2L 17s

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↖ 1L 16s ↑ 2L 16s 3L 16s ↗
← 1L 17s 2L 17s 3L 17s →
↙ 1L 18s ↓ 2L 18s 3L 18s ↘ 
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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 ¢), having minimum harmonic entropy at 7/5.

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 diatonic interval categories.

Intervals

The intervals of 2L 17s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 19-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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 ¢

Generator chain

A chain of bright generators, each a perfect 9-mosstep, produces the following scale degrees. A chain of 19 bright generators contains the scale degrees of one of the modes of 2L 17s. Expanding the chain to 21 scale degrees produces the modes of either 19L 2s (for soft-of-basic tunings) or 2L 19s (for hard-of-basic tunings).

Generator chain of 2L 17s
Bright gens Scale degree Abbrev.
20 Augmented 9-mosdegree A9md
19 Augmented 0-mosdegree A0md
18 Augmented 10-mosdegree A10md
17 Major 1-mosdegree M1md
16 Major 11-mosdegree M11md
15 Major 2-mosdegree M2md
14 Major 12-mosdegree M12md
13 Major 3-mosdegree M3md
12 Major 13-mosdegree M13md
11 Major 4-mosdegree M4md
10 Major 14-mosdegree M14md
9 Major 5-mosdegree M5md
8 Major 15-mosdegree M15md
7 Major 6-mosdegree M6md
6 Major 16-mosdegree M16md
5 Major 7-mosdegree M7md
4 Major 17-mosdegree M17md
3 Major 8-mosdegree M8md
2 Major 18-mosdegree M18md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 10-mosdegree P10md
−2 Minor 1-mosdegree m1md
−3 Minor 11-mosdegree m11md
−4 Minor 2-mosdegree m2md
−5 Minor 12-mosdegree m12md
−6 Minor 3-mosdegree m3md
−7 Minor 13-mosdegree m13md
−8 Minor 4-mosdegree m4md
−9 Minor 14-mosdegree m14md
−10 Minor 5-mosdegree m5md
−11 Minor 15-mosdegree m15md
−12 Minor 6-mosdegree m6md
−13 Minor 16-mosdegree m16md
−14 Minor 7-mosdegree m7md
−15 Minor 17-mosdegree m17md
−16 Minor 8-mosdegree m8md
−17 Minor 18-mosdegree m18md
−18 Diminished 9-mosdegree d9md
−19 Diminished 19-mosdegree d19md
−20 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 2L 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
18|0 1 LssssssssLsssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 10 LsssssssssLssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 19 sLssssssssLssssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|3 9 sLsssssssssLsssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|4 18 ssLssssssssLsssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|5 8 ssLsssssssssLssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|6 17 sssLssssssssLssssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
11|7 7 sssLsssssssssLsssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
10|8 16 ssssLssssssssLsssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
9|9 6 ssssLsssssssssLssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
8|10 15 sssssLssssssssLssss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
7|11 5 sssssLsssssssssLsss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
6|12 14 ssssssLssssssssLsss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
5|13 4 ssssssLsssssssssLss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
4|14 13 sssssssLssssssssLss Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
3|15 3 sssssssLsssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
2|16 12 ssssssssLssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
1|17 2 ssssssssLsssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|18 11 sssssssssLssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

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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