5L 20s

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↖ 4L 19s ↑ 5L 19s 6L 19s ↗
← 4L 20s 5L 20s 6L 20s →
↙ 4L 21s ↓ 5L 21s 6L 21s ↘ 
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│││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLssssLssssLssssLssss
ssssLssssLssssLssssLssssL
Equave 2/1 (1200.0¢)
Period 1\5 (240.0¢)
Generator size
Bright 4\25 to 1\5 (192.0¢ to 240.0¢)
Dark 0\5 to 1\25 (0.0¢ to 48.0¢)
TAMNAMS information
Descends from 5L 5s
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 5L 15s
Sister 20L 5s
Daughters 25L 5s, 5L 25s
Neutralized 10L 15s
2-Flought 30L 20s, 5L 45s
Equal tunings
Equalized (L:s = 1:1) 4\25 (192.0¢)
Supersoft (L:s = 4:3) 13\80 (195.0¢)
Soft (L:s = 3:2) 9\55 (196.4¢)
Semisoft (L:s = 5:3) 14\85 (197.6¢)
Basic (L:s = 2:1) 5\30 (200.0¢)
Semihard (L:s = 5:2) 11\65 (203.1¢)
Hard (L:s = 3:1) 6\35 (205.7¢)
Superhard (L:s = 4:1) 7\40 (210.0¢)
Collapsed (L:s = 1:0) 1\5 (240.0¢)

5L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 20 small steps, with a period of 1 large step and 4 small steps that repeats every 240.0¢, or 5 times every octave. 5L 20s is a great-grandchild scale of 5L 5s, expanding it by 15 tones. Generators that produce this scale range from 192¢ to 240¢, or from 0¢ to 48¢.

Modes

Modes of 5L 20s
UDP Cyclic
order		 Step
pattern
20|0(5) 1 LssssLssssLssssLssssLssss
15|5(5) 5 sLssssLssssLssssLssssLsss
10|10(5) 4 ssLssssLssssLssssLssssLss
5|15(5) 3 sssLssssLssssLssssLssssLs
0|20(5) 2 ssssLssssLssssLssssLssssL

Intervals

Intervals of 5L 20s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Perfect 1-mosstep P1ms s 0.0¢ to 48.0¢
Augmented 1-mosstep A1ms L 48.0¢ to 240.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 96.0¢
Major 2-mosstep M2ms L + s 96.0¢ to 240.0¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0¢ to 144.0¢
Major 3-mosstep M3ms L + 2s 144.0¢ to 240.0¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0¢ to 192.0¢
Perfect 4-mosstep P4ms L + 3s 192.0¢ to 240.0¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 240.0¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 240.0¢ to 288.0¢
Augmented 6-mosstep A6ms 2L + 4s 288.0¢ to 480.0¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0¢ to 336.0¢
Major 7-mosstep M7ms 2L + 5s 336.0¢ to 480.0¢
8-mosstep Minor 8-mosstep m8ms L + 7s 240.0¢ to 384.0¢
Major 8-mosstep M8ms 2L + 6s 384.0¢ to 480.0¢
9-mosstep Diminished 9-mosstep d9ms L + 8s 240.0¢ to 432.0¢
Perfect 9-mosstep P9ms 2L + 7s 432.0¢ to 480.0¢
10-mosstep Perfect 10-mosstep P10ms 2L + 8s 480.0¢
11-mosstep Perfect 11-mosstep P11ms 2L + 9s 480.0¢ to 528.0¢
Augmented 11-mosstep A11ms 3L + 8s 528.0¢ to 720.0¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 480.0¢ to 576.0¢
Major 12-mosstep M12ms 3L + 9s 576.0¢ to 720.0¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 480.0¢ to 624.0¢
Major 13-mosstep M13ms 3L + 10s 624.0¢ to 720.0¢
14-mosstep Diminished 14-mosstep d14ms 2L + 12s 480.0¢ to 672.0¢
Perfect 14-mosstep P14ms 3L + 11s 672.0¢ to 720.0¢
15-mosstep Perfect 15-mosstep P15ms 3L + 12s 720.0¢
16-mosstep Perfect 16-mosstep P16ms 3L + 13s 720.0¢ to 768.0¢
Augmented 16-mosstep A16ms 4L + 12s 768.0¢ to 960.0¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 720.0¢ to 816.0¢
Major 17-mosstep M17ms 4L + 13s 816.0¢ to 960.0¢
18-mosstep Minor 18-mosstep m18ms 3L + 15s 720.0¢ to 864.0¢
Major 18-mosstep M18ms 4L + 14s 864.0¢ to 960.0¢
19-mosstep Diminished 19-mosstep d19ms 3L + 16s 720.0¢ to 912.0¢
Perfect 19-mosstep P19ms 4L + 15s 912.0¢ to 960.0¢
20-mosstep Perfect 20-mosstep P20ms 4L + 16s 960.0¢
21-mosstep Perfect 21-mosstep P21ms 4L + 17s 960.0¢ to 1008.0¢
Augmented 21-mosstep A21ms 5L + 16s 1008.0¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 4L + 18s 960.0¢ to 1056.0¢
Major 22-mosstep M22ms 5L + 17s 1056.0¢ to 1200.0¢
23-mosstep Minor 23-mosstep m23ms 4L + 19s 960.0¢ to 1104.0¢
Major 23-mosstep M23ms 5L + 18s 1104.0¢ to 1200.0¢
24-mosstep Diminished 24-mosstep d24ms 4L + 20s 960.0¢ to 1152.0¢
Perfect 24-mosstep P24ms 5L + 19s 1152.0¢ to 1200.0¢
25-mosstep Perfect 25-mosstep P25ms 5L + 20s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 20s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\25 192.000 48.000 1:1 1.000 Equalized 5L 20s
21\130 193.846 46.154 6:5 1.200
17\105 194.286 45.714 5:4 1.250
30\185 194.595 45.405 9:7 1.286
13\80 195.000 45.000 4:3 1.333 Supersoft 5L 20s
35\215 195.349 44.651 11:8 1.375
22\135 195.556 44.444 7:5 1.400
31\190 195.789 44.211 10:7 1.429
9\55 196.364 43.636 3:2 1.500 Soft 5L 20s
32\195 196.923 43.077 11:7 1.571
23\140 197.143 42.857 8:5 1.600
37\225 197.333 42.667 13:8 1.625
14\85 197.647 42.353 5:3 1.667 Semisoft 5L 20s
33\200 198.000 42.000 12:7 1.714
19\115 198.261 41.739 7:4 1.750
24\145 198.621 41.379 9:5 1.800
5\30 200.000 40.000 2:1 2.000 Basic 5L 20s
Scales with tunings softer than this are proper
21\125 201.600 38.400 9:4 2.250
16\95 202.105 37.895 7:3 2.333
27\160 202.500 37.500 12:5 2.400
11\65 203.077 36.923 5:2 2.500 Semihard 5L 20s
28\165 203.636 36.364 13:5 2.600
17\100 204.000 36.000 8:3 2.667
23\135 204.444 35.556 11:4 2.750
6\35 205.714 34.286 3:1 3.000 Hard 5L 20s
19\110 207.273 32.727 10:3 3.333
13\75 208.000 32.000 7:2 3.500
20\115 208.696 31.304 11:3 3.667
7\40 210.000 30.000 4:1 4.000 Superhard 5L 20s
15\85 211.765 28.235 9:2 4.500
8\45 213.333 26.667 5:1 5.000
9\50 216.000 24.000 6:1 6.000
1\5 240.000 0.000 1:0 → ∞ Collapsed 5L 20s
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