7L 9s

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↖ 6L 8s ↑ 7L 8s 8L 8s ↗
← 6L 9s 7L 9s 8L 9s →
↙ 6L 10s ↓ 7L 10s 8L 10s ↘ 
┌╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐
│║│║│║│║││║│║│║│││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLssLsLsLss
ssLsLsLssLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\16 to 4\7 (675.0 ¢ to 685.7 ¢)
Dark 3\7 to 7\16 (514.3 ¢ to 525.0 ¢)
TAMNAMS information
Related to 7L 2s (armotonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 7L 2s
Sister 9L 7s
Daughters 16L 7s, 7L 16s
Neutralized 14L 2s
2-Flought 23L 9s, 7L 25s
Equal tunings
Equalized (L:s = 1:1) 9\16 (675.0 ¢)
Supersoft (L:s = 4:3) 31\55 (676.4 ¢)
Soft (L:s = 3:2) 22\39 (676.9 ¢)
Semisoft (L:s = 5:3) 35\62 (677.4 ¢)
Basic (L:s = 2:1) 13\23 (678.3 ¢)
Semihard (L:s = 5:2) 30\53 (679.2 ¢)
Hard (L:s = 3:1) 17\30 (680.0 ¢)
Superhard (L:s = 4:1) 21\37 (681.1 ¢)
Collapsed (L:s = 1:0) 4\7 (685.7 ¢)

7L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 9 small steps, repeating every octave. 7L 9s is a child scale of 7L 2s, expanding it by 7 tones. Generators that produce this scale range from 675 ¢ to 685.7 ¢, or from 514.3 ¢ to 525 ¢.

Most notable as the 16-tone Mavila scale, although there are mavila tunings that generate 9L 7s. The entire range is suitable for mavila, but generators around 520 to 522 ¢ are perhaps "best" if you wish to approximate 4/3 with the generator.

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 9s
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 75.0 ¢
Major 1-mosstep M1ms L 75.0 ¢ to 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 150.0 ¢
Major 2-mosstep M2ms L + s 150.0 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 225.0 ¢
Major 3-mosstep M3ms 2L + s 225.0 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 300.0 ¢
Major 4-mosstep M4ms 2L + 2s 300.0 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 342.9 ¢ to 375.0 ¢
Major 5-mosstep M5ms 3L + 2s 375.0 ¢ to 514.3 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9 ¢ to 450.0 ¢
Major 6-mosstep M6ms 3L + 3s 450.0 ¢ to 514.3 ¢
7-mosstep Perfect 7-mosstep P7ms 3L + 4s 514.3 ¢ to 525.0 ¢
Augmented 7-mosstep A7ms 4L + 3s 525.0 ¢ to 685.7 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 514.3 ¢ to 600.0 ¢
Major 8-mosstep M8ms 4L + 4s 600.0 ¢ to 685.7 ¢
9-mosstep Diminished 9-mosstep d9ms 3L + 6s 514.3 ¢ to 675.0 ¢
Perfect 9-mosstep P9ms 4L + 5s 675.0 ¢ to 685.7 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 685.7 ¢ to 750.0 ¢
Major 10-mosstep M10ms 5L + 5s 750.0 ¢ to 857.1 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 685.7 ¢ to 825.0 ¢
Major 11-mosstep M11ms 5L + 6s 825.0 ¢ to 857.1 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 857.1 ¢ to 900.0 ¢
Major 12-mosstep M12ms 6L + 6s 900.0 ¢ to 1028.6 ¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 857.1 ¢ to 975.0 ¢
Major 13-mosstep M13ms 6L + 7s 975.0 ¢ to 1028.6 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 1028.6 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 7L + 7s 1050.0 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 1028.6 ¢ to 1125.0 ¢
Major 15-mosstep M15ms 7L + 8s 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 7L + 9s 1200.0 ¢

