7L 10s

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↖ 6L 9s ↑ 7L 9s 8L 9s ↗
← 6L 10s 7L 10s 8L 10s →
↙ 6L 11s ↓ 7L 11s 8L 11s ↘ 
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║││║│║│││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Related to 7L 3s (dicoid)
With tunings 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 ¢) and its entire spectrum is 2\7edo (342.857 ¢) to 5\17edo (352.941 ¢).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 7L 10s
Bright gens Scale degree Abbrev.
23 Augmented 4-mosdegree A4md
22 Augmented 9-mosdegree A9md
21 Augmented 14-mosdegree A14md
20 Augmented 2-mosdegree A2md
19 Augmented 7-mosdegree A7md
18 Augmented 12-mosdegree A12md
17 Augmented 0-mosdegree A0md
16 Augmented 5-mosdegree A5md
15 Major 10-mosdegree M10md
14 Major 15-mosdegree M15md
13 Major 3-mosdegree M3md
12 Major 8-mosdegree M8md
11 Major 13-mosdegree M13md
10 Major 1-mosdegree M1md
9 Major 6-mosdegree M6md
8 Major 11-mosdegree M11md
7 Major 16-mosdegree M16md
6 Major 4-mosdegree M4md
5 Major 9-mosdegree M9md
4 Major 14-mosdegree M14md
3 Major 2-mosdegree M2md
2 Major 7-mosdegree M7md
1 Perfect 12-mosdegree P12md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 15-mosdegree m15md
−4 Minor 3-mosdegree m3md
−5 Minor 8-mosdegree m8md
−6 Minor 13-mosdegree m13md
−7 Minor 1-mosdegree m1md
−8 Minor 6-mosdegree m6md
−9 Minor 11-mosdegree m11md
−10 Minor 16-mosdegree m16md
−11 Minor 4-mosdegree m4md
−12 Minor 9-mosdegree m9md
−13 Minor 14-mosdegree m14md
−14 Minor 2-mosdegree m2md
−15 Minor 7-mosdegree m7md
−16 Diminished 12-mosdegree d12md
−17 Diminished 17-mosdegree d17md
−18 Diminished 5-mosdegree d5md
−19 Diminished 10-mosdegree d10md
−20 Diminished 15-mosdegree d15md
−21 Diminished 3-mosdegree d3md
−22 Diminished 8-mosdegree d8md
−23 Diminished 13-mosdegree d13md

Modes

Scale degrees of the modes of 7L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LsLsLssLsLssLsLss Perf. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
15|1 13 LsLssLsLsLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
14|2 8 LsLssLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
13|3 3 LsLssLsLssLsLssLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
12|4 15 LssLsLsLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
11|5 10 LssLsLssLsLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
10|6 5 LssLsLssLsLssLsLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
9|7 17 sLsLsLssLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
8|8 12 sLsLssLsLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
7|9 7 sLsLssLsLssLsLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Perf.
6|10 2 sLsLssLsLssLsLssL Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
5|11 14 sLssLsLsLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
4|12 9 sLssLsLssLsLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Perf.
3|13 4 sLssLsLssLsLssLsL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
2|14 16 ssLsLsLssLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|15 11 ssLsLssLsLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|16 6 ssLsLssLsLssLsLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Perf.

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 Hemif / hemififths
99\140 848.571 351.429 10:7 1.429
29\41 848.780 351.220 3:2 1.500 Soft 7L 10s
Mohaha / neutrominant / mohamaq
104\147 848.980 351.020 11:7 1.571
75\106 849.057 350.943 8:5 1.600 Hemif / salsa / karadeniz
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
Mohaha / migration / mohajira
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 Mohaha / ptolemy
37\52 853.846 346.154 6:1 6.000 Artoneutral ↓
5\7 857.143 342.857 1:0 → ∞ Collapsed 7L 10s
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