Sirius

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EDTs compatible with the Sirius triskaidecatonic scale[edit]

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 4L+5s 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 L s 2g 3g 4g notes
1/6 316.99 0 633.985 950.98 1267.97
8/49 310.52 271.71 38.815 621.05 931.57 1242.09
7/43 309.62 265.389 44.23 619.24 928.86 1238.48
13/80 309.07 261.52 47.55 618.14 927.2 1236.27
6/37 308.425 257.02 51.4 616.85 925.275 1233.7
17/105 307.94 253.59 54.34 615.87 923.81 1231.74
11/68 307.67 251.73 55.94 615.34 923.01 1230.68
16/99 307.39 249.75 57.635 614.77 922.16 1229.55
5/31 306.77 245.41 61.35 613.53 920.3 1227.07
19/118 306.25 241.77 64.47 612.49 918.74 1224.99
14/87 306.06 240.47 65.585 612.12 918.19 1224.25
23/143 305.91 239.41 66.5 611.82 917.73 1223.64
9/56 305.67 237.74 67.93 611.34 917.01 1222.68
22/137 305.42 236.01 69.41 610.85 916.27 1221.69
13/81 305.25 234.81 70.44 610.5 915.76 1221.01
17/106 305.03 233.26 71.77 610.06 915.09 1220.12
304.73 231.15 73.58 609.46 914.19 1218.92
4/25 304.31 228.235 76.08 608.63 912.94 1217.25
19/119 303.67 223.76 79.91 607.35 911.02 1214.69
15/94 303.5 222.57 80.93 607.01 910.51 1214.01
303.39 221.8 81.595 606.79 910.18 1213.57
26/163 303.38 221.7 81.67 606.76 910.14 1213.52
11/69 303.21 220.52 82.69 606.42 909.63 1212.84
29/182 303.06 219.46 83.6 606.12 909.18 1212.84
18/113 302.97 218.81 84.16 605.93 908.9 1211.86
25/157 302.86 218.06 84.8 605.72 908.58 1211.44
7/44 302.58 216.13 86.45 605.17 907.75 1210.34
24/151 302.3 214.13 88.17 604.59 906.89 1209.19
17/107 302.18 213.3 88.88 604.36 906.54 1208.72
27/170 302.075 212.57 89.5 604.15 906.225 1208.3
10/63 301.898 211.33 90.57 603.8 905.69 1207.59
23/145 301.69 209.87 91.82 603.38 905.07 1207.76
13/82 301.53 208.75 92.78 603.06 904.59 1206.12
16/101 301.3 207.14 94.16 602.6 903.9 1205.2
3/19 300.31 200.21 100.1 600.62 900.93 1201.235 Boundary of propriety for major Sirius scale
17/108 299.38 193.72 105.66 598.76 898.15 1197.53
14/89 299.18 192.33 106.85 598.37 897.55 1196.74
25/159 299.05 191.39 107.66 598.1 897.15 1196.2
11/70 298.88 190.2 108.68 597.76 896.64 1195.52
30/191 298.74 189.2 109.54 597.47 896.21 1194.94
19/121 298.65 188.62 110.03 597.31 895.96 1194.62
27/172 298.56 187.98 110.58 597.13 895.69 1194.25
8/51 298.35 186.47 111.88 596.69 895.04 1193.38
29/185 298.14 185.055 113.09 596.29 894.43 1192.58
21/134 298.07 184.52 113.55 596.14 894.2 1192.27
34/217 298 184.06 113.94 596 894.01 1192.01 Golden major Sirius scale is near here
13/83 297.9 183.32 114.58 595.79 893.69 1191.59
31/198 297.78 182.51 115.27 595.56 893.34 1191.12
18/115 297.7 181.93 115.71 595.39 893.09 1190.79
23/147 297.585 181.14 116.45 595.17 892.755 1190.34
5/32 297.18 178.31 118.87 594.36 891.54 1188.72
22/141 296.76 175.36 121.4 593.52 890.28 1187.04
17/109 296.635 174.49 122.14 593.27 889.905 1186.54
29/186 296.54 173.835 122.71 593.08 889.62 1186.16
12/77 296.41 172.905 123.5 592.82 889.23 1185.64
31/199 296.28 172.04 124.25 592.57 888.85 1185.14
19/122 296.21 171.49 124.718 592.41 888.62 1184.82
26/167 296.11 170.83 125.28 592.23 888.34 1184.45
7/45 295.86 169.06 126.8 591.72 887.57 1183.44
23/148 295.57 167.06 128.51 591.15 886.72 1182.3
16/103 295.45 166.19 129.26 590.9 886.35 1181.8
25/161 295.335 165.39 129.95 590.67 896.005 1181.34
9/58 295.13 163.96 131.17 590.26 885.39 1180.52
20/129 294.88 162.18 132.695 589.75 884.63 1179.51
11/71 294.67 160.73 133.94 589.34 884.01 1178.68
13/84 294.35 158.5 135.85 588.7 883.05 1177.4
2/13 292.61 146.3 585.22 877.825 1170.43 Separatrix of major and minor Sirius scales
13/85 290.89 156.63 134.26 581.77 872.66 1163.55
11/72 290.58 158.5 132.08 581.15 871.73 1162.3
20/131

