Canopus
Canopus is the rank two 3.5.7 temperament tempering out 16875/16807. Having a generator of ~7:5, it possesses non-trivial MOS of the families 1L 2s (triad), 3L 1s (tetrad), 3L 4s ("neutral" diatonic) and 3L 7s (augmented neutral decatonic). On either side the greater region where it appears, there appear the most important, though as yet unnamed, tritave-equivalent temperaments which retain twos, they being important for using a (smeary) ~4:3 or 3:2 as a generator.
The Sigma and Anti-Sigma (Mu) MOS families of 8L+3s and 3L+8s (unfair) or 4L+7s and 7L+4s (fair), but especially the unfair families which by definition include an interval for the function of an "ordinary" ~2:1, are good scales to know for the conceptualizations they provide of how an "ordinary" diatonic or anti-diatonic scale extends into a tritave equivalence (8L+3s being in fact the Obikhod pitch set used in Russian Orthodox chants). These scales are neighbors of the 7&3 region where the 3L+7s Canopus decatonic scale appears. Below is a list of equal temperaments which contain these scales using generators between or 475.5 and 713.2 cents:
| L=1 s=0 8 edt | L=1 s=0 7 edt | L=1 s=0 3 edt |
| L=7 s=1 59 | L=7 s=1 53 | L=7 s=1 28 |
| L=6 s=1 51 | L=6 s=1 46 | L=6 s=1 25 |
| L=5 s=1 43 | L=5 s=1 39 | L=5 s=1 22 |
| L=4 s=1 35 | L=4 s=1 32 | L=4 s=1 19 |
| L=7 s=2 62 | L=7 s=2 57 | L=7 s=2 35 |
| L=3 s=1 27 | L=3 s=1 25 | L=3 s=1 16 |
| L=5 s=2 46 | L=5 s=2 43 | L=5 s=2 29 |
| L=7 s=3 65 | L=7 s=3 61 | L=7 s=3 42 |
| L=2 s=1 19 | L=2 s=1 18 | L=2 s=1 13 |
| L=7 s=4 68 | L=7 s=4 65 | L=7 s=4 49 |
| L=5 s=3 49 | L=5 s=3 47 | L=5 s=3 36 |
| L=3 s=2 30 | L=3 s=2 29 | L=3 s=2 23 |
| L=7 s=5 71 | L=7 s=5 69 | L=7 s=5 56 |
| L=4 s=3 41 | L=4 s=3 40 | L=4 s=3 33 |
| L=5 s=4 52 | L=5 s=4 51 | L=5 s=4 43 |
| L=6 s=5 63 | L=6 s=5 62 | L=6 s=5 53 |
| L=7 s=6 74 | L=7 s=6 73 | L=7 s=6 63 |
| L=1 s=1 11 edt | L=1 s=1 10 edt | |
| L=7 s=6 69 | L=7 s=6 70 | L=7 s=6 67 |
| L=6 s=5 58 | L=6 s=5 59 | L=6 s=5 57 |
| L=5 s=4 47 | L=5 s=4 48 | L=5 s=4 47 |
| L=4 s=3 36 | L=4 s=3 37 | L=4 s=3 37 |
| L=7 s=5 61 | L=7 s=5 63 | L=7 s=5 64 |
| L=3 s=2 25 | L=3 s=2 26 | L=3 s=2 27 |
| L=5 s=3 39 | L=5 s=3 41 | L=5 s=3 44 |
| L=7 s=4 53 | L=7 s=4 56 | L=7 s=4 61 |
| L=2 s=1 14 | L=2 s=1 15 | L=2 s=1 17 |
| L=7 s=3 45 | L=7 s=3 49 | L=7 s=3 58 |
| L=5 s=2 31 | L=5 s=2 30 | L=5 s=2 41 |
| L=3 s=1 17 | L=3 s=1 19 | L=3 s=1 24 |
| L=7 s=2 37 | L=7 s=2 42 | L=7 s=2 55 |
| L=4 s=1 20 | L=4 s=1 23 | L=4 s=1 31 |
| L=5 s=1 23 | L=5 s=1 27 | L=5 s=1 38 |
| L=6 s=1 26 | L=6 s=1 31 | L=6 s=1 45 |
| L=7 s=1 29 | L=7 s=1 35 | L=7 s=1 52 |
| L=1 s=0 3 edt | L=1 s=0 4 edt | L=1 s=0 7 edt |
As the table shows, the two families overlap at several equal temperaments within the first sixteen proper members of each tree due to the fact that the chain of ~4:3s forms an index-2 subtemperament of a chain of ~3:2s under tritave equivalence. Beyond that, the unfair Sigma and Mu scales match the EDO-EDT correspondences due to their definition including an interval with the function of an "ordinary" ~2:1 which can nevertheless be off by up to +68.0 cents and the fair scales compare to 5a+2b edos in a completely backwards way, with 7L+4s actually comparing to the anti-diatonic scale but being contained in the larger edts. This backward way that the fair scales compare to edos creates an interesting coincidence between 27edt and 27edo both as generated by an ~4:3.
