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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.
{{Infobox regtemp
| Title = Canopus
| Subgroups = 3.5.7
| Comma basis = [[16875/16807]]
| Edo join 1 = b13 | Edo join 2 = b88
| Mapping = 1; -5 -4
| Generators = 7/5
| Generators tuning = 583.986
| Optimization method = CWE
| MOS scales = [[3L 1s (3/1-equivalent)|3L 1s <3/1>]], [[3L 4s (3/1-equivalent)|3L 4s <3/1>]], [[3L 7s (3/1-equivalent)|3L 7s <3/1>]]
| Color name =
| Odd limit 1 = 3.5.7 7 | Mistuning 1 = 1.40 | Complexity 1 = 7
| Odd limit 2 = 3.5.7 49 | Mistuning 2 = 2.80 | Complexity 2 = 13
}}
'''Canopus''' is the [[Rank-2 temperament|rank two]] [[3.5.7 subgroup]] temperament [[Temper out|tempering out]] [[16875/16807]], the amount by which [[27/7]] exceeds four 7/5s. Having a generator of [[~]][[7/5|7:5]], it possesses non-trivial [[MOS]] of the families [[1L 2s (3/1-equivalent)|1L 2s]], [[3L 1s (3/1-equivalent)|3L 1s]], [[3L 4s (3/1-equivalent)|3L 4s]], [[3L 7s (3/1-equivalent)|3L 7s]], and (in most cases) [[10L 3s (3/1-equivalent)|10L 3s]]. As 16875/16807 = ([[540/539]])<sup>2</sup>*([[3025/3024]]), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out [[1325/1323]], equating (7/5)<sup>2</sup> = [[49/25]] to 53/27.


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 [[wikipedia:Obikhod|Obikhod]] pitch set used in Russian Orthodox chants). These scales are neighbors of the 7&amp;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:
For technical information see [[No-twos subgroup temperaments #Canopus]].  


{| class="wikitable"
== Interval table ==
|-
In the below, tritave-reduced harmonics and subharmonics are indicated in '''bold'''.
| | L=1 s=0 8 edt
 
| | L=1 s=0 7 edt
<div style="display: inline-grid; margin-right: 25px;">
| | L=1 s=0 3 edt
{| class="wikitable center-1 right-2"
|-
|+ style="font-size: 105%;" | Canopus
| | 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
! rowspan="2" | &#35; !! rowspan="2" | Cents* !! colspan="1" | Approximate Ratios
| | L=5 s=4 51
| | L=5 s=4 43
|-
|-
| | L=6 s=5 63
! 3.5.7.11/4.53 subgroup
| | L=6 s=5 62
| | L=6 s=5 53
|-
|-
| | L=7 s=6 74
| &minus;3 || 149.9 || 12/11, 49/45
| | L=7 s=6 73
| | L=7 s=6 63
|-
|-
| colspan="2" style="text-align:center;" | L=1 s=1 11 edt
| &minus;2 || 733.9 || 55/36, 75/49, '''81/53''', 84/55
| | L=1 s=1 10 edt
|-
|-
| | L=7 s=6 69
| &minus;1 || 1318.0 || 15/7
| | L=7 s=6 70
| | L=7 s=6 67
|-
|-
| | L=6 s=5 58
| 0 || 0.0 || 1/1
| | L=6 s=5 59
| | L=6 s=5 57
|-
|-
| | L=5 s=4 47
| 1 || 584.0 || 7/5
| | L=5 s=4 48
| | L=5 s=4 47
|-
|-
| | L=4 s=3 36
| 2 || 1168.0 || 49/25, '''53/27''', 55/28, 108/55
| | L=4 s=3 37
| | L=4 s=3 37
|-
|-
| | L=7 s=5 61
| 3 || 1752.0 || 11/4, 135/49
| | L=7 s=5 63
| | L=7 s=5 64
|-
|-
| | L=3 s=2 25
| 4 || 434.1 || '''9/7'''
| | L=3 s=2 26
| | L=3 s=2 27
|-
|-
| | L=5 s=3 39
| 5 || 1018.1 || '''9/5'''
| | L=5 s=3 41
| | L=5 s=3 44
|-
|-
| | L=7 s=4 53
| 6 || 1602.1 || 53/21, 63/25
| | L=7 s=4 56
| | L=7 s=4 61
|-
|-
| | L=2 s=1 14
| 7 || 284.1 || 33/28, 53/45
| | L=2 s=1 15
| | L=2 s=1 17
|-
|-
| | L=7 s=3 45
| 8 || 868.1 || 33/20, '''81/49'''
| | L=7 s=3 49
| | L=7 s=3 58
|-
|-
| | L=5 s=2 31
| 9 || 1452.1 || '''81/35'''
| | L=5 s=2 30
| | L=5 s=2 41
|-
|-
| | L=3 s=1 17
| 10 || 134.2 || '''27/25''', 53/49
| | 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.
<nowiki />* In 3.5.7-targeted [[DKW theory|DKW]] tuning
</div>


