User:Contribution/Successive superparticular complementary pair

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: Tables Explain the tables.

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.

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
Name	Equal division	Steps per octave	Equave	SSC pair	Steps (Equave, SSC pair)	Errors (cent)
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
Beta 3/1	5ed3/1	3.15464876785729			5\5<3/1>, 3\5<3/1>, 2\5<3/1>	0, -58.827, 58.827
Gamma 3/1	8ed3/1	5.04743802857166			8\8<3/1>, 5\8<3/1>, 3\8<3/1>	0, -11.278, 11.278
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
Beta 2/1	7ed2/1	7			7\7<2/1>, 4\7<2/1>, 3\7<2/1>	0, -16.241, 16.241
Gamma 2/1	12ed2/1	12			12\12<2/1>, 7\12<2/1>, 5\12<2/1>	0, -1.955, 1.955
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
Beta 5/3	9ed5/3	12.2122390397105			9\9<5/3>, 5\9<5/3>, 4\9<5/3>	0, -6.735, 6.735
Gamma 5/3	16ed5/3	21.7106471817076			16\16<5/3>, 9\16<5/3>, 7\16<5/3>	0, -0.593, 0.593
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
Beta 3/2	11ed3/2	18.8046242048660			11\11<3/2>, 6\11<3/2>, 5\11<3/2>	0, -3.429, 3.429
Gamma 3/2	20ed3/2	34.1902258270291			20\20<3/2>, 11\20<3/2>, 9\20<3/2>	0, -0.238, 0.238
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
Beta 7/5	13ed7/5	26.7805553223799			13\13<7/5>, 7\13<7/5>, 6\13<7/5>	0, -1.981, 1.981
Gamma 7/5	24ed7/5	49.4410252105475			24\24<7/5>, 13\24<7/5>, 11\24<7/5>	0, -0.114, 0.114
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
Beta 4/3	15ed4/3	36.1413125947981			15\15<4/3>, 8\15<4/3>, 7\15<4/3>	0, -1.247, 1.247
Gamma 4/3	28ed4/3	67.4637835102899			28\28<4/3>, 15\28<4/3>, 13\28<4/3>	0, -0.061, 0.061
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
Beta 9/7	17ed9/7	46.8874873206567			17\17<9/7>, 9\17<9/7>, 8\17<9/7>	0, -0.835, 0.835
Gamma 9/7	32ed9/7	88.2587996624126			32\32<9/7>, 17\32<9/7>, 15\32<9/7>	0, -0.036, 0.036
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
Beta 5/4	19ed5/4	59.0193906706024			19\19<5/4>, 10\19<5/4>, 9\19<5/4>	0, -0.587, 0.587
Gamma 5/4	36ed5/4	111.826213902194			36\36<5/4>, 19\36<5/4>, 17\36<5/4>	0, -0.022, 0.022
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
Beta 11/9	21ed11/9	72.5372020973750			21\21<11/9>, 11\21<11/9>, 10\21<11/9>	0, -0.428, 0.428
Gamma 11/9	40ed11/9	138.166099233095			40\40<11/9>, 21\40<11/9>, 19\40<11/9>	0, -0.015, 0.015
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
Beta 6/5	23ed6/5	87.4410323892504			23\23<6/5>, 12\23<6/5>, 11\23<6/5>	0, -0.322, 0.322
Gamma 6/5	44ed6/5	167.278496744653			44\44<6/5>, 23\44<6/5>, 21\44<6/5>	0, -0.010, 0.010
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
Beta 13/11	25ed13/11	103.730953654553			25\25<13/11>, 13\25<13/11>, 12\25<13/11>	0, -0.248, 0.248
Gamma 13/11	48ed13/11	199.163431016741			48\48<13/11>, 25\48<13/11>, 23\48<13/11>	0, -0.007, 0.007
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
Beta 7/6	27ed7/6	121.407014851252			27\27<7/6>, 14\27<7/6>, 13\27<7/6>	0, -0.195, 0.195
Gamma 7/6	52ed7/6	233.820917491300			52\52<7/6>, 27\52<7/6>, 25\52<7/6>	0, -0.005, 0.005
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
Beta 15/13	29ed15/13	140.469250388997			29\29<15/13>, 15\29<15/13>, 14\29<15/13>	0, -0.156, 0.156
Gamma 15/13	56ed15/13	271.250966268408			56\56<15/13>, 29\56<15/13>, 27\56<15/13>	0, -0.004, 0.004
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
Beta 8/7	31ed8/7	160.917685160217			31\31<8/7>, 16\31<8/7>, 15\31<8/7>	0, -0.127, 0.127
Gamma 8/7	60ed8/7	311.453584181066			60\60<8/7>, 31\60<8/7>, 29\60<8/7>	0, -0.003, 0.003

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

The fact

As a fact, 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