6L 17s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 5L 16s ↑ 6L 16s 7L 16s ↗
← 5L 17s 6L 17s 7L 17s →
↙ 5L 18s ↓ 6L 18s 7L 18s ↘ 
┌╥┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┐
│║││║│││║│││║│││║│││║││││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLsssLsssLsssLsssLsss
sssLsssLsssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 19\23 to 5\6 (991.3 ¢ to 1000.0 ¢)
Dark 1\6 to 4\23 (200.0 ¢ to 208.7 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent 6L 11s
Sister 17L 6s
Daughters 23L 6s, 6L 23s
Neutralized 12L 11s
2-Flought 29L 17s, 6L 40s
Equal tunings
Equalized (L:s = 1:1) 19\23 (991.3 ¢)
Supersoft (L:s = 4:3) 62\75 (992.0 ¢)
Soft (L:s = 3:2) 43\52 (992.3 ¢)
Semisoft (L:s = 5:3) 67\81 (992.6 ¢)
Basic (L:s = 2:1) 24\29 (993.1 ¢)
Semihard (L:s = 5:2) 53\64 (993.8 ¢)
Hard (L:s = 3:1) 29\35 (994.3 ¢)
Superhard (L:s = 4:1) 34\41 (995.1 ¢)
Collapsed (L:s = 1:0) 5\6 (1000.0 ¢)

6L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 17 small steps, repeating every octave. 6L 17s is a great-grandchild scale of 5L 1s, expanding it by 17 tones. Generators that produce this scale range from 991.3 ¢ to 1000 ¢, or from 200 ¢ to 208.7 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 6L 17s
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 52.2 ¢
Major 1-mosstep M1ms L 52.2 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 104.3 ¢
Major 2-mosstep M2ms L + s 104.3 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms L + 2s 156.5 ¢ to 200.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 200.0 ¢ to 208.7 ¢
Augmented 4-mosstep A4ms 2L + 2s 208.7 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 200.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 2L + 3s 260.9 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 200.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 2L + 4s 313.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 200.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms 2L + 5s 365.2 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 400.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 3L + 5s 417.4 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 400.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 3L + 6s 469.6 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 400.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 3L + 7s 521.7 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 400.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 3L + 8s 573.9 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 600.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 4L + 8s 626.1 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 4L + 9s 678.3 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 600.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 4L + 10s 730.4 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 600.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 4L + 11s 782.6 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 800.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 5L + 11s 834.8 ¢ to 1000.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 800.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 5L + 12s 887.0 ¢ to 1000.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 800.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 5L + 13s 939.1 ¢ to 1000.0 ¢
19-mosstep Diminished 19-mosstep d19ms 4L + 15s 800.0 ¢ to 991.3 ¢
Perfect 19-mosstep P19ms 5L + 14s 991.3 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 5L + 15s 1000.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 6L + 14s 1043.5 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 5L + 16s 1000.0 ¢ to 1095.7 ¢
Major 21-mosstep M21ms 6L + 15s 1095.7 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 5L + 17s 1000.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 6L + 16s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 6L + 17s 1200.0 ¢

Generator chain

Generator chain of 6L 17s
Bright gens Scale degree Abbrev.
28 Augmented 3-mosdegree A3md
27 Augmented 7-mosdegree A7md
26 Augmented 11-mosdegree A11md
25 Augmented 15-mosdegree A15md
24 Augmented 19-mosdegree A19md
23 Augmented 0-mosdegree A0md
22 Augmented 4-mosdegree A4md
21 Major 8-mosdegree M8md
20 Major 12-mosdegree M12md
19 Major 16-mosdegree M16md
18 Major 20-mosdegree M20md
17 Major 1-mosdegree M1md
16 Major 5-mosdegree M5md
15 Major 9-mosdegree M9md
14 Major 13-mosdegree M13md
13 Major 17-mosdegree M17md
12 Major 21-mosdegree M21md
11 Major 2-mosdegree M2md
10 Major 6-mosdegree M6md
9 Major 10-mosdegree M10md
8 Major 14-mosdegree M14md
7 Major 18-mosdegree M18md
6 Major 22-mosdegree M22md
5 Major 3-mosdegree M3md
4 Major 7-mosdegree M7md
3 Major 11-mosdegree M11md
2 Major 15-mosdegree M15md
1 Perfect 19-mosdegree P19md
0 Perfect 0-mosdegree
Perfect 23-mosdegree		 P0md
P23md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 12-mosdegree m12md
−4 Minor 16-mosdegree m16md
−5 Minor 20-mosdegree m20md
−6 Minor 1-mosdegree m1md
−7 Minor 5-mosdegree m5md
−8 Minor 9-mosdegree m9md
−9 Minor 13-mosdegree m13md
−10 Minor 17-mosdegree m17md
−11 Minor 21-mosdegree m21md
−12 Minor 2-mosdegree m2md
−13 Minor 6-mosdegree m6md
−14 Minor 10-mosdegree m10md
−15 Minor 14-mosdegree m14md
−16 Minor 18-mosdegree m18md
−17 Minor 22-mosdegree m22md
−18 Minor 3-mosdegree m3md
−19 Minor 7-mosdegree m7md
−20 Minor 11-mosdegree m11md
−21 Minor 15-mosdegree m15md
−22 Diminished 19-mosdegree d19md
−23 Diminished 23-mosdegree d23md
−24 Diminished 4-mosdegree d4md
−25 Diminished 8-mosdegree d8md
−26 Diminished 12-mosdegree d12md
−27 Diminished 16-mosdegree d16md
−28 Diminished 20-mosdegree d20md

