17L 2s (3/1-equivalent)
↖ 16L 1s⟨3/1⟩ | ↑ 17L 1s⟨3/1⟩ | 18L 1s⟨3/1⟩ ↗ |
← 16L 2s⟨3/1⟩ | 17L 2s (3/1-equivalent) | 18L 2s⟨3/1⟩ → |
↙ 16L 3s⟨3/1⟩ | ↓ 17L 3s⟨3/1⟩ | 18L 3s⟨3/1⟩ ↘ |
┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║│║║║║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLsLLLLLLLLL
17L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 17 large steps and 2 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1001¢ to 1006.9¢, or from 895¢ to 900.9¢.
Using a generator as which is as sharp as possible for an 'ordinary' ~5:3, this MOS is the most complex parent scale for an Arcturus-like temperament. It is also the most complex parent MOS for a temperament where two generators make an "ordinary" ~14:5 (the simplest is the proper Arcturus scale).
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
18|0 | 1 | LLLLLLLLLsLLLLLLLLs |
17|1 | 11 | LLLLLLLLsLLLLLLLLLs |
16|2 | 2 | LLLLLLLLsLLLLLLLLsL |
15|3 | 12 | LLLLLLLsLLLLLLLLLsL |
14|4 | 3 | LLLLLLLsLLLLLLLLsLL |
13|5 | 13 | LLLLLLsLLLLLLLLLsLL |
12|6 | 4 | LLLLLLsLLLLLLLLsLLL |
11|7 | 14 | LLLLLsLLLLLLLLLsLLL |
10|8 | 5 | LLLLLsLLLLLLLLsLLLL |
9|9 | 15 | LLLLsLLLLLLLLLsLLLL |
8|10 | 6 | LLLLsLLLLLLLLsLLLLL |
7|11 | 16 | LLLsLLLLLLLLLsLLLLL |
6|12 | 7 | LLLsLLLLLLLLsLLLLLL |
5|13 | 17 | LLsLLLLLLLLLsLLLLLL |
4|14 | 8 | LLsLLLLLLLLsLLLLLLL |
3|15 | 18 | LsLLLLLLLLLsLLLLLLL |
2|16 | 9 | LsLLLLLLLLsLLLLLLLL |
1|17 | 19 | sLLLLLLLLLsLLLLLLLL |
0|18 | 10 | sLLLLLLLLsLLLLLLLLL |
Intervals
Intervals | Steps subtended |
Range in cents | ||
---|---|---|---|---|
Generic | Specific | Abbrev. | ||
0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 100.1¢ |
Major 1-mosstep | M1ms | L | 100.1¢ to 111.9¢ | |
2-mosstep | Minor 2-mosstep | m2ms | L + s | 111.9¢ to 200.2¢ |
Major 2-mosstep | M2ms | 2L | 200.2¢ to 223.8¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 223.8¢ to 300.3¢ |
Major 3-mosstep | M3ms | 3L | 300.3¢ to 335.6¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 335.6¢ to 400.4¢ |
Major 4-mosstep | M4ms | 4L | 400.4¢ to 447.5¢ | |
5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 447.5¢ to 500.5¢ |
Major 5-mosstep | M5ms | 5L | 500.5¢ to 559.4¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 559.4¢ to 600.6¢ |
Major 6-mosstep | M6ms | 6L | 600.6¢ to 671.3¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 671.3¢ to 700.7¢ |
Major 7-mosstep | M7ms | 7L | 700.7¢ to 783.2¢ | |
8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 783.2¢ to 800.8¢ |
Major 8-mosstep | M8ms | 8L | 800.8¢ to 895.0¢ | |
9-mosstep | Perfect 9-mosstep | P9ms | 8L + s | 895.0¢ to 900.9¢ |
Augmented 9-mosstep | A9ms | 9L | 900.9¢ to 1006.9¢ | |
10-mosstep | Diminished 10-mosstep | d10ms | 8L + 2s | 895.0¢ to 1001.0¢ |
Perfect 10-mosstep | P10ms | 9L + s | 1001.0¢ to 1006.9¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 9L + 2s | 1006.9¢ to 1101.1¢ |
Major 11-mosstep | M11ms | 10L + s | 1101.1¢ to 1118.8¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 10L + 2s | 1118.8¢ to 1201.2¢ |
Major 12-mosstep | M12ms | 11L + s | 1201.2¢ to 1230.7¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 11L + 2s | 1230.7¢ to 1301.3¢ |
Major 13-mosstep | M13ms | 12L + s | 1301.3¢ to 1342.6¢ | |
14-mosstep | Minor 14-mosstep | m14ms | 12L + 2s | 1342.6¢ to 1401.4¢ |
