3L 17s

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↖ 2L 16s ↑ 3L 16s 4L 16s ↗
← 2L 17s 3L 17s 4L 17s →
↙ 2L 18s ↓ 3L 18s 4L 18s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┐
│║│││││║││││││║│││││││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLssssssLssssss
ssssssLssssssLsssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 13\20 to 2\3 (780.0¢ to 800.0¢)
Dark 1\3 to 7\20 (400.0¢ to 420.0¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 5:1 to 1:0
Related MOS scales
Parent 3L 14s
Sister 17L 3s
Daughters 20L 3s, 3L 20s
Neutralized 6L 14s
2-Flought 23L 17s, 3L 37s
Equal tunings
Equalized (L:s = 1:1) 13\20 (780.0¢)
Supersoft (L:s = 4:3) 41\63 (781.0¢)
Soft (L:s = 3:2) 28\43 (781.4¢)
Semisoft (L:s = 5:3) 43\66 (781.8¢)
Basic (L:s = 2:1) 15\23 (782.6¢)
Semihard (L:s = 5:2) 32\49 (783.7¢)
Hard (L:s = 3:1) 17\26 (784.6¢)
Superhard (L:s = 4:1) 19\29 (786.2¢)
Collapsed (L:s = 1:0) 2\3 (800.0¢)

3L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 17 small steps, repeating every octave. 3L 17s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 780¢ to 800¢, or from 400¢ to 420¢.

This is the MOS which splits its small steps 6-6-5 between its large steps. Its most consonant generator is a 14/11 supermajor third, and its generator in general is a major third of no more than 7\20edo (420 cents).

Modes

Modes of 3L 17s
UDP Cyclic
order		 Step
pattern
19|0 1 LsssssLssssssLssssss
18|1 14 LssssssLsssssLssssss
17|2 7 LssssssLssssssLsssss
16|3 20 sLsssssLssssssLsssss
15|4 13 sLssssssLsssssLsssss
14|5 6 sLssssssLssssssLssss
13|6 19 ssLsssssLssssssLssss
12|7 12 ssLssssssLsssssLssss
11|8 5 ssLssssssLssssssLsss
10|9 18 sssLsssssLssssssLsss
9|10 11 sssLssssssLsssssLsss
8|11 4 sssLssssssLssssssLss
7|12 17 ssssLsssssLssssssLss
6|13 10 ssssLssssssLsssssLss
5|14 3 ssssLssssssLssssssLs
4|15 16 sssssLsssssLssssssLs
3|16 9 sssssLssssssLsssssLs
2|17 2 sssssLssssssLssssssL
1|18 15 ssssssLsssssLssssssL
0|19 8 ssssssLssssssLsssssL

Intervals

Intervals of 3L 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 60.0¢
Major 1-mosstep M1ms L 60.0¢ to 400.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 120.0¢
Major 2-mosstep M2ms L + s 120.0¢ to 400.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 180.0¢
Major 3-mosstep M3ms L + 2s 180.0¢ to 400.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 240.0¢
Major 4-mosstep M4ms L + 3s 240.0¢ to 400.0¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0¢ to 300.0¢
Major 5-mosstep M5ms L + 4s 300.0¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0¢ to 360.0¢
Major 6-mosstep M6ms L + 5s 360.0¢ to 400.0¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 400.0¢ to 420.0¢
Augmented 7-mosstep A7ms 2L + 5s 420.0¢ to 800.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0¢ to 480.0¢
Major 8-mosstep M8ms 2L + 6s 480.0¢ to 800.0¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0¢ to 540.0¢
Major 9-mosstep M9ms 2L + 7s 540.0¢ to 800.0¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0¢ to 600.0¢
Major 10-mosstep M10ms 2L + 8s 600.0¢ to 800.0¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0¢ to 660.0¢
Major 11-mosstep M11ms 2L + 9s 660.0¢ to 800.0¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0¢ to 720.0¢
Major 12-mosstep M12ms 2L + 10s 720.0¢ to 800.0¢
13-mosstep Diminished 13-mosstep d13ms L + 12s 400.0¢ to 780.0¢
Perfect 13-mosstep P13ms 2L + 11s 780.0¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 800.0¢ to 840.0¢
Major 14-mosstep M14ms 3L + 11s 840.0¢ to 1200.0¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 800.0¢ to 900.0¢
Major 15-mosstep M15ms 3L + 12s 900.0¢ to 1200.0¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0¢ to 960.0¢
Major 16-mosstep M16ms 3L + 13s 960.0¢ to 1200.0¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 800.0¢ to 1020.0¢
Major 17-mosstep M17ms 3L + 14s 1020.0¢ to 1200.0¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0¢ to 1080.0¢
Major 18-mosstep M18ms 3L + 15s 1080.0¢ to 1200.0¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0¢ to 1140.0¢
Major 19-mosstep M19ms 3L + 16s 1140.0¢ to 1200.0¢
20-mosstep Perfect 20-mosstep P20ms 3L + 17s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\20 780.000 420.000 1:1 1.000 Equalized 3L 17s
67\103 780.583 419.417 6:5 1.200
54\83 780.723 419.277 5:4 1.250
95\146 780.822 419.178 9:7 1.286
41\63 780.952 419.048 4:3 1.333 Supersoft 3L 17s
110\169 781.065 418.935 11:8 1.375
69\106 781.132 418.868 7:5 1.400
97\149 781.208 418.792 10:7 1.429
28\43 781.395 418.605 3:2 1.500 Soft 3L 17s
99\152 781.579 418.421 11:7 1.571
71\109 781.651 418.349 8:5 1.600
114\175 781.714 418.286 13:8 1.625
43\66 781.818 418.182 5:3 1.667 Semisoft 3L 17s
101\155 781.935 418.065 12:7 1.714
58\89 782.022 417.978 7:4 1.750
73\112 782.143 417.857 9:5 1.800
15\23 782.609 417.391 2:1 2.000 Basic 3L 17s
Scales with tunings softer than this are proper
62\95 783.158 416.842 9:4 2.250
47\72 783.333 416.667 7:3 2.333
79\121 783.471 416.529 12:5 2.400
32\49 783.673 416.327 5:2 2.500 Semihard 3L 17s
81\124 783.871 416.129 13:5 2.600
49\75 784.000 416.000 8:3 2.667
66\101 784.158 415.842 11:4 2.750
17\26 784.615 415.385 3:1 3.000 Hard 3L 17s
53\81 785.185 414.815 10:3 3.333
36\55 785.455 414.545 7:2 3.500
55\84 785.714 414.286 11:3 3.667
19\29 786.207 413.793 4:1 4.000 Superhard 3L 17s
40\61 786.885 413.115 9:2 4.500
21\32 787.500 412.500 5:1 5.000
23\35 788.571 411.429 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 17s
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