| Generator | cents
hekts |
L | s | notes | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 3\8 | 713.23
487.5 |
237.74
162.5 |
0 | |||||||
| 22\59 | 709.2
484.75 |
225.66
154.24 |
32.24
22.03 |
|||||||
| 19\51 | 708.57
484.31 |
223.76
152.94 |
37.29
25.49 |
|||||||
| 35\94 | 708.175
484.04 |
222.57
152.13 |
40.47
27.66 |
|||||||
| 16\43 | 707.74
483.72 |
221.16
151.16 |
44.23
29.23 |
|||||||
| 45\121 | 707.34
483.47 |
220.06
150.41 |
47.16
32.23 |
|||||||
| 29\78 | 707.14
483.33 |
219.46
150 |
48.77
33.33 |
|||||||
| 42\113 | 706.92
483.19 |
218.81
149.56 |
50.49
34.51 |
|||||||
| 13\35 | 706.44
482.86 |
217.37
148.57 |
54.34
35.71 |
|||||||
| 49\132 | 706.03
482.58 |
216.13
147.73 |
57.635
39.39 |
|||||||
| 36\97 | 705.88
482.47 |
215.69
147.42 |
58.82
40.21 |
|||||||
| 59\159 | 705.76
482.39 |
216.32
147.17 |
59.81
40.88 |
|||||||
| 23\62 | 705.56
482.26 |
214.74
146.77 |
61.35
41.935 |
|||||||
| 56\151 | 705.36
482.12 |
214.13
146.36 |
62.98
43.05 |
|||||||
| 33\89 | 705.22
482.02 |
213.7
146.07 |
64.11
43.82 |
|||||||
| 43\116 | 705.035
481.9 |
213.15
145.69 |
65.585
44.83 |
|||||||
| 10\27 | 704.43
481.48 |
211.33
144.44 |
70.44
48.15 |
|||||||
| 47\127 | 703.87
481.1 |
209.66
143.31 |
74.88
51.18 |
|||||||
| 37\100 | 703.72
481 |
209.215
143 |
76.08
52 |
|||||||
| 64\173 | 703.61
480.925 |
208.885
142.775 |
76,96
52.6 |
|||||||
| 27\73 | 703.46
480.82 |
208.43
142.47 |
78.16
53.425 |
|||||||
| 71\192 | 703.33
480.73 |
208.03
142.19 |
79.25
54.17 |
|||||||
| 44\119 | 703.24
480.67 |
207.78
142.02 |
79.91
54.62 |
|||||||
| 61\165 | 703.15
480.61 |
207.49
141.82 |
80.69
55.15 |
|||||||
| 17\46 | 702.9
480.435 |
206.73
141.3 |
82.69
56.52 |
|||||||
| 58\157 | 702.63
480.255 |
205.94
140.76 |
84.8
57.96 |
|||||||
| 41\111 | 702.52
480.18 |
205.62
140.54 |
85.67
58.56 |
|||||||
| 65\176 | 702.43
480.11 |
205.325
140.34 |
86.45
59.09 |
|||||||
| 24\65 | 702.26
480 |
204.83
140 |
87.78
60 |
|||||||
| 55\149 | 702.06
479.87 |
204.24
139.6 |
89.35
61.07 |
|||||||
| 31\84 | 701.91
479.76 |
203.78
139.29 |
90.57
61.905 |
|||||||
| 38\103 | 701.69
479.61 |
203.12
138.835 |
92.34
63.11 |
|||||||
| 7\19 | 700.72
478.95 |
200.21
136.84 |
100.1
68.42 |
Boundary of propriety for unfair Sigma scale | ||||||
| 39\106 | 699.78
478.3 |
197.37
134.91 |
107.66
73.585 |
|||||||
| 32\87 | 699.57
478.16 |
196.75
134.48 |
109.31
74.71 |
|||||||
| 57\155 | 699.43
478.065 |
196.33
134.19 |
110.44
75.48 |
|||||||
| 25\68 | 699.25
477.94 |
195.71
133.82 |
111.88
76.47 |
|||||||
| 68\185 | 699.1
477.84 |
195.34
133.51 |
113.09
77.3 |
|||||||
| 43\117 | 699.01
477.78 |
195.07
133.33 |
113.79
77.78 |
|||||||
| 61\166 | 698.91
477.71 |
194.78
133.13 |
114.58
78.31 |
|||||||
| 18\49 | 698.68
477.55 |
194.08
132.65 |
116.45
79.59 |
|||||||
| 65\177 | 698.46
477.4 |
193.42
132.2 |
118.2
80.79 |
|||||||
| 47\128 | 698.37
477.34 |
193.17
132.03 |
118.87
81.25 |
|||||||
| 76\207 | 698.3
477.295 |
192.95
131.88 |
119.45
81.64 |
Golden unfair Sigma scale is near here | ||||||
| 29\79 | 698.19
477.215 |
192.6
131.65 |
120.38
82.28 |
|||||||
| 69\188 | 698.05
477.13 |
192.22
131.38 |
121.4
82.98 |
|||||||
| 40\109 | 697.965
477.06 |
191.94
131.19 |
122.14
83.49 |
|||||||
| 51\139 | 697.84
476.98 |
191.56
130.935 |
123.15
84.17 |
|||||||
| 11\30 | 697.38
476.67 |
190.2
130 |
126.8
86.67 |
|||||||
| 48\131 | 696.9
476.34 |
188.74
129.01 |
130.67
89.31 |
|||||||
| 37\101 | 696.76
176.24 |
188.31
128.71 |
131.82
90.1 |
|||||||
| 63\172 | 696.65
176.16 |
187.98
128.49 |
132.695
90.7 |
|||||||
| 26\71 | 696.49
476.06 |
187.52
128.17 |
133.94
91.55 |
|||||||
| 67\183 | 696.34