290.375

159.71

132.695

580.75 871.125 1161.5
9/59

290.13

161.18

128.95

580.26 870.38 1160.52
25/164

289.93

162.36

127.57

579.86 869.8 1159.73
16/105

289.82

163.025

126.8

579.66 869.47 1159.29
23/151

289.7

163.74

125.96

579.4 869.11 1158.81
7/46

289.43

165.39

124.04

578.86 868.28 1157.71
26/171

289.19

166.84

122.74

578.37 867.56 1156.74
19/125

289.1

167.37

121.725

578.19 867.29 1156.39
31/204

289.02

167.82

121.2

578.05 867.07 1156.092
12/79

288.905

168.53

120.38

577.81 866.715 1155.62
29/191 288.78 169.28 119.495 577.56 866.34 1155.12
17/112

288.69

169.82

118.87

577.38 866.07 1154.76
22/145

288.57

170.52

118.05

577.14 865.72 1154.29
5/33 288.175

172.905

115.27

576.35 864.525 1152.7
23/152

287.8

175.18

112.62

575.59 863.39 1151.18
18/119

287.69

175.81

111.88

575.38 863.07 1150.76
31/205

287.61

176.28

111.33

575.23 862.84 1150.54
13/86 287.505 176.93 110.58 575.01 862.515 1150.02
34/225 287.41 177.52 109.89 574.81 862.22 1149.63 Golden minor Sirius scale is near here
21/139 287.35 177.88 109.465 574.69 862.02 1149.38
29/192 287.27 178.31 108.97 574.55 861.82 1149.1
8/53 287.09 179.43 107.66 574.18 861.26 1148.35
27/179 286.88 180.63 106.25 573.77 860.66 1147.55
19/126 286.8 181.14 105.66 573.61 860.41 1147.21
30/199 286.73 181.59 105.13 573.45 860.18 1146.91
11/73 286.6 182.38 104.22 573.19 859.79 1146.38
25/166 286.44 183.32 103.12 572.88 859.32 1145.76
14/93 286.32 184.06 102.26 572.63 858.95 1145.26
17/113 286.135 185.15 100.99 572.27 858.405 1144.54
3/20 285.29 190.2 95.1 570.59 855.88 1141.17 Boundary of propriety for minor Sirius scale
16/107 284.4 195.52 88.88 568.81 853.21 1137.6
13/87 284.2 196.75 87.45 568.4 852.6 1136.8
23/154 284.06 197.61 86.45 568.12 852.17 1136.23
10/67 283.87 198.71 85.16 567.75 851.62 1135.5
27/181 283.72 199.65 84.06 567.43 851.15 1134.87
17/114 283.625 200.21 83.42 567.25 850.875 1134.5
24/161 283.52 200.83 82.69 567.04 850.56 1134.08
7/47 283.27 202.34 80.93 566.54 849.81 1133.08
25/168 283.03 203.78 79.25 566.06 849.09 1132.12
18/121 282.935 204.34 78.59 565.87 848.805 1131.74
29/195 282.855 204.83 78.03 565.71 848.565 1131.42
11/74 282.72 205.62 77.11 565.45 848.17 1130.89
26/175 282.58 206.5 76.08 565.15 847.73 1130.3
282.56 206.57 75.99 565.13 847.69 1130.26
15/101 282.47 207.14 75.325 564.94 847.41 1129.88
19/128 282.32 208.03 74.295 564.64 846.96 1129.28
4/27 281.77 211.33 70.44 563.54 845.31 1127.08
281.415 213.47 67.95 562.83 844.24 1125.66
17/115 281.16 215 66.155 562.32 843.48 1124.64
13/88 280.97 216.13 64.84 561.94 842.91 1123.88
22/149 280.83 217 63.82 561.65 842.48 1123.3
9/61 280.62 218.26 62.36 561.23 841.85 1122.46
23/156 280.42 219.46 60.96 560.83 841.25 1121.66
14/95 280.29 220.23 60.06 560.58 840.86 1121.15
19/129 280.13 221.16 58.975 560.27 840.4 1120.53
5/34 279.7 223.76 55.94 559.4 839.1 1118.8
16/109 279.19 226.84 52.35 558.37 837.56 1116.74
11/75 278.95 228.235 50.72 557.91 836.86 1115.81
17/116 278.735 229.55 49.19 557.47 836.205 1114.94
6/41 278.335 231.95 46.39 556.67 835.005 1113.34
13/89 277.81 235.07 42.74 555.63 833.44 1111.26
7/48 277.37 237.74 39.62 554.74 832.1 1109.47
8/55 276.65 242.07 34.58 553.3 829.94 1106.59
1/7 271,71 0 543.42 815.12 1086.83

236.009

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