Canopus

From Xenharmonic Wiki
Jump to: navigation, search

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