17L 12s

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↖16L 11s ↑17L 11s 18L 11s↗
←16L 12s17L 12s 18L 12s→
↙16L 13s ↓17L 13s 18L 13s↘
Scale structure
Brightest mode LLsLsLLsLsLLsLsLsLLsLsLLsLsLs
Equave (cents) 2/1 (1200.0¢)
Period (cents) 2/1 (1200.0¢)
Generator ranges
Bright 17\29 (703.4¢) to 10\17 (705.9¢)
Dark 7\17 (494.1¢) to 12\29 (496.6¢)
Related scales
Parent 12L 5s
Sister 12L 17s
Daughters 29L 17s, 17L 29s
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¢)

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.

Scale tree

Scale tree and tuning spectrum of 17L 12s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\29 703.448 496.552 1:1 1.000 Equalized 17L 12s
129\220 703.636 496.364 8:7 1.143
112\191 703.665 496.335 7:6 1.167
207\353 703.683 496.317 13:11 1.182
95\162 703.704 496.296 6:5 1.200
268\457 703.720 496.280 17:14 1.214
173\295 703.729 496.271 11:9 1.222
251\428 703.738 496.262 16:13 1.231
78\133 703.759 496.241 5:4 1.250
295\503 703.777 496.223 19:15 1.267
217\370 703.784 496.216 14:11 1.273
356\607 703.789 496.211 23:18 1.278
139\237 703.797 496.203 9:7 1.286
339\578 703.806 496.194 22:17 1.294
200\341 703.812 496.188 13:10 1.300
261\445 703.820 496.180 17:13 1.308
61\104 703.846 496.154 4:3 1.333 Supersoft 17L 12s
288\491 703.870 496.130 19:14 1.357
227\387 703.876 496.124 15:11 1.364
393\670 703.881 496.119 26:19 1.368
166\283 703.887 496.113 11:8 1.375
437\745 703.893 496.107 29:21 1.381
271\462 703.896 496.104 18:13 1.385
376\641 703.900 496.100 25:18 1.389
105\179 703.911 496.089 7:5 1.400
359\612 703.922 496.078 24:17 1.412
254\433 703.926 496.074 17:12 1.417
403\687 703.930 496.070 27:19 1.421
149\254 703.937 496.063 10:7 1.429
342\583 703.945 496.055 23:16 1.438
193\329 703.951 496.049 13:9 1.444
237\404 703.960 496.040 16:11 1.455
44\75 704.000 496.000 3:2 1.500 Soft 17L 12s
247\421 704.038 495.962 17:11 1.545
203\346 704.046 495.954 14:9 1.556
362\617 704.052 495.948 25:16 1.562
159\271 704.059 495.941 11:7 1.571
433\738 704.065 495.935 30:19 1.579
274\467 704.069 495.931 19:12 1.583
389\663 704.072 495.928 27:17 1.588
115\196 704.082 495.918 8:5 1.600
416\709 704.090 495.910 29:18 1.611
301\513 704.094 495.906 21:13 1.615
487\830 704.096 495.904 34:21 1.619
186\317 704.101 495.899 13:8 1.625
443\755 704.106 495.894 31:19 1.632
257\438 704.110 495.890 18:11 1.636
328\559 704.114 495.886 23:14 1.643
71\121 704.132 495.868 5:3 1.667 Semisoft 17L 12s
311\530 704.151 495.849 22:13 1.692
240\409 704.156 495.844 17:10 1.700
409\697 704.161 495.839 29:17 1.706
169\288 704.167 495.833 12:7 1.714
436\743 704.172 495.828 31:18 1.722
267\455 704.176 495.824 19:11 1.727
365\622 704.180 495.820 26:15 1.733
98\167 704.192 495.808 7:4 1.750
321\547 704.205 495.795 23:13 1.769
223\380 704.211 495.789 16:9 1.778
348\593 704.216 495.784 25:14 1.786
125\213 704.225 495.775 9:5 1.800
277\472 704.237 495.763 20:11 1.818
152\259 704.247 495.753 11:6 1.833
179\305 704.262 495.738 13:7 1.857
27\46 704.348 495.652 2:1 2.000 Basic 17L 12s
Scales with tunings softer than this are proper
172\293 704.437 495.563 13:6 2.167
145\247 704.453 495.547 11:5 2.200
263\448 704.464 495.536 20:9 2.222
118\201 704.478 495.522 9:4 2.250
327\557 704.488 495.512 25:11 2.273
209\356 704.494 495.506 16:7 2.286
300\511 704.501 495.499 23:10 2.300
91\155 704.516 495.484 7:3 2.333
337\574 704.530 495.470 26:11 2.364
246\419 704.535 495.465 19:8 2.375
401\683 704.539 495.461 31:13 2.385
155\264 704.545 495.455 12:5 2.400
374\637 704.553 495.447 29:12 2.417
219\373 704.558 495.442 17:7 2.429
283\482 704.564 495.436 22:9 2.444
64\109 704.587 495.413 5:2 2.500 Semihard 17L 12s
293\499 704.609 495.391 23:9 2.556
229\390 704.615 495.385 18:7 2.571
394\671 704.620 495.380 31:12 2.583
165\281 704.626 495.374 13:5 2.600
431\734 704.632 495.368 34:13 2.615
266\453 704.636 495.364 21:8 2.625
367\625 704.640 495.360 29:11 2.636
101\172 704.651 495.349 8:3 2.667
340\579 704.663 495.337 27:10 2.700
239\407 704.668 495.332 19:7 2.714
377\642 704.673 495.327 30:11 2.727
138\235 704.681 495.319 11:4 2.750
313\533 704.690 495.310 25:9 2.778
175\298 704.698 495.302 14:5 2.800
212\361 704.709 495.291 17:6 2.833
37\63 704.762 495.238 3:1 3.000 Hard 17L 12s
195\332 704.819 495.181 16:5 3.200
158\269 704.833 495.167 13:4 3.250
279\475 704.842 495.158 23:7 3.286
121\206 704.854 495.146 10:3 3.333
326\555 704.865 495.135 27:8 3.375
205\349 704.871 495.129 17:5 3.400
289\492 704.878 495.122 24:7 3.429
84\143 704.895 495.105 7:2 3.500
299\509 704.912 495.088 25:7 3.571
215\366 704.918 495.082 18:5 3.600
346\589 704.924 495.076 29:8 3.625
131\223 704.933 495.067 11:3 3.667
309\526 704.943 495.057 26:7 3.714
178\303 704.950 495.050 15:4 3.750
225\383 704.961 495.039 19:5 3.800
47\80 705.000 495.000 4:1 4.000 Superhard 17L 12s
198\337 705.045 494.955 17:4 4.250
151\257 705.058 494.942 13:3 4.333
255\434 705.069 494.931 22:5 4.400
104\177 705.085 494.915 9:2 4.500
265\451 705.100 494.900 23:5 4.600
161\274 705.109 494.891 14:3 4.667
218\371 705.121 494.879 19:4 4.750
57\97 705.155 494.845 5:1 5.000
181\308 705.195 494.805 16:3 5.333
124\211 705.213 494.787 11:2 5.500
191\325 705.231 494.769 17:3 5.667
67\114 705.263 494.737 6:1 6.000
144\245 705.306 494.694 13:2 6.500
77\131 705.344 494.656 7:1 7.000
87\148 705.405 494.595 8:1 8.000
10\17 705.882 494.118 1:0 → ∞ Collapsed 17L 12s