9L 2s (3/1-equivalent)

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↖ 8L 1s⟨3/1⟩ ↑ 9L 1s⟨3/1⟩ 10L 1s⟨3/1⟩ ↗
← 8L 2s⟨3/1⟩ 9L 2s (3/1-equivalent) 10L 2s⟨3/1⟩ →
↙ 8L 3s⟨3/1⟩ ↓ 9L 3s⟨3/1⟩ 10L 3s⟨3/1⟩ ↘ 
┌╥╥╥╥╥┬╥╥╥╥┬┐
│║║║║║│║║║║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLsLLLLs
sLLLLsLLLLL
Equave 3/1 (1902.0¢)
Period 3/1 (1902.0¢)
Generator size(edt)
Bright 6\11 to 5\9 (1037.4¢ to 1056.6¢)
Dark 4\9 to 5\11 (845.3¢ to 864.5¢)
Related MOS scales
Parent 2L 7s⟨3/1⟩
Sister 2L 9s⟨3/1⟩
Daughters 11L 9s⟨3/1⟩, 9L 11s⟨3/1⟩
Neutralized 7L 4s⟨3/1⟩
2-Flought 20L 2s⟨3/1⟩, 9L 13s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 6\11 (1037.4¢)
Supersoft (L:s = 4:3) 23\42 (1041.5¢)
Soft (L:s = 3:2) 17\31 (1043.0¢)
Semisoft (L:s = 5:3) 28\51 (1044.2¢)
Basic (L:s = 2:1) 11\20 (1046.1¢)
Semihard (L:s = 5:2) 27\49 (1048.0¢)
Hard (L:s = 3:1) 16\29 (1049.4¢)
Superhard (L:s = 4:1) 21\38 (1051.1¢)
Collapsed (L:s = 1:0) 5\9 (1056.6¢)

9L 2s⟨3/1⟩, also called sub-Arcturus, is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 9 large steps and 2 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1037.4¢ to 1056.6¢, or from 845.3¢ to 864.5¢.

This MOS family is the simplest tritave-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth.

Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila continuum and the bottom of the syntonic continuum.

Modes

Modes of 9L 2s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
10|0 1 LLLLLsLLLLs
9|1 7 LLLLsLLLLLs
8|2 2 LLLLsLLLLsL
7|3 8 LLLsLLLLLsL
6|4 3 LLLsLLLLsLL
5|5 9 LLsLLLLLsLL
4|6 4 LLsLLLLsLLL
3|7 10 LsLLLLLsLLL
2|8 5 LsLLLLsLLLL
1|9 11 sLLLLLsLLLL
0|10 6 sLLLLsLLLLL

Intervals

Intervals of 9L 2s⟨3/1⟩
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 172.9¢
Major 1-mosstep M1ms L 172.9¢ to 211.3¢
2-mosstep Minor 2-mosstep m2ms L + s 211.3¢ to 345.8¢
Major 2-mosstep M2ms 2L 345.8¢ to 422.7¢
3-mosstep Minor 3-mosstep m3ms 2L + s 422.7¢ to 518.7¢
Major 3-mosstep M3ms 3L 518.7¢ to 634.0¢
4-mosstep Minor 4-mosstep m4ms 3L + s 634.0¢ to 691.6¢
Major 4-mosstep M4ms 4L 691.6¢ to 845.3¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 845.3¢ to 864.5¢
Augmented 5-mosstep A5ms 5L 864.5¢ to 1056.6¢
6-mosstep Diminished 6-mosstep d6ms 4L + 2s 845.3¢ to 1037.4¢
Perfect 6-mosstep P6ms 5L + s 1037.4¢ to 1056.6¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 1056.6¢ to 1210.3¢
Major 7-mosstep M7ms 6L + s 1210.3¢ to 1268.0¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1268.0¢ to 1383.2¢
Major 8-mosstep M8ms 7L + s 1383.2¢ to 1479.3¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 1479.3¢ to 1556.1¢
Major 9-mosstep M9ms 8L + s 1556.1¢ to 1690.6¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 1690.6¢ to 1729.1¢
Major 10-mosstep M10ms 9L + s 1729.1¢ to 1902.0¢
11-mosstep Perfect 11-mosstep P11ms 9L + 2s 1902.0¢

