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17L 12s

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17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4 ¢ to 705.9 ¢, or from 494.1 ¢ to 496.6 ¢. This MOS, belonging to the Leapday and Grackle temperaments, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 cents sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and a yet-unnamed region extending up to 17edo.

↖ 16L 11s ↑ 17L 11s 18L 11s ↗
← 16L 12s 17L 12s 18L 12s →
↙ 16L 13s ↓ 17L 13s 18L 13s ↘
Scale structure
Step pattern LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 17\29 to 10\17 (703.4 ¢ to 705.9 ¢)
Dark 7\17 to 12\29 (494.1 ¢ to 496.6 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 5:2 to 3:1 (quasihard)
Related MOS scales
Parent 12L 5s
Sister 12L 17s
Daughters 29L 17s, 17L 29s
Neutralized 5L 24s
2-Flought 46L 12s, 17L 41s
Equal tunings
Equalized (L:s = 1:1) 17\29 (703.4 ¢)
Supersoft (L:s = 4:3) 61\104 (703.8 ¢)
Soft (L:s = 3:2) 44\75 (704.0 ¢)
Semisoft (L:s = 5:3) 71\121 (704.1 ¢)
Basic (L:s = 2:1) 27\46 (704.3 ¢)
Semihard (L:s = 5:2) 64\109 (704.6 ¢)
Hard (L:s = 3:1) 37\63 (704.8 ¢)
Superhard (L:s = 4:1) 47\80 (705.0 ¢)
Collapsed (L:s = 1:0) 10\17 (705.9 ¢)
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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 17L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\29 703.448 496.552 1:1 1.000 Equalized 17L 12s
146\249 703.614 496.386 9:8 1.125
129\220 703.636 496.364 8:7 1.143
241\411 703.650 496.350 15:13 1.154
112\191 703.665 496.335 7:6 1.167
319\544 703.676 496.324 20:17 1.176
207\353 703.683 496.317 13:11 1.182
302\515 703.689 496.311 19:16 1.188
95\162 703.704 496.296 6:5 1.200
363\619 703.716 496.284 23:19 1.211
268\457 703.720 496.280 17:14 1.214
441\752 703.723 496.277 28:23 1.217
173\295 703.729 496.271 11:9 1.222
424\723 703.734 496.266 27:22 1.227
251\428 703.738 496.262 16:13 1.231
329\561 703.743 496.257 21:17 1.235
78\133 703.759 496.241 5:4 1.250
373\636 703.774 496.226 24:19 1.263
295\503 703.777 496.223 19:15 1.267
512\873 703.780 496.220 33:26 1.269
217\370 703.784 496.216 14:11 1.273
573\977 703.787 496.213 37:29 1.276
356\607 703.789 496.211 23:18 1.278
495\844 703.791 496.209 32:25 1.280
139\237 703.797 496.203 9:7 1.286
478\815 703.804 496.196 31:24 1.292
339\578 703.806 496.194 22:17 1.294
539\919 703.808 496.192 35:27 1.296
200\341 703.812 496.188 13:10 1.300
461\786 703.817 496.183 30:23 1.304
261\445 703.820 496.180 17:13 1.308
322\549 703.825 496.175 21:16 1.312
61\104 703.846 496.154 4:3 1.333 Supersoft 17L 12s
349\595 703.866 496.134 23:17 1.353
288\491 703.870 496.130 19:14 1.357
515\878 703.872 496.128 34:25 1.360
227\387 703.876 496.124 15:11 1.364
620\1057 703.879 496.121 41:30 1.367
393\670 703.881 496.119 26:19 1.368
559\953 703.882 496.118 37:27 1.370
166\283 703.887 496.113 11:8 1.375
603\1028 703.891 496.109 40:29 1.379
437\745 703.893 496.107 29:21 1.381
708\1207 703.894 496.106 47:34 1.382
271\462 703.896 496.104 18:13 1.385
647\1103 703.898 496.102 43:31 1.387
376\641 703.900 496.100 25:18 1.389
481\820 703.902 496.098 32:23 1.391
105\179 703.911 496.089 7:5 1.400
464\791 703.919 496.081 31:22 1.409
359\612 703.922 496.078 24:17 1.412
613\1045 703.923 496.077 41:29 1.414
254\433 703.926 496.074 17:12 1.417
657\1120 703.929 496.071 44:31 1.419
403\687 703.930 496.070 27:19 1.421
552\941 703.932 496.068 37:26 1.423
149\254 703.937 496.063 10:7 1.429
491\837 703.943 496.057 33:23 1.435
342\583 703.945 496.055 23:16 1.438
535\912 703.947 496.053 36:25 1.440
193\329 703.951 496.049 13:9 1.444
