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=1 13 edt
L=7 s=3 63 (~40edo) and 67 (~42edo)
[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 |
||||||||