Scale tree

Scale Tree and Tuning Spectrum of 9L 2s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
6\11 1037.430 864.525 1:1 1.000 Equalized 9L 2s⟨3/1⟩
41\75 1039.735 862.220 7:6 1.167
35\64 1040.132 861.823 6:5 1.200
64\117 1040.386 861.569 11:9 1.222
29\53 1040.692 861.263 5:4 1.250
81\148 1040.935 861.020 14:11 1.273
52\95 1041.070 860.885 9:7 1.286
75\137 1041.216 860.739 13:10 1.300
23\42 1041.547 860.408 4:3 1.333 Supersoft 9L 2s⟨3/1⟩
86\157 1041.835 860.120 15:11 1.364
63\115 1041.941 860.014 11:8 1.375
103\188 1042.029 859.926 18:13 1.385
40\73 1042.167 859.788 7:5 1.400
97\177 1042.314 859.641 17:12 1.417
57\104 1042.418 859.537 10:7 1.429
74\135 1042.553 859.402 13:9 1.444
17\31 1043.008 858.947 3:2 1.500 Soft 9L 2s⟨3/1⟩
79\144 1043.434 858.521 14:9 1.556
62\113 1043.551 858.404 11:7 1.571
107\195 1043.637 858.318 19:12 1.583
45\82 1043.756 858.199 8:5 1.600
118\215 1043.864 858.091 21:13 1.615 Golden Sub-Arcturus is near here
73\133 1043.930 858.025 13:8 1.625
101\184 1044.008 857.947 18:11 1.636
28\51 1044.211 857.744 5:3 1.667 Semisoft 9L 2s⟨3/1⟩
95\173 1044.426 857.529 17:10 1.700
67\122 1044.516 857.439 12:7 1.714
106\193 1044.597 857.358 19:11 1.727
39\71 1044.736 857.219 7:4 1.750
89\162 1044.901 857.054 16:9 1.778
50\91 1045.030 856.925 9:5 1.800
61\111 1045.219 856.736 11:6 1.833
11\20 1046.075 855.880 2:1 2.000 Basic 9L 2s⟨3/1⟩
Scales with tunings softer than this are proper
60\109 1046.948 855.007 11:5 2.200
49\89 1047.144 854.811 9:4 2.250
87\158 1047.279 854.676 16:7 2.286
38\69 1047.453 854.502 7:3 2.333
103\187 1047.601 854.354 19:8 2.375
65\118 1047.687 854.268 12:5 2.400
92\167 1047.784 854.171 17:7 2.429
27\49 1048.016 853.939 5:2 2.500 Semihard 9L 2s⟨3/1⟩
97\176 1048.237 853.718 18:7 2.571
70\127 1048.322 853.633 13:5 2.600
113\205 1048.395 853.560 21:8 2.625
43\78 1048.514 853.441 8:3 2.667
102\185 1048.645 853.310 19:7 2.714
59\107 1048.742 853.213 11:4 2.750
75\136 1048.872 853.083 14:5 2.800
16\29 1049.354 852.601 3:1 3.000 Hard 9L 2s⟨3/1⟩
69\125 1049.879 852.076 13:4 3.250
53\96 1050.038 851.917 10:3 3.333
90\163 1050.159 851.796 17:5 3.400
37\67 1050.333 851.622 7:2 3.500
95\172 1050.498 851.457 18:5 3.600
58\105 1050.604 851.351 11:3 3.667
79\143 1050.730 851.225 15:4 3.750
21\38 1051.080 850.875 4:1 4.000 Superhard 9L 2s⟨3/1⟩
68\123 1051.487 850.468 13:3 4.333
47\85 1051.669 850.286 9:2 4.500
73\132 1051.839 850.116 14:3 4.667
26\47 1052.145 849.810 5:1 5.000
57\103 1052.538 849.417 11:2 5.500
31\56 1052.868 849.087 6:1 6.000
36\65 1053.390 848.565 7:1 7.000
5\9 1056.642 845.313 1:0 → ∞ Collapsed 9L 2s⟨3/1⟩
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