Sirius

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This page on a regular temperament, temperament collection, or aspect of regular temperament theory is under the jurisdiction of WikiProject TempClean and is being revised for clarity.

Technical data: Gariboh clan#Sirius

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 and, 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
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