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.

Intervals		Tuning			Mapping		Various optimizations (cents)
Equave	SSCP	Equal division	Name	Steps per octave	Mappings (Equave, SSCP)	Errors	Pure Equave	Dave Benson
3/1	2/1, 3/2	3ed3/1	Alpha 3/1	1.89278926071437	3\3<3/1>, 2\3<3/1>, 1\3<3/1>	0, 67.970, -67.970	633.985000288462	629.130000247254
		5ed3/1	Beta 3/1	3.15464876785729	5\5<3/1>, 3\5<3/1>, 2\5<3/1>	0, -58.827, 58.827	380.391000173077	381.939079106782
		8ed3/1	Gamma 3/1	5.04743802857166	8\8<3/1>, 5\8<3/1>, 3\8<3/1>	0, -11.278, 11.278	237.744375108173	237.974540913462
2/1	3/2, 4/3	5ed2/1	Alpha 2/1	5.00000000000000	5\5<2/1>, 3\5<2/1>, 2\5<2/1>	0, 18.045, -18.045	240.000000000000	239.525131601721
		7ed2/1	Beta 2/1	7.00000000000000	7\7<2/1>, 4\7<2/1>, 3\7<2/1>	0, -16.241, 16.241	171.428571428571	171.648040552235
		12ed2/1	Gamma 2/1	12.0000000000000	12\12<2/1>, 7\12<2/1>, 5\12<2/1>	0, -1.955, 1.955	100.000000000000	100.017935787756
5/3	4/3, 5/4	7ed5/3	Alpha 5/3	9.49840814199707	7\7<5/3>, 4\7<5/3>, 3\7<5/3>	0, 7.303, -7.303	126.336958999921	126.238272015258
		9ed5/3	Beta 5/3	12.2122390397105	9\9<5/3>, 5\9<5/3>, 4\9<5/3>	0, -6.735, 6.735	98.2620792221608	98.3172808862904
		16ed5/3	Gamma 5/3	21.7106471817076	16\16<5/3>, 9\16<5/3>, 7\16<5/3>	0, -0.593, 0.593	55.2724195624655	55.2754932571412
3/2	5/4, 6/5	9ed3/2	Alpha 3/2	15.3856016221631	9\9<3/2>, 5\9<3/2>, 4\9<3/2>	0, 3.661, -3.661	77.9950000961542	77.9649895501219
		11ed3/2	Beta 3/2	18.8046242048660	11\11<3/2>, 6\11<3/2>, 5\11<3/2>	0, -3.429, 3.429	63.8140909877625	63.8329325698408
		20ed3/2	Gamma 3/2	34.1902258270291	20\20<3/2>, 11\20<3/2>, 9\20<3/2>	0, -0.238, 0.238	35.0977500432694	35.0985422804417
7/5	6/5, 7/6	11ed7/5	Alpha 7/5	22.6604698881676	11\11<7/5>, 6\11<7/5>, 5\11<7/5>	0, 2.093, -2.093	52.9556538731173	52.9441558718088
		13ed7/5	Beta 7/5	26.7805553223799	13\13<7/5>, 7\13<7/5>, 6\13<7/5>	0, -1.981, 1.981	44.8086302003300	44.8164289231577
		24ed7/5	Gamma 7/5	49.4410252105475	24\24<7/5>, 13\24<7/5>, 11\24<7/5>	0, -0.114, 0.114	24.2713413585121	24.2716042900130
4/3	7/6, 8/7	13ed4/3	Alpha 4/3	31.3224709154917	13\13<4/3>, 7\13<4/3>, 6\13<4/3>	0, 1.307, -1.307	38.3111537795856	38.3060074376432
		15ed4/3	Beta 4/3	36.1413125947981	15\15<4/3>, 8\15<4/3>, 7\15<4/3>	0, -1.247, 1.247	33.2029999423075	33.2066890135066
		28ed4/3	Gamma 4/3	67.4637835102899	28\28<4/3>, 15\28<4/3>, 13\28<4/3>	0, -0.061, 0.061	17.7873213976647	17.7874251067289
9/7	8/7, 9/8	15ed9/7	Alpha 9/7	41.3713123417559	15\15<9/7>, 8\15<9/7>, 7\15<9/7>	0, 0.871, -0.871	29.0056063507767	29.0030301458200
		17ed9/7	Beta 9/7	46.8874873206567	17\17<9/7>, 9\17<9/7>, 8\17<9/7>	0, -0.835, 0.835	25.5931820742147	25.5951070854196
		32ed9/7	Gamma 9/7	88.2587996624126	32\32<9/7>, 17\32<9/7>, 15\32<9/7>	0, -0.036, 0.036	13.5963779769266	13.5964243591413
