10L 11s
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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)
Related MOS scales
Parent
10L 1s
Sister
11L 10s
Daughters
21L 10s
10L 21s
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¢)
| ↖9L 10s | ↑10L 10s | 11L 10s↗ |
| ←9L 11s | 10L 11s | 11L 11s→ |
| ↙9L 12s | ↓10L 12s | 11L 12s↘ |
┌╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│║│║│║│║│║│║│││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLsLsLsLsLsLsLsLsL
10L 21s
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.
| Generator (in steps of 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 | |||||