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.

3/1	2/1, 3/2	3ed3/1	Alpha 3/1	1.892789	633.985000	1.907395926960071	629.130000247253548	3\3<3/1>, 2\3<3/1>, 1\3<3/1>	0, 67.970001, -67.970001	-14.565000, 58.260000, -72.825001
		5ed3/1	Beta 3/1	3.154649	380.391000	3.141862316907629	381.939079106781893	5\5<3/1>, 3\5<3/1>, 2\5<3/1>	0, -58.826999, 58.826999	7.740395, -54.182763, 61.923157
		8ed3/1	Gamma 3/1	5.047438	237.744375	5.042556213760587	237.974540913461853	8\8<3/1>, 5\8<3/1>, 3\8<3/1>	0, -11.278124, 11.278124	1.841326, -10.127295, 11.968622
2/1	3/2, 4/3	5ed2/1	Alpha 2/1	5.000000	240.000000	5.009912705090773	239.525131601720722	5\5<2/1>, 3\5<2/1>, 2\5<2/1>	0, 18.044999, -18.044999	-2.374342, 16.620394, -18.994736
		7ed2/1	Beta 2/1	7.000000	171.428571	6.991049802487100	171.648040552234965	7\7<2/1>, 4\7<2/1>, 3\7<2/1>	0, -16.240715, 16.240715	1.536284, -15.362839, 16.899123
		12ed2/1	Gamma 2/1	12.000000	100.000000	11.997848091431052	100.017935787755848	12\12<2/1>, 7\12<2/1>, 5\12<2/1>	0, -1.955001, 1.955001	0.215229, -1.829450, 2.044680
5/3	4/3, 5/4	7ed5/3	Alpha 5/3	9.498408	126.336959	9.505833538777849	126.238272015257927	7\7<5/3>, 4\7<5/3>, 3\7<5/3>	0, 7.302837, -7.302837	-0.690809, 6.908089, -7.598898
		9ed5/3	Beta 5/3	12.212239	98.262079	12.205382300878206	98.317280886290400	9\9<5/3>, 5\9<5/3>, 4\9<5/3>	0, -6.734603, 6.734603	0.496815, -6.458595, 6.955410
		16ed5/3	Gamma 5/3	21.710647	55.272420	21.709439921550910	55.275493257141231	16\16<5/3>, 9\16<5/3>, 7\16<5/3>	0, -0.593223, 0.593223	0.049179, -0.565560, 0.614739
3/2	5/4, 6/5	9ed3/2	Alpha 3/2	15.385602	77.995000	15.391523899692793	77.964989550121895	9\9<3/2>, 5\9<3/2>, 4\9<3/2>	0, 3.661287, -3.661287	-0.270095, 3.511234, -3.781329
		11ed3/2	Beta 3/2	18.804624	63.814091	18.799073639411081	63.832932569840843	11\11<3/2>, 6\11<3/2>, 5\11<3/2>	0, -3.429168, 3.429168	0.207257, -3.316118, 3.523376
		20ed3/2	Gamma 3/2	34.190226	35.097750	34.189454092191388	35.098542280441702	20\20<3/2>, 11\20<3/2>, 9\20<3/2>	0, -0.238463, 0.238463	0.015845, -0.229749, 0.245594
7/5	6/5, 7/6	11ed7/5	Alpha 7/5	22.660470	52.955654	22.665391113336561	52.944155871808760	11\11<7/5>, 6\11<7/5>, 5\11<7/5>	0, 2.092636, -2.092636	-0.126478, 2.023648, -2.150126
		13ed7/5	Beta 7/5	26.780555	44.808630	26.775895108856630	44.816428923157735	13\13<7/5>, 7\13<7/5>, 6\13<7/5>	0, -1.980876, 1.980876	0.101383, -1.926285, 2.027668
		24ed7/5	Gamma 7/5	49.441025	24.271341	49.440489621601243	24.271604290013001	24\24<7/5>, 13\24<7/5>, 11\24<7/5>	0, -0.113849, 0.113849	0.006310, -0.110431, 0.116742
4/3	7/6, 8/7	13ed4/3	Alpha 4/3	31.322471	38.311154	31.326679032092577	38.306007437643215	13\13<4/3>, 7\13<4/3>, 6\13<4/3>	0, 1.307171, -1.307171	-0.066902, 1.271146, -1.338049
		15ed4/3	Beta 4/3	36.141313	33.203000	36.137297503882719	33.206689013506551	15\15<4/3>, 8\15<4/3>, 7\15<4/3>	0, -1.246906, 1.246906	0.055336, -1.217393, 1.272730
		28ed4/3	Gamma 4/3	67.463784	17.787321	67.463390164664623	17.787425106728855	28\28<4/3>, 15\28<4/3>, 13\28<4/3>	0, -0.061085, 0.061085	0.002904, -0.059529, 0.062433
9/7	8/7, 9/8	15ed9/7	Alpha 9/7	41.371312	29.005606	41.374987163985893	29.003030145820039	15\15<9/7>, 8\15<9/7>, 7\15<9/7>	0, 0.870757, -0.870757	-0.038643, 0.850148, -0.888791
		17ed9/7	Beta 9/7	46.887487	25.593182	46.883960906871343	25.595107085419638	17\17<9/7>, 9\17<9/7>, 8\17<9/7>	0, -0.835455, 0.835455	0.032725, -0.818130, 0.850855
		32ed9/7	Gamma 9/7	88.258800	13.596378	88.258498580415662	13.596424359141285	32\32<9/7>, 17\32<9/7>, 15\32<9/7>	0, -0.035668, 0.035668	0.001484, -0.034879, 0.036364
