0.69 74ed6/5 1.35
75ed3/1 8.11 75ed2/1 2.04 75ed5/3 2.80 75ed3/2 2.58 75ed7/5 2.80 75ed4/3 1.25 75ed9/7 0.87 75ed5/4 2.12 75ed11/9 1.75 75ed6/5 0.87
76ed3/1 1.23 76ed2/1 7.22 76ed5/3 2.32 76ed3/2 1.61 76ed7/5 1.39 76ed4/3 1.81 76ed9/7 2.18 76ed5/4 0.59 76ed11/9 0.44 76ed6/5 1.12
77ed3/1 10.34 77ed2/1 0.66 77ed5/3 4.18 77ed3/2 3.43 77ed7/5 2.09 77ed4/3 1.68 77ed9/7 0.49 77ed5/4 1.79 77ed11/9 1.93 77ed6/5 1.03
78ed3/1 5.18 78ed2/1 5.74 78ed5/3 0.82 78ed3/2 0.66 78ed7/5 1.98 78ed4/3 1.31 78ed9/7 2.48 78ed5/4 0.85 78ed11/9 0.21 78ed6/5 0.91
79ed3/1 3.77 79ed2/1 3.22 79ed5/3 5.49 79ed3/2 4.24 79ed7/5 1.42 79ed4/3 2.09 79ed9/7 0.14 79ed5/4 1.47 79ed11/9 2.10 79ed6/5 1.19
80ed3/1 11.28 80ed2/1 3.04 80ed5/3 0.59 80ed3/2 0.24 80ed7/5 2.54 80ed4/3 0.83 80ed9/7 2.68 80ed5/4 1.10 80ed11/9 0.01 80ed6/5 0.71
81ed3/1 2.47 81ed2/1 5.66 81ed5/3 4.18 81ed3/2 3.66 81ed7/5 0.79 81ed4/3 2.48 81ed9/7 0.20 81ed5/4 1.17 81ed11/9 2.02 81ed6/5 1.34
82ed3/1 6.12 82ed2/1 0.48 82ed5/3 1.94 82ed3/2 1.09 82ed7/5 3.07 82ed4/3 0.37 82ed9/7 2.29 82ed5/4 1.33 82ed11/9 0.23 82ed6/5 0.51
83ed3/1 8.41 83ed2/1 6.48 83ed5/3 2.74 83ed3/2 2.72 83ed7/5 0.18 83ed4/3 2.85 83ed9/7 0.53 83ed5/4 0.88 83ed11/9 1.76 83ed6/5 1.48
84ed3/1 0.04 84ed2/1 1.96 84ed5/3 3.23 84ed3/2 1.91 84ed7/5 3.35 84ed4/3 0.06 84ed9/7 1.91 84ed5/4 1.56 84ed11/9 0.43 84ed6/5 0.33
85ed3/1 8.30 85ed2/1 3.93 85ed5/3 1.36 85ed3/2 1.83 85ed7/5 0.40 85ed4/3 2.66 85ed9/7 0.84 85ed5/4 0.61 85ed11/9 1.52 85ed6/5 1.61
86ed3/1 5.75 86ed2/1 4.28 86ed5/3 4.45 86ed3/2 2.69 86ed7/5 2.71 86ed4/3 0.47 86ed9/7 1.55 86ed5/4 1.77 86ed11/9 0.62 86ed6/5 0.16
87ed3/1 2.39 87ed2/1 1.49 87ed5/3 0.04 87ed3/2 0.97 87ed7/5 0.95 87ed4/3 2.19 87ed9/7 1.13 87ed5/4 0.35 87ed11/9 1.28 87ed6/5 1.74
88ed3/1 10.34 88ed2/1 6.50 88ed5/3 4.43 88ed3/2 3.43 88ed7/5 2.09 88ed4/3 0.87 88ed9/7 1.20 88ed5/4 1.97 88ed11/9 0.80 88ed6/5 0.01
89ed3/1 3.26 89ed2/1 0.83 89ed5/3 1.21 89ed3/2 0.16 89ed7/5 1.48 89ed4/3 1.74 89ed9/7 1.41 89ed5/4 0.10 89ed11/9 1.06 89ed6/5 1.68
90ed3/1 4.57 90ed2/1 4.71 90ed5/3 3.09 90ed3/2 3.66 90ed7/5 1.50 90ed4/3 1.25 90ed9/7 0.87 90ed5/4 2.12 90ed11/9 0.98 90ed6/5 0.17
91ed3/1 8.67 91ed2/1 3.05 91ed5/3 2.42 91ed3/2 0.62 91ed7/5 1.98 91ed4/3 1.31 91ed9/7 1.68 91ed5/4 0.14 91ed11/9 0.84 91ed6/5 1.49
92ed3/1 0.94 92ed2/1 2.39 92ed5/3 1.81 92ed3/2 2.81 92ed7/5 0.94 92ed4/3 1.61 92ed9/7 0.56 92ed5/4 1.84 92ed11/9 1.15 92ed6/5 0.32
93ed3/1 6.62 93ed2/1 5.18 93ed5/3 3.56 93ed3/2 1.37 93ed7/5 2.46 93ed4/3 0.90 93ed9/7 1.94 93ed5/4 0.37 93ed11/9 0.64 93ed6/5 1.30
94ed3/1 6.22 94ed2/1 0.17 94ed5/3 0.58 94ed3/2 2.00 94ed7/5 0.40 94ed4/3 1.95 94ed9/7 0.25 94ed5/4 1.58 94ed11/9 1.31 94ed6/5 0.47
95ed3/1 1.23 95ed2/1 5.41 95ed5/3 4.64 95ed3/2 2.09 95ed7/5 2.92 95ed4/3 0.50 95ed9/7 2.18 95ed5/4 0.59 95ed11/9 0.44 95ed6/5 1.12
96ed3/1 8.53 96ed2/1 1.96 96ed5/3 0.59 96ed3/2 1.22 96ed7/5 0.11 96ed4/3 2.28 96ed9/7 0.04 96ed5/4 1.32 96ed11/9 1.46 96ed6/5 0.61
97ed3/1 3.93 97ed2/1 3.20 97ed5/3 3.40 97ed3/2 2.77 97ed7/5 2.64 97ed4/3 0.12 97ed9/7 2.07 97ed5/4 0.80 97ed11/9 0.25 97ed6/5 0.95
98ed3/1 3.28 98ed2/1 4.00 98ed5/3 1.72 98ed3/2 0.48 98ed7/5 0.61 98ed4/3 2.48 98ed9/7 0.31 98ed5/4 1.07 98ed11/9 1.61 98ed6/5 0.74
99ed3/1 8.88 99ed2/1 1.08 99ed5/3 2.20 99ed3/2 3.43 99ed7/5 2.09 99ed4/3 0.24 99ed9/7 1.75 99ed5/4 1.00 99ed11/9 0.07 99ed6/5 0.79
100ed3/1 1.77 100ed2/1 5.96 100ed5/3 2.80 100ed3/2 0.24 100ed7/5 1.08 100ed4/3 2.07 100ed9/7 0.58 100ed5/4 0.84 100ed11/9 1.72 100ed6/5 0.87
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