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19L 12s

Revision as of 00:54, 21 June 2023 by CompactStar (talk | contribs) (Replaced content with "{{Infobox MOS}} {{MOS intro}} == Modes == {{MOS modes}} == Scale tree == {{Scale tree|depth=8}}")

19L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 12 small steps, repeating every octave. 19L 12s is a great-grandchild scale of 5L 2s, expanding it by 24 tones. Generators that produce this scale range from 503.2 ¢ to 505.3 ¢, or from 694.7 ¢ to 696.8 ¢.

↖ 18L 11s ↑ 19L 11s 20L 11s ↗
← 18L 12s 19L 12s 20L 12s →
↙ 18L 13s ↓ 19L 13s 20L 13s ↘
Scale structure
Step pattern LLsLLsLsLLsLsLLsLLsLsLLsLsLLsLs
sLsLLsLsLLsLsLLsLLsLsLLsLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\31 to 8\19 (503.2 ¢ to 505.3 ¢)
Dark 11\19 to 18\31 (694.7 ¢ to 696.8 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:2 to 5:3 (quasisoft)
Related MOS scales
Parent 12L 7s
Sister 12L 19s
Daughters 31L 19s, 19L 31s
Neutralized 7L 24s
2-Flought 50L 12s, 19L 43s
Equal tunings
Equalized (L:s = 1:1) 13\31 (503.2 ¢)
Supersoft (L:s = 4:3) 47\112 (503.6 ¢)
Soft (L:s = 3:2) 34\81 (503.7 ¢)
Semisoft (L:s = 5:3) 55\131 (503.8 ¢)
Basic (L:s = 2:1) 21\50 (504.0 ¢)
Semihard (L:s = 5:2) 50\119 (504.2 ¢)
Hard (L:s = 3:1) 29\69 (504.3 ¢)
Superhard (L:s = 4:1) 37\88 (504.5 ¢)
Collapsed (L:s = 1:0) 8\19 (505.3 ¢)
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Modes

Modes of 19L 12s
UDP Cyclic
order		 Step
pattern
30|0 1 LLsLLsLsLLsLsLLsLLsLsLLsLsLLsLs
29|1 14 LLsLLsLsLLsLsLLsLsLLsLLsLsLLsLs
28|2 27 LLsLsLLsLLsLsLLsLsLLsLLsLsLLsLs
27|3 9 LLsLsLLsLLsLsLLsLsLLsLsLLsLLsLs
26|4 22 LLsLsLLsLsLLsLLsLsLLsLsLLsLLsLs
25|5 4 LLsLsLLsLsLLsLLsLsLLsLsLLsLsLLs
24|6 17 LLsLsLLsLsLLsLsLLsLLsLsLLsLsLLs
23|7 30 LsLLsLLsLsLLsLsLLsLLsLsLLsLsLLs
22|8 12 LsLLsLLsLsLLsLsLLsLsLLsLLsLsLLs
21|9 25 LsLLsLsLLsLLsLsLLsLsLLsLLsLsLLs
20|10 7 LsLLsLsLLsLLsLsLLsLsLLsLsLLsLLs
19|11 20 LsLLsLsLLsLsLLsLLsLsLLsLsLLsLLs
18|12 2 LsLLsLsLLsLsLLsLLsLsLLsLsLLsLsL
17|13 15 LsLLsLsLLsLsLLsLsLLsLLsLsLLsLsL
16|14 28 LsLsLLsLLsLsLLsLsLLsLLsLsLLsLsL
15|15 10 LsLsLLsLLsLsLLsLsLLsLsLLsLLsLsL
14|16 23 LsLsLLsLsLLsLLsLsLLsLsLLsLLsLsL
13|17 5 LsLsLLsLsLLsLLsLsLLsLsLLsLsLLsL
12|18 18 LsLsLLsLsLLsLsLLsLLsLsLLsLsLLsL
11|19 31 sLLsLLsLsLLsLsLLsLLsLsLLsLsLLsL
10|20 13 sLLsLLsLsLLsLsLLsLsLLsLLsLsLLsL
9|21 26 sLLsLsLLsLLsLsLLsLsLLsLLsLsLLsL
8|22 8 sLLsLsLLsLLsLsLLsLsLLsLsLLsLLsL
7|23 21 sLLsLsLLsLsLLsLLsLsLLsLsLLsLLsL
6|24 3 sLLsLsLLsLsLLsLLsLsLLsLsLLsLsLL
5|25 16 sLLsLsLLsLsLLsLsLLsLLsLsLLsLsLL
4|26 29 sLsLLsLLsLsLLsLsLLsLLsLsLLsLsLL
3|27 11 sLsLLsLLsLsLLsLsLLsLsLLsLLsLsLL
2|28 24 sLsLLsLsLLsLLsLsLLsLsLLsLLsLsLL
1|29 6 sLsLLsLsLLsLLsLsLLsLsLLsLsLLsLL
0|30 19 sLsLLsLsLLsLsLLsLLsLsLLsLsLLsLL

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 19L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\31 503.226 696.774 1:1 1.000 Equalized 19L 12s
112\267 503.371 696.629 9:8 1.125
99\236 503.390 696.610 8:7 1.143
185\441 503.401 696.599 15:13 1.154
86\205 503.415 696.585 7:6 1.167
245\584 503.425 696.575 20:17 1.176
