User:Contribution/Successive superparticular complementary pair

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

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

Icon-Todo.png Todo: Tables
Explain the tables.
Icon-Todo.png 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.
Icon-Todo.png Todo: Add data
Include columns for the following optimizations: Pure Equave, Dave Benson, TE, POTE, and CTE. To prevent the table from becoming overcrowded, choose between using cents or EDO. Cents are preferable since these are EDONOI. Retain the EDO column for pure equaves to provide a sense of scale, but place it outside the optimization subgroup column.
Tuning Intervals Mappings Various optimizations (cent)
Name Equal division Steps per octave Equave SSC pair Steps (Equave, SSC pair) Errors (cent) Pure Equave Dave Benson
Alpha 3/1 3ed3/1 1.89278926071437 3/1 2/1, 3/2 3\3<3/1>, 2\3<3/1>, 1\3<3/1> 0, 67.970, -67.970 633.985000288462 629.130000247254
Beta 3/1 5ed3/1 3.15464876785729 5\5<3/1>, 3\5<3/1>, 2\5<3/1> 0, -58.827, 58.827 380.391000173077 381.939079106782
Gamma 3/1 8ed3/1 5.04743802857166 8\8<3/1>, 5\8<3/1>, 3\8<3/1> 0, -11.278, 11.278 237.744375108173 237.974540913462
Alpha 2/1 5ed2/1 5 2/1 3/2, 4/3 5\5<2/1>, 3\5<2/1>, 2\5<2/1> 0, 18.045, -18.045 240 239.525131601721
Beta 2/1 7ed2/1 7 7\7<2/1>, 4\7<2/1>, 3\7<2/1> 0, -16.241, 16.241 171.428571428571 171.648040552235
Gamma 2/1 12ed2/1 12 12\12<2/1>, 7\12<2/1>, 5\12<2/1> 0, -1.955, 1.955 100 100.017935787756
Alpha 5/3 7ed5/3 9.49840814199707 5/3 4/3, 5/4 7\7<5/3>, 4\7<5/3>, 3\7<5/3> 0, 7.303, -7.303 126.336958999921 126.238272015258
Beta 5/3 9ed5/3 12.2122390397105 9\9<5/3>, 5\9<5/3>, 4\9<5/3> 0, -6.735, 6.735 98.2620792221608 98.3172808862904
Gamma 5/3 16ed5/3 21.7106471817076 16\16<5/3>, 9\16<5/3>, 7\16<5/3> 0, -0.593, 0.593 55.2724195624655 55.2754932571412
Alpha 3/2 9ed3/2 15.3856016221631 3/2 5/4, 6/5 9\9<3/2>, 5\9<3/2>, 4\9<3/2> 0, 3.661, -3.661 77.9950000961542 77.9649895501219
Beta 3/2 11ed3/2 18.8046242048660 11\11<3/2>, 6\11<3/2>, 5\11<3/2> 0, -3.429, 3.429 63.8140909877625 63.8329325698408
Gamma 3/2 20ed3/2 34.1902258270291 20\20<3/2>, 11\20<3/2>, 9\20<3/2> 0, -0.238, 0.238 35.0977500432694 35.0985422804417
Alpha 7/5 11ed7/5 22.6604698881676 7/5 6/5, 7/6 11\11<7/5>, 6\11<7/5>, 5\11<7/5> 0, 2.093, -2.093 52.9556538731173 52.9441558718088
Beta 7/5 13ed7/5 26.7805553223799 13\13<7/5>, 7\13<7/5>, 6\13<7/5> 0, -1.981, 1.981 44.8086302003300 44.8164289231577
Gamma 7/5 24ed7/5 49.4410252105475 24\24<7/5>, 13\24<7/5>, 11\24<7/5> 0, -0.114, 0.114 24.2713413585121 24.2716042900130
Alpha 4/3 13ed4/3 31.3224709154917 4/3 7/6, 8/7 13\13<4/3>, 7\13<4/3>, 6\13<4/3> 0, 1.307, -1.307 38.3111537795856 38.3060074376432
Beta 4/3 15ed4/3 36.1413125947981 15\15<4/3>, 8\15<4/3>, 7\15<4/3> 0, -1.247, 1.247 33.2029999423075 33.2066890135066
Gamma 4/3 28ed4/3 67.4637835102899 28\28<4/3>, 15\28<4/3>, 13\28<4/3> 0, -0.061, 0.061 17.7873213976647 17.7874251067289
Alpha 9/7 15ed9/7 41.3713123417559 9/7 8/7, 9/8 15\15<9/7>, 8\15<9/7>, 7\15<9/7> 0, 0.871, -0.871 29.0056063507767 29.0030301458200
