10L 11s

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↖ 9L 10s ↑ 10L 10s 11L 10s ↗
← 9L 11s 10L 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)
Ancestor'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.

Intervals

Intervals of 10L 11s
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 57.1¢
Major 1-mosstep M1ms L 57.1¢ to 120.0¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0¢ to 114.3¢
Perfect 2-mosstep P2ms L + s 114.3¢ to 120.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0¢ to 171.4¢
Major 3-mosstep M3ms 2L + s 171.4¢ to 240.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 120.0¢ to 228.6¢
Major 4-mosstep M4ms 2L + 2s 228.6¢ to 240.0¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 240.0¢ to 285.7¢
Major 5-mosstep M5ms 3L + 2s 285.7¢ to 360.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 240.0¢ to 342.9¢
Major 6-mosstep M6ms 3L + 3s 342.9¢ to 360.0¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 360.0¢ to 400.0¢
Major 7-mosstep M7ms 4L + 3s 400.0¢ to 480.0¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 360.0¢ to 457.1¢
Major 8-mosstep M8ms 4L + 4s 457.1¢ to 480.0¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 480.0¢ to 514.3¢
Major 9-mosstep M9ms 5L + 4s 514.3¢ to 600.0¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 480.0¢ to 571.4¢
Major 10-mosstep M10ms 5L + 5s 571.4¢ to 600.0¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 600.0¢ to 628.6¢
Major 11-mosstep M11ms 6L + 5s 628.6¢ to 720.0¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 600.0¢ to 685.7¢
Major 12-mosstep M12ms 6L + 6s 685.7¢ to 720.0¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 720.0¢ to 742.9¢
Major 13-mosstep M13ms 7L + 6s 742.9¢ to 840.0¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 720.0¢ to 800.0¢
Major 14-mosstep M14ms 7L + 7s 800.0¢ to 840.0¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 840.0¢ to 857.1¢
Major 15-mosstep M15ms 8L + 7s 857.1¢ to 960.0¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 840.0¢ to 914.3¢
Major 16-mosstep M16ms 8L + 8s 914.3¢ to 960.0¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 960.0¢ to 971.4¢
Major 17-mosstep M17ms 9L + 8s 971.4¢ to 1080.0¢
18-mosstep Minor 18-mosstep m18ms 8L + 10s 960.0¢ to 1028.6¢
Major 18-mosstep M18ms 9L + 9s 1028.6¢ to 1080.0¢
19-mosstep Perfect 19-mosstep P19ms 9L + 10s 1080.0¢ to 1085.7¢
Augmented 19-mosstep A19ms 10L + 9s 1085.7¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 9L + 11s 1080.0¢ to 1142.9¢
Major 20-mosstep M20ms 10L + 10s 1142.9¢ to 1200.0¢
21-mosstep Perfect 21-mosstep P21ms 10L + 11s 1200.0¢

Scale tree

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
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