Major 14-mosstep | M14ms | 13L + s | 1401.4¢ to 1454.4¢ | |
15-mosstep | Minor 15-mosstep | m15ms | 13L + 2s | 1454.4¢ to 1501.5¢ |
Major 15-mosstep | M15ms | 14L + s | 1501.5¢ to 1566.3¢ | |
16-mosstep | Minor 16-mosstep | m16ms | 14L + 2s | 1566.3¢ to 1601.6¢ |
Major 16-mosstep | M16ms | 15L + s | 1601.6¢ to 1678.2¢ | |
17-mosstep | Minor 17-mosstep | m17ms | 15L + 2s | 1678.2¢ to 1701.7¢ |
Major 17-mosstep | M17ms | 16L + s | 1701.7¢ to 1790.1¢ | |
18-mosstep | Minor 18-mosstep | m18ms | 16L + 2s | 1790.1¢ to 1801.9¢ |
Major 18-mosstep | M18ms | 17L + s | 1801.9¢ to 1902.0¢ | |
19-mosstep | Perfect 19-mosstep | P19ms | 17L + 2s | 1902.0¢ |
Scale tree
Generator | cents | L | s | 2g | Notes | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
8\17 | 895.038
611.765 |
111.88
76.471 |
0.00 | 1790.075
1223.529 |
L=1 s=0 | ||||||
57\121 | 895.962
612.397 |
110.0305
75.207 |
15.719
10.744 |
1791.925
1224.793 |
L=7 s=1 | ||||||
49\104 | 896.113
612.5 |
109.728
75 |
18.288
12.5 |
1792.227
1225 |
L=6 s=1 | ||||||
90\191 | 896.209
612.565 |
109.537
74.869 |
19.916
13.913 |
1792.418
1225.131 |
|||||||
41\87 | 896.324
612.644 |
109.308
74.713 |
21.862
14.9425 |
1792.647
1225.287 |
L=5 s=1 | ||||||
115\244 | 896.413
612.705 |
109.129
74.59 |
23.385
15.984 |
1792.826
1225.41 |
|||||||
74\157 | 896.463
612.739 |
109.029
74.522 |
24.229
16.5605 |
1792.926
1225.478 |
|||||||
107\227 | 896.516
612.775 |
108.9225
74.449 |
25.136
17.181 |
1793.032
1225.551 |
|||||||
33\70 | 896.636
612.857 |
108.683
74.286 |
27.171
18.571 |
1793.272
1225.714 |
L=4 s=1 | ||||||
124\263 | 896.739
612.928 |
108.4765
74.1445 |
28.927
19.772 |
1793.478
1225.8555 |
|||||||
91\193 | 896.777
612.953 |
108.402
74.093 |
33.368
20.207 |
1793.553
1225.907 |
|||||||
149\316 | 896.808
612.975 |
108.339
74.051 |
30.094
20.57 |
1793.616
1225.949 |
|||||||
58\123 | 896.857
613.008 |
108.241
73.984 |
30.926
21.138 |
1793.714
1226.016 |
L=7 s=2 | ||||||
141\299 | 896.9085
613.0435 |
108.138
73.913 |
31.805
21.739 |
1793.817
1226.087 |
|||||||
83\176 | 896.945
613.068 |
108.066
73.864 |
32.42
22.159 |
1793.889
1226.136 |
|||||||
108\229 | 896.992
613.1 |
107.971
73.799 |
33.222
22.707 |
1793.984
1226.201 |
|||||||
25\53 | 897.149
613.2075 |
107.658
73.585 |
35.886
24.528 |
1794.297
1226.415 |
L=3 s=1 | ||||||
117\248 | 897.293
613.3065 |
107.368
73.381 |
38.346
26.21 |
1794.587
1226.613 |
|||||||
92\195 | 897.333
613.333 |
107.29
73.333 |
39.0145
26.667 |
1794.665
1226.667 |
|||||||
159\337 | 897.362
613.353 |
107.232
73.294 |
39.5065
27.003 |
1794.723
1226.706 |
|||||||
67\142 | 897.401
613.38 |
107.152
73.239 |
40.182
27.465 |
1794.803
1226.761 |
|||||||
176\373 | 897.437
613.405 |
107.081
73.19 |
40.793
27.397 |
1794.874
1226.81 |
|||||||
109\231 | 897.459
613.42 |
107.036
73.16 |
41.168
28.1385 |
1794.919
1226.84 |
|||||||
151\320 | 897.485
613.4375 |
106.985
73.125 |
41.605
28.4375 |
1794.97
1226.875 |
|||||||
42\89 | 897.552
613.483 |
106.851
73.034 |
42.741
29.2135 |
1795.104
1226.966 |
L=5 s=2 | ||||||
143\303 | 897.622
613.531 |
106.71
72.947 |
43.94
30.033 |
1795.245
1227.063 |
|||||||
101\214 | 897.652
613.551 |
106.652
72.897 |
44.438
30.374 |
1795.303
1227.103 |
|||||||
160\339 | 897.678
613.569 |
106.599
72.86 |
44.884
30.6785 |
1795.356
1227.14 |
|||||||
59\125 | 897.723
613.6 |
106.5095
72.8 |
45.647
