2L 20s

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↖1L 19s ↑2L 19s 3L 19s↗
←1L 20s2L 20s 3L 20s→
↙1L 21s ↓2L 21s 3L 21s↘
┌╥┬┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┐
│║││││││││││║│││││││││││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssssssLssssssssss
ssssssssssLssssssssssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Step size ranges
Large 1\22 to 1\2 (54.5¢ to 600.0¢)
Small 0\2 to 1\22 (0.0¢ to 54.5¢)
Generator size
Bright 10\22 to 1\2 (545.5¢ to 600.0¢)
Dark 0\2 to 1\22 (0.0¢ to 54.5¢)
TAMNAMS information
Descends from 2L 8s (jaric)
Related MOS scales
Parent 2L 18s
Sister 20L 2s
Daughters 22L 2s
2L 22s
Equal tunings
Equalized (L:s = 1:1) 10\22 (545.5¢)
Supersoft (L:s = 4:3) 31\68 (547.1¢)
Soft (L:s = 3:2) 21\46 (547.8¢)
Semisoft (L:s = 5:3) 32\70 (548.6¢)
Basic (L:s = 2:1) 11\24 (550.0¢)
Semihard (L:s = 5:2) 23\50 (552.0¢)
Hard (L:s = 3:1) 12\26 (553.8¢)
Superhard (L:s = 4:1) 13\28 (557.1¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

2L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 20 small steps, with a period of 1 large step and 10 small steps that repeats every 600.0¢, or twice every octave. 2L 20s is related to 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 545.5¢ to 600¢, or from 0¢ to 54.5¢.

This scale is the quarter tone scale of Shrutar temperament.

Scale tree and tuning spectrum of 2L 20s
Generator (in steps of edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\22 545.455 54.545 1:1 1.000 Equalized 2L 20s
51\112 546.429 53.571 6:5 1.200
41\90 546.667 53.333 5:4 1.250
72\158 546.835 53.165 9:7 1.286
31\68 547.059 52.941 4:3 1.333 Supersoft 2L 20s
83\182 547.253 52.747 11:8 1.375
52\114 547.368 52.632 7:5 1.400
73\160 547.500 52.500 10:7 1.429
21\46 547.826 52.174 3:2 1.500 Soft 2L 20s
74\162 548.148 51.852 11:7 1.571
53\116 548.276 51.724 8:5 1.600
85\186 548.387 51.613 13:8 1.625
32\70 548.571 51.429 5:3 1.667 Semisoft 2L 20s
75\164 548.780 51.220 12:7 1.714
43\94 548.936 51.064 7:4 1.750
54\118 549.153 50.847 9:5 1.800
11\24 550.000 50.000 2:1 2.000 Basic 2L 20s
Scales with tunings softer than this are proper
45\98 551.020 48.980 9:4 2.250
34\74 551.351 48.649 7:3 2.333
57\124 551.613 48.387 12:5 2.400
23\50 552.000 48.000 5:2 2.500 Semihard 2L 20s
58\126 552.381 47.619 13:5 2.600
35\76 552.632 47.368 8:3 2.667
47\102 552.941 47.059 11:4 2.750
12\26 553.846 46.154 3:1 3.000 Hard 2L 20s
37\80 555.000 45.000 10:3 3.333
25\54 555.556 44.444 7:2 3.500
38\82 556.098 43.902 11:3 3.667
13\28 557.143 42.857 4:1 4.000 Superhard 2L 20s
27\58 558.621 41.379 9:2 4.500
14\30 560.000 40.000 5:1 5.000
15\32 562.500 37.500 6:1 6.000
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 20s