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: 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.

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
Equave	SSCP	Equal division	Name	Mappings (Equave, SSCP)	Errors	Pure Equave (EDO)	Pure Equave (Cent)	Dave Benson (EDO)	Dave Benson (Cent)
3/1	2/1, 3/2	3ed3/1	Alpha 3/1	3\3<3/1>, 2\3<3/1>, 1\3<3/1>	0, 67.970, -67.970	1.89278926071437	633.985000288462	1.90739592696007	629.130000247254
		5ed3/1	Beta 3/1	5\5<3/1>, 3\5<3/1>, 2\5<3/1>	0, -58.827, 58.827	3.15464876785729	380.391000173077	3.14186231690763	381.939079106782
		8ed3/1	Gamma 3/1	8\8<3/1>, 5\8<3/1>, 3\8<3/1>	0, -11.278, 11.278	5.04743802857166	237.744375108173	5.04255621376059	237.974540913462
2/1	3/2, 4/3	5ed2/1	Alpha 2/1	5\5<2/1>, 3\5<2/1>, 2\5<2/1>	0, 18.045, -18.045	5.00000000000000	240.000000000000	5.00991270509077	239.525131601721
		7ed2/1	Beta 2/1	7\7<2/1>, 4\7<2/1>, 3\7<2/1>	0, -16.241, 16.241	7.00000000000000	171.428571428571	6.99104980248710	171.648040552235
		12ed2/1	Gamma 2/1	12\12<2/1>, 7\12<2/1>, 5\12<2/1>	0, -1.955, 1.955	12.0000000000000	100.000000000000	11.9978480914311	100.017935787756
5/3	4/3, 5/4	7ed5/3	Alpha 5/3	7\7<5/3>, 4\7<5/3>, 3\7<5/3>	0, 7.303, -7.303	9.49840814199707	126.336958999921	9.50583353877785	126.238272015258
		9ed5/3	Beta 5/3	9\9<5/3>, 5\9<5/3>, 4\9<5/3>	0, -6.735, 6.735	12.2122390397105	98.2620792221608	12.2053823008782	98.3172808862904
		16ed5/3	Gamma 5/3	16\16<5/3>, 9\16<5/3>, 7\16<5/3>	0, -0.593, 0.593	21.7106471817076	55.2724195624655	21.7094399215509	55.2754932571412
3/2	5/4, 6/5	9ed3/2	Alpha 3/2	9\9<3/2>, 5\9<3/2>, 4\9<3/2>	0, 3.661, -3.661	15.3856016221631	77.9950000961542	15.3915238996928	77.9649895501219
		11ed3/2	Beta 3/2	11\11<3/2>, 6\11<3/2>, 5\11<3/2>	0, -3.429, 3.429	18.8046242048660	63.8140909877625	18.7990736394111	63.8329325698408
		20ed3/2	Gamma 3/2	20\20<3/2>, 11\20<3/2>, 9\20<3/2>	0, -0.238, 0.238	34.1902258270291	35.0977500432694	34.1894540921914	35.0985422804417
7/5	6/5, 7/6	11ed7/5	Alpha 7/5	11\11<7/5>, 6\11<7/5>, 5\11<7/5>	0, 2.093, -2.093	22.6604698881676	52.9556538731173	22.6653911133366	52.9441558718088
		13ed7/5	Beta 7/5	13\13<7/5>, 7\13<7/5>, 6\13<7/5>	0, -1.981, 1.981	26.7805553223799	44.8086302003300	26.7758951088566	44.8164289231577
		24ed7/5	Gamma 7/5	24\24<7/5>, 13\24<7/5>, 11\24<7/5>	0, -0.114, 0.114	49.4410252105475	24.2713413585121	49.4404896216012	24.2716042900130
4/3	7/6, 8/7	13ed4/3	Alpha 4/3	13\13<4/3>, 7\13<4/3>, 6\13<4/3>	0, 1.307, -1.307	31.3224709154917	38.3111537795856	31.3266790320926	38.3060074376432
		15ed4/3	Beta 4/3	15\15<4/3>, 8\15<4/3>, 7\15<4/3>	0, -1.247, 1.247	36.1413125947981	33.2029999423075	36.1372975038827	33.2066890135066
		28ed4/3	Gamma 4/3	28\28<4/3>, 15\28<4/3>, 13\28<4/3>	0, -0.061, 0.061	67.4637835102899	17.7873213976647	67.4633901646646	17.7874251067289
9/7	8/7, 9/8	15ed9/7	Alpha 9/7	15\15<9/7>, 8\15<9/7>, 7\15<9/7>	0, 0.871, -0.871	41.3713123417559	29.0056063507767	41.3749871639859	29.0030301458200
		17ed9/7	Beta 9/7	17\17<9/7>, 9\17<9/7>, 8\17<9/7>	0, -0.835, 0.835	46.8874873206567	25.5931820742147	46.8839609068713	25.5951070854196
		32ed9/7	Gamma 9/7	32\32<9/7>, 17\32<9/7>, 15\32<9/7>	0, -0.036, 0.036	88.2587996624126	13.5963779769266	88.2584985804157	13.5964243591413