{| class="wikitable"
{{Todo|inline=1|expand|comment=add tuning spectrum}}
|-
[[Category:Canopus| ]] <!-- main article -->
! colspan="7" | Generator
[[Category:Rank-2 temperaments]]
! | cents
[[Category:Non-octave temperaments]]
hekts
[[Category:Canopic clan]]
! | 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
| colspan="2" style="text-align:center;" | 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
| |
| |
| |
| |
| |
| |
| colspan="2" style="text-align:center;" | 633.985
433.33
| | 0
| |
|-
| |
| |
| |
| |
| |
| |
| | 9\28
| | 611.34
| | 475.49
| | 67.92
| |
|-
| |
| |
| |
| |
| |
| | 8\25
| |
| | 608.63
| | 456.47
| | 76.08
| |
|-
| |
| |
| |
| |
| |
| |
| | 15\47
| | 607.01
| | 445.39
| | 80.93
| |
|-
| |
| |
| |
| |
| | 7\22
| |
| |
| | 605.18
| | 432.26
| | 86.45
| |
|-
| |
| |
| |
| |
| |
| |
| | 20\63
| | 603.795
| | 422.66
| | 90.57
| |
|-
| |
| |
| |
| |
| |
| | 13\41
| |
| | 603.06
| | 417.50
| | 92.78
| |
|-
| |
| |
| |
| |
| |
| |
| | 19\60
| | 602.29
| | 412.09
| | 95.10
| |
|-
| |
| |
| |
| | 6\19
| |
| |
| |
| | 600.62
| | 400.41
| | 100.11
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\73
| | 599.25
| | 390.81
| | 104.22
| |
|-
| |
| |
| |
| |
| |
| | 17\54
| |
| | 598.76
| | 387.425
| | 105.66
| |
|-
| |
| |
| |
| |
| |
| |
| | 28\89
| | 598.37
| | 384.665
| | 106.85
| |
|-
| |
| |
| |
| |
| | 11\35
| |
| |
| | 597.76
| | 380.39
| | 108.68
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\86
| | 597.125
| | 375.97
| | 110.58
| |
|-
| |
| |
| |
| |
| |
| | 16\51
| |
| | 596.69
| | 372.93
| | 111.88
| |
|-
| |
| |
| |
| |
| |
| |
| | 21\67
| | 596.135
| | 369.04
| | 113.55
| |
|-
| |
| |
| | 5\16
| |
| |
| |
| |
| | 594.36
| | 356.62
| | 118.87
| |
|-
| |
| |
| |
| |
| |
| |
| | 24\77
| | 592.82
| | 345.81
| | 123.50
| |
|-
| |
| |
| |
| |
| |
| | 19\61
| |
| | 592.41
| | 342.975
| | 124.72
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\106
| | 592.12
| | 340.92
| | 125.60
| |
|-
| |
| |
| |
| |
| | 14\45
| |
| |
| | 591.72
| | 338.125
| | 126.80
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\119
| | 591.36
| | 335.64
| | 127.86
| |
|-
| |
| |
| |
| |
| |
| | 23\74
| |
| | 591.15
| | 334.13
| | 128.51
| |
|-
| |
| |
| |
| |
| |
| |
| | 32\103
| | 590.90
| | 332.38
| | 129.26
| |
|-
| |
| |
| |
| | 9\29
| |
| |
| |
| | 590.26
| | 327.92
| | 131.17
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\100
| | 589.61
| | 323.33
| | 133.14
| |
|-
| |
| |
| |
| |
| |
| | 22\71
| |
| | 589.34
| | 321.46
| | 133.94
| |
|-
| |
| |
| |
| |
| |
| |
| | 35\113
| | 589.10
| | 319.80
| | 134.65
| |
|-
| |
| |
| |
| |
| | 13\42
| |
| |
| | 588.70
| | 316.99
| | 135.85
| |
|-
| |
| |
| |
| |
| |
| |
| | 30\97
| | 588.23
| | 313.725
| | 137.25
| |
|-
| |
| |
| |
| |
| |
| | 17\55
| |
| | 587.88
| | 311.23
| | 138.32
| |
|-
| |
| |
| |
| |
| |
| |
| | 21\68
| | 587.37
| | 307.67
| | 139.85
| |
|-
| |
| | 4\13
| |
| |
| |
| |
| |
| | 585.22
| | 292.61
| | 146.30
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\75
| | 583.27
| | 278.95
| | 152.16
| |
|-
| |
| |
| |
| |
| |
| | 19\62
| |
| | 582.86
| | 276.09
| | 153.38
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\111
| | 582.58
| | 274.16
| | 154.21
| |
|-
| |
| |
| |
| |
| | 15\49
| |
| |
| | 582.23
| | 271.71
| | 155.26
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\134
| | 581.94
| | 269.68
| | 156.13
| |
|-
| |
| |
| |
| |
| |
| | 26\85
| |
| | 581.77