5/4	9/8, 10/9	17ed5/4	Alpha 5/4	52.8068232315916	17\17<5/4>, 9\17<5/4>, 8\17<5/4>	0, 0.609, -0.609	22.7243361096962	22.7229328303033
		19ed5/4	Beta 5/4	59.0193906706024	19\19<5/4>, 10\19<5/4>, 9\19<5/4>	0, -0.587, 0.587	20.3323007297281	20.3333837452881
		36ed5/4	Gamma 5/4	111.826213902194	36\36<5/4>, 19\36<5/4>, 17\36<5/4>	0, -0.022, 0.022	10.7309364962454	10.7309593208108
11/9	10/9, 11/10	19ed11/9	Alpha 11/9	65.6288971357202	19\19<11/9>, 10\19<11/9>, 9\19<11/9>	0, 0.443, -0.443	18.2846284544201	18.2838119001578
		21ed11/9	Beta 11/9	72.5372020973750	21\21<11/9>, 11\21<11/9>, 10\21<11/9>	0, -0.428, 0.428	16.5432352682849	16.5438819815521
		40ed11/9	Gamma 11/9	138.166099233095	40\40<11/9>, 21\40<11/9>, 19\40<11/9>	0, -0.015, 0.015	8.68519851584955	8.68521062517612
6/5	11/10, 12/11	21ed6/5	Alpha 6/5	79.8374643554025	21\21<6/5>, 11\21<6/5>, 10\21<6/5>	0, 0.332, -0.332	15.0305374762168	15.0300364433792
		23ed6/5	Beta 6/5	87.4410323892504	23\23<6/5>, 12\23<6/5>, 11\23<6/5>	0, -0.322, 0.322	13.7235342174153	13.7239395296205
		44ed6/5	Gamma 6/5	167.278496744653	44\44<6/5>, 23\44<6/5>, 21\44<6/5>	0, -0.010, 0.010	7.17366561364892	7.17367244048030
13/11	12/11, 13/12	23ed13/11	Alpha 13/11	95.4324773621886	23\23<13/11>, 12\23<13/11>, 11\23<13/11>	0, 0.255, -0.255	12.5743356262850	12.5740145066190
		25ed13/11	Beta 13/11	103.730953654553	25\25<13/11>, 13\25<13/11>, 12\25<13/11>	0, -0.248, 0.248	11.5683887761822	11.5686531732080
		48ed13/11	Gamma 13/11	199.163431016741	48\48<13/11>, 25\48<13/11>, 23\48<13/11>	0, -0.007, 0.007	6.02520248759487	6.02520653404413
7/6	13/12, 14/13	25ed7/6	Alpha 7/6	112.413902640048	25\25<7/6>, 13\25<7/6>, 12\25<7/6>	0, 0.200, -0.200	10.6748362241495	10.6746227806420
		27ed7/6	Beta 7/6	121.407014851252	27\27<7/6>, 14\27<7/6>, 13\27<7/6>	0, -0.195, 0.195	9.88410761495324	9.88428600096291
		52ed7/6	Gamma 7/6	233.820917491300	52\52<7/6>, 27\52<7/6>, 25\52<7/6>	0, -0.005, 0.005	5.13213280007188	5.13213530145284
15/13	14/13, 15/14	27ed15/13	Alpha 15/13	130.781715879411	27\27<15/13>, 14\27<15/13>, 13\27<15/13>	0, 0.160, -0.160	9.17559455410784	9.17544822955784
		29ed15/13	Beta 15/13	140.469250388997	29\29<15/13>, 15\29<15/13>, 14\29<15/13>	0, -0.156, 0.156	8.54279492968661	8.54291879716245
		56ed15/13	Gamma 15/13	271.250966268408	56\56<15/13>, 29\56<15/13>, 27\56<15/13>	0, -0.004, 0.004	4.42394737430199	4.42394897687108
8/7	15/14, 16/15	29ed8/7	Alpha 8/7	150.535899020849	29\29<8/7>, 15\29<8/7>, 14\29<8/7>	0, 0.130, -0.130	7.97152046658190	7.97141745648869
		31ed8/7	Beta 8/7	160.917685160217	31\31<8/7>, 16\31<8/7>, 15\31<8/7>	0, -0.127, 0.127	7.45722882357662	7.45731699769858
		60ed8/7	Gamma 8/7	311.453584181066	60\60<8/7>, 31\60<8/7>, 29\60<8/7>	0, -0.003, 0.003	3.85290155884792	3.85290261769161

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