Sirius

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EDTs compatible with the Sirius triskaidecatonic scale

The Sirius MOS families of 6L+7s and 6L+7s are good scales to know for representing "ordinary" diminished chords with stack of their generators. In fact, 0-1-2-3-4 generators is an "ordinary" dim7dim9 pentad, and by a weird coincidence, numbered 1-3-5-7-9 just as if arranged in an "ordinary" diatonic scale. Below is a list of the equal-temperaments which contain a 6L+1s scale using generators between 271.7 cents and 317.0 cents.

L=1 s=0 6 and 7 edt

L=1 s=1 13 edt

L=2 s=1 19 (~12edo) and 20

L=3 s=1 25 and 27 (~17edo)

L=3 s=2 32 and 33 (~21edo)

L=4 s=1 31 and 34

L=4 s=3 45 and 46 (~29edo)

L=5 s=1 37 and 41

L=5 s=2 44 and 47

L=5 s=3 51 (~32edo) and 53

L=5 s=4 58 and 59 (~37edo)

L=6 s=1 43 (~27edo) and 48

L=6 s=5 71 and 72

L=7 s=1 49 (~31edo) and 55

L=7 s=2 56 and 61

L=7 s=3 63 (~40edo) and 67 (~42edo)

L=7 s=4 64 and 68 (~43edo)

L=7 s=5 77 and 79 (~50edo)

L=7 s=6 84 (~53edo) and 85

[For what it's worth, as 6edt and 7edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be dodecatonic and tetradecatonic, eg. 18edt and 21edt.]