| | 268.51
| | 156.63
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\121
| | 581.59
| | 267.22
| | 157.19
| |
|-
| |
| |
| |
| | 11\36
| |
| |
| |
| | 581.15
| | 264.16
| | 158.50
| |
|-
| |
| |
| |
| |
| |
| |
| | 40\131
| | 580.75
| | 261.34
| | 150.71
| |
|-
| |
| |
| |
| |
| |
| | 29\95
| |
| | 580.60
| | 260.27
| | 160.165
| |
|-
| |
| |
| |
| |
| |
| |
| | 47\154
| | 580.47
| | 259.36
| | 160.555
| |
|-
| |
| |
| |
| |
| | 18\59
| |
| |
| | 580.26
| | 257.89
| | 161.18
| |
|-
| |
| |
| |
| |
| |
| |
| | 43\141
| | 580.03
| | 259.29
| | 161.87
| |
|-
| |
| |
| |
| |
| |
| | 25\82
| |
| | 579.86
| | 255.14
| | 162.36
| |
|-
| |
| |
| |
| |
| |
| |
| | 32\105
| | 579.64
| | 253.59
| | 163.025
| |
|-
| |
| |
| | 7\23
| |
| |
| |
| |
| | 578.86
| | 248.08
| | 165.39
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\102
| | 578.045
| | 242.41
| | 167.82
| |
|-
| |
| |
| |
| |
| |
| | 24\79
| |
| | 577.81
| | 240.75
| | 168.53
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\135
| | 577.63
| | 239.505
| | 169.06
| |
|-
| |
| |
| |
| |
| | 17\56
| |
| |
| | 577.38
| | 237.74
| | 169.82
| |
|-
| |
| |
| |
| |
| |
| |
| | 44\145
| | 577.145
| | 236.105
| | 170.52
| |
|-
| |
| |
| |
| |
| |
| | 27\89
| |
| | 577.00
| | 235.07
| | 170.96
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\122
| | 576.82
| | 233.85
| | 171.49
| |
|-
| |
| |
| |
| | 10\33
| |
| |
| |
| | 576.35
| | 230.54
| | 172.905
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\109
| | 575.82
| | 226.84
| | 174.49
| |
|-
| |
| |
| |
| |
| |
| | 23\76
| |
| | 575.59
| | 225.23
| | 175.18
| |
|-
| |
| |
| |
| |
| |
| |
| | 36\119
| | 575.38
| | 223.76
| | 175.81
| |
|-
| |
| |
| |
| |
| | 13\43
| |
| |
| | 575.01
| | 221.16
| | 176.93
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\96
| | 574,55
| | 217.93
| | 178.31
| |
|-
| |
| |
| |
| |
| |
| | 16\53
| |
| | 574.175
| | 215.32
| | 179.43
| |
|-
| |
| |
| |
| |
| |
| |
| | 19\63
| | 573.605
| | 211.33
| | 181.14
| |
|-
| | 3\10
| |
| |
| |
| |
| |
| |
| | 570.59
| colspan="2" style="text-align:center;" | 190.20
| |
|-
| |
| |
| |
| |
| |
| |
| | 20\67
| | 567.75
| | 198.72
| | 170.32
| |
|-
| |
| |
| |
| |
| |
| | 17\57
| |
| | 567.25
| | 200.21
| | 166.84
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\104
| | 566.93
| | 201.17
| | 164.50
| |
|-
| |
| |
| |
| |
| | 14\47
| |
| |
| | 566.54
| | 202.34
| | 161.87
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\131
| | 566.23
| | 203.26
| | 159.71
| |
|-
| |
| |
| |
| |
| |
| | 25\84
| |
| | 566.06
| | 203.78
| | 158.50
| |
|-
| |
| |
| |
| |
| |
| |
| | 36\121
| | 565.87
| | 204.34
| | 157.19
| |
|-
| |
| |
| |
| | 11\37
| |
| |
| |
| | 565.45
| | 205.62
| | 154.21
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\138
| | 565.07
| | 206.73
| | 151.605
| |
|-
| |
| |
| |
| |
| |
| | 30\101
| |
| | 564.94
| | 207.14
| | 150.65
| |
|-
| |
| |
| |
| |
| |
| |
| | 49\165
| | 564.82
| | 207.49
| | 149.85
| |
|-
| |
| |
| |
| |
| | 19\64
| |
| |
| | 564.64
| | 208.03
| | 148.59
| |
|-
| |
| |
| |
| |
| |
| |
| | 46\155
| | 564.45
| | 208.60
| | 147.25
| |
|-
| |
| |
| |
| |
| |
| | 27\91
| |
| | 564.32
| | 209.00
| | 146.30
| |
|-
| |
| |
| |
| |
| |
| |
| | 35\118
| | 564.14
| | 209.54
| | 145.06
| |
|-
| |
| |
| | 8\27
| |
| |
| |
| |
| | 563.54
| | 211.33
| | 140.89
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\125
| | 562.98
| | 213.02
| | 136.94
