2L 21s

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↖ 1L 20s ↑ 2L 20s 3L 20s ↗
← 1L 21s 2L 21s 3L 21s →
↙ 1L 22s ↓ 2L 22s 3L 22s ↘
Scale structure
Step pattern LssssssssssLsssssssssss
sssssssssssLssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\23 to 1\2 (573.9 ¢ to 600.0 ¢)
Dark 1\2 to 12\23 (600.0 ¢ to 626.1 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 8:1 to 1:0
Related MOS scales
Parent 2L 19s
Sister 21L 2s
Daughters 23L 2s, 2L 23s
Neutralized 4L 19s
2-Flought 25L 21s, 2L 44s
Equal tunings
Equalized (L:s = 1:1) 11\23 (573.9 ¢)
Supersoft (L:s = 4:3) 34\71 (574.6 ¢)
Soft (L:s = 3:2) 23\48 (575.0 ¢)
Semisoft (L:s = 5:3) 35\73 (575.3 ¢)
Basic (L:s = 2:1) 12\25 (576.0 ¢)
Semihard (L:s = 5:2) 25\52 (576.9 ¢)
Hard (L:s = 3:1) 13\27 (577.8 ¢)
Superhard (L:s = 4:1) 14\29 (579.3 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)
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2L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 21 small steps, repeating every octave. 2L 21s is related to 2L 7s, expanding it by 14 tones. Generators that produce this scale range from 573.9 ¢ to 600 ¢, or from 600 ¢ to 626.1 ¢.

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 2L 21s
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 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 104.3 ¢
Major 2-mosstep M2ms L + s 104.3 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms L + 2s 156.5 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 208.7 ¢
Major 4-mosstep M4ms L + 3s 208.7 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms L + 4s 260.9 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms L + 5s 313.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms L + 6s 365.2 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms L + 7s 417.4 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms L + 8s 469.6 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 10s 0.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms L + 9s 521.7 ¢ to 600.0 ¢
11-mosstep Diminished 11-mosstep d11ms 11s 0.0 ¢ to 573.9 ¢
Perfect 11-mosstep P11ms L + 10s 573.9 ¢ to 600.0 ¢
12-mosstep Perfect 12-mosstep P12ms L + 11s 600.0 ¢ to 626.1 ¢
Augmented 12-mosstep A12ms 2L + 10s 626.1 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 2L + 11s 678.3 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 2L + 12s 730.4 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 2L + 13s 782.6 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 2L + 14s 834.8 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms L + 16s 600.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 2L + 15s 887.0 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms L + 17s 600.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 2L + 16s 939.1 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms L + 18s 600.0 ¢ to 991.3 ¢
Major 19-mosstep M19ms 2L + 17s 991.3 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms L + 19s 600.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 2L + 18s 1043.5 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms L + 20s 600.0 ¢ to 1095.7 ¢
Major 21-mosstep M21ms 2L + 19s 1095.7 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms L + 21s 600.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 2L + 20s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 2L + 21s 1200.0 ¢