Generator chain

Generator chain of 7L 9s
Bright gens Scale degree Abbrev.
22 Augmented 6-mosdegree A6md
21 Augmented 13-mosdegree A13md
20 Augmented 4-mosdegree A4md
19 Augmented 11-mosdegree A11md
18 Augmented 2-mosdegree A2md
17 Augmented 9-mosdegree A9md
16 Augmented 0-mosdegree A0md
15 Augmented 7-mosdegree A7md
14 Major 14-mosdegree M14md
13 Major 5-mosdegree M5md
12 Major 12-mosdegree M12md
11 Major 3-mosdegree M3md
10 Major 10-mosdegree M10md
9 Major 1-mosdegree M1md
8 Major 8-mosdegree M8md
7 Major 15-mosdegree M15md
6 Major 6-mosdegree M6md
5 Major 13-mosdegree M13md
4 Major 4-mosdegree M4md
3 Major 11-mosdegree M11md
2 Major 2-mosdegree M2md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 16-mosdegree		 P0md
P16md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 5-mosdegree m5md
−4 Minor 12-mosdegree m12md
−5 Minor 3-mosdegree m3md
−6 Minor 10-mosdegree m10md
−7 Minor 1-mosdegree m1md
−8 Minor 8-mosdegree m8md
−9 Minor 15-mosdegree m15md
−10 Minor 6-mosdegree m6md
−11 Minor 13-mosdegree m13md
−12 Minor 4-mosdegree m4md
−13 Minor 11-mosdegree m11md
−14 Minor 2-mosdegree m2md
−15 Diminished 9-mosdegree d9md
−16 Diminished 16-mosdegree d16md
−17 Diminished 7-mosdegree d7md
−18 Diminished 14-mosdegree d14md
−19 Diminished 5-mosdegree d5md
−20 Diminished 12-mosdegree d12md
−21 Diminished 3-mosdegree d3md
−22 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 7L 9s
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
15|0 1 LsLsLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|1 10 LsLsLssLsLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|2 3 LsLsLssLsLsLssLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
12|3 12 LsLssLsLsLsLssLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
11|4 5 LsLssLsLsLssLsLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
10|5 14 LssLsLsLsLssLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
9|6 7 LssLsLsLssLsLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
8|7 16 sLsLsLsLssLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
7|8 9 sLsLsLssLsLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
6|9 2 sLsLsLssLsLsLssL Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
5|10 11 sLsLssLsLsLsLssL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
4|11 4 sLsLssLsLsLssLsL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
3|12 13 sLssLsLsLsLssLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
2|13 6 sLssLsLsLssLsLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|14 15 ssLsLsLsLssLsLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|15 8 ssLsLsLssLsLsLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\16 675.000 525.000 1:1 1.000 Equalized 7L 9s
49\87 675.862 524.138 6:5 1.200
40\71 676.056 523.944 5:4 1.250
71\126 676.190 523.810 9:7 1.286
31\55 676.364 523.636 4:3 1.333 Supersoft 7L 9s
84\149 676.510 523.490 11:8 1.375
53\94 676.596 523.404 7:5 1.400
75\133 676.692 523.308 10:7 1.429
22\39 676.923 523.077 3:2 1.500 Soft 7L 9s
79\140 677.143 522.857 11:7 1.571
57\101 677.228 522.772 8:5 1.600
92\163 677.301 522.699 13:8 1.625
35\62 677.419 522.581 5:3 1.667 Semisoft 7L 9s
83\147 677.551 522.449 12:7 1.714
48\85 677.647 522.353 7:4 1.750
61\108 677.778 522.222 9:5 1.800
13\23 678.261 521.739 2:1 2.000 Basic 7L 9s
Scales with tunings softer than this are proper
56\99 678.788 521.212 9:4 2.250
43\76 678.947 521.053 7:3 2.333 Hornbostel is around here
73\129 679.070 520.930 12:5 2.400
30\53 679.245 520.755 5:2 2.500 Semihard 7L 9s
77\136 679.412 520.588 13:5 2.600
47\83 679.518 520.482 8:3 2.667
64\113 679.646 520.354 11:4 2.750
17\30 680.000 520.000 3:1 3.000 Hard 7L 9s
55\97 680.412 519.588 10:3 3.333
38\67 680.597 519.403 7:2 3.500
59\104 680.769 519.231 11:3 3.667
21\37 681.081 518.919 4:1 4.000 Superhard 7L 9s
46\81 681.481 518.519 9:2 4.500
25\44 681.818 518.182 5:1 5.000
29\51 682.353 517.647 6:1 6.000 Gravity ↓, Marvo ↓
4\7 685.714 514.286 1:0 → ∞ Collapsed 7L 9s
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