| |
|-
| |
| |
| |
| |
| |
| | 29\98
| |
| | 562.82
| | 213.485
| | 135.85
| |
|-
| |
| |
| |
| |
| |
| |
| | 50\169
| | 562.71
| | 213.83
| | 135.05
| |
|-
| |
| |
| |
| |
| | 21\71
| |
| |
| | 562.55
| | 214.30
| | 133.94
| |
|-
| |
| |
| |
| |
| |
| |
| | 55\186
| | 562.41
| | 214.74
| | 132.93
| |
|-
| |
| |
| |
| |
| |
| | 34\115
| |
| | 562.32
| | 215.00
| | 132.31
| |
|-
| |
| |
| |
| |
| |
| |
| | 47\159
| | 562.21
| | 215.32
| | 131.58
| |
|-
| |
| |
| |
| | 13\44
| |
| |
| |
| | 561.94
| | 216.13
| | 129.68
| |
|-
| |
| |
| |
| |
| |
| |
| | 44\149
| | 561.65
| | 217.00
| | 127.65
| |
|-
| |
| |
| |
| |
| |
| | 31\105
| |
| | 561.53
| | 217.37
| | 126.80
| |
|-
| |
| |
| |
| |
| |
| |
| | 49\166
| | 561.42
| | 217.69
| | 126.03
| |
|-
| |
| |
| |
| |
| | 18\61
| |
| |
| | 561.23
| | 218.26
| | 124.72
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\139
| | 561.01
| | 218.93
| | 123.15
| |
|-
| |
| |
| |
| |
| |
| | 23\78
| |
| | 560.83
| | 219.46
| | 121.92
| |
|-
| |
| |
| |
| |
| |
| |
| | 28\95
| | 560.58
| | 220.23
| | 120.12
| |
|-
| |
| | 5\17
| |
| |
| |
| |
| |
| | 559.40
| | 223.76
| | 111.88
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\92
| | 558.18
| | 227.41
| | 103.37
| |
|-
| |
| |
| |
| |
| |
| | 22\75
| |
| | 557.91
| | 228.235
| | 101.44
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\133
| | 557.72
| | 228.81
| | 100.10
| |
|-
| |
| |
| |
| |
| | 17\58
| |
| |
| | 557.47
| | 229.55
| | 98.38
| |
|-
| |
| |
| |
| |
| |
| |
| | 46\157
| | 557.26
| | 230.17
| | 96.915
| |
|-
| |
| |
| |
| |
| |
| | 29\99
| |
| | 557.14
| | 230.54
| | 96.06
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\140
| | 557.00
| | 230.95
| | 95.10
| |
|-
| |
| |
| |
| | 12\41
| |
| |
| |
| | 556.67
| | 231.95
| | 92.78
| |
|-
| |
| |
| |
| |
| |
| |
| | 43\147
| | 556.35
| | 232.89
| | 90.57
| |
|-
| |
| |
| |
| |
| |
| | 31\106
| |
| | 556.23
| | 233.26
| | 89.715
| |
|-
| |
| |
| |
| |
| |
| |
| | 50\171
| | 556.13
| | 233.57
| | 88.98
| |
|-
| |
| |
| |
| |
| | 19\65
| |
| |
| | 555.96
| | 234.09
| | 87.78
| |
|-
| |
| |
| |
| |
| |
| |
| | 45\154
| | 555.77
| | 234.66
| | 86.45
| |
|-
| |
| |
| |
| |
| |
| | 26\89
| |
| | 555.63
| | 235.07
| | 85.48
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\113
| | 555.44
| | 235.64
| | 84.16
| |
|-
| |
| |
| | 7\24
| |
| |
| |
| |
| | 554.74
| | 237.74
| | 79.25
| |
|-
| |
| |
| |
| |
| |
| |
| | 30\103
| | 553.97
| | 240.05
| | 73.86
| |
|-
| |
| |
| |
| |
| |
| | 23\79
| |
| | 553.73
| | 240.75
| | 72.23
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\134
| | 553.55
| | 241.29
| | 70.97
| |
|-
| |
| |
| |
| |
| | 16\55
| |
| |
| | 553.30
| | 242.07
| | 69.16
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\141
| | 553.05
| | 242.80
| | 67.445
| |
|-
| |
| |
| |
| |
| |
| | 25\86
| |
| | 552.89
| | 243.27
| | 66.35
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\117
| | 552.805
| | 243.84
| | 65.02
| |
|-
| |
| |
| |
| | 9\31
| |
| |
| |
| | 552.18
| | 245.41
| | 61.35
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\100
| | 551.57
| | 247.25
| | 57.06
| |
|-
| |
| |
| |
| |
| |
| | 20\69
| |
| | 551.29
| | 248.08
| | 55.13
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\107
| | 551.03
| | 248.85
| | 53.33
| |
|-
| |
| |
| |
| |
| | 11\38
| |
| |
| | 550.57
| | 250.26
| | 50.05
| |
|-
| |
| |
| |
| |
| |
| |
| | 24\83
| | 549.96
| | 252.07
| | 45.83
| |
|-