430\733 703.956 496.044 29:20 1.450
237\404 703.960 496.040 16:11 1.455
281\479 703.967 496.033 19:13 1.462
44\75 704.000 496.000 3:2 1.500 Soft 17L 12s
291\496 704.032 495.968 20:13 1.538
247\421 704.038 495.962 17:11 1.545
450\767 704.042 495.958 31:20 1.550
203\346 704.046 495.954 14:9 1.556
565\963 704.050 495.950 39:25 1.560
362\617 704.052 495.948 25:16 1.562
521\888 704.054 495.946 36:23 1.565
159\271 704.059 495.941 11:7 1.571
592\1009 704.063 495.937 41:26 1.577
433\738 704.065 495.935 30:19 1.579
707\1205 704.066 495.934 49:31 1.581
274\467 704.069 495.931 19:12 1.583
663\1130 704.071 495.929 46:29 1.586
389\663 704.072 495.928 27:17 1.588
504\859 704.075 495.925 35:22 1.591
115\196 704.082 495.918 8:5 1.600
531\905 704.088 495.912 37:23 1.609
416\709 704.090 495.910 29:18 1.611
717\1222 704.092 495.908 50:31 1.613
301\513 704.094 495.906 21:13 1.615
788\1343 704.095 495.905 55:34 1.618
487\830 704.096 495.904 34:21 1.619
673\1147 704.098 495.902 47:29 1.621
186\317 704.101 495.899 13:8 1.625
629\1072 704.104 495.896 44:27 1.630
443\755 704.106 495.894 31:19 1.632
700\1193 704.107 495.893 49:30 1.633
257\438 704.110 495.890 18:11 1.636
585\997 704.112 495.888 41:25 1.640
328\559 704.114 495.886 23:14 1.643
399\680 704.118 495.882 28:17 1.647
71\121 704.132 495.868 5:3 1.667 Semisoft 17L 12s
382\651 704.147 495.853 27:16 1.688
311\530 704.151 495.849 22:13 1.692
551\939 704.153 495.847 39:23 1.696
240\409 704.156 495.844 17:10 1.700
649\1106 704.159 495.841 46:27 1.704
409\697 704.161 495.839 29:17 1.706
578\985 704.162 495.838 41:24 1.708
169\288 704.167 495.833 12:7 1.714
605\1031 704.171 495.829 43:25 1.720
436\743 704.172 495.828 31:18 1.722
703\1198 704.174 495.826 50:29 1.724
267\455 704.176 495.824 19:11 1.727
632\1077 704.178 495.822 45:26 1.731
365\622 704.180 495.820 26:15 1.733
463\789 704.183 495.817 33:19 1.737
98\167 704.192 495.808 7:4 1.750
419\714 704.202 495.798 30:17 1.765
321\547 704.205 495.795 23:13 1.769
544\927 704.207 495.793 39:22 1.773
223\380 704.211 495.789 16:9 1.778
571\973 704.214 495.786 41:23 1.783
348\593 704.216 495.784 25:14 1.786
473\806 704.218 495.782 34:19 1.789
125\213 704.225 495.775 9:5 1.800
402\685 704.234 495.766 29:16 1.812
277\472 704.237 495.763 20:11 1.818
429\731 704.241 495.759 31:17 1.824
152\259 704.247 495.753 11:6 1.833
331\564 704.255 495.745 24:13 1.846
179\305 704.262 495.738 13:7 1.857
206\351 704.274 495.726 15:8 1.875
27\46 704.348 495.652 2:1 2.000 Basic 17L 12s
Scales with tunings softer than this are proper
199\339 704.425 495.575 15:7 2.143
172\293 704.437 495.563 13:6 2.167
317\540 704.444 495.556 24:11 2.182
145\247 704.453 495.547 11:5 2.200
408\695 704.460 495.540 31:14 2.214
263\448 704.464 495.536 20:9 2.222
381\649 704.468 495.532 29:13 2.231
118\201 704.478 495.522 9:4 2.250
445\758 704.485 495.515 34:15 2.267
327\557 704.488 495.512 25:11 2.273
536\913 704.491 495.509 41:18 2.278
209\356 704.494 495.506 16:7 2.286
509\867 704.498 495.502 39:17 2.294
300\511 704.501 495.499 23:10 2.300
391\666 704.505 495.495 30:13 2.308
91\155 704.516 495.484 7:3 2.333
428\729 704.527 495.473 33:14 2.357
337\574 704.530 495.470 26:11 2.364
583\993 704.532 495.468 45:19 2.368
246\419 704.535 495.465 19:8 2.375
647\1102 704.537 495.463 50:21 2.381
401\683 704.539 495.461 31:13 2.385
556\947 704.541 495.459 43:18 2.389
155\264 704.545 495.455 12:5 2.400
529\901 704.550 495.450 41:17 2.412
374\637 704.553 495.447 29:12 2.417
593\1010 704.554 495.446 46:19 2.421
219\373 704.558 495.442 17:7 2.429
502\855 704.561 495.439 39:16 2.438