Modes

Scale degrees of the modes of 6L 17s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
22|0 1 LssLsssLsssLsssLsssLsss Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
21|1 20 LsssLssLsssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
20|2 16 LsssLsssLssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
19|3 12 LsssLsssLsssLssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
18|4 8 LsssLsssLsssLsssLssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
17|5 4 LsssLsssLsssLsssLsssLss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
16|6 23 sLssLsssLsssLsssLsssLss Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
15|7 19 sLsssLssLsssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
14|8 15 sLsssLsssLssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
13|9 11 sLsssLsssLsssLssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
12|10 7 sLsssLsssLsssLsssLssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf.
11|11 3 sLsssLsssLsssLsssLsssLs Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
10|12 22 ssLssLsssLsssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
9|13 18 ssLsssLssLsssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
8|14 14 ssLsssLsssLssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
7|15 10 ssLsssLsssLsssLssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
6|16 6 ssLsssLsssLsssLsssLssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf.
5|17 2 ssLsssLsssLsssLsssLsssL Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
4|18 21 sssLssLsssLsssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
3|19 17 sssLsssLssLsssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
2|20 13 sssLsssLsssLssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|21 9 sssLsssLsssLsssLssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|22 5 sssLsssLsssLsssLsssLssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
19\23 991.304 208.696 1:1 1.000 Equalized 6L 17s
138\167 991.617 208.383 8:7 1.143
119\144 991.667 208.333 7:6 1.167
219\265 991.698 208.302 13:11 1.182
100\121 991.736 208.264 6:5 1.200
281\340 991.765 208.235 17:14 1.214
181\219 991.781 208.219 11:9 1.222
262\317 991.798 208.202 16:13 1.231
81\98 991.837 208.163 5:4 1.250
305\369 991.870 208.130 19:15 1.267
224\271 991.882 208.118 14:11 1.273
367\444 991.892 208.108 23:18 1.278
143\173 991.908 208.092 9:7 1.286
348\421 991.924 208.076 22:17 1.294
205\248 991.935 208.065 13:10 1.300
267\323 991.950 208.050 17:13 1.308
62\75 992.000 208.000 4:3 1.333 Supersoft 6L 17s
291\352 992.045 207.955 19:14 1.357
229\277 992.058 207.942 15:11 1.364
396\479 992.067 207.933 26:19 1.368
167\202 992.079 207.921 11:8 1.375
439\531 992.090 207.910 29:21 1.381
272\329 992.097 207.903 18:13 1.385
377\456 992.105 207.895 25:18 1.389
105\127 992.126 207.874 7:5 1.400
358\433 992.148 207.852 24:17 1.412
253\306 992.157 207.843 17:12 1.417
401\485 992.165 207.835 27:19 1.421
148\179 992.179 207.821 10:7 1.429
339\410 992.195 207.805 23:16 1.438
191\231 992.208 207.792 13:9 1.444
234\283 992.226 207.774 16:11 1.455
43\52 992.308 207.692 3:2 1.500 Soft 6L 17s
239\289 992.388 207.612 17:11 1.545
196\237 992.405 207.595 14:9 1.556
349\422 992.417 207.583 25:16 1.562
153\185 992.432 207.568 11:7 1.571
416\503 992.445 207.555 30:19 1.579
263\318 992.453 207.547 19:12 1.583
373\451 992.461 207.539 27:17 1.588
