10L 11s

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↖ 9L 10s ↑10L 10s 11L 10s ↗
← 9L 11s10L 11s 11L 11s →
↙ 9L 12s ↓10L 12s 11L 12s ↘
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Scale structure
Step pattern LsLsLsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 2\21 to 1\10 (114.3¢ to 120.0¢)
Dark 9\10 to 19\21 (1080.0¢ to 1085.7¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Descendant's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 10L 1s
Sister 11L 10s
Daughters 21L 10s, 10L 21s
Neutralized 20L 1s
2-Flought 31L 11s, 10L 32s
Equal tunings
Equalized (L:s = 1:1) 2\21 (114.3¢)
Supersoft (L:s = 4:3) 7\73 (115.1¢)
Soft (L:s = 3:2) 5\52 (115.4¢)
Semisoft (L:s = 5:3) 8\83 (115.7¢)
Basic (L:s = 2:1) 3\31 (116.1¢)
Semihard (L:s = 5:2) 7\72 (116.7¢)
Hard (L:s = 3:1) 4\41 (117.1¢)
Superhard (L:s = 4:1) 5\51 (117.6¢)
Collapsed (L:s = 1:0) 1\10 (120.0¢)

10L 11s, also called miracloid, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 11 small steps, repeating every octave. 10L 11s is a grandchild scale of 1L 9s, expanding it by 11 tones. Generators that produce this scale range from 114.3¢ to 120¢, or from 1080¢ to 1085.7¢. This is the simplest MOS for which miracle temperament can be used[clarification needed], placing the low estimate for the boundary of "practicality" at 41edo (L:s = 3:1). Eliora has proposed the name miracloid for this pattern.

Scale Tree and Tuning Spectrum of 10L 11s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
2\21 114.286 1085.714 1:1 1.000 Equalized 10L 11s
11\115 114.783 1085.217 6:5 1.200
9\94 114.894 1085.106 5:4 1.250
16\167 114.970 1085.030 9:7 1.286
7\73 115.068 1084.932 4:3 1.333 Supersoft 10L 11s
19\198 115.152 1084.848 11:8 1.375
12\125 115.200 1084.800 7:5 1.400
17\177 115.254 1084.746 10:7 1.429
5\52 115.385 1084.615 3:2 1.500 Soft 10L 11s
Approximate range for using 31/29 as a generator
18\187 115.508 1084.492 11:7 1.571
13\135 115.556 1084.444 8:5 1.600
21\218 115.596 1084.404 13:8 1.625
8\83 115.663 1084.337 5:3 1.667 Semisoft 10L 11s
19\197 115.736 1084.264 12:7 1.714
11\114 115.789 1084.211 7:4 1.750
14\145 115.862 1084.138 9:5 1.800
3\31 116.129 1083.871 2:1 2.000 Basic 10L 11s
Scales with tunings softer than this are proper
Approximate range for using 46/43 as a generator
13\134 116.418 1083.582 9:4 2.250
10\103 116.505 1083.495 7:3 2.333
17\175 116.571 1083.429 12:5 2.400
7\72 116.667 1083.333 5:2 2.500 Semihard 10L 11s
18\185 116.757 1083.243 13:5 2.600
11\113 116.814 1083.186 8:3 2.667
15\154 116.883 1083.117 11:4 2.750
4\41 117.073 1082.927 3:1 3.000 Hard 10L 11s
13\133 117.293 1082.707 10:3 3.333
9\92 117.391 1082.609 7:2 3.500
14\143 117.483 1082.517 11:3 3.667
5\51 117.647 1082.353 4:1 4.000 Superhard 10L 11s
11\112 117.857 1082.143 9:2 4.500
6\61 118.033 1081.967 5:1 5.000
7\71 118.310 1081.690 6:1 6.000
1\10 120.000 1080.000 1:0 → ∞ Collapsed 10L 11s