| |
| |
| |
| |
| |
| | 13\45
| |
| | 549.45
| | 253.59
| | 42.27
| |
|-
| |
| |
| |
| |
| |
| |
| | 15\52
| | 548.64
| | 256.03
| | 36.58
| |
|-
| | 2\7
| |
| |
| |
| |
| |
| |
| | 543.42
| | 271.71
| | 0
| |
|-
| |
| |
| |
| |
| |
| |
| | 15\53
| | 538.29
| | 251.20
| | 35.89
| |
|-
| |
| |
| |
| |
| |
| | 13\46
| |
| | 537.51
| | 248.08
| | 41.35
| |
|-
| |
| |
| |
| |
| |
| |
| | 24\85
| | 537.02
| | 246.135
| | 44.75
| |
|-
| |
| |
| |
| |
| | 11\39
| |
| |
| | 536.45
| | 243.84
| | 48.77
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\110
| | 536.00
| | 242.07
| | 51.87
| |
|-
| |
| |
| |
| |
| |
| | 20\71
| |
| | 535.76
| | 241.09
| | 53.58
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\103
| | 535.50
| | 240.05
| | 55.40
| |
|-
| |
| |
| |
| | 9\32
| |
| |
| |
| | 534.925
| | 237.74
| | 59.44
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\121
| | 534.43
| | 235.78
| | 62.875
| |
|-
| |
| |
| |
| |
| |
| | 25\89
| |
| | 534.26
| | 235.07
| | 64.11
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\146
| | 534.11
| | 234.49
| | 65.135
| |
|-
| |
| |
| |
| |
| | 16\57
| |
| |
| | 533.88
| | 233.57
| | 66.735
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\139
| | 533.6
| | 232.61
| | 68.42
| |
|-
| |
| |
| |
| |
| |
| | 23\82
| |
| | 533.475
| | 231.95
| | 69.58
| |
|-
| |
| |
| |
| |
| |
| |
| | 30\107
| | 533.26
| | 231.09
| | 71.10
| |
|-
| |
| |
| | 7\25
| |
| |
| |
| |
| | 532.55
| | 228.235
| | 76.08
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\118
| | 531.90
| | 225.66
| | 80.59
| |
|-
| |
| |
| |
| |
| |
| | 26\93
| |
| | 531.73
| | 224.96
| | 81.805
| |
|-
| |
| |
| |
| |
| |
| |
| | 45\161
| | 531.60
| | 224.45
| | 82,69
| |
|-
| |
| |
| |
| |
| | 19\68
| |
| |
| | 531.43
| | 223.76
| | 83.91
| |
|-
| |
| |
| |
| |
| |
| |
| | 50\179
| | 531.27
| | 223.13
| | 85.00
| |
|-
| |
| |
| |
| |
| |
| | 31\111
| |
| | 531.18
| | 222.75
| | 85.67
| |
|-
| |
| |
| |
| |
| |
| |
| | 43\154
| | 531.065
| | 222.31
| | 86.45
| |
|-
| |
| |
| |
| | 12\43
| |
| |
| |
| | 530.78
| | 221.16
| | 88.46
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\147
| | 530.48
| | 218.95
| | 90.57
| |
|-
| |
| |
| |
| |
| |
| | 29\104
| |
| | 530.35
| | 219.46
| | 91.44
| |
|-
| |
| |
| |
| |
| |
| |
| | 46\165
| | 530.24
| | 219.01
| | 92.22
| |
|-
| |
| |
| |
| |
| | 17\61
| |
| |
| | 530.05
| | 218.26
| | 93.54
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\140
| | 529.83
| | 217.37
| | 95.10
| |
|-
| |
| |
| |
| |
| |
| | 22\79
| |
| | 529.66
| | 216.68
| | 96.30
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\97
| | 529.41
| | 215.69
| | 98.04
| |
|-
| |
| | 5\18
| |
| |
| |
| |
| |
| | 528.32
| | 211.33
| | 105.66
| | Boundary of propriety for fair Mu scale
|-
| |
| |
| |
| |
| |
| |
| | 28\101
| | 527.275
| | 207.14
| | 112.99
| |
|-
| |
| |
| |
| |
| |
| | 23\83
| |
| | 527.05
| | 206.23
| | 114.58
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\148
| | 526.89
| | 205.62
| | 115.66
| |
|-
| |
| |
| |
| |
| | 18\65
| |
| |
| | 526.695
| | 204.83
| | 117.04
| |
|-
| |
| |
| |
| |
| |
| |
| | 49\177
| | 526.53
| | 204.165
| | 118.20
| |
|-
| |
| |
| |
| |
| |
| | 31\112
| |
| | 526.43
| | 203.78
| | 118.87
| |
|-
| |
| |
| |
| |
| |
| |
| | 44\159
| | 526.53
| | 203.35
| | 119.62
| |
|-
| |
| |
| |
| | 13\47
| |
| |
| |
| | 526.07
| | 202.34
| | 121.40
| |
|-
| |
| |
| |
| |
| |
| |
| | 47\170
| | 525.835
| | 201.38