283\482 704.564 495.436 22:9 2.444
347\591 704.569 495.431 27:11 2.455
64\109 704.587 495.413 5:2 2.500 Semihard 17L 12s
357\608 704.605 495.395 28:11 2.545
293\499 704.609 495.391 23:9 2.556
522\889 704.612 495.388 41:16 2.562
229\390 704.615 495.385 18:7 2.571
623\1061 704.618 495.382 49:19 2.579
394\671 704.620 495.380 31:12 2.583
559\952 704.622 495.378 44:17 2.588
165\281 704.626 495.374 13:5 2.600
596\1015 704.631 495.369 47:18 2.611
431\734 704.632 495.368 34:13 2.615
697\1187 704.634 495.366 55:21 2.619
266\453 704.636 495.364 21:8 2.625
633\1078 704.638 495.362 50:19 2.632
367\625 704.640 495.360 29:11 2.636
468\797 704.642 495.358 37:14 2.643
101\172 704.651 495.349 8:3 2.667
441\751 704.660 495.340 35:13 2.692
340\579 704.663 495.337 27:10 2.700
579\986 704.665 495.335 46:17 2.706
239\407 704.668 495.332 19:7 2.714
616\1049 704.671 495.329 49:18 2.722
377\642 704.673 495.327 30:11 2.727
515\877 704.675 495.325 41:15 2.733
138\235 704.681 495.319 11:4 2.750
451\768 704.688 495.313 36:13 2.769
313\533 704.690 495.310 25:9 2.778
488\831 704.693 495.307 39:14 2.786
175\298 704.698 495.302 14:5 2.800
387\659 704.704 495.296 31:11 2.818
212\361 704.709 495.291 17:6 2.833
249\424 704.717 495.283 20:7 2.857
37\63 704.762 495.238 3:1 3.000 Hard 17L 12s
232\395 704.810 495.190 19:6 3.167
195\332 704.819 495.181 16:5 3.200
353\601 704.825 495.175 29:9 3.222
158\269 704.833 495.167 13:4 3.250
437\744 704.839 495.161 36:11 3.273
279\475 704.842 495.158 23:7 3.286
400\681 704.846 495.154 33:10 3.300
121\206 704.854 495.146 10:3 3.333
447\761 704.862 495.138 37:11 3.364
326\555 704.865 495.135 27:8 3.375
531\904 704.867 495.133 44:13 3.385
205\349 704.871 495.129 17:5 3.400
494\841 704.875 495.125 41:12 3.417
289\492 704.878 495.122 24:7 3.429
373\635 704.882 495.118 31:9 3.444
84\143 704.895 495.105 7:2 3.500
383\652 704.908 495.092 32:9 3.556
299\509 704.912 495.088 25:7 3.571
514\875 704.914 495.086 43:12 3.583
215\366 704.918 495.082 18:5 3.600
561\955 704.921 495.079 47:13 3.615
346\589 704.924 495.076 29:8 3.625
477\812 704.926 495.074 40:11 3.636
131\223 704.933 495.067 11:3 3.667
440\749 704.940 495.060 37:10 3.700
309\526 704.943 495.057 26:7 3.714
487\829 704.946 495.054 41:11 3.727
178\303 704.950 495.050 15:4 3.750
403\686 704.956 495.044 34:9 3.778
225\383 704.961 495.039 19:5 3.800
272\463 704.968 495.032 23:6 3.833
47\80 705.000 495.000 4:1 4.000 Superhard 17L 12s
245\417 705.036 494.964 21:5 4.200
198\337 705.045 494.955 17:4 4.250
349\594 705.051 494.949 30:7 4.286
151\257 705.058 494.942 13:3 4.333
406\691 705.065 494.935 35:8 4.375
255\434 705.069 494.931 22:5 4.400
359\611 705.074 494.926 31:7 4.429
104\177 705.085 494.915 9:2 4.500
369\628 705.096 494.904 32:7 4.571
265\451 705.100 494.900 23:5 4.600
426\725 705.103 494.897 37:8 4.625
161\274 705.109 494.891 14:3 4.667
379\645 705.116 494.884 33:7 4.714
218\371 705.121 494.879 19:4 4.750
275\468 705.128 494.872 24:5 4.800
57\97 705.155 494.845 5:1 5.000
238\405 705.185 494.815 21:4 5.250
181\308 705.195 494.805 16:3 5.333
305\519 705.202 494.798 27:5 5.400
124\211 705.213 494.787 11:2 5.500
315\536 705.224 494.776 28:5 5.600
191\325 705.231 494.769 17:3 5.667
258\439 705.239 494.761 23:4 5.750
67\114 705.263 494.737 6:1 6.000
211\359 705.292 494.708 19:3 6.333
144\245 705.306 494.694 13:2 6.500
221\376 705.319 494.681 20:3 6.667
77\131 705.344 494.656 7:1 7.000
164\279 705.376 494.624 15:2 7.500
87\148 705.405 494.595 8:1 8.000
97\165 705.455 494.545 9:1 9.000
10\17 705.882 494.118 1:0 → ∞ Collapsed 17L 12s
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