Generator cents

hekts

L s 2g 3g 4g notes
1/6 316.99

216.67

0 633.985

433.33

950.98

650

1267.97

866.67

8/49 310.52

212.245

271.71

185.71

38.815

26.53

621.05

424.49

931.57

636.735

1242.09

848.98

7/43 309.62

211.63

265.39

181.395

44.23

30.23

619.24

423.26

928.86

634.88

1238.48

846.51

13/80 309.07

211.25

261.52

178.75

47.55

32.5

618.14

422.5

927.2

633.75

1236.27

845

6/37 308.425

210.81

257.02

175.68

51.4

35.135

616.85

421.62

925.275

632.43

1233.7

843.24

17/105 307.94

210.48

253.59

173.33

54.34

37.14

615.87

420.95

923.81

631.43

1231.74

841.905

11/68 307.67

210.29

251.73

172.06

55.94

38.235

615.34

420.59

923.01

630.88

1230.68

841.18

16/99 307.39

210.1

249.75

170.71

57.635

39.39

614.77

420.2

922.16

630.3

1229.55

840.4

5/31 306.77

209.68

245.41

167.74

61.35

41.935

613.53

419.355

920.3

629.03

1227.07

838.71

19/118 306.25

209.32

241.77

165.25

64.47

44.07

612.49

418.64

918.74

627.97

1224.99

837.29

14/87 306.06

209.195

240.47

164.37

65.585

44.83

612.12

418.39

918.19

627.59

1224.25

836.78

23/143 305.91

209.09

239.41

163.64

66.5

46.36

611.82

418.18

917.73

627.27

1223.64

836.36

9/56 305.67

208.93

237.74

162.5

67.93

46.43

611.34

417.86

917.01

626.79

1222.68

835.71

22/137 305.42

208.76

236.01

161.31

69.41

47.445

610.85

417.52

916.27

626.28

1221.69

835.04

13/81 305.25

208.64

234.81

160.49

70.44

48.15

610.5

417.28

915.76

625.93

1221.01

834.57

17/106 305.03

208.49

233.26

159.43

71.77

49.06

610.06

416.98

915.09

625.47

1220.12

833.96

304.73

208.285

231.15

157.99

73.58

50.29

609.46

416.57

914.19

624.855

1218.92

833.14

L=8/7 essentially here
4/25 304.31

208

228.235

156

76.08

52

608.63

416

912.94

624

1217.25

832

19/119 303.67

207.56

223.76

152.94

79.91

54.62

607.35

415.13

911.02

622.69

1214.69

830.25

15/94 303.5

207.45

222.57

152.13

80.93

55.32

607.01

414.89

910.51

622.34

1214.01

829.79

303.39

207.37

221.8

151.61

81.595

55.77

606.79

414.74

910.18

622.115

1213.57

829.49

26/163 303.38

207.36

221.7

151.53

81.67

55.83

606.76

414.72

910.14

622.08

1213.52

829.45

11/69 303.21

207.25

220.52

150.725

82.69

56.52

606.42

414.49

909.63

621.74

1212.84

828.99

29/182 303.06

207.14

219.46

150

83.6

57.14

606.12

414.29

909.18

621.43

1212.84

828.57

18/113 302.97

207.08

218.81

149.56

84.16

57.52

605.93

414.16

908.9

621.24

1211.86

828.32

25/157 302.86

207.01

218.06

149.045

84.8

57.96

605.72

414.01

908.58

621.02

1211.44

828.025

7/44 302.58

206.82

216.13

147.73

86.45

59.09

605.17

413.63

907.75

620.455

1210.34

827.27

24/151 302.3

206.62

214.13

146.36

88.17

60.265

604.59

413.245

906.89

619.87

1209.19

826.49

17/107 302.18

206.54

213.3

145.79

88.88

60.75

604.36

413.08

906.54

619.63

1208.72

826.17

27/170 302.075

206.47

212.57

145.29

89.5

61.18

604.15

412.94

906.225

619.41

1208.3

825.88

10/63 301.9

206.35

211.33

144.44

90.57

61.905

603.8

412.7

905.7

619.05

1207.59

825.4

23/145 301.69

206.21

209.87

143.45

91.82

62.76

603.38

412.41

905.07

618.62

1207.76

824.83

13/82 301.53

206.1

208.75

142.68

92.78

63.415

603.06

412.195

904.59

618.29

1206.12

824.39

16/101 301.3

205.94

207.14

141.58

94.16

64.36

602.6

411.88

903.9

617.82

1205.2

823.76

3/19 300.31

205.26

200.21

136.84

100.1

68.42

600.62

410.52

900.93

615.79

1201.235

821.05

Boundary of propriety for major Sirius scale
17/108 299.38

204.63

193.72

132.41

105.66

72.22

598.76

409.26

898.15

613.89

1197.53

818.52

14/89 299.18

204.49

192.33

131.46

106.85

73.03

598.37

408.99

897.55

613.48

1196.74

816.98

25/159 299.05

204.4

191.39

130.82

107.66

73.585

598.1

408.805

897.15

613.21

1196.2

817.61

11/70 298.88

204.29

190.2

130

108.68

74.29

597.76

408.57

896.64

612.86

1195.52

817.14

30/191 298.74

204.19

189.2

129.32

109.54

74.87

597.47

408.38

896.21

612.565

1194.94

816.75

19/121 298.65

204.13

188.62

128.93

110.03

75.21

597.31

408.26

895.96

612.4

1194.62

816.53

27/172 298.56

204.07

187.98

128.49

110.58

75.58

597.13

408.14

895.69

612.21

1194.25

816.28

8/51 298.35

203.92

186.47

127.45

111.88

76.47

596.69

407.84

895.04

611.765

1193.38

815.69

29/185 298.14

203.78

185.055

126.49

113.09

77.3

596.29

407.57

894.43

611.35

1192.58

815.135

21/134 298.07

203.73

184.52

126.12