475.96 |
187.08
127.87 |
135.11
92.35 |
|||||||
| 41\112 | 696.25
475.89 |
186.8
127.68 |
135.85
92.86 |
|||||||
| 56\153 | 696.14
475.82 |
186.47
127.45 |
136.74
93.46 |
|||||||
| 15\41 | 695.84
475.61 |
185.56
126.83 |
139.17
95.12 |
|||||||
| 49\134 | 695.49
475.37 |
184.52
126.12 |
141.94
97.01 |
|||||||
| 34\93 | 695.34
475.27 |
184.06
125.81 |
143.16
97.85 |
|||||||
| 53\145 | 695.2
475.17 |
183.64
125.51 |
144.29
98.62 |
|||||||
| 19\52 | 694.945
475 |
182.88
125 |
146.3
100 |
|||||||
| 42\115 | 694.63
474.78 |
181.93
124.35 |
148.85
131.74 |
|||||||
| 23\63 | 694.365
474.6 |
181.14
123.81 |
150.95
103.175 |
|||||||
| 27\74 | 693.96
474.32 |
179.915
122.97 |
154.21
105.405 |
|||||||
| 4\11 | 691.62
472.73 |
172.905
118.18 |
Separatrix of unfair Sigma and Mu scales | |||||||
| 25\69 | 689.11
471.01 |
192.95
131.88 |
165.39
113.04 |
|||||||
| 21\58 | 688.64
470.69 |
196.75
134.48 |
163.96
112.07 |
|||||||
| 38\105 | 688.33
470.48 |
199.25
136.19 |
163.025
111.43 |
|||||||
| 17\47 | 687.94
470.21 |
202.34
138.3 |
161.87
110.64 |
|||||||
| 47\130 | 687.63
470 |
204.83
140 |
160.935
110 |
|||||||
| 30\83 | 687.45
469.88 |
206.24
140.96 |
160.41
109.64 |
|||||||
| 43\119 | 687.26
469.75 |
207.78
142.02 |
159.83
109.24 |
|||||||
| 13\36 | 686.82
469.44 |
211.33
144.44 |
158.5
108.33 |
|||||||
| 48\133 | 686.42
469.17 |
214.51
146.62 |
157.305
107.52 |
|||||||
| 35\97 | 686.27
469.07 |
215.69
147.42 |
156.86
107.22 |
|||||||
| 57\158 | 686.15
468.99 |
216.68
148.1 |
156.49
106.96 |
|||||||
| 22\61 | 685.95
468.85 |
218.26
149.18 |
155.9
106.56 |
|||||||
| 53\147 | 685.74
468.71 |
219.95
150.34 |
155.26
106.12 |
|||||||
| 31\86 | 685.59
468.605 |
221.16
151.16 |
154.81
105.81 |
|||||||
| 40\111 | 685.39
468.47 |
222.75
152.25 |
154.21
105.405 |
|||||||
| 9\25 | 684.7
468 |
228.235
156 |
152.16
104 |
|||||||
| 41\114 | 684.04
467.54 |
233.57
159.65 |
150.15
102.63 |
|||||||
| 32\89 | 683.85
467.42 |
235.07
160.67 |
149.59
102.25 |
|||||||
| 55\153 | 683.71
467.37 |
236.19
161.44 |
149.17
101.96 |
|||||||
| 23\64 | 683.515
467.19 |
237.74
162.5 |
148.5
101.56 |
|||||||
| 60\167 | 683.34
467.07 |
239.17
163.47 |
148.06
101.2 |
Golden unfair Mu scale is near here | ||||||
| 37\103 | 683.23
466.99 |
240.05
164.08 |
147.725
100.97 |
|||||||
| 51\142 | 683.1
466.9 |
241.09
164.79 |
147.335
100.7 |
|||||||
| 14\39 | 682.75
466.67 |
243.84
166.67 |
146.3
100 |
|||||||
| 47\131 | 682.38
466.41 |
246.815
168.7 |
145.19
99.24 |
|||||||
| 33\92 | 682.22
466.3 |
248.08
169.565 |
144.71
98.91 |
|||||||
| 52\145 | 682.08
466.21 |
249.22
170.345 |
144.29
98.62 |
|||||||
| 19\53 | 681.83
466.04 |
251.2
171.7 |
143.54
98.11 |
|||||||
| 43\120 | 681.53
465.83 |
253.59
173.33 |
142.65
97.5 |
|||||||
| 24\67 | 681.3
465.67 |
255.49
174.63 |
141.94
97.015 |
|||||||
| 29\81 | 680.95
465.43 |
258.29
176.54 |
140.89
96.3 |
|||||||
| 5\14 | 679.27
464.29 |
271.71
185.71 |
135.85
92.86 |
Boundary of propriety for unfair Mu scale | ||||||
| 26\73 | 677.48
463.01 |
286.6
195.89 |
130.27
89.04 |
|||||||
| 21\59 | 676.97
462.71 |
290.13
198.305 |
128.95
88.14 |
|||||||
| 37\104 | 676.66
462.5 |
292.61
200 |
128.02
87.5 |
|||||||
| 16\45 | 676.25
462.22 |
295.86
202.22 |
126.78
86.67 |
|||||||
| 43\121 | 675.9
461.98 |
298.65
204.13 |
125.75
85.95 |
|||||||
| 27\76 | 675.695
461.84 |
300.31
205.26 |
125.13
85.53 |
|||||||
| 38\107 | 675.46
461.68 |
302.18
206.54 |
124.43
85.05 |
|||||||
| 11\31 | 674.89
461.29 |
306.77
209.68 |
122.71
83.87 |
|||||||
| 39\110 | 674.33
460.91 |
311.23
212.73 |
121.03
82.73 |
|||||||
| 28\79 | 674.12
460.76 |
312.98
213.92 |
120.38
82.28 |
|||||||