159\379 503.430 696.570 13:11 1.182
232\553 503.436 696.564 19:16 1.188
73\174 503.448 696.552 6:5 1.200
279\665 503.459 696.541 23:19 1.211
206\491 503.462 696.538 17:14 1.214
339\808 503.465 696.535 28:23 1.217
133\317 503.470 696.530 11:9 1.222
326\777 503.475 696.525 27:22 1.227
193\460 503.478 696.522 16:13 1.231
253\603 503.483 696.517 21:17 1.235
60\143 503.497 696.503 5:4 1.250
287\684 503.509 696.491 24:19 1.263
227\541 503.512 696.488 19:15 1.267
394\939 503.514 696.486 33:26 1.269
167\398 503.518 696.482 14:11 1.273
441\1051 503.520 696.480 37:29 1.276
274\653 503.522 696.478 23:18 1.278
381\908 503.524 696.476 32:25 1.280
107\255 503.529 696.471 9:7 1.286
368\877 503.535 696.465 31:24 1.292
261\622 503.537 696.463 22:17 1.294
415\989 503.539 696.461 35:27 1.296
154\367 503.542 696.458 13:10 1.300
355\846 503.546 696.454 30:23 1.304
201\479 503.549 696.451 17:13 1.308
248\591 503.553 696.447 21:16 1.312
47\112 503.571 696.429 4:3 1.333 Supersoft 19L 12s
269\641 503.588 696.412 23:17 1.353
222\529 503.592 696.408 19:14 1.357
397\946 503.594 696.406 34:25 1.360
175\417 503.597 696.403 15:11 1.364
478\1139 503.600 696.400 41:30 1.367
303\722 503.601 696.399 26:19 1.368
431\1027 503.603 696.397 37:27 1.370
128\305 503.607 696.393 11:8 1.375
465\1108 503.610 696.390 40:29 1.379
337\803 503.611 696.389 29:21 1.381
546\1301 503.613 696.387 47:34 1.382
209\498 503.614 696.386 18:13 1.385
499\1189 503.616 696.384 43:31 1.387
290\691 503.618 696.382 25:18 1.389
371\884 503.620 696.380 32:23 1.391
81\193 503.627 696.373 7:5 1.400
358\853 503.634 696.366 31:22 1.409
277\660 503.636 696.364 24:17 1.412
473\1127 503.638 696.362 41:29 1.414
196\467 503.640 696.360 17:12 1.417
507\1208 503.642 696.358 44:31 1.419
311\741 503.644 696.356 27:19 1.421
426\1015 503.645 696.355 37:26 1.423
115\274 503.650 696.350 10:7 1.429
379\903 503.654 696.346 33:23 1.435
264\629 503.657 696.343 23:16 1.438
413\984 503.659 696.341 36:25 1.440
149\355 503.662 696.338 13:9 1.444
332\791 503.666 696.334 29:20 1.450
183\436 503.670 696.330 16:11 1.455
217\517 503.675 696.325 19:13 1.462
34\81 503.704 696.296 3:2 1.500 Soft 19L 12s
225\536 503.731 696.269 20:13 1.538
191\455 503.736 696.264 17:11 1.545
348\829 503.739 696.261 31:20 1.550
157\374 503.743 696.257 14:9 1.556
437\1041 503.746 696.254 39:25 1.560
280\667 503.748 696.252 25:16 1.562
403\960 503.750 696.250 36:23 1.565
123\293 503.754 696.246 11:7 1.571
458\1091 503.758 696.242 41:26 1.577
335\798 503.759 696.241 30:19 1.579
547\1303 503.761 696.239 49:31 1.581
212\505 503.762 696.238 19:12 1.583
513\1222 503.764 696.236 46:29 1.586
301\717 503.766 696.234 27:17 1.588
390\929 503.767 696.233 35:22 1.591
89\212 503.774 696.226 8:5 1.600
411\979 503.779 696.221 37:23 1.609
322\767 503.781 696.219 29:18 1.611
555\1322 503.782 696.218 50:31 1.613
233\555 503.784 696.216 21:13 1.615
610\1453 503.785 696.215 55:34 1.618
377\898 503.786 696.214 34:21 1.619
521\1241 503.787 696.213 47:29 1.621
144\343 503.790 696.210 13:8 1.625
487\1160 503.793 696.207 44:27 1.630