5/4	9/8, 10/9	17ed5/4	Alpha 5/4	52.806823	22.724336	52.810084374305705	22.722932830303330	17\17<5/4>, 9\17<5/4>, 8\17<5/4>	0, 0.609023, -0.609023	-0.023856, 0.596394, -0.620249
		19ed5/4	Beta 5/4	59.019391	20.332301	59.016247125030467	20.333383745288099	19\19<5/4>, 10\19<5/4>, 9\19<5/4>	0, -0.586994, 0.586994	0.020577, -0.576164, 0.596742
		36ed5/4	Gamma 5/4	111.826214	10.730936	111.825976049765954	10.730959320810789	36\36<5/4>, 19\36<5/4>, 17\36<5/4>	0, -0.022208, 0.022208	0.000822, -0.021775, 0.022596
11/9	10/9, 11/10	19ed11/9	Alpha 11/9	65.628897	18.284628	65.631828119476568	18.283811900157846	19\19<11/9>, 10\19<11/9>, 9\19<11/9>	0, 0.442572, -0.442572	-0.015515, 0.434407, -0.449921
		21ed11/9	Beta 11/9	72.537202	16.543235	72.534366561494206	16.543881981552112	21\21<11/9>, 11\21<11/9>, 10\21<11/9>	0, -0.428124, 0.428124	0.013581, -0.421010, 0.434591
		40ed11/9	Gamma 11/9	138.166099	8.685199	138.165906595462172	8.685210625176124	40\40<11/9>, 21\40<11/9>, 19\40<11/9>	0, -0.014543, 0.014543	0.000484, -0.014289, 0.014773
6/5	11/10, 12/11	21ed6/5	Alpha 6/5	79.837464	15.030537	79.840125772190183	15.030036443379233	21\21<6/5>, 11\21<6/5>, 10\21<6/5>	0, 0.331684, -0.331684	-0.010522, 0.326172, -0.336694
		23ed6/5	Beta 6/5	87.441032	13.723534	87.438449973495273	13.723939529620542	23\23<6/5>, 12\23<6/5>, 11\23<6/5>	0, -0.321818, 0.321818	0.009322, -0.316954, 0.326276
		44ed6/5	Gamma 6/5	167.278497	7.173666	167.278337553931523	7.173672440480304	44\44<6/5>, 23\44<6/5>, 21\44<6/5>	0, -0.009919, 0.009919	0.000300, -0.009762, 0.010063
13/11	12/11, 13/12	23ed13/11	Alpha 13/11	95.432477	12.574336	95.434914550823771	12.574014506618971	23\23<13/11>, 12\23<13/11>, 11\23<13/11>	0, 0.254969, -0.254969	-0.007386, 0.251116, -0.258501
		25ed13/11	Beta 13/11	103.730954	11.568389	103.728582924336770	11.568653173208022	25\25<13/11>, 13\25<13/11>, 12\25<13/11>	0, -0.248004, 0.248004	0.006610, -0.244567, 0.251177
		48ed13/11	Gamma 13/11	199.163431	6.025202	199.163297261207502	6.025206534044126	48\48<13/11>, 25\48<13/11>, 23\48<13/11>	0, -0.006996, 0.006996	0.000194, -0.006895, 0.007089
7/6	13/12, 14/13	25ed7/6	Alpha 7/6	112.413903	10.674836	112.416150402630623	10.674622780642016	25\25<7/6>, 13\25<7/6>, 12\25<7/6>	0, 0.200210, -0.200210	-0.005336, 0.197435, -0.202771
		27ed7/6	Beta 7/6	121.407015	9.884108	121.404823766036118	9.884286000962910	27\27<7/6>, 14\27<7/6>, 13\27<7/6>	0, -0.195154, 0.195154	0.004816, -0.192657, 0.197473
		52ed7/6	Gamma 7/6	233.820917	5.132133	233.820803527976982	5.132135301452842	52\52<7/6>, 27\52<7/6>, 25\52<7/6>	0, -0.005075, 0.005075	0.000130, -0.005008, 0.005138
15/13	14/13, 15/14	27ed15/13	Alpha 15/13	130.781716	9.175595	130.783801507844919	9.175448229557843	27\27<15/13>, 14\27<15/13>, 13\27<15/13>	0, 0.160079, -0.160079	-0.003951, 0.158031, -0.161981
		29ed15/13	Beta 15/13	140.469250	8.542795	140.467213664559518	8.542918797162452	29\29<15/13>, 15\29<15/13>, 14\29<15/13>	0, -0.156321, 0.156321	0.003592, -0.154463, 0.158055
		56ed15/13	Gamma 15/13	271.250966	4.423947	271.250868008139347	4.423948976871078	56\56<15/13>, 29\56<15/13>, 27\56<15/13>	0, -0.003771, 0.003771	0.000090, -0.003724, 0.003814
8/7	15/14, 16/15	29ed8/7	Alpha 8/7	150.535899	7.971520	150.537844310638475	7.971417456488689	29\29<8/7>, 15\29<8/7>, 14\29<8/7>	0, 0.129999, -0.129999	-0.002987, 0.128454, -0.131441
		31ed8/7	Beta 8/7	160.917685	7.457229	160.915782495277457	7.457316997698579	31\31<8/7>, 16\31<8/7>, 15\31<8/7>	0, -0.127147, 0.127147	0.002733, -0.125736, 0.128470
		60ed8/7	Gamma 8/7	311.453584	3.852902	311.453498588281532	3.852902617691610	60\60<8/7>, 31\60<8/7>, 29\60<8/7>	0, -0.002860, 0.002860	0.000064, -0.002827, 0.002891

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