Canopus
For technical information see Mirkwai clan#Canopus
Canopus is the rank two 3.5.7 temperament tempering out 16875/16807, the amount by which 27/7 exceeds four 7/5s. 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.
Relationship between MOS with P4 generator and MOS with P5 generator
| This page on a regular temperament, temperament collection, or aspect of RTT is under the jurisdiction of WikiProject TempClean and is being revised for clarity. |
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 and in fiction, most obviously speaking, the secondary traditional tuning of cylindrical wind instrument humans e. g. clarinets). 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 | ||||||||