343\817 503.794 696.206 31:19 1.632
542\1291 503.796 696.204 49:30 1.633
199\474 503.797 696.203 18:11 1.636
453\1079 503.800 696.200 41:25 1.640
254\605 503.802 696.198 23:14 1.643
309\736 503.804 696.196 28:17 1.647
55\131 503.817 696.183 5:3 1.667 Semisoft 19L 12s
296\705 503.830 696.170 27:16 1.688
241\574 503.833 696.167 22:13 1.692
427\1017 503.835 696.165 39:23 1.696
186\443 503.837 696.163 17:10 1.700
503\1198 503.840 696.160 46:27 1.704
317\755 503.841 696.159 29:17 1.706
448\1067 503.843 696.157 41:24 1.708
131\312 503.846 696.154 12:7 1.714
469\1117 503.850 696.150 43:25 1.720
338\805 503.851 696.149 31:18 1.722
545\1298 503.852 696.148 50:29 1.724
207\493 503.854 696.146 19:11 1.727
490\1167 503.856 696.144 45:26 1.731
283\674 503.858 696.142 26:15 1.733
359\855 503.860 696.140 33:19 1.737
76\181 503.867 696.133 7:4 1.750
325\774 503.876 696.124 30:17 1.765
249\593 503.879 696.121 23:13 1.769
422\1005 503.881 696.119 39:22 1.773
173\412 503.883 696.117 16:9 1.778
443\1055 503.886 696.114 41:23 1.783
270\643 503.888 696.112 25:14 1.786
367\874 503.890 696.110 34:19 1.789
97\231 503.896 696.104 9:5 1.800
312\743 503.903 696.097 29:16 1.812
215\512 503.906 696.094 20:11 1.818
333\793 503.909 696.091 31:17 1.824
118\281 503.915 696.085 11:6 1.833
257\612 503.922 696.078 24:13 1.846
139\331 503.927 696.073 13:7 1.857
160\381 503.937 696.063 15:8 1.875
21\50 504.000 696.000 2:1 2.000 Basic 19L 12s
Scales with tunings softer than this are proper
155\369 504.065 695.935 15:7 2.143
134\319 504.075 695.925 13:6 2.167
247\588 504.082 695.918 24:11 2.182
113\269 504.089 695.911 11:5 2.200
318\757 504.095 695.905 31:14 2.214
205\488 504.098 695.902 20:9 2.222
297\707 504.102 695.898 29:13 2.231
92\219 504.110 695.890 9:4 2.250
347\826 504.116 695.884 34:15 2.267
255\607 504.119 695.881 25:11 2.273
418\995 504.121 695.879 41:18 2.278
163\388 504.124 695.876 16:7 2.286
397\945 504.127 695.873 39:17 2.294
234\557 504.129 695.871 23:10 2.300
305\726 504.132 695.868 30:13 2.308
71\169 504.142 695.858 7:3 2.333
334\795 504.151 695.849 33:14 2.357
263\626 504.153 695.847 26:11 2.364
455\1083 504.155 695.845 45:19 2.368
192\457 504.158 695.842 19:8 2.375
505\1202 504.160 695.840 50:21 2.381
313\745 504.161 695.839 31:13 2.385
434\1033 504.163 695.837 43:18 2.389
121\288 504.167 695.833 12:5 2.400
413\983 504.171 695.829 41:17 2.412
292\695 504.173 695.827 29:12 2.417
463\1102 504.174 695.826 46:19 2.421
171\407 504.177 695.823 17:7 2.429
392\933 504.180 695.820 39:16 2.438
221\526 504.183 695.817 22:9 2.444
271\645 504.186 695.814 27:11 2.455
50\119 504.202 695.798 5:2 2.500 Semihard 19L 12s
279\664 504.217 695.783 28:11 2.545
229\545 504.220 695.780 23:9 2.556
408\971 504.222 695.778 41:16 2.562
179\426 504.225 695.775 18:7 2.571
487\1159 504.228 695.772 49:19 2.579
308\733 504.229 695.771 31:12 2.583
437\1040 504.231 695.769 44:17 2.588
129\307 504.235 695.765 13:5 2.600
466\1109 504.238 695.762 47:18 2.611
337\802 504.239 695.761 34:13 2.615
545\1297 504.241 695.759 55:21 2.619
208\495 504.242 695.758 21:8 2.625
