10L 7s

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↖ 9L 6s ↑ 10L 6s 11L 6s ↗
← 9L 7s 10L 7s 11L 7s →
↙ 9L 8s ↓ 10L 8s 11L 8s ↘ 
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLsLLsLsLs
sLsLsLLsLsLLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\17 to 3\10 (352.9¢ to 360.0¢)
Dark 7\10 to 12\17 (840.0¢ to 847.1¢)
TAMNAMS information
Descends from 7L 3s (dicoid)
Ancestor's step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 7L 3s
Sister 7L 10s
Daughters 17L 10s, 10L 17s
Neutralized 3L 14s
2-Flought 27L 7s, 10L 24s
Equal tunings
Equalized (L:s = 1:1) 5\17 (352.9¢)
Supersoft (L:s = 4:3) 18\61 (354.1¢)
Soft (L:s = 3:2) 13\44 (354.5¢)
Semisoft (L:s = 5:3) 21\71 (354.9¢)
Basic (L:s = 2:1) 8\27 (355.6¢)
Semihard (L:s = 5:2) 19\64 (356.2¢)
Hard (L:s = 3:1) 11\37 (356.8¢)
Superhard (L:s = 4:1) 14\47 (357.4¢)
Collapsed (L:s = 1:0) 3\10 (360.0¢)

10L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 7 small steps, repeating every octave. 10L 7s is a child scale of 7L 3s, expanding it by 7 tones. Generators that produce this scale range from 352.9¢ to 360¢, or from 840¢ to 847.1¢. This scale is the neutral thirds version of Schismic temperament. The range of the bright generator also makes it an improper MOS of Beatles temperament (generator = c. 19\64 ~ 356.25 ¢).

Modes

Modes of 10L 7s
UDP Cyclic
order		 Step
pattern
16|0 1 LLsLsLLsLsLLsLsLs
15|1 6 LLsLsLLsLsLsLLsLs
14|2 11 LLsLsLsLLsLsLLsLs
13|3 16 LsLLsLsLLsLsLLsLs
12|4 4 LsLLsLsLLsLsLsLLs
11|5 9 LsLLsLsLsLLsLsLLs
10|6 14 LsLsLLsLsLLsLsLLs
9|7 2 LsLsLLsLsLLsLsLsL
8|8 7 LsLsLLsLsLsLLsLsL
7|9 12 LsLsLsLLsLsLLsLsL
6|10 17 sLLsLsLLsLsLLsLsL
5|11 5 sLLsLsLLsLsLsLLsL
4|12 10 sLLsLsLsLLsLsLLsL
3|13 15 sLsLLsLsLLsLsLLsL
2|14 3 sLsLLsLsLLsLsLsLL
1|15 8 sLsLLsLsLsLLsLsLL
0|16 13 sLsLsLLsLsLLsLsLL

Intervals

Intervals of 10L 7s
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 70.6¢
Major 1-mosstep M1ms L 70.6¢ to 120.0¢
2-mosstep Minor 2-mosstep m2ms L + s 120.0¢ to 141.2¢
Major 2-mosstep M2ms 2L 141.2¢ to 240.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0¢ to 211.8¢
Major 3-mosstep M3ms 2L + s 211.8¢ to 240.0¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 240.0¢ to 282.4¢
Major 4-mosstep M4ms 3L + s 282.4¢ to 360.0¢
5-mosstep Diminished 5-mosstep d5ms 2L + 3s 240.0¢ to 352.9¢
Perfect 5-mosstep P5ms 3L + 2s 352.9¢ to 360.0¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 360.0¢ to 423.5¢
Major 6-mosstep M6ms 4L + 2s 423.5¢ to 480.0¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 480.0¢ to 494.1¢
Major 7-mosstep M7ms 5L + 2s 494.1¢ to 600.0¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 480.0¢ to 564.7¢
Major 8-mosstep M8ms 5L + 3s 564.7¢ to 600.0¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 600.0¢ to 635.3¢
Major 9-mosstep M9ms 6L + 3s 635.3¢ to 720.0¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 600.0¢ to 705.9¢
Major 10-mosstep M10ms 6L + 4s 705.9¢ to 720.0¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 720.0¢ to 776.5¢
Major 11-mosstep M11ms 7L + 4s 776.5¢ to 840.0¢
12-mosstep Perfect 12-mosstep P12ms 7L + 5s 840.0¢ to 847.1¢
Augmented 12-mosstep A12ms 8L + 4s 847.1¢ to 960.0¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 840.0¢ to 917.6¢
Major 13-mosstep M13ms 8L + 5s 917.6¢ to 960.0¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 960.0¢ to 988.2¢
Major 14-mosstep M14ms 9L + 5s 988.2¢ to 1080.0¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 960.0¢ to 1058.8¢
Major 15-mosstep M15ms 9L + 6s 1058.8¢ to 1080.0¢
16-mosstep Minor 16-mosstep m16ms 9L + 7s 1080.0¢ to 1129.4¢
Major 16-mosstep M16ms 10L + 6s 1129.4¢ to 1200.0¢
17-mosstep Perfect 17-mosstep P17ms 10L + 7s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 10L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\17 352.941 847.059 1:1 1.000 Equalized 10L 7s
28\95 353.684 846.316 6:5 1.200
23\78 353.846 846.154 5:4 1.250
41\139 353.957 846.043 9:7 1.286
18\61 354.098 845.902 4:3 1.333 Supersoft 10L 7s
49\166 354.217 845.783 11:8 1.375
31\105 354.286 845.714 7:5 1.400
44\149 354.362 845.638 10:7 1.429
13\44 354.545 845.455 3:2 1.500 Soft 10L 7s
47\159 354.717 845.283 11:7 1.571
34\115 354.783 845.217 8:5 1.600
55\186 354.839 845.161 13:8 1.625
21\71 354.930 845.070 5:3 1.667 Semisoft 10L 7s
50\169 355.030 844.970 12:7 1.714
29\98 355.102 844.898 7:4 1.750
37\125 355.200 844.800 9:5 1.800
8\27 355.556 844.444 2:1 2.000 Basic 10L 7s
Scales with tunings softer than this are proper
35\118 355.932 844.068 9:4 2.250
27\91 356.044 843.956 7:3 2.333
46\155 356.129 843.871 12:5 2.400
19\64 356.250 843.750 5:2 2.500 Semihard 10L 7s
49\165 356.364 843.636 13:5 2.600
30\101 356.436 843.564 8:3 2.667
41\138 356.522 843.478 11:4 2.750
11\37 356.757 843.243 3:1 3.000 Hard 10L 7s
36\121 357.025 842.975 10:3 3.333
25\84 357.143 842.857 7:2 3.500
39\131 357.252 842.748 11:3 3.667
14\47 357.447 842.553 4:1 4.000 Superhard 10L 7s
31\104 357.692 842.308 9:2 4.500
17\57 357.895 842.105 5:1 5.000
20\67 358.209 841.791 6:1 6.000
3\10 360.000 840.000 1:0 → ∞ Collapsed 10L 7s
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