10L 1s

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← 9L 1s10L 1s 11L 1s →
↙ 9L 2s ↓10L 2s 11L 2s ↘
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└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLLLs
sLLLLLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\11 to 1\10 (109.1¢ to 120.0¢)
Dark 9\10 to 10\11 (1080.0¢ to 1090.9¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Required step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 1L 9s
Sister 1L 10s
Daughters 11L 10s, 10L 11s
Neutralized 9L 2s
2-Flought 21L 1s, 10L 12s
Equal tunings
Equalized (L:s = 1:1) 1\11 (109.1¢)
Supersoft (L:s = 4:3) 4\43 (111.6¢)
Soft (L:s = 3:2) 3\32 (112.5¢)
Semisoft (L:s = 5:3) 5\53 (113.2¢)
Basic (L:s = 2:1) 2\21 (114.3¢)
Semihard (L:s = 5:2) 5\52 (115.4¢)
Hard (L:s = 3:1) 3\31 (116.1¢)
Superhard (L:s = 4:1) 4\41 (117.1¢)
Collapsed (L:s = 1:0) 1\10 (120.0¢)

10L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 1 small step, repeating every octave. 10L 1s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 109.1¢ to 120¢, or from 1080¢ to 1090.9¢. Scales of this form are always proper because there is only one small step. This MOS functions as the superdiatonic scale[clarification needed] of Miracle temperment.

Modes

Modes of 10L 1s
UDP Rotational order Step pattern
10|0 1 LLLLLLLLLLs
9|1 2 LLLLLLLLLsL
8|2 3 LLLLLLLLsLL
7|3 4 LLLLLLLsLLL
6|4 5 LLLLLLsLLLL
5|5 6 LLLLLsLLLLL
4|6 7 LLLLsLLLLLL
3|7 8 LLLsLLLLLLL
2|8 9 LLsLLLLLLLL
1|9 10 LsLLLLLLLLL
0|10 11 sLLLLLLLLLL

Scale tree

Scale Tree and Tuning Spectrum of 10L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\11 109.091 1090.909 1:1 1.000 Equalized 10L 1s
6\65 110.769 1089.231 6:5 1.200
5\54 111.111 1088.889 5:4 1.250
9\97 111.340 1088.660 9:7 1.286
4\43 111.628 1088.372 4:3 1.333 Supersoft 10L 1s
11\118 111.864 1088.136 11:8 1.375
7\75 112.000 1088.000 7:5 1.400
10\107 112.150 1087.850 10:7 1.429
3\32 112.500 1087.500 3:2 1.500 Soft 10L 1s
11\117 112.821 1087.179 11:7 1.571
8\85 112.941 1087.059 8:5 1.600
13\138 113.043 1086.957 13:8 1.625
5\53 113.208 1086.792 5:3 1.667 Semisoft 10L 1s
12\127 113.386 1086.614 12:7 1.714
7\74 113.514 1086.486 7:4 1.750
9\95 113.684 1086.316 9:5 1.800
2\21 114.286 1085.714 2:1 2.000 Basic 10L 1s
Simplest tuning for miracle
9\94 114.894 1085.106 9:4 2.250
7\73 115.068 1084.932 7:3 2.333
12\125 115.200 1084.800 12:5 2.400
5\52 115.385 1084.615 5:2 2.500 Semihard 10L 1s
13\135 115.556 1084.444 13:5 2.600
8\83 115.663 1084.337 8:3 2.667
11\114 115.789 1084.211 11:4 2.750
3\31 116.129 1083.871 3:1 3.000 Hard 10L 1s
10\103 116.505 1083.495 10:3 3.333
7\72 116.667 1083.333 7:2 3.500 Miracle
11\113 116.814 1083.186 11:3 3.667
4\41 117.073 1082.927 4:1 4.000 Superhard 10L 1s
9\92 117.391 1082.609 9:2 4.500
5\51 117.647 1082.353 5:1 5.000
6\61 118.033 1081.967 6:1 6.000
1\10 120.000 1080.000 1:0 → ∞ Collapsed 10L 1s