495\1178 504.244 695.756 50:19 2.632
287\683 504.246 695.754 29:11 2.636
366\871 504.248 695.752 37:14 2.643
79\188 504.255 695.745 8:3 2.667
345\821 504.263 695.737 35:13 2.692
266\633 504.265 695.735 27:10 2.700
453\1078 504.267 695.733 46:17 2.706
187\445 504.270 695.730 19:7 2.714
482\1147 504.272 695.728 49:18 2.722
295\702 504.274 695.726 30:11 2.727
403\959 504.275 695.725 41:15 2.733
108\257 504.280 695.720 11:4 2.750
353\840 504.286 695.714 36:13 2.769
245\583 504.288 695.712 25:9 2.778
382\909 504.290 695.710 39:14 2.786
137\326 504.294 695.706 14:5 2.800
303\721 504.300 695.700 31:11 2.818
166\395 504.304 695.696 17:6 2.833
195\464 504.310 695.690 20:7 2.857
29\69 504.348 695.652 3:1 3.000 Hard 19L 12s
182\433 504.388 695.612 19:6 3.167
153\364 504.396 695.604 16:5 3.200
277\659 504.401 695.599 29:9 3.222
124\295 504.407 695.593 13:4 3.250
343\816 504.412 695.588 36:11 3.273
219\521 504.415 695.585 23:7 3.286
314\747 504.418 695.582 33:10 3.300
95\226 504.425 695.575 10:3 3.333
351\835 504.431 695.569 37:11 3.364
256\609 504.433 695.567 27:8 3.375
417\992 504.435 695.565 44:13 3.385
161\383 504.439 695.561 17:5 3.400
388\923 504.442 695.558 41:12 3.417
227\540 504.444 695.556 24:7 3.429
293\697 504.448 695.552 31:9 3.444
66\157 504.459 695.541 7:2 3.500
301\716 504.469 695.531 32:9 3.556
235\559 504.472 695.528 25:7 3.571
404\961 504.475 695.525 43:12 3.583
169\402 504.478 695.522 18:5 3.600
441\1049 504.480 695.520 47:13 3.615
272\647 504.482 695.518 29:8 3.625
375\892 504.484 695.516 40:11 3.636
103\245 504.490 695.510 11:3 3.667
346\823 504.496 695.504 37:10 3.700
243\578 504.498 695.502 26:7 3.714
383\911 504.501 695.499 41:11 3.727
140\333 504.505 695.495 15:4 3.750
317\754 504.509 695.491 34:9 3.778
177\421 504.513 695.487 19:5 3.800
214\509 504.519 695.481 23:6 3.833
37\88 504.545 695.455 4:1 4.000 Superhard 19L 12s
193\459 504.575 695.425 21:5 4.200
156\371 504.582 695.418 17:4 4.250
275\654 504.587 695.413 30:7 4.286
119\283 504.594 695.406 13:3 4.333
320\761 504.599 695.401 35:8 4.375
201\478 504.603 695.397 22:5 4.400
283\673 504.606 695.394 31:7 4.429
82\195 504.615 695.385 9:2 4.500
291\692 504.624 695.376 32:7 4.571
209\497 504.628 695.372 23:5 4.600
336\799 504.631 695.369 37:8 4.625
127\302 504.636 695.364 14:3 4.667
299\711 504.641 695.359 33:7 4.714
172\409 504.645 695.355 19:4 4.750
217\516 504.651 695.349 24:5 4.800
45\107 504.673 695.327 5:1 5.000
188\447 504.698 695.302 21:4 5.250
143\340 504.706 695.294 16:3 5.333
241\573 504.712 695.288 27:5 5.400
98\233 504.721 695.279 11:2 5.500
249\592 504.730 695.270 28:5 5.600
151\359 504.735 695.265 17:3 5.667
204\485 504.742 695.258 23:4 5.750
53\126 504.762 695.238 6:1 6.000
167\397 504.786 695.214 19:3 6.333
114\271 504.797 695.203 13:2 6.500
175\416 504.808 695.192 20:3 6.667
61\145 504.828 695.172 7:1 7.000
130\309 504.854 695.146 15:2 7.500
69\164 504.878 695.122 8:1 8.000
77\183 504.918 695.082 9:1 9.000
8\19 505.263 694.737 1:0 → ∞ Collapsed 19L 12s
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