| | 123.07
| |
|-
| |
| |
| |
| |
| |
| | 34\123
| |
| | 525.74
| | 201.02
| | 123.70
| |
|-
| |
| |
| |
| |
| |
| |
| | 55\199
| | 525.67
| | 200.71
| | 124.25
| | Golden fair Mu scale is near here
|-
| |
| |
| |
| |
| | 21\76
| |
| |
| | 525.54
| | 200.21
| | 125.13
| |
|-
| |
| |
| |
| |
| |
| |
| | 50\181
| | 525.40
| | 199.65
| | 126.10
| |
|-
| |
| |
| |
| |
| |
| | 29\105
| |
| | 525.30
| | 199.25
| | 126.80
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\134
| | 525.17
| | 198.71
| | 127.74
| |
|-
| |
| |
| | 8\29
| |
| |
| |
| |
| | 524.68
| | 196.75
| | 131.17
| |
|-
| |
| |
| |
| |
| |
| |
| | 35\127
| | 524.16
| | 194.69
| | 134.78
| |
|-
| |
| |
| |
| |
| |
| | 27\98
| |
| | 524.01
| | 194.08
| | 135.85
| |
|-
| |
| |
| |
| |
| |
| |
| | 46\167
| | 523.89
| | 193.61
| | 136.67
| |
|-
| |
| |
| |
| |
| | 19\69
| |
| |
| | 523.73
| | 192.95
| | 137.82
| |
|-
| |
| |
| |
| |
| |
| |
| | 49\178
| | 523.57
| | 192.33
| | 138.91
| |
|-
| |
| |
| |
| |
| |
| | 30\109
| |
| | 523.47
| | 191.94
| | 139.59
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\149
| | 523.37
| | 191.47
| | 140.41
| |
|-
| |
| |
| |
| | 11\40
| |
| |
| |
| | 523.04
| | 190.20
| | 142.65
| |
|-
| |
| |
| |
| |
| |
| |
| | 36\131
| | 522.675
| | 188.74
| | 145.19
| |
|-
| |
| |
| |
| |
| |
| | 25\91
| |
| | 522.515
| | 188.105
| | 146.30
| |
|-
| |
| |
| |
| |
| |
| |
| | 39\142
| | 522.37
| | 187.52
| | 147.335
| |
|-
| |
| |
| |
| |
| | 14\51
| |
| |
| | 522.105
| | 186.466
| | 149.17
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\113
| | 521.78
| | 185.15
| | 151.48
| |
|-
| |
| |
| |
| |
| |
| | 17\62
| |
| | 521.50
| | 184.06
| | 153.38
| |
|-
| |
| |
| |
| |
| |
| |
| | 20\73
| | 521.08
| | 182.38
| | 156.325
| |
|-
| | 3\11
| |
| |
| |
| |
| |
| |
| | 518.715
| colspan="2" style="text-align:center;" | 172.905
| | Separatrix of fair Sigma and Mu scales
|-
| |
| |
| |
| |
| |
| |
| | 19\70
| | 516.24
| | 190.20
| | 163.025
| |
|-
| |
| |
| |
| |
| |
| | 16\59
| |
| | 512.78
| | 193.42
| | 161.18
| |
|-
| |
| |
| |
| |
| |
| |
| | 29\107
| | 515.48
| | 195.53
| | 159.98
| |
|-
| |
| |
| |
| |
| | 13\48
| |
| |
| | 515.11
| | 198.12
| | 158.50
| |
|-
| |
| |
| |
| |
| |
| |
| | 36\133
| | 514.815
| | 200.21
| | 157.305
| |
|-
| |
| |
| |
| |
| |
| | 23\85
| |
| | 514.65
| | 201.38
| | 156.63
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\122
| | 514.46
| | 202.67
| | 155.90
| |
|-
| |
| |
| |
| | 10\37
| |
| |
| |
| | 514.04
| | 205.62
| | 154.21
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\137
| | 513.67
| | 208.24
| | 152.71
| |
|-
| |
| |
| |
| |
| |
| | 27\100
| |
| | 513.53
| | 209.215
| | 152.16
| |
|-
| |
| |
| |
| |
| |
| |
| | 44\163
| | 513.41
| | 210.03
| | 151.69
| |
|-
| |
| |
| |
| |
| | 17\63
| |
| |
| | 513.23
| | 211.33
| | 150.95
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\152
| | 513.03
| | 212.72
| | 150.15
| |
|-
| |
| |
| |
| |
| |
| | 24\89
| |
| | 512.89
| | 213.70
| | 149.59
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\115
| | 512.70
| | 215.00
| | 148.85
| |
|-
| |
| |
| | 7\26
| |
| |
| |
| |
| | 512.59
| | 219.68
| | 146.30
| |
|-
| |
| |
| |
| |
| |
| |
| | 32\119
| | 511.45
| | 223.76
| | 143.845
| |
|-
| |
| |
| |
| |
| |
| | 25\93
| |
| | 511.28
| | 224.96
| | 143.16
| |
|-
| |
| |
| |
| |
| |
| |
| | 43\160
| | 511.10
| | 225.86
| | 142.65
| |
|-
| |
| |
| |
| |
| | 18\67
| |
| |
| | 510.97
