2L 17s

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↖ 1L 16s ↑ 2L 16s 3L 16s ↗
← 1L 17s 2L 17s 3L 17s →
↙ 1L 18s ↓ 2L 18s 3L 18s ↘ 
┌╥┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┐
│║││││││││║││││││││││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssssLsssssssss
sssssssssLssssssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\19 to 1\2 (568.4¢ to 600.0¢)
Dark 1\2 to 10\19 (600.0¢ to 631.6¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 6:1 to 1:0
Related MOS scales
Parent 2L 15s
Sister 17L 2s
Daughters 19L 2s, 2L 19s
Neutralized 4L 15s
2-Flought 21L 17s, 2L 36s
Equal tunings
Equalized (L:s = 1:1) 9\19 (568.4¢)
Supersoft (L:s = 4:3) 28\59 (569.5¢)
Soft (L:s = 3:2) 19\40 (570.0¢)
Semisoft (L:s = 5:3) 29\61 (570.5¢)
Basic (L:s = 2:1) 10\21 (571.4¢)
Semihard (L:s = 5:2) 21\44 (572.7¢)
Hard (L:s = 3:1) 11\23 (573.9¢)
Superhard (L:s = 4:1) 12\25 (576.0¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

2L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 17 small steps, repeating every octave. 2L 17s is related to 2L 7s, expanding it by 10 tones. Generators that produce this scale range from 568.4¢ to 600¢, or from 600¢ to 631.6¢.

This is the MOS where the small steps divide 9-8 between the large steps. The generator is a tritone of no less than 9/19edo (568.421 cents), having minimum harmonic entropy at 7/5.

Modes

Modes of 2L 17s
UDP Cyclic
order		 Step
pattern
18|0 1 LssssssssLsssssssss
17|1 10 LsssssssssLssssssss
16|2 19 sLssssssssLssssssss
15|3 9 sLsssssssssLsssssss
14|4 18 ssLssssssssLsssssss
13|5 8 ssLsssssssssLssssss
12|6 17 sssLssssssssLssssss
11|7 7 sssLsssssssssLsssss
10|8 16 ssssLssssssssLsssss
9|9 6 ssssLsssssssssLssss
8|10 15 sssssLssssssssLssss
7|11 5 sssssLsssssssssLsss
6|12 14 ssssssLssssssssLsss
5|13 4 ssssssLsssssssssLss
4|14 13 sssssssLssssssssLss
3|15 3 sssssssLsssssssssLs
2|16 12 ssssssssLssssssssLs
1|17 2 ssssssssLsssssssssL
0|18 11 sssssssssLssssssssL

Intervals

Intervals of 2L 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 63.2¢
Major 1-mosstep M1ms L 63.2¢ to 600.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 126.3¢
Major 2-mosstep M2ms L + s 126.3¢ to 600.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 189.5¢
Major 3-mosstep M3ms L + 2s 189.5¢ to 600.0¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0¢ to 252.6¢
Major 4-mosstep M4ms L + 3s 252.6¢ to 600.0¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0¢ to 315.8¢
Major 5-mosstep M5ms L + 4s 315.8¢ to 600.0¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0¢ to 378.9¢
Major 6-mosstep M6ms L + 5s 378.9¢ to 600.0¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0¢ to 442.1¢
Major 7-mosstep M7ms L + 6s 442.1¢ to 600.0¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0¢ to 505.3¢
Major 8-mosstep M8ms L + 7s 505.3¢ to 600.0¢
9-mosstep Diminished 9-mosstep d9ms 9s 0.0¢ to 568.4¢
Perfect 9-mosstep P9ms L + 8s 568.4¢ to 600.0¢
10-mosstep Perfect 10-mosstep P10ms L + 9s 600.0¢ to 631.6¢
Augmented 10-mosstep A10ms 2L + 8s 631.6¢ to 1200.0¢
11-mosstep Minor 11-mosstep m11ms L + 10s 600.0¢ to 694.7¢
Major 11-mosstep M11ms 2L + 9s 694.7¢ to 1200.0¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0¢ to 757.9¢
Major 12-mosstep M12ms 2L + 10s 757.9¢ to 1200.0¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0¢ to 821.1¢
Major 13-mosstep M13ms 2L + 11s 821.1¢ to 1200.0¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0¢ to 884.2¢
Major 14-mosstep M14ms 2L + 12s 884.2¢ to 1200.0¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0¢ to 947.4¢
Major 15-mosstep M15ms 2L + 13s 947.4¢ to 1200.0¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0¢ to 1010.5¢
Major 16-mosstep M16ms 2L + 14s 1010.5¢ to 1200.0¢
17-mosstep Minor 17-mosstep m17ms L + 16s 600.0¢ to 1073.7¢
Major 17-mosstep M17ms 2L + 15s 1073.7¢ to 1200.0¢
18-mosstep Minor 18-mosstep m18ms L + 17s 600.0¢ to 1136.8¢
Major 18-mosstep M18ms 2L + 16s 1136.8¢ to 1200.0¢
19-mosstep Perfect 19-mosstep P19ms 2L + 17s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 2L 17s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\19 568.421 631.579 1:1 1.000 Equalized 2L 17s
46\97 569.072 630.928 6:5 1.200
37\78 569.231 630.769 5:4 1.250
65\137 569.343 630.657 9:7 1.286
28\59 569.492 630.508 4:3 1.333 Supersoft 2L 17s
75\158 569.620 630.380 11:8 1.375
47\99 569.697 630.303 7:5 1.400
66\139 569.784 630.216 10:7 1.429
19\40 570.000 630.000 3:2 1.500 Soft 2L 17s
67\141 570.213 629.787 11:7 1.571
48\101 570.297 629.703 8:5 1.600
77\162 570.370 629.630 13:8 1.625
29\61 570.492 629.508 5:3 1.667 Semisoft 2L 17s
68\143 570.629 629.371 12:7 1.714
39\82 570.732 629.268 7:4 1.750
49\103 570.874 629.126 9:5 1.800
10\21 571.429 628.571 2:1 2.000 Basic 2L 17s
Scales with tunings softer than this are proper
41\86 572.093 627.907 9:4 2.250
31\65 572.308 627.692 7:3 2.333
52\109 572.477 627.523 12:5 2.400
21\44 572.727 627.273 5:2 2.500 Semihard 2L 17s
53\111 572.973 627.027 13:5 2.600
32\67 573.134 626.866 8:3 2.667
43\90 573.333 626.667 11:4 2.750
11\23 573.913 626.087 3:1 3.000 Hard 2L 17s
34\71 574.648 625.352 10:3 3.333
23\48 575.000 625.000 7:2 3.500
35\73 575.342 624.658 11:3 3.667
12\25 576.000 624.000 4:1 4.000 Superhard 2L 17s
25\52 576.923 623.077 9:2 4.500
13\27 577.778 622.222 5:1 5.000
14\29 579.310 620.690 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 17s
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