| 45\127 | 673.92
460.63 |
314.5
214.96 |
119.81
81.89 |
|||||||
| 17\48 | 673.61
460.42 |
316.99
216.67 |
118.87
81.25 |
|||||||
| 40\113 | 673.26
460.18 |
319.8
218.58 |
117.82
80.53 |
|||||||
| 23\65 | 673
460 |
321.89
220 |
117.04
80 |
|||||||
| 29\82 | 672.64
459.76 |
324.72
221.95 |
115.97
79.27 |
|||||||
| 6\17 | 671.28
458.82 |
335.64
229.41 |
111.88
76.47 |
|||||||
| 25\71 | 669.7
457.75 |
348.245
238.03 |
107.15
73.24 |
|||||||
| 19\54 | 669.21
457.41 |
352.21
240.74 |
105.66
72.22 |
|||||||
| 32\91 | 668.82
457.14 |
355.31
242.86 |
104.5
71.43 |
|||||||
| 13\37 | 668.25
456.76 |
359.83
245.95 |
102.81
70.27 |
|||||||
| 33\94 | 667.71
456.38 |
364.2
248.94 |
101.17
69.15 |
|||||||
| 20\57 | 667.35
456.14 |
367.04
250.88 |
100.1
68.42 |
|||||||
| 27\77 | 666.92
455.84 |
370.51
253.25 |
98.8
67.53 |
|||||||
| 7\20 | 665.68
455 |
380.39
260 |
95.1
65 |
|||||||
| 22\63 | 664.175
453.97 |
392.37
268.25 |
90.57
61.905 |
|||||||
| 15\43 | 663.47
453.49 |
398.08
272.09 |
88.46
60.465 |
|||||||
| 23\66 | 662.8
453.03 |
403.445
275.76 |
86.45
59.09 |
|||||||
| 8\23 | 661.55
452.17 |
413.47
282.61 |
82.69
56.52 |
|||||||
| 17\49 | 659.86
451.02 |
426.97
291.84 |
73.63
53.06 |
|||||||
| 9\26 | 658.37
450 |
439.81
300 |
73.15
50 |
|||||||
| 10\29 | 655.85
448.28 |
459.09
313.79 |
65.585
44.83 |
|||||||
| 1\3 | 633.985
433.33 |
0 | ||||||||
| 9\28 | 611.34
417.86 |
475.49
325 |
67.92
46.43 |
|||||||
| 8\25 | 608.63
416 |
456.47
312 |
76.08
52 |
|||||||
| 15\47 | 607.01
414.89 |
445.39
304.255 |
80.93
55.32 |
|||||||
| 7\22 | 605.18
413.64 |
432.26
295.455 |
86.45
59.09 |
|||||||
| 20\63 | 603.795
412.7 |
422.66
288.89 |
90.57
61.905 |
|||||||
| 13\41 | 603.06
412.195 |
417.5
285.37 |
92.78
63.415 |
|||||||
| 19\60 | 602.29
411.67 |
412.09
281.67 |
95.1
65 |
|||||||
| 6\19 | 600.62
410.53 |
400.41
273.68 |
100.11
68.42 |
|||||||
| 23\73 | 599.25
409.59 |
390.81
267.12 |
104.22
71.23 |
|||||||
| 17\54 | 598.76
409.26 |
387.425
264.815 |
105.66
72.22 |
|||||||
| 28\89 | 598.37
408.99 |
384.665
262.92 |
106.85
73.03 |
|||||||
| 11\35 | 597.76
408.57 |
380.39
260 |
108.68
74.29 |
|||||||
| 27\86 | 597.125
408.14 |
375.97
256.98 |
110.58
75.58 |
|||||||
| 16\51 | 596.69
407.84 |
372.93
254.9 |
111.88
76.47 |
|||||||
| 21\67 | 596.135
407.46 |
369.04
252.24 |
113.55
77.61 |
|||||||
| 5\16 | 594.36
406.25 |
356.62
243.75 |
118.87
81.25 |
|||||||
| 24\77 | 592.82
405.195 |
345.81
236.36 |
123.5
84.42 |
|||||||
| 19\61 | 592.41
404.92 |
342.975
234.43 |
124.72
85.25 |
|||||||
| 33\106 | 592.12
404.72 |
340.92
233.02 |
125.6
85.85 |
|||||||
| 14\45 | 591.72
404.44 |
338.125
231.11 |
126.8
86.67 |
|||||||
| 37\119 | 591.36
404.2 |
335.64
229.41 |
127.86
87.395 |
|||||||
| 23\74 | 591.15
404.05 |
334.13
228.38 |
128.51
87.84 |
|||||||
| 32\103 | 590.9
403.88 |
332.38
227.18 |
129.26
88.35 |
|||||||
| 9\29 | 590.26
403.45 |
327.92
224.14 |
131.17
89.655 |
|||||||
| 31\100 | 589.61
403 |
323.33
221 |
133.14
91 |
|||||||
| 22\71 | 589.34
402.82 |
321.46
219.72 |
133.94
91.55 |
|||||||
| 35\113 | 589.1
402.655 |
319.8
218.58 |
134.65
92.035 |
|||||||
| 13\42 | 588.7
402.38 |
316.99
216.67 |
135.85
92.86 |
|||||||
| 30\97 | 588.23
402.06 |
313.725
214.43 |
137.25
93.81 |
|||||||
| 17\55 | 587.88
401.82 |
311.23
212.73 |
138.32
94.545 |
|||||||
| 21\68 | 587.37
401.47 |
307.67
210.29 |
139.85
95.59 |
|||||||
| 4\13 | 585.22
400 |
292.61
200 |
146.3
100 |
|||||||
| 23\75 | 583.27
398.67 |
278.95
190.67 |
152.16
104 |
|||||||
| 19\62 | 582.86
398.39 |
276.09
188.71 |
153.38
104.84 |
|||||||
| 34\111 | 582.58
398.2 |
274.16
187.39 |
154.21
105.405 |
|||||||