113.55

77.61

596.14

407.46

894.2

611.19

1192.27

814.925

34/217 298

203.69

184.06

125.81

113.94

77.88

596

407.37

894.01

611.06

1192.01

814.75

Golden major Sirius scale is near here
13/83 297.9

203.61

183.32

125.3

114.58

78.31

595.79

407.23

893.69

610.84

1191.59

814.46

31/198 297.78

203.535

182.51

124.75

115.27

78.79

595.56

407.07

893.34

610.61

1191.12

814.14

18/115 297.7

203.48

181.93

124.35

115.71

79.13

595.39

406.96

893.09

610.435

1190.79

813.91

23/147 297.585

203.4

181.14

123.81

116.45

79.59

595.17

406.8

892.755

610.2

1190.34

813.605

5/32 297.18

203.125

178.31

121.875

118.87

81.25

594.36

406.25

891.54

609.375

1188.72

812.5

22/141 296.76

202.84

175.36

119.86

121.4

82.98

593.52

405.67

890.28

608.51

1187.04

811.34

17/109 296.635

202.75

174.49

119.27

122.14

83.48

593.27

405.505

889.905

608.26

1186.54

811.01

29/186 296.54

202.69

173.835

118.82

122.71

83.87

593.08

405.38

889.62

608.065

1186.16

810.75

12/77 296.41

202.6

172.905

118.18

123.5

84.42

592.82

405.195

889.23

607.79

1185.64

810.39

31/199 296.28

202.51

172.04

117.59

124.25

84.925

592.57

405.025

888.85

607.54

1185.14

810.05

19/122 296.21

202.46

171.49

117.21

124.718

85.25

592.41

404.92

888.62

607.38

1184.82

809.84

26/167 296.11

202.395

170.83

116.77

125.28

85.63

592.23

404.79

888.34

607.19

1184.45

809.58

7/45 295.86

202.22

169.06

115.56

126.8

86.67

591.72

404.44

887.57

606.67

1183.44

808.89

23/148 295.57

202.03

167.06

114.19

128.51

87.84

591.15

404.05

886.72

606.08

1182.3

806.11

16/103 295.45

201.94

166.19

113.59

129.26

88.35

590.9

403.88

886.35

605.825

1181.8

807.77

25/161 295.335

201.86

165.39

113.04

129.95

88.82

590.67

403.73

886.005

605.59

1181.34

807.45

9/58 295.13

201.72

163.96

112.07

131.17

89.655

590.26

403.45

885.39

605.17

1180.52

806.9

20/129 294.88

201.55

162.18

110.85

132.695

90.7

589.75

403.1

884.63

604.65

1179.51

806.2

11/71 294.67

201.41

160.73

109.86

133.94

91.55

589.34

402.82

884.01

604.225

1178.68

805.63

13/84 294.35

201.19

158.5

108.33

135.85

92.86

588.7

402.38

883.05

603.57

1177.4

804.76

2/13 292.61

200

146.3

100

585.22

400

877.825

600

1170.43

800

Separatrix of major and minor Sirius scales
13/85 290.89

198.82

156.63

107.06

134.26

91.765

581.77

397.65

872.66

596.47

1163.55

795.29

11/72 290.58

198.61

158.5

108.33

132.08

90.28

581.15

397.22

871.73

595.83

1162.3

794.44

20/131 290.375

198.47

159.71

109.16

132.695

89.31

580.75

396.95

871.125

595.42

1161.5

793.89

9/59 290.13

198.305

161.18

110.17

128.95

88.14

580.26

396.61

870.38

594.915

1160.52

793.22

25/164 289.93

198.17

162.36

110.98

127.57

87.195

579.86

396.34

869.8

594.51

1159.73

792.68

16/105 289.82

198.095

163.025

111.43

126.8

86.67

579.66

396.19

869.47

594.29

1159.29

792.38

23/151 289.7

198.01

163.74

111.92

125.96

85.09

579.4

396.03

869.11

594.04

1158.81

792.05

7/46 289.43

197.83

165.39

113.04

124.04

84.78

578.86

395.65

868.28

593.48

1157.71

791.3

26/171 289.19

197.66

166.84

114.035

122.74

83.63

578.37

395.32

867.56

592.98

1156.74

790.64

19/125 289.1

197.6

167.37

114.4

121.725

83.2

578.19

395.2

867.29

592.8

1156.39

790.4

31/204 289.02

197.55

167.82

114.71

121.2

82.84

578.05

395.1

867.07

592.65

1156.092

790.2

12/79 288.905

197.47

168.53

115.19

120.38

82.28

577.81

394.94

866.715

592.405

1155.62

789.87

29/191 288.78

197.38

169.28

115.71

119.495

81.675

577.56

394.76

866.34

592.15

1155.12

789.35

17/112 288.69

197.32

169.82

116.07

118.87

81.25

577.38

394.64

866.07

591.69

1154.76

789.29

22/145 288.57

197.24

170.52

116.55

118.05

80.69

577.14

394.48

865.72

591.72

1154.29

788.965

5/33 288.175

196.97

172.905

118.18

115.27

78.79

576.35

393.94

864.525

590.91

1152.7

787.88

23/152 287.8

196.71

175.18

119.74

112.62

76.97

575.59

393.42

863.39

590.13

1151.18

786.84

18/119 287.69

196.64

175.81

120.17

111.88

76.47

575.38

393.28

863.07

589.92

1150.76

786.555

31/205 287.61

196.585

176.28

120.49

111.33

76.1

575.23

393.17

862.84

589.76

1150.54

786.34

13/86 287.505

196.51

176.93

120.93

110.58

75.58

575.01

393.02

862.515

589.535

1150.02

786.05

34/225 287.41

196.44

177.52

121.33

109.89

75.11

574.81

392.89

862.22

589.22

1149.63

785.67

Golden minor Sirius scale is near here
