7L 10s

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↖ 6L 9s ↑ 7L 9s 8L 9s ↗
← 6L 10s 7L 10s 8L 10s →
↙ 6L 11s ↓ 7L 11s 8L 11s ↘ 
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Scale structure
Step pattern LsLsLssLsLssLsLss
ssLsLssLsLssLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 12\17 to 5\7 (847.1¢ to 857.1¢)
Dark 2\7 to 5\17 (342.9¢ to 352.9¢)
TAMNAMS information
Descends from 7L 3s (dicoid)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 7L 3s
Sister 10L 7s
Daughters 17L 7s, 7L 17s
Neutralized 14L 3s
2-Flought 24L 10s, 7L 27s
Equal tunings
Equalized (L:s = 1:1) 12\17 (847.1¢)
Supersoft (L:s = 4:3) 41\58 (848.3¢)
Soft (L:s = 3:2) 29\41 (848.8¢)
Semisoft (L:s = 5:3) 46\65 (849.2¢)
Basic (L:s = 2:1) 17\24 (850.0¢)
Semihard (L:s = 5:2) 39\55 (850.9¢)
Hard (L:s = 3:1) 22\31 (851.6¢)
Superhard (L:s = 4:1) 27\38 (852.6¢)
Collapsed (L:s = 1:0) 5\7 (857.1¢)

7L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 10 small steps, repeating every octave. 7L 10s is a child scale of 7L 3s, expanding it by 7 tones. Generators that produce this scale range from 847.1¢ to 857.1¢, or from 342.9¢ to 352.9¢.

This MOS is a neutral thirds-style meantone scale which spaces its large steps 2s-s-s-2s-s-s-s-2s. It is an improper Mohajira scale when the generator is c. 9/31edo (348.387 cents) and its entire spectrum is 2/7edo (342.857) to 5/17edo (352.941).

Modes

Modes of 7L 10s
UDP Cyclic
order		 Step
pattern
16|0 1 LsLsLssLsLssLsLss
15|1 13 LsLssLsLsLssLsLss
14|2 8 LsLssLsLssLsLsLss
13|3 3 LsLssLsLssLsLssLs
12|4 15 LssLsLsLssLsLssLs
11|5 10 LssLsLssLsLsLssLs
10|6 5 LssLsLssLsLssLsLs
9|7 17 sLsLsLssLsLssLsLs
8|8 12 sLsLssLsLsLssLsLs
7|9 7 sLsLssLsLssLsLsLs
6|10 2 sLsLssLsLssLsLssL
5|11 14 sLssLsLsLssLsLssL
4|12 9 sLssLsLssLsLsLssL
3|13 4 sLssLsLssLsLssLsL
2|14 16 ssLsLsLssLsLssLsL
1|15 11 ssLsLssLsLsLssLsL
0|16 6 ssLsLssLsLssLsLsL

Intervals

Intervals of 7L 10s
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 171.4¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 141.2¢
Major 2-mosstep M2ms L + s 141.2¢ to 171.4¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4¢ to 211.8¢
Major 3-mosstep M3ms 2L + s 211.8¢ to 342.9¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4¢ to 282.4¢
Major 4-mosstep M4ms 2L + 2s 282.4¢ to 342.9¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 342.9¢ to 352.9¢
Augmented 5-mosstep A5ms 3L + 2s 352.9¢ to 514.3¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9¢ to 423.5¢
Major 6-mosstep M6ms 3L + 3s 423.5¢ to 514.3¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9¢ to 494.1¢
Major 7-mosstep M7ms 3L + 4s 494.1¢ to 514.3¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 514.3¢ to 564.7¢
Major 8-mosstep M8ms 4L + 4s 564.7¢ to 685.7¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 514.3¢ to 635.3¢
Major 9-mosstep M9ms 4L + 5s 635.3¢ to 685.7¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 685.7¢ to 705.9¢
Major 10-mosstep M10ms 5L + 5s 705.9¢ to 857.1¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 685.7¢ to 776.5¢
Major 11-mosstep M11ms 5L + 6s 776.5¢ to 857.1¢
12-mosstep Diminished 12-mosstep d12ms 4L + 8s 685.7¢ to 847.1¢
Perfect 12-mosstep P12ms 5L + 7s 847.1¢ to 857.1¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 857.1¢ to 917.6¢
Major 13-mosstep M13ms 6L + 7s 917.6¢ to 1028.6¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 857.1¢ to 988.2¢
Major 14-mosstep M14ms 6L + 8s 988.2¢ to 1028.6¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 1028.6¢ to 1058.8¢
Major 15-mosstep M15ms 7L + 8s 1058.8¢ to 1200.0¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 1028.6¢ to 1129.4¢
Major 16-mosstep M16ms 7L + 9s 1129.4¢ to 1200.0¢
17-mosstep Perfect 17-mosstep P17ms 7L + 10s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 7L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
12\17 847.059 352.941 1:1 1.000 Equalized 7L 10s
65\92 847.826 352.174 6:5 1.200
53\75 848.000 352.000 5:4 1.250
94\133 848.120 351.880 9:7 1.286
41\58 848.276 351.724 4:3 1.333 Supersoft 7L 10s
111\157 848.408 351.592 11:8 1.375
70\99 848.485 351.515 7:5 1.400
99\140 848.571 351.429 10:7 1.429
29\41 848.780 351.220 3:2 1.500 Soft 7L 10s
104\147 848.980 351.020 11:7 1.571
75\106 849.057 350.943 8:5 1.600
121\171 849.123 350.877 13:8 1.625
46\65 849.231 350.769 5:3 1.667 Semisoft 7L 10s
109\154 849.351 350.649 12:7 1.714
63\89 849.438 350.562 7:4 1.750
80\113 849.558 350.442 9:5 1.800
17\24 850.000 350.000 2:1 2.000 Basic 7L 10s
Scales with tunings softer than this are proper
73\103 850.485 349.515 9:4 2.250
56\79 850.633 349.367 7:3 2.333
95\134 850.746 349.254 12:5 2.400
39\55 850.909 349.091 5:2 2.500 Semihard 7L 10s
100\141 851.064 348.936 13:5 2.600
61\86 851.163 348.837 8:3 2.667
83\117 851.282 348.718 11:4 2.750
22\31 851.613 348.387 3:1 3.000 Hard 7L 10s
71\100 852.000 348.000 10:3 3.333
49\69 852.174 347.826 7:2 3.500
76\107 852.336 347.664 11:3 3.667
27\38 852.632 347.368 4:1 4.000 Superhard 7L 10s
59\83 853.012 346.988 9:2 4.500
32\45 853.333 346.667 5:1 5.000
37\52 853.846 346.154 6:1 6.000
5\7 857.143 342.857 1:0 → ∞ Collapsed 7L 10s
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