| 15\49 | 582.23
397.96 |
271.71
185.71 |
155.26
106.12 |
|||||||
| 41\134 | 581.94
397.76 |
269.68
184.33 |
156.13
106.72 |
|||||||
| 26\85 | 581.77
397.65 |
268.51
183.53 |
156.63
107.06 |
|||||||
| 37\121 | 581.59
397.52 |
267.22
182.645 |
157.19
107.44 |
|||||||
| 11\36 | 581.15
397.22 |
264.16
180.56 |
158.5
108.33 |
|||||||
| 40\131 | 580.75
396.95 |
261.34
178.63 |
150.71
109.16 |
|||||||
| 29\95 | 580.6
396.84 |
260.27
177.895 |
160.165
109.47 |
|||||||
| 47\154 | 580.47
396.75 |
259.36
177.27 |
160.555
109.74 |
|||||||
| 18\59 | 580.26
396.61 |
257.89
176.27 |
161.18
110.17 |
|||||||
| 43\141 | 580.03
396.45 |
259.29
175.18 |
161.87
110.64 |
|||||||
| 25\82 | 579.86
396.34 |
255.14
174.39 |
162.36
110.98 |
|||||||
| 32\105 | 579.64
396.19 |
253.59
173.33 |
163.025
111.43 |
|||||||
| 7\23 | 578.86
395.65 |
248.08
169.565 |
165.39
113.04 |
|||||||
| 31\102 | 578.045
395.1 |
242.41
165.69 |
167.82
114.71 |
|||||||
| 24\79 | 577.81
394.94 |
240.75
164.56 |
168.53
115.19 |
|||||||
| 41\135 | 577.63
394.815 |
239.505
163.7 |
169.06
115.56 |
|||||||
| 17\56 | 577.38
394.64 |
237.74
162.5 |
169.82
116.07 |
|||||||
| 44\145 | 577.145
394.48 |
236.105
161.38 |
170.52
116.55 |
|||||||
| 27\89 | 577
394.38 |
235.07
160.67 |
170.96
116.85 |
|||||||
| 37\122 | 576.82
394.26 |
233.85
159.84 |
171.49
117.21 |
|||||||
| 10\33 | 576.35
393.94 |
230.54
157.58 |
172.905
118.18 |
|||||||
| 33\109 | 575.82
393.58 |
226.84
155.05 |
174.49
119.27 |
|||||||
| 23\76 | 575.59
393.42 |
225.23
153.95 |
175.18
119.74 |
|||||||
| 36\119 | 575.38
393.28 |
223.76
152.94 |
175.81
120.17 |
|||||||
| 13\43 | 575.01
393.02 |
221.16
151.16 |
176.93
120.93 |
|||||||
| 29\96 | 574,55
392.71 |
217.93
148.96 |
178.31
121.875 |
|||||||
| 16\53 | 574.175
392.45 |
215.32
147.17 |
179.43
122.64 |
|||||||
| 19\63 | 573.605
392.06 |
211.33
144.44 |
181.14
123.81 |
|||||||
| 3\10 | 570.59
390 |
190.2
130 |
||||||||
| 20\67 | 567.75
388.06 |
198.72
135.82 |
170.32
116.42 |
|||||||
| 17\57 | 567.25
387.72 |
200.21
136.84 |
166.84
114.035 |
|||||||
| 31\104 | 566.93
387.5 |
201.17
137.5 |
164.5
112.5 |
|||||||
| 14\47 | 566.54
387.23 |
202.34
138.3 |
161.87
110.64 |
|||||||
| 39\131 | 566.23
387.02 |
203.26
138.93 |
159.71
109.16 |
|||||||
| 25\84 | 566.06
386.905 |
203.78
139.29 |
158.5
108.33 |
|||||||
| 36\121 | 565.87
386.78 |
204.34
139.67 |
157.19
107.44 |
|||||||
| 11\37 | 565.45
386.49 |
205.62
140.54 |
154.21
105.405 |
|||||||
| 41\138 | 565.07
386.23 |
206.73
141.3 |
151.605
103.62 |
|||||||
| 30\101 | 564.94
386.14 |
207.14
141.58 |
150.65
102.97 |
|||||||
| 49\165 | 564.82
386.06 |
207.49
141.82 |
149.85
102.42 |
|||||||
| 19\64 | 564.64
385.94 |
208.03
142.18 |
148.59
101.625 |
|||||||
| 46\155 | 564.45
385.81 |
208.6
142.58 |
147.25
100.645 |
|||||||
| 27\91 | 564.32
385.71 |
209
142.86 |
146.3
100 |
|||||||
| 35\118 | 564.14
385.59 |
209.54
143.22 |
145.06
99.15 |
|||||||
| 8\27 | 563.54
385.185 |
211.33
144.44 |
140.89
96.3 |
|||||||
| 37\125 | 562.98
384.8 |
213.02
145.6 |
136.94
93.6 |
|||||||
| 29\98 | 562.82
384.693 |
213.485
145.92 |
135.85
92.86 |
|||||||
| 50\169 | 562.71
384.615 |
213.83
146.15 |
135.05
92.31 |
|||||||
| 21\71 | 562.55
384.51 |
214.3
146.48 |
133.94
91.55 |
|||||||
| 55\186 | 562.41
384.41 |
214.74
146.77 |
132.93
90.86 |
|||||||
| 34\115 | 562.32
384.35 |
215
146.96 |
132.31
90.435 |
|||||||
| 47\159 | 562.21
384.28 |
215.32
147.17 |
131.58
89.94 |
|||||||
| 13\44 | 561.94
384.09 |
216.13
147.73 |
129.68
88.64 |
|||||||
| 44\149 | 561.65
383.89 |
217
148.32 |
127.65
87.25 |
|||||||
| 31\105 | 561.53
383.81 |
217.37
148.57 |
126.8
86.67 |
|||||||