5/4	9/8, 10/9	17ed5/4	Alpha 5/4	17\17<5/4>, 9\17<5/4>, 8\17<5/4>	0, 0.609, -0.609	52.8068232315916	22.7243361096962	52.8100843743057	22.7229328303033
		19ed5/4	Beta 5/4	19\19<5/4>, 10\19<5/4>, 9\19<5/4>	0, -0.587, 0.587	59.0193906706024	20.3323007297281	59.0162471250305	20.3333837452881
		36ed5/4	Gamma 5/4	36\36<5/4>, 19\36<5/4>, 17\36<5/4>	0, -0.022, 0.022	111.826213902194	10.7309364962454	111.825976049766	10.7309593208108
11/9	10/9, 11/10	19ed11/9	Alpha 11/9	19\19<11/9>, 10\19<11/9>, 9\19<11/9>	0, 0.443, -0.443	65.6288971357202	18.2846284544201	65.6318281194766	18.2838119001578
		21ed11/9	Beta 11/9	21\21<11/9>, 11\21<11/9>, 10\21<11/9>	0, -0.428, 0.428	72.5372020973750	16.5432352682849	72.5343665614942	16.5438819815521
		40ed11/9	Gamma 11/9	40\40<11/9>, 21\40<11/9>, 19\40<11/9>	0, -0.015, 0.015	138.166099233095	8.68519851584955	138.165906595462	8.68521062517612
6/5	11/10, 12/11	21ed6/5	Alpha 6/5	21\21<6/5>, 11\21<6/5>, 10\21<6/5>	0, 0.332, -0.332	79.8374643554025	15.0305374762168	79.8401257721902	15.0300364433792
		23ed6/5	Beta 6/5	23\23<6/5>, 12\23<6/5>, 11\23<6/5>	0, -0.322, 0.322	87.4410323892504	13.7235342174153	87.4384499734953	13.7239395296205
		44ed6/5	Gamma 6/5	44\44<6/5>, 23\44<6/5>, 21\44<6/5>	0, -0.010, 0.010	167.278496744653	7.17366561364892	167.278337553932	7.17367244048030
13/11	12/11, 13/12	23ed13/11	Alpha 13/11	23\23<13/11>, 12\23<13/11>, 11\23<13/11>	0, 0.255, -0.255	95.4324773621886	12.5743356262850	95.4349145508238	12.5740145066190
		25ed13/11	Beta 13/11	25\25<13/11>, 13\25<13/11>, 12\25<13/11>	0, -0.248, 0.248	103.730953654553	11.5683887761822	103.728582924337	11.5686531732080
		48ed13/11	Gamma 13/11	48\48<13/11>, 25\48<13/11>, 23\48<13/11>	0, -0.007, 0.007	199.163431016741	6.02520248759487	199.163297261208	6.02520653404413
7/6	13/12, 14/13	25ed7/6	Alpha 7/6	25\25<7/6>, 13\25<7/6>, 12\25<7/6>	0, 0.200, -0.200	112.413902640048	10.6748362241495	112.416150402631	10.6746227806420
		27ed7/6	Beta 7/6	27\27<7/6>, 14\27<7/6>, 13\27<7/6>	0, -0.195, 0.195	121.407014851252	9.88410761495324	121.404823766036	9.88428600096291
		52ed7/6	Gamma 7/6	52\52<7/6>, 27\52<7/6>, 25\52<7/6>	0, -0.005, 0.005	233.820917491300	5.13213280007188	233.820803527977	5.13213530145284
15/13	14/13, 15/14	27ed15/13	Alpha 15/13	27\27<15/13>, 14\27<15/13>, 13\27<15/13>	0, 0.160, -0.160	130.781715879411	9.17559455410784	130.783801507845	9.17544822955784
		29ed15/13	Beta 15/13	29\29<15/13>, 15\29<15/13>, 14\29<15/13>	0, -0.156, 0.156	140.469250388997	8.54279492968661	140.467213664560	8.54291879716245
		56ed15/13	Gamma 15/13	56\56<15/13>, 29\56<15/13>, 27\56<15/13>	0, -0.004, 0.004	271.250966268408	4.42394737430199	271.250868008139	4.42394897687108
8/7	15/14, 16/15	29ed8/7	Alpha 8/7	29\29<8/7>, 15\29<8/7>, 14\29<8/7>	0, 0.130, -0.130	150.535899020849	7.97152046658190	150.537844310638	7.97141745648869
		31ed8/7	Beta 8/7	31\31<8/7>, 16\31<8/7>, 15\31<8/7>	0, -0.127, 0.127	160.917685160217	7.45722882357662	160.915782495277	7.45731699769858
		60ed8/7	Gamma 8/7	60\60<8/7>, 31\60<8/7>, 29\60<8/7>	0, -0.003, 0.003	311.453584181066	3.85290155884792	311.453498588282	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