Beta 9/7 17ed9/7 46.8874873206567 17\17<9/7>, 9\17<9/7>, 8\17<9/7> 0, -0.835, 0.835 25.5931820742147 25.5951070854196
Gamma 9/7 32ed9/7 88.2587996624126 32\32<9/7>, 17\32<9/7>, 15\32<9/7> 0, -0.036, 0.036 13.5963779769266 13.5964243591413
Alpha 5/4 17ed5/4 52.8068232315916 5/4 9/8, 10/9 17\17<5/4>, 9\17<5/4>, 8\17<5/4> 0, 0.609, -0.609 22.7243361096962 22.7229328303033
Beta 5/4 19ed5/4 59.0193906706024 19\19<5/4>, 10\19<5/4>, 9\19<5/4> 0, -0.587, 0.587 20.3323007297281 20.3333837452881
Gamma 5/4 36ed5/4 111.826213902194 36\36<5/4>, 19\36<5/4>, 17\36<5/4> 0, -0.022, 0.022 10.7309364962454 10.7309593208108
Alpha 11/9 19ed11/9 65.6288971357202 11/9 10/9, 11/10 19\19<11/9>, 10\19<11/9>, 9\19<11/9> 0, 0.443, -0.443 18.2846284544201 18.2838119001578
Beta 11/9 21ed11/9 72.5372020973750 21\21<11/9>, 11\21<11/9>, 10\21<11/9> 0, -0.428, 0.428 16.5432352682849 16.5438819815521
Gamma 11/9 40ed11/9 138.166099233095 40\40<11/9>, 21\40<11/9>, 19\40<11/9> 0, -0.015, 0.015 8.68519851584955 8.68521062517612
Alpha 6/5 21ed6/5 79.8374643554025 6/5 11/10, 12/11 21\21<6/5>, 11\21<6/5>, 10\21<6/5> 0, 0.332, -0.332 15.0305374762168 15.0300364433792
Beta 6/5 23ed6/5 87.4410323892504 23\23<6/5>, 12\23<6/5>, 11\23<6/5> 0, -0.322, 0.322 13.7235342174153 13.7239395296205
Gamma 6/5 44ed6/5 167.278496744653 44\44<6/5>, 23\44<6/5>, 21\44<6/5> 0, -0.010, 0.010 7.17366561364892 7.17367244048030
Alpha 13/11 23ed13/11 95.4324773621886 13/11 12/11, 13/12 23\23<13/11>, 12\23<13/11>, 11\23<13/11> 0, 0.255, -0.255 12.5743356262850 12.5740145066190
Beta 13/11 25ed13/11 103.730953654553 25\25<13/11>, 13\25<13/11>, 12\25<13/11> 0, -0.248, 0.248 11.5683887761822 11.5686531732080
Gamma 13/11 48ed13/11 199.163431016741 48\48<13/11>, 25\48<13/11>, 23\48<13/11> 0, -0.007, 0.007 6.02520248759487 6.02520653404413
Alpha 7/6 25ed7/6 112.413902640048 7/6 13/12, 14/13 25\25<7/6>, 13\25<7/6>, 12\25<7/6> 0, 0.200, -0.200 10.6748362241495 10.6746227806420
Beta 7/6 27ed7/6 121.407014851252 27\27<7/6>, 14\27<7/6>, 13\27<7/6> 0, -0.195, 0.195 9.88410761495324 9.88428600096291
Gamma 7/6 52ed7/6 233.820917491300 52\52<7/6>, 27\52<7/6>, 25\52<7/6> 0, -0.005, 0.005 5.13213280007188 5.13213530145284
Alpha 15/13 27ed15/13 130.781715879411 15/13 14/13, 15/14 27\27<15/13>, 14\27<15/13>, 13\27<15/13> 0, 0.160, -0.160 9.17559455410784 9.17544822955784
Beta 15/13 29ed15/13 140.469250388997 29\29<15/13>, 15\29<15/13>, 14\29<15/13> 0, -0.156, 0.156 8.54279492968661 8.54291879716245
Gamma 15/13 56ed15/13 271.250966268408 56\56<15/13>, 29\56<15/13>, 27\56<15/13> 0, -0.004, 0.004 4.42394737430199 4.42394897687108
Alpha 8/7 29ed8/7 150.535899020849 8/7 15/14, 16/15 29\29<8/7>, 15\29<8/7>, 14\29<8/7> 0, 0.130, -0.130 7.97152046658190 7.97141745648869
Beta 8/7 31ed8/7 160.917685160217 31\31<8/7>, 16\31<8/7>, 15\31<8/7> 0, -0.127, 0.127 7.45722882357662 7.45731699769858
Gamma 8/7 60ed8/7 311.453584181066 60\60<8/7>, 31\60<8/7>, 29\60<8/7> 0, -0.003, 0.003 3.85290155884792 3.85290261769161
Icon-Todo.png 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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