21/139 287.35

196.4

177.88

121.58

109.465

74.82

574.69

392.81

862.02

589.21

1149.38

785.61

29/192 287.27

196.35

178.31

121.875

108.97

74.48

574.55

392.71

861.82

589.06

1149.1

785.42

8/53 287.09

196.23

179.43

122.64

107.66

73.585

574.18

392.45

861.26

588.68

1148.35

784.91

27/179 286.88

196.09

180.63

123.46

106.25

72.63

573.77

392.18

860.66

588.27

1147.55

784.36

19/126 286.8

196.03

181.14

123.81

105.66

72.22

573.61

392.06

860.41

588.095

1147.21

784.13

30/199 286.73

195.98

181.59

124.12

105.13

71.86

573.45

391.96

860.18

587.94

1146.91

783.92

11/73 286.6

195.89

182.38

124.66

104.22

71.23

573.19

396.78

859.79

587.67

1146.38

783.56

25/166 286.44

195.78

183.32

125.3

103.12

70.48

572.88

391.57

859.32

587.35

1145.76

783.13

14/93 286.32

195.7

184.06

125.81

102.26

69.89

572.63

391.4

858.95

587.1

1145.26

782.8

17/113 286.135

195.575

185.15

126.55

100.99

69.03

572.27

391.15

858.405

586.73

1144.54

782.3

3/20 285.29

195

190.2

130

95.1

65

570.59

390

855.88

585

1141.17

780

Boundary of propriety for minor Sirius scale
16/107 284.4

194.39

195.52

133.645

88.88

60.75

568.81

388.785

853.21

583.18

1137.6

777.57

13/87 284.2

194.25

196.75

134.48

87.45

59.77

568.4

388.51

852.6

582.76

1136.8

777.01

23/154 284.06

194.16

197.61

135.065

86.45

59.09

568.12

388.31

852.17

582.47

1136.23

776.62

10/67 283.87

194.03

198.71

135.82

85.16

58.21

567.75

388.06

851.62

582.09

1135.5

776.12

27/181 283.72

193.92

199.65

136.46

84.06

57.46

567.43

387.845

851.15

581.77

1134.87

775.69

17/114 283.625

193.86

200.21

136.84

83.42

57.02

567.25

387.72

850.875

581.58

1134.5

775.44

24/161 283.52

193.79

200.83

137.27

82.69

56.52

567.04

387.58

850.56

581.37

1134.08

775.155

7/47 283.27

193.62

202.34

138.3

80.93

55.32

566.54

387.24

849.81

580.86

1133.08

774.48

25/168 283.03

193.45

203.78

139.29

79.25

54.16

566.06

386.905

849.09

580.36

1132.12

773.81

18/121 282.935

193.39

204.34

139.67

78.59

53.72

565.87

386.78

848.805

580.165

1131.74

773.55

29/195 282.855

193.33

204.83

140

78.03

53.33

565.71

386.67

848.565

580

1131.42

773.33

11/74 282.72

193.24

205.62

140.54

77.11

52.7

565.45

386.49

848.17

579.73

1130.89

772.97

26/175 282.58

193.14

206.5

141.14

76.08

52

565.15

386.29

847.73

579.43

1130.3

772.57

282.56

193.135

206.57

141.19

75.99

51.94

565.13

386.27

847.69

579.4

1130.26

772.54

15/101 282.47

193.07

207.14

141.58

75.325

51.485

564.94

386.14

847.41

579.21

1129.88

772.28

19/128 282.32

192.97

208.03

142.19

74.295

50.78

564.64

385.94

846.96

578.91

1129.28

771.875

4/27 281.77

192.59

211.33

144.44

70.44

48.15

563.54

385.185

845.31

577.78

1127.08

770.37

281.415

192.35

213.47

145.91

67.95

46.44

562.83

384.7

844.24

577.05

1125.66

769.4

17/115 281.16

192.17

215

146.96

66.155

45.22

562.32

384.35

843.48

576.52

1124.64

768.69

13/88 280.97

192.045

216.13

147.73

64.84

44.31

561.94

384.09

842.91

576.14

1123.88

768.18

22/149 280.83

191.95

217

148.32

63.82

43.62

561.65

383.89

842.48

575.84

1123.3

767.785

9/61 280.62

191.8

218.26

149.18

62.36

42.62

561.23

191.61

841.85

575.41

1122.46

767.21

23/156 280.42

191.67

219.46

150

60.96

41.67

560.83

383.33

841.25

575

1121.66

766.67

14/95 280.29

191.58

220.23

150.53

60.06

41.05

560.58

383.16

840.86

574.74

1121.15

766.32

19/129 280.13

191.47

221.16

151.16

58.975

40.31

560.27

382.95

840.4

574.42

1120.53

765.89

5/34 279.7

191.18

223.76

152.94

55.94

38.235

559.4

382.35

839.1

573.52

1118.8

764.71

16/109 279.19

190.83

226.84

155.05

52.35

35.78

558.37

381.65

837.56

572.48

1116.74

763.3

11/75 278.95

190.67

228.235

156

50.72

34.67

557.91

381.33

836.86

572

1115.81

762.67

17/116 278.735

190.52

229.55

156.9

49.19

33.62

557.47

381.03

836.205

571.55

1114.94

762.07

6/41 278.335

190.24

231.95

158.54

46.39

31.71

556.67

380.49

835.005

570.73

1113.34

760.98

13/89 277.81

189.89

235.07

160.67

42.74

29.21

555.63

379.775

833.44

569.66

1111.26

759.55

7/48 277.37

189.58

237.74

162.5

39.62

27.08

554.74

379.17

832.1

568.75

1109.47

758.33

8/55 276.65

189.09

242.07

165.455

34.58

23.64

553.3

378.18

829.94

567.27

1106.59

756.36

1/7 271.71

185.71

0 543.42

371.43

815.12

557.14

1086.83

742.86