| 49\166 | 561.42
383.735 |
217.69
148.795 |
126.03
86.145 |
|||||||
| 18\61 | 561.23
383.61 |
218.26
149.18 |
124.72
85.25 |
|||||||
| 41\139 | 561.01
383.45 |
218.93
149.64 |
123.15
85.17 |
|||||||
| 23\78 | 560.83
383.33 |
219.46
150 |
121.92
83.33 |
|||||||
| 28\95 | 560.58
383.16 |
220.23
150.53 |
120.12
82.105 |
|||||||
| 5\17 | 559.4
382.35 |
223.76
152.94 |
111.88
76.47 |
|||||||
| 27\92 | 558.18
381.51 |
227.41
155.435 |
103.37
70.65 |
|||||||
| 22\75 | 557.91
381.33 |
228.235
156 |
101.44
69.33 |
|||||||
| 39\133 | 557.72
381.2 |
228.81
156.39 |
100.1
68.42 |
|||||||
| 17\58 | 557.47
381.03 |
229.55
156.9 |
98.38
67.24 |
|||||||
| 46\157 | 557.26
380.89 |
230.17
157.325 |
96.915
66.24 |
|||||||
| 29\99 | 557.14
380.81 |
230.54
157.58 |
96.06
65.66 |
|||||||
| 41\140 | 557
380.71 |
230.95
157.86 |
95.1
65 |
|||||||
| 12\41 | 556.67
380.49 |
231.95
158.54 |
92.78
63.415 |
|||||||
| 43\147 | 556.35
380.27 |
232.89
159.18 |
90.57
61.905 |
|||||||
| 31\106 | 556.23
380.19 |
233.26
159.43 |
89.715
61.32 |
|||||||
| 50\171 | 556.13
380.12 |
233.57
159.65 |
88.98
60.82 |
|||||||
| 19\65 | 555.96
380 |
234.09
160 |
87.78
60 |
|||||||
| 45\154 | 555.77
379.87 |
234.66
160.39 |
86.45
59.09 |
|||||||
| 26\89 | 555.63
379.775 |
235.07
160.67 |
85.48
58.43 |
|||||||
| 33\113 | 555.44
379.65 |
235.64
161.06 |
84.16
57.52 |
|||||||
| 7\24 | 554.74
379.17 |
237.74
162.5 |
79.25
54.17 |
|||||||
| 30\103 | 553.97
378.64 |
240.05
164.08 |
73.86
50.485 |
|||||||
| 23\79 | 553.73
378.48 |
240.75
164.56 |
72.23
49.37 |
|||||||
| 39\134 | 553.55
378.36 |
241.29
164.925 |
70.97
48.51 |
|||||||
| 16\55 | 553.3
378.18 |
242.07
165.455 |
69.16
47.27 |
|||||||
| 41\141 | 553.05
378.015 |
242.8
165.96 |
67.445
46.1 |
|||||||
| 25\86 | 552.89
377.91 |
243.27
166.28 |
66.35
45.35 |
|||||||
| 34\117 | 552.805
377.78 |
243.84
166.67 |
65.02
44.44 |
|||||||
| 9\31 | 552.18
377.42 |
245.41
167.74 |
61.35
41.935 |
|||||||
| 29\100 | 551.57
377 |
247.25
169 |
57.06
39 |
|||||||
| 20\69 | 551.29
376.81 |
248.08
169.565 |
55.13
37.68 |
|||||||
| 31\107 | 551.03
376.64 |
248.85
170.09 |
53.33
36.45 |
|||||||
| 11\38 | 550.57
376.32 |
250.26
171.05 |
50.05
34.21 |
|||||||
| 24\83 | 549.96
375.9 |
252.07
172.29 |
45.83
31.325 |
|||||||
| 13\45 | 549.45
375.56 |
253.59
173.33 |
42.27
28.89 |
|||||||
| 15\52 | 548.64
375 |
256.03
175 |
36.58
25 |
|||||||
| 2\7 | 543.42
371.43 |
271.71
185.71 |
0 | |||||||
| 15\53 | 538.29
367.925 |
251.2
171.7 |
35.89
24.53 |
|||||||
| 13\46 | 537.51
367.39 |
248.08
169.565 |
41.35
28.26 |
|||||||
| 24\85 | 537.02
367.06 |
246.135
168.235 |
44.75
30.59 |
|||||||
| 11\39 | 536.45
366.67 |
243.84
166.67 |
48.77
33.33 |
|||||||
| 31\110 | 536
366.36 |
242.07
165.455 |
51.87
35.455 |
|||||||
| 20\71 | 535.76
366.2 |
241.09
164.79 |
53.58
36.62 |
|||||||
| 29\103 | 535.5
366.02 |
240.05
164.08 |
55.4
37.86 |
|||||||
| 9\32 | 534.925
365.625 |
237.74
162.5 |
59.44
40.625 |
|||||||
| 34\121 | 534.43
365.29 |
235.78
161.16 |
62.875
42.975 |
|||||||
| 25\89 | 534.26
365.17 |
235.07
160.67 |
64.11
43.82 |
|||||||
| 41\146 | 534.11
365.07 |
234.49
160.27 |
65.135
44.52 |
|||||||
| 16\57 | 533.88
364.91 |
233.57
159.65 |
66.735
45.61 |
|||||||
| 39\139 | 533.6
364.75 |
232.61
158.99 |
68.42
46.76 |
|||||||
| 23\82 | 533.475
364.63 |
231.95
158.54 |
69.58
47.56 |
|||||||
| 30\107 | 533.26
364.49 |
231.09
157.94 |
71.1
48.6 |
|||||||
| 7\25 | 532.55
364 |
228.235
156 |
76.08
52 |
|||||||
| 33\118 | 531.9
363.56 |
225.66
154.237 |
80.59
55.085 |
|||||||
| 26\93 | 531.73
363.44 |
224.96
153.76 |
81.805
55.91 |
|||||||
| 45\161 | 531.6
363.35 |
224.45