110\133 992.481 207.519 8:5 1.600
397\480 992.500 207.500 29:18 1.611
287\347 992.507 207.493 21:13 1.615
464\561 992.513 207.487 34:21 1.619
177\214 992.523 207.477 13:8 1.625
421\509 992.534 207.466 31:19 1.632
244\295 992.542 207.458 18:11 1.636
311\376 992.553 207.447 23:14 1.643
67\81 992.593 207.407 5:3 1.667 Semisoft 6L 17s
292\353 992.635 207.365 22:13 1.692
225\272 992.647 207.353 17:10 1.700
383\463 992.657 207.343 29:17 1.706
158\191 992.670 207.330 12:7 1.714
407\492 992.683 207.317 31:18 1.722
249\301 992.691 207.309 19:11 1.727
340\411 992.701 207.299 26:15 1.733
91\110 992.727 207.273 7:4 1.750
297\359 992.758 207.242 23:13 1.769
206\249 992.771 207.229 16:9 1.778
321\388 992.784 207.216 25:14 1.786
115\139 992.806 207.194 9:5 1.800
254\307 992.834 207.166 20:11 1.818
139\168 992.857 207.143 11:6 1.833
163\197 992.893 207.107 13:7 1.857
24\29 993.103 206.897 2:1 2.000 Basic 6L 17s
Scales with tunings softer than this are proper
149\180 993.333 206.667 13:6 2.167
125\151 993.377 206.623 11:5 2.200
226\273 993.407 206.593 20:9 2.222
101\122 993.443 206.557 9:4 2.250
279\337 993.472 206.528 25:11 2.273
178\215 993.488 206.512 16:7 2.286
255\308 993.506 206.494 23:10 2.300
77\93 993.548 206.452 7:3 2.333
284\343 993.586 206.414 26:11 2.364
207\250 993.600 206.400 19:8 2.375
337\407 993.612 206.388 31:13 2.385
130\157 993.631 206.369 12:5 2.400
313\378 993.651 206.349 29:12 2.417
183\221 993.665 206.335 17:7 2.429
236\285 993.684 206.316 22:9 2.444
53\64 993.750 206.250 5:2 2.500 Semihard 6L 17s
241\291 993.814 206.186 23:9 2.556
188\227 993.833 206.167 18:7 2.571
323\390 993.846 206.154 31:12 2.583
135\163 993.865 206.135 13:5 2.600
352\425 993.882 206.118 34:13 2.615
217\262 993.893 206.107 21:8 2.625
299\361 993.906 206.094 29:11 2.636
82\99 993.939 206.061 8:3 2.667
275\332 993.976 206.024 27:10 2.700
193\233 993.991 206.009 19:7 2.714
304\367 994.005 205.995 30:11 2.727
111\134 994.030 205.970 11:4 2.750
251\303 994.059 205.941 25:9 2.778
140\169 994.083 205.917 14:5 2.800
169\204 994.118 205.882 17:6 2.833
29\35 994.286 205.714 3:1 3.000 Hard 6L 17s
150\181 994.475 205.525 16:5 3.200
121\146 994.521 205.479 13:4 3.250
213\257 994.553 205.447 23:7 3.286
92\111 994.595 205.405 10:3 3.333
247\298 994.631 205.369 27:8 3.375
155\187 994.652 205.348 17:5 3.400
218\263 994.677 205.323 24:7 3.429
63\76 994.737 205.263 7:2 3.500
223\269 994.796 205.204 25:7 3.571
160\193 994.819 205.181 18:5 3.600
257\310 994.839 205.161 29:8 3.625
97\117 994.872 205.128 11:3 3.667
228\275 994.909 205.091 26:7 3.714
131\158 994.937 205.063 15:4 3.750
165\199 994.975 205.025 19:5 3.800
34\41 995.122 204.878 4:1 4.000 Superhard 6L 17s
Quadrimage
141\170 995.294 204.706 17:4 4.250
107\129 995.349 204.651 13:3 4.333
180\217 995.392 204.608 22:5 4.400
73\88 995.455 204.545 9:2 4.500
185\223 995.516 204.484 23:5 4.600
112\135 995.556 204.444 14:3 4.667
151\182 995.604 204.396 19:4 4.750
39\47 995.745 204.255 5:1 5.000
122\147 995.918 204.082 16:3 5.333 Baldy is optimal around here
83\100 996.000 204.000 11:2 5.500
127\153 996.078 203.922 17:3 5.667
44\53 996.226 203.774 6:1 6.000
93\112 996.429 203.571 13:2 6.500
49\59 996.610 203.390 7:1 7.000
54\65 996.923 203.077 8:1 8.000
5\6 1000.000 200.000 1:0 → ∞ Collapsed 6L 17s
This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=6L_17s&oldid=195348"