Generator chain

Generator chain of 2L 21s
Bright gens Scale degree Abbrev.
24 Augmented 11-mosdegree A11md
23 Augmented 0-mosdegree A0md
22 Augmented 12-mosdegree A12md
21 Major 1-mosdegree M1md
20 Major 13-mosdegree M13md
19 Major 2-mosdegree M2md
18 Major 14-mosdegree M14md
17 Major 3-mosdegree M3md
16 Major 15-mosdegree M15md
15 Major 4-mosdegree M4md
14 Major 16-mosdegree M16md
13 Major 5-mosdegree M5md
12 Major 17-mosdegree M17md
11 Major 6-mosdegree M6md
10 Major 18-mosdegree M18md
9 Major 7-mosdegree M7md
8 Major 19-mosdegree M19md
7 Major 8-mosdegree M8md
6 Major 20-mosdegree M20md
5 Major 9-mosdegree M9md
4 Major 21-mosdegree M21md
3 Major 10-mosdegree M10md
2 Major 22-mosdegree M22md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 23-mosdegree		 P0md
P23md
−1 Perfect 12-mosdegree P12md
−2 Minor 1-mosdegree m1md
−3 Minor 13-mosdegree m13md
−4 Minor 2-mosdegree m2md
−5 Minor 14-mosdegree m14md
−6 Minor 3-mosdegree m3md
−7 Minor 15-mosdegree m15md
−8 Minor 4-mosdegree m4md
−9 Minor 16-mosdegree m16md
−10 Minor 5-mosdegree m5md
−11 Minor 17-mosdegree m17md
−12 Minor 6-mosdegree m6md
−13 Minor 18-mosdegree m18md
−14 Minor 7-mosdegree m7md
−15 Minor 19-mosdegree m19md
−16 Minor 8-mosdegree m8md
−17 Minor 20-mosdegree m20md
−18 Minor 9-mosdegree m9md
−19 Minor 21-mosdegree m21md
−20 Minor 10-mosdegree m10md
−21 Minor 22-mosdegree m22md
−22 Diminished 11-mosdegree d11md
−23 Diminished 23-mosdegree d23md
−24 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 2L 21s
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 LssssssssssLsssssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|1 12 LsssssssssssLssssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|2 23 sLssssssssssLssssssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|3 11 sLsssssssssssLsssssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|4 22 ssLssssssssssLsssssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|5 10 ssLsssssssssssLssssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|6 21 sssLssssssssssLssssssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|7 9 sssLsssssssssssLsssssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|8 20 ssssLssssssssssLsssssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|9 8 ssssLsssssssssssLssssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|10 19 sssssLssssssssssLssssss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
11|11 7 sssssLsssssssssssLsssss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
10|12 18 ssssssLssssssssssLsssss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
9|13 6 ssssssLsssssssssssLssss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
8|14 17 sssssssLssssssssssLssss Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
7|15 5 sssssssLsssssssssssLsss Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
6|16 16 ssssssssLssssssssssLsss Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
5|17 4 ssssssssLsssssssssssLss Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
4|18 15 sssssssssLssssssssssLss Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
3|19 3 sssssssssLsssssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
2|20 14 ssssssssssLssssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
1|21 2 ssssssssssLsssssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|22 13 sssssssssssLssssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 21s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\23 573.913 626.087 1:1 1.000 Equalized 2L 21s
56\117 574.359 625.641 6:5 1.200
45\94 574.468 625.532 5:4 1.250
79\165 574.545 625.455 9:7 1.286
34\71 574.648 625.352 4:3 1.333 Supersoft 2L 21s
91\190 574.737 625.263 11:8 1.375
57\119 574.790 625.210 7:5 1.400
80\167 574.850 625.150 10:7 1.429
23\48 575.000 625.000 3:2 1.500 Soft 2L 21s
81\169 575.148 624.852 11:7 1.571
58\121 575.207 624.793 8:5 1.600
93\194 575.258 624.742 13:8 1.625
35\73 575.342 624.658 5:3 1.667 Semisoft 2L 21s
82\171 575.439 624.561 12:7 1.714
47\98 575.510 624.490 7:4 1.750
59\123 575.610 624.390 9:5 1.800
12\25 576.000 624.000 2:1 2.000 Basic 2L 21s
Scales with tunings softer than this are proper
49\102 576.471 623.529 9:4 2.250
37\77 576.623 623.377 7:3 2.333
62\129 576.744 623.256 12:5 2.400
25\52 576.923 623.077 5:2 2.500 Semihard 2L 21s
63\131 577.099 622.901 13:5 2.600
38\79 577.215 622.785 8:3 2.667
51\106 577.358 622.642 11:4 2.750
13\27 577.778 622.222 3:1 3.000 Hard 2L 21s
40\83 578.313 621.687 10:3 3.333
27\56 578.571 621.429 7:2 3.500
41\85 578.824 621.176 11:3 3.667
14\29 579.310 620.690 4:1 4.000 Superhard 2L 21s
29\60 580.000 620.000 9:2 4.500
15\31 580.645 619.355 5:1 5.000
16\33 581.818 618.182 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 21s
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