| | 227.10
| | 141.94
| |
|-
| |
| |
| |
| |
| |
| |
| | 47\175
| | 510.81
| | 228.23
| | 141.29
| | Golden fair Sigma scale is near here
|-
| |
| |
| |
| |
| |
| | 29\108
| |
| | 510.71
| | 228.94
| | 140.89
| |
|-
| |
| |
| |
| |
| |
| |
| | 40\149
| | 510.59
| | 229.77
| | 140.41
| |
|-
| |
| |
| |
| | 11\41
| |
| |
| |
| | 510.28
| | 231.95
| | 139.17
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\138
| | 509.94
| | 234.30
| | 137.82
| |
|-
| |
| |
| |
| |
| |
| | 26\97
| |
| | 509.80
| | 235.29
| | 137.25
| |
|-
| |
| |
| |
| |
| |
| |
| | 41\153
| | 509.67
| | 236.19
| | 136.71
| |
|-
| |
| |
| |
| |
| | 15\56
| |
| |
| | 509.45
| | 237.74
| | 135.85
| |
|-
| |
| |
| |
| |
| |
| |
| | 34\127
| | 509.185
| | 239.62
| | 134.78
| |
|-
| |
| |
| |
| |
| |
| | 19\71
| |
| | 507.97
| | 241.09
| | 133.94
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\86
| | 506.66
| | 243.27
| | 132.695
| |
|-
| |
| | 4\15
| |
| |
| |
| |
| |
| | 507.19
| | 253.59
| | 126.80
| | Boundary of propriety for fair Sigma scale
|-
| |
| |
| |
| |
| |
| |
| | 21\79
| | 505.58
| | 264.83
| | 120.38
| |
|-
| |
| |
| |
| |
| |
| | 17\64
| |
| | 505.21
| | 267.42
| | 118.87
| |
|-
| |
| |
| |
| |
| |
| |
| | 30\113
| | 504.94
| | 269.30
| | 117.82
| |
|-
| |
| |
| |
| |
| | 13\49
| |
| |
| | 504.60
| | 271.71
| | 116.45
| |
|-
| |
| |
| |
| |
| |
| |
| | 35\132
| | 504.30
| | 273.77
| | 115.27
| |
|-
| |
| |
| |
| |
| |
| | 22\83
| |
| | 504.13
| | 274.98
| | 114.58
| |
|-
| |
| |
| |
| |
| |
| |
| | 31\117
| | 503.94
| | 265.35
| | 113.79
| |
|-
| |
| |
| |
| | 9\34
| |
| |
| |
| | 503.46
| | 279.70
| | 111.88
| |
|-
| |
| |
| |
| |
| |
| |
| | 32\121
| | 503.00
| | 282.935
| | 110.03
| |
|-
| |
| |
| |
| |
| |
| | 23\87
| |
| | 502.82
| | 284.20
| | 109.31
| |
|-
| |
| |
| |
| |
| |
| |
| | 37\140
| | 502.66
| | 285.29
| | 108.68
| |
|-
| |
| |
| |
| |
| | 14\53
| |
| |
| | 502.40
| | 287.09
| | 107.66
| |
|-
| |
| |
| |
| |
| |
| |
| | 33\125
| | 502.12
| | 289.10
| | 106.51
| |
|-
| |
| |
| |
| |
| |
| | 19\72
| |
| | 501.90
| | 290.58
| | 105.66
| |
|-
| |
| |
| |
| |
| |
| |
| | 24\91
| | 501.615
| | 292.61
| | 104.50
| |
|-
| |
| |
| | 5\19
| |
| |
| |
| |
| | 500.51
| | 300.31
| | 100.10
| |
|-
| |
| |
| |
| |
| |
| |
| | 21\80
| | 499.26
| | 309.07
| | 95.10
| |
|-
| |
| |
| |
| |
| |
| | 16\61
| |
| | 498.87
| | 311.80
| | 93.54
| |
|-
| |
| |
| |
| |
| |
| |
| | 27\103
| | 498.57
| | 313.915
| | 92.33
| |
|-
| |
| |
| |
| |
| | 11\42
| |
| |
| | 498.13
| | 316.99
| | 90.57
| |
|-
| |
| |
| |
| |
| |
| |
| | 28\107
| | 497.71
| | 319.955
| | 88.88
| |
|-
| |
| |
| |
| |
| |
| | 17\65
| |
| | 497.43
| | 321.87
| | 87.78
| |
|-
| |
| |
| |
| |
| |
| |
| | 23\88
| | 497.10
| | 324.20
| | 86.42
| |
|-
| |
| |
| |
| | 6\23
| |
| |
| |
| | 496.16
| | 330.775
| | 82.69
| |
|-
| |
| |
| |
| |
| |
| |
| | 19\73
| | 495.03
| | 338.70
| | 78.16
| |
|-
| |
| |
| |
| |
| |
| | 13\50
| |
| | 494.51
| | 342.35
| | 76.08
| |
|-
| |
| |
| |
| |
| |
| |
| | 20\77
| | 494.01
| | 345.81
| | 74.10
| |
|-
| |
| |
| |
| |
| | 7\27
| |
| |
| | 493.10
| | 352.21
| | 70.44
| |
|-
| |
| |
| |
| |
| |
| |
| | 15\58
| | 491.885
| | 360.72
| | 65.585
| |
|-
| |
| |
| |
| |
| |
| | 8\31
| |
| | 490.83
| | 368.12
| | 61.35
| |
|-
| |
| |
| |
| |
| |
| |
| | 9\35
| | 489.07
| | 380.39
| | 54.34
| |
|-
| | 1\4
| |
| |
| |
| |
| |
| |
| colspan="2" style="text-align:center;" | 475.49
| | 0
| |
|}