153.42 |
82,69
56.52 |
|||||||
| 19\68 | 531.43
363.235 |
223.76
152.94 |
83.91
57.35 |
|||||||
| 50\179 | 531.27
363.13 |
223.13
152.51 |
85
58.11 |
|||||||
| 31\111 | 531.18
363.06 |
222.75
152.25 |
85.67
58.56 |
|||||||
| 43\154 | 531.065
362.99 |
222.31
151.95 |
86.45
59.09 |
|||||||
| 12\43 | 530.78
362.79 |
221.16
151.16 |
88.46
60.465 |
|||||||
| 41\147 | 530.48
362.585 |
218.95
150.34 |
90.57
61.905 |
|||||||
| 29\104 | 530.35
362.5 |
219.46
150 |
91.44
62.5 |
|||||||
| 46\165 | 530.24
362.42 |
219.01
149.7 |
92.22
63.03 |
|||||||
| 17\61 | 530.05
362.295 |
218.26
149.18 |
93.54
63.93 |
|||||||
| 39\140 | 529.83
362.14 |
217.37
148.57 |
95.1
65 |
|||||||
| 22\79 | 529.66
362.025 |
216.68
148.1 |
96.3
65.82 |
|||||||
| 27\97 | 529.41
361.86 |
215.69
147.42 |
98.04
67.01 |
|||||||
| 5\18 | 528.32
361.11 |
211.33
144.44 |
105.66
72.22 |
Boundary of propriety for fair Mu scale | ||||||
| 28\101 | 527.275
360.4 |
207.14
141.58 |
112.99
77.23 |
|||||||
| 23\83 | 527.05
360.24 |
206.23
140.96 |
114.58
78.31 |
|||||||
| 41\148 | 526.89
360.135 |
205.62
140.54 |
115.66
79.05 |
|||||||
| 18\65 | 526.695
360 |
204.83
140 |
117.04
80 |
|||||||
| 49\177 | 526.53
359.89 |
204.165
139.55 |
118.2
80.79 |
|||||||
| 31\112 | 526.43
359.82 |
203.78
139.29 |
118.87
81.24 |
|||||||
| 44\159 | 526.53
359.75 |
203.35
138.99 |
119.62
81.76 |
|||||||
| 13\47 | 526.07
359.57 |
202.34
138.3 |
121.4
82.98 |
|||||||
| 47\170 | 525.835
359.41 |
201.38
137.65 |
123.07
84.12 |
|||||||
| 34\123 | 525.74
359.35 |
201.02
137.4 |
123.7
84.55 |
|||||||
| 55\199 | 525.67
359.3 |
200.71
137.19 |
124.25
84.925 |
Golden fair Mu scale is near here | ||||||
| 21\76 | 525.54
359.21 |
200.21
136.84 |
125.13
85.53 |
|||||||
| 50\181 | 525.4
359.12 |
199.65
136.46 |
126.1
86.3 |
|||||||
| 29\105 | 525.3
359.05 |
199.25
136.19 |
126.8
86.67 |
|||||||
| 37\134 | 525.17
358.955 |
198.71
135.82 |
127.74
87.31 |
|||||||
| 8\29 | 524.68
358.62 |
196.75
134.48 |
131.17
89.655 |
|||||||
| 35\127 | 524.16
358.27 |
194.69
133.07 |
134.78
92.125 |
|||||||
| 27\98 | 524.01
358.16 |
194.08
132.65 |
135.85
92.86 |
|||||||
| 46\167 | 523.89
358.08 |
193.61
132.335 |
136.67
93.41 |
|||||||
| 19\69 | 523.73
357.97 |
192.95
131.88 |
137.82
94.2 |
|||||||
| 49\178 | 523.57
357.865 |
192.33
131.46 |
138.91
94.94 |
|||||||
| 30\109 | 523.47
357.8 |
191.94
131.19 |
139.59
95.41 |
|||||||
| 41\149 | 523.37
357.72 |
191.47
130.87 |
140.41
95.97 |
|||||||
| 11\40 | 523.04
357.5 |
190.2
130 |
142.65
97.5 |
|||||||
| 36\131 | 522.675
357.25 |
188.74
129.01 |
145.19
99.24 |
|||||||
| 25\91 | 522.515
357.14 |
188.105
128.57 |
146.3
100 |
|||||||
| 39\142 | 522.37
357.04 |
187.52
128.17 |
147.335
100.7 |
|||||||
| 14\51 | 522.105
356.86 |
186.47
127.75 |
149.17
101.96 |
|||||||
| 31\113 | 521.78
356.64 |
185.15
126.55 |
151.48
103.54 |
|||||||
| 17\62 | 521.5
356.45 |
184.06
125.81 |
153.38
104.84 |
|||||||
| 20\73 | 521.08
356.16 |
182.38
124.63 |
156.325
106.85 |
|||||||
| 3\11 | 518.715
354.545 |
172.905
118.18 |
Separatrix of fair Sigma and Mu scales | |||||||
| 19\70 | 516.24
352.86 |
190.2
130 |
163.025
111.43 |
|||||||
| 16\59 | 512.78
352.54 |
193.42
132.2 |
161.18
110.17 |
|||||||
| 29\107 | 515.48
352.34 |
195.53
133.645 |
159.98
109.35 |
|||||||
| 13\48 | 515.11
352.08 |
198.12
135.42 |
158.5
108.33 |
|||||||
| 36\133 | 514.815
351.88 |
200.21
136.84 |
157.305
107.52 |
|||||||
| 23\85 | 514.65
351.765 |
201.38
137.65 |
156.63
107.06 |
|||||||
| 33\122 | 514.46
351.64 |
202.67
138.525 |
155.9
106.56 |
|||||||
| 10\37 | 514.04
351.35 |
205.62
140.54 |
154.21
105.405 |
|||||||
| 37\137 | 513.67
351.095 |
