9L 2s (3/1-equivalent)

From Xenharmonic Wiki
Revision as of 01:50, 7 June 2023 by CompactStar (talk | contribs)
Jump to navigation Jump to search
↖ 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 ¢)
View • Talk • Edit

9L 2s<3/1> or sub-Arcturus is a tritave-repeating MOS scale having 9 large steps and 2 small steps. 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.

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


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⟩
47\86 1039.441 862.514 8:7 1.143
41\75 1039.735 862.220 7:6 1.167
76\139 1039.918 862.037 13:11 1.182
35\64 1040.132 861.823 6:5 1.200
99\181 1040.296 861.659 17:14 1.214
64\117 1040.386 861.569 11:9 1.222
93\170 1040.481 861.474 16:13 1.231
29\53 1040.692 861.263 5:4 1.250
110\201 1040.871 861.084 19:15 1.267
81\148 1040.935 861.020 14:11 1.273
133\243 1040.988 860.967 23:18 1.278
52\95 1041.070 860.885 9:7 1.286
127\232 1041.156 860.799 22:17 1.294
75\137 1041.216 860.739 13:10 1.300
98\179 1041.294 860.661 17:13 1.308
23\42 1041.547 860.408 4:3 1.333 Supersoft 9L 2s⟨3/1⟩
109\199 1041.774 860.181 19:14 1.357
86\157 1041.835 860.120 15:11 1.364
149\272 1041.880 860.075 26:19 1.368
63\115 1041.941 860.014 11:8 1.375
166\303 1041.995 859.960 29:21 1.381
103\188 1042.029 859.926 18:13 1.385
143\261 1042.067 859.888 25:18 1.389
40\73 1042.167 859.788 7:5 1.400
137\250 1042.271 859.684 24:17 1.412
97\177 1042.314 859.641 17:12 1.417
154\281 1042.353 859.602 27:19 1.421
57\104 1042.418 859.537 10:7 1.429
131\239 1042.494 859.461 23:16 1.438
74\135 1042.553 859.402 13:9 1.444
91\166 1042.638 859.317 16:11 1.455
17\31 1043.008 858.947 3:2 1.500 Soft 9L 2s⟨3/1⟩
96\175 1043.358 858.597 17:11 1.545
79\144 1043.434 858.521 14:9 1.556
141\257 1043.485 858.470 25:16 1.562
62\113 1043.551 858.404 11:7 1.571
169\308 1043.605 858.350 30:19 1.579
107\195 1043.637 858.318 19:12 1.583
152\277 1043.672 858.283 27:17 1.588
45\82 1043.756 858.199 8:5 1.600
163\297 1043.834 858.121 29:18 1.611
118\215 1043.864 858.091 21:13 1.615
191\348 1043.889 858.066 34:21 1.619
73\133 1043.930 858.025 13:8 1.625
174\317 1043.975 857.980 31:19 1.632
101\184 1044.008 857.947 18:11 1.636
129\235 1044.052 857.903 23:14 1.643
28\51 1044.211 857.744 5:3 1.667 Semisoft 9L 2s⟨3/1⟩
123\224 1044.377 857.578 22:13 1.692
95\173 1044.426 857.529 17:10 1.700
162\295 1044.463 857.492 29:17 1.706
67\122 1044.516 857.439 12:7 1.714
173\315 1044.566 857.389 31:18 1.722
106\193 1044.597 857.358 19:11 1.727
145\264 1044.634 857.321 26:15 1.733
39\71 1044.736 857.219 7:4 1.750
128\233 1044.851 857.104 23:13 1.769
89\162 1044.901 857.054 16:9 1.778
139\253 1044.948 857.007 25:14 1.786
50\91 1045.030 856.925 9:5 1.800
111\202 1045.134 856.821 20:11 1.818
61\111 1045.219 856.736 11:6 1.833
72\131 1045.349 856.606 13:7 1.857
11\20 1046.075 855.880 2:1 2.000 Basic 9L 2s⟨3/1⟩
Scales with tunings softer than this are proper
71\129 1046.812 855.143 13:6 2.167
60\109 1046.948 855.007 11:5 2.200
109\198 1047.036 854.919 20:9 2.222
49\89 1047.144 854.811 9:4 2.250
136\247 1047.230 854.725 25:11 2.273
87\158 1047.279 854.676 16:7 2.286
125\227 1047.332 854.623 23:10 2.300
38\69 1047.453 854.502 7:3 2.333
141\256 1047.561 854.394 26:11 2.364
103\187 1047.601 854.354 19:8 2.375
168\305 1047.634 854.321 31:13 2.385
65\118 1047.687 854.268 12:5 2.400
157\285 1047.744 854.211 29:12 2.417
92\167 1047.784 854.171 17:7 2.429
119\216 1047.836 854.119 22:9 2.444
27\49 1048.016 853.939 5:2 2.500 Semihard 9L 2s⟨3/1⟩
124\225 1048.189 853.766 23:9 2.556
97\176 1048.237 853.718 18:7 2.571
167\303 1048.272 853.683 31:12 2.583
70\127 1048.322 853.633 13:5 2.600
183\332 1048.367 853.588 34:13 2.615
113\205 1048.395 853.560 21:8 2.625
156\283 1048.427 853.528 29:11 2.636
43\78 1048.514 853.441 8:3 2.667
145\263 1048.606 853.349 27:10 2.700
102\185 1048.645 853.310 19:7 2.714
161\292 1048.681 853.274 30:11 2.727
59\107 1048.742 853.213 11:4 2.750
134\243 1048.815 853.140 25:9 2.778
75\136 1048.872 853.083 14:5 2.800
91\165 1048.957 852.998 17:6 2.833
16\29 1049.354 852.601 3:1 3.000 Hard 9L 2s⟨3/1⟩
85\154 1049.780 852.175 16:5 3.200
69\125 1049.879 852.076 13:4 3.250
122\221 1049.948 852.007 23:7 3.286
53\96 1050.038 851.917 10:3 3.333
143\259 1050.114 851.841 27:8 3.375
90\163 1050.159 851.796 17:5 3.400
127\230 1050.210 851.745 24:7 3.429
37\67 1050.333 851.622 7:2 3.500
132\239 1050.452 851.503 25:7 3.571
95\172 1050.498 851.457 18:5 3.600
153\277 1050.538 851.417 29:8 3.625
58\105 1050.604 851.351 11:3 3.667
137\248 1050.677 851.278 26:7 3.714
79\143 1050.730 851.225 15:4 3.750
100\181 1050.804 851.151 19:5 3.800
21\38 1051.080 850.875 4:1 4.000 Superhard 9L 2s⟨3/1⟩
89\161 1051.391 850.564 17:4 4.250
68\123 1051.487 850.468 13:3 4.333
115\208 1051.562 850.393 22:5 4.400
47\85 1051.669 850.286 9:2 4.500
120\217 1051.772 850.183 23:5 4.600
73\132 1051.839 850.116 14:3 4.667
99\179 1051.919 850.036 19:4 4.750
26\47 1052.145 849.810 5:1 5.000
83\150 1052.415 849.540 16:3 5.333
57\103 1052.538 849.417 11:2 5.500
88\159 1052.654 849.301 17:3 5.667
31\56 1052.868 849.087 6:1 6.000
67\121 1053.149 848.806 13:2 6.500
36\65 1053.390 848.565 7:1 7.000
41\74 1053.786 848.169 8:1 8.000
5\9 1056.642 845.313 1:0 → ∞ Collapsed 9L 2s⟨3/1⟩
Retrieved from "https://en.xen.wiki/index.php?title=9L_2s_(3/1-equivalent)&oldid=115852"