Latest revision as of 10:30, 6 June 2026

Canopus
Subgroups 3.5.7
Comma basis 16875/16807
Reduced mapping ⟨1; -5 -4]
ET join b13 & b88
Generators (CWE) ~7/5 = 583.986 ¢
MOS scales 3L 1s <3/1>, 3L 4s <3/1>, 3L 7s <3/1>
Ploidacot beta-tetragem
Minimax error 3.5.7 7-throdd-limit: 1.40 ¢;
3.5.7 49-throdd-limit: 2.80 ¢
Target scale size 3.5.7 7-throdd-limit: 7 notes;
3.5.7 49-throdd-limit: 13 notes

Canopus is the rank two 3.5.7 subgroup 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, 3L 1s, 3L 4s, 3L 7s, and (in most cases) 10L 3s. As 16875/16807 = (540/539)2*(3025/3024), Canopus can be extended to the 3.5.7.11/4 subgroup extremely naturally by tempering out these two commas; prime 53 can additionally be incorporated by means of tempering out 1325/1323, equating (7/5)2 = 49/25 to 53/27.

For technical information see No-twos subgroup temperaments #Canopus.

Interval table

In the below, tritave-reduced harmonics and subharmonics are indicated in bold.

Canopus
# Cents* Approximate Ratios
3.5.7.11/4.53 subgroup
−3 149.9 12/11, 49/45
−2 733.9 55/36, 75/49, 81/53, 84/55
−1 1318.0 15/7
0 0.0 1/1
1 584.0 7/5
2 1168.0 49/25, 53/27, 55/28, 108/55
3 1752.0 11/4, 135/49
4 434.1 9/7
5 1018.1 9/5
6 1602.1 53/21, 63/25
7 284.1 33/28, 53/45
8 868.1 33/20, 81/49
9 1452.1 81/35
10 134.2 27/25, 53/49

* In 3.5.7-targeted DKW tuning

Todo: expand

add tuning spectrum

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