208.24
142.34 |
152.71
104.38 |
|||||||
| 27\100 | 513.53
351 |
209.215
143 |
152.16
104 |
|||||||
| 44\163 | 513.41
350.92 |
210.03
143.56 |
151.69
103.68 |
|||||||
| 17\63 | 513.23
350.79 |
211.33
144.44 |
150.95
103.175 |
|||||||
| 41\152 | 513.03
350.66 |
212.72
145.695 |
150.15
102.63 |
|||||||
| 24\89 | 512.89
350.56 |
213.7
146.07 |
149.59
102.25 |
|||||||
| 31\115 | 512.7
350.435 |
215
146.96 |
148.85
101.74 |
|||||||
| 7\26 | 512.59
350 |
219.68
150 |
146.3
100 |
|||||||
| 32\119 | 511.45
349.58 |
223.76
152.94 |
143.845
98.32 |
|||||||
| 25\93 | 511.28
349.46 |
224.96
153.76 |
143.16
97.85 |
|||||||
| 43\160 | 511.1
349.375 |
225.8
154.375 |
142.65
97.5 |
|||||||
| 18\67 | 510.97
349.25 |
227.1
155.22 |
141.94
97.015 |
|||||||
| 47\175 | 510.81
349.14 |
228.23
156 |
141.29
96.57 |
Golden fair Sigma scale is near here | ||||||
| 29\108 | 510.71
349.07 |
228.94
156.48 |
140.89
96.3 |
|||||||
| 40\149 | 510.59
348.99 |
229.77
157.05 |
140.41
95.97 |
|||||||
| 11\41 | 510.28
348.78 |
231.95
158.54 |
139.17
95.12 |
|||||||
| 37\138 | 509.94
348.55 |
234.3
160.145 |
137.82
94.2 |
|||||||
| 26\97 | 509.8
348.45 |
235.29
160.825 |
137.25
93.81 |
|||||||
| 41\153 | 509.67
348.37 |
236.19
161.44 |
136.71
93.46 |
|||||||
| 15\56 | 509.45
348.21 |
237.74
162.5 |
135.85
92.86 |
|||||||
| 34\127 | 509.185
348.03 |
239.62
163.78 |
134.78
92.13 |
|||||||
| 19\71 | 508.97
347.89 |
241.09
164.79 |
133.94
91.55 |
|||||||
| 23\86 | 508.66
347.67 |
243.27
166.28 |
132.695
90.7 |
|||||||
| 4\15 | 507.19
346.67 |
253.59
173.33 |
126.8
86.67 |
Boundary of propriety for fair Sigma scale | ||||||
| 21\79 | 505.58
345.57 |
264.83
181.01 |
120.38
82.28 |
|||||||
| 17\64 | 505.21
343.31 |
267.42
182.81 |
118.87
81.25 |
|||||||
| 30\113 | 504.94
345.13 |
269.3
184.07 |
117.82
80.53 |
|||||||
| 13\49 | 504.6
344.9 |
271.71
185.71 |
116.45
79.59 |
|||||||
| 35\132 | 504.3
344.7 |
273.77
187.12 |
115.27
78.79 |
|||||||
| 22\83 | 504.13
344.58 |
274.98
187.95 |
114.58
78.31 |
|||||||
| 31\117 | 503.94
344.44 |
265.35
188.89 |
113.79
77.78 |
|||||||
| 9\34 | 503.46
344.12 |
279.7
191.18 |
111.88
76.47 |
|||||||
| 32\121 | 503
343.8 |
282.935
193.39 |
110.03
75.21 |
|||||||
| 23\87 | 502.82
343.68 |
284.2
194.25 |
109.31
74.71 |
|||||||
| 37\140 | 502.66
343.57 |
285.29
195 |
108.68
74.29 |
|||||||
| 14\53 | 502.4
343.4 |
287.09
196.23 |
107.66
73.585. |
|||||||
| 33\125 | 502.12
343.2 |
289.1
197.6 |
106.51
72.8 |
|||||||
| 19\72 | 501.9
343.06 |
290.58
198.61 |
105.66
72.22 |
|||||||
| 24\91 | 501.615
342.86 |
292.61
200 |
104.5
71.43 |
|||||||
| 5\19 | 500.51
342.105 |
300.31
205.26 |
100.1
68.42 |
|||||||
| 21\80 | 499.26
341.25 |
309.07
211.25 |
95.1
65 |
|||||||
| 16\61 | 498.87
340.98 |
311.8
213.115 |
93.54
63.93 |
|||||||
| 27\103 | 498.57
340.78 |
313.915
214.56 |
92.33
63.11 |
|||||||
| 11\42 | 498.13
340.48 |
316.99
216.67 |
90.57
61.905 |
|||||||
| 28\107 | 497.71
340.19 |
319.955
218.69 |
88.88
60.75 |
|||||||
| 17\65 | 497.43
340 |
321.87
220 |
87.78
60 |
|||||||
| 23\88 | 497.1
339.77 |
324.2
221.59 |
86.42
59.09 |
|||||||
| 6\23 | 496.16
339.13 |
330.775
226.09 |
82.69
56.52 |
|||||||
| 19\73 | 495.03
338.36 |
338.7
231.51 |
78.16
53.425 |
|||||||
| 13\50 | 494.51
338 |
342.35
234 |
76.08
52 |
|||||||
| 20\77 | 494.01
337.66 |
345.81
236.36 |
74.1
50.65 |
|||||||
| 7\27 | 493.1
337.04 |
352.21
240.74 |
70.44
48.15 |
|||||||
| 15\58 | 491.885
336.21 |
360.72
246.55 |
65.585
44.83 |
|||||||
| 8\31 | 490.83
335.48 |
368.12
251.61 |
61.35
41.935 |
|||||||
| 9\35 | 489.07
334.29 |
380.39
260 |
54.34
37.14 |
|||||||
| 1\4 | 475.49
325 |
0 | ||||||||