31.2 |
1795.446
1227.2 |
L=7 s=3 | ||||||
135\286 | 897.776
613.636 |
106.403
72.727 |
46.551
31.818 |
1795.552
1227.273 |
|||||||
76\161 | 897.817
613.665 |
106.3205
72.671 |
47.2535
32.298 |
1795.635
1227.329 |
|||||||
93\197 | 897.877
613.706 |
106.2005
72.589 |
48.273
32.995 |
1795.754
1227.411 |
|||||||
17\36 | 898.145
613.889 |
105.664
72.222 |
52.832
36.111 |
1796.291
1227.778 |
L=2 s=1 | ||||||
94\199 | 898.411
614.07 |
105.133
71.859 |
57.345
39.196 |
1796.822
1228.141 |
|||||||
77\163 | 898.4695
614.11 |
105.016
71.779 |
58.342
39.877 |
1796.939
1228.221 |
|||||||
137\290 | 898.51
614.138 |
104.935
71.732 |
59.026
40.345 |
1797.02
1228.276 |
|||||||
60\127 | 898.561
614.173 |
104.832
71.654 |
59.904
40.945 |
1797.123
1228.346 |
L=7 s=4 | ||||||
163\345 | 898.605
614.203 |
104.745
71.594 |
60.642
41.449 |
1797.201
1228.406 |
|||||||
103\218 | 898.63
614.22 |
104.695
71.56 |
61.072
41.743 |
1797.26
1228.44 |
|||||||
146\309 | 898.658
614.2395 |
104.638
71.521 |
61.552
42.071 |
1797.317
1228.479 |
|||||||
43\91 | 898.726
614.286 |
104.503
71.571 |
62.702
42.857 |
1797.452
1228.571 |
L=5 s=3 | ||||||
155\328 | 898.79
614.329 |
104.376
71.3415 |
63.785
43.598 |
1797.579
1228.6585 |
|||||||
112\237 | 898.814
614.346 |
104.327
71.308 |
64.201
43.882 |
1797.628
1228.692 |
|||||||
181\383 | 898.835
614.36 |
104.285
71.28 |
64.557
44.125 |
1797.67
1228.72 |
Golden Super-Arcturus[19] is near here | ||||||
69\146 | 898.869
614.384 |
104.217
71.231 |
65.135
44.5205 |
1797.738
1228.769 |
|||||||
164\347 | 898.901
614.409 |
104.142
71.182 |
65.774
44.957 |
1797.813
1228.818 |
|||||||
95\201 | 898.934
614.428 |
104.087
71.144 |
66.237
45.274 |
1797.868
1228.856 |
|||||||
121\256 | 898.971
614.453 |
104.013
71.094 |
66.866
45.703 |
1797.942
1228.906 |
|||||||
26\55 | 899.106
614.5455 |
103.743
70.909 |
69.162
47.273 |
1798.212
1229.091 |
L=3 s=2 | ||||||
113\239 | 899.251
614.644 |
103.454
70.711 |
71.622
48.954 |
1798.501
1229.289 |
|||||||
87\184 | 899.294
614.674 |
103.367
70.652 |
72.357
49.4565 |
1798.589
1229.348 |
|||||||
148\313 | 899.327
614.6965 |
103.301
70.607 |
72.918
49.84 |
1798.654
1229.393 |
|||||||
61\129 | 899.374
614.729 |
103.207
70.543 |
73.719
50.388 |
1798.748
1229.457 |
L=7 s=5 | ||||||
157\332 | 899.4185
614.759 |
103.118
70.482 |
74.474
50.904 |
1798.837
1229.518 |
|||||||
96\203 | 899.447
614.778 |
103.062
70.443 |
74.954
51.2315 |
1798.893
1229.557 |
|||||||
131\277 | 899.4805
614.801 |
102.994
70.397 |
75.529
51.6245 |
1798.961
1229.603 |
|||||||
35\74 | 899.573
614.865 |
102.808
70.37 |
77.106
52.703 |
1799.147
1229.63 |
L=4 s=3 | ||||||
114/241 | 899.68
614.938 |
102.595
70.1345 |
78.919
53.942 |
1799.36
1229.8655 |
|||||||
79\167 | 899.727
614.97 |
102.501
70.06 |
79.723
54.491 |
1799.454
1229.94 |
|||||||
123\260 | 899.771
615 |
102.413
70 |
80.467
55 |
1799.542
1230 |
|||||||
44\93 | 899.85
615.054 |
102.256
69.8925 |
81.8045
55.914 |
1799.699
1230.1075 |
L=5 s=4 | ||||||
97\205 | 899.949
615.122 |
102.056
69.756 |
83.5005
57.073 |
1799.899
1230.244 |
|||||||
53\112 | 900.032
615.179 |
101.89
69.643 |
84.909
58.036 |
1800.065
1230.357 |
L=6 s=5 | ||||||
62\131 | 900.162
615.267 |
101.631
69.466 |
87.112
59.542 |
1800.324
1230.534 |
L=7 s=6 | ||||||
9\19 | 900.926
615.7895 |
100.103
68.421 |
1801.852
1231.579 |
L=1 s=1 |