9L 7s

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Scale structure
Step pattern LLsLsLsLLsLsLsLs
sLsLsLsLLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\16 to 4\9 (525.0 ¢ to 533.3 ¢)
Dark 5\9 to 9\16 (666.7 ¢ to 675.0 ¢)
TAMNAMS information
Related to 7L 2s (armotonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 7L 2s
Sister 7L 9s
Daughters 16L 9s, 9L 16s
Neutralized 2L 14s
2-Flought 25L 7s, 9L 23s
Equal tunings
Equalized (L:s = 1:1) 7\16 (525.0 ¢)
Supersoft (L:s = 4:3) 25\57 (526.3 ¢)
Soft (L:s = 3:2) 18\41 (526.8 ¢)
Semisoft (L:s = 5:3) 29\66 (527.3 ¢)
Basic (L:s = 2:1) 11\25 (528.0 ¢)
Semihard (L:s = 5:2) 26\59 (528.8 ¢)
Hard (L:s = 3:1) 15\34 (529.4 ¢)
Superhard (L:s = 4:1) 19\43 (530.2 ¢)
Collapsed (L:s = 1:0) 4\9 (533.3 ¢)
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9L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 7 small steps, repeating every octave. 9L 7s is a child scale of 7L 2s, expanding it by 7 tones. Generators that produce this scale range from 525 ¢ to 533.3 ¢, or from 666.7 ¢ to 675 ¢.

This can be seen as a Mavila chromatic scale, but some mavila tunings generate 7L 9s. The entire range can be used as a mavila tuning, but tunings around 671-673c are perhaps best if you wish to generate an accurately-tuned 5/4 with the generator. As a result, this range also is characteristic of trismegistus.

This scale is also generated by the golden antidiatonic tuning of around 672.8 cents.

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 9L 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 75.0 ¢
Major 1-mosstep M1ms L 75.0 ¢ to 133.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 133.3 ¢ to 150.0 ¢
Major 2-mosstep M2ms 2L 150.0 ¢ to 266.7 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 133.3 ¢ to 225.0 ¢
Major 3-mosstep M3ms 2L + s 225.0 ¢ to 266.7 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 266.7 ¢ to 300.0 ¢
Major 4-mosstep M4ms 3L + s 300.0 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 266.7 ¢ to 375.0 ¢
Major 5-mosstep M5ms 3L + 2s 375.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 400.0 ¢ to 450.0 ¢
Major 6-mosstep M6ms 4L + 2s 450.0 ¢ to 533.3 ¢
7-mosstep Diminished 7-mosstep d7ms 3L + 4s 400.0 ¢ to 525.0 ¢
Perfect 7-mosstep P7ms 4L + 3s 525.0 ¢ to 533.3 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 533.3 ¢ to 600.0 ¢
Major 8-mosstep M8ms 5L + 3s 600.0 ¢ to 666.7 ¢
9-mosstep Perfect 9-mosstep P9ms 5L + 4s 666.7 ¢ to 675.0 ¢
Augmented 9-mosstep A9ms 6L + 3s 675.0 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 666.7 ¢ to 750.0 ¢
Major 10-mosstep M10ms 6L + 4s 750.0 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 800.0 ¢ to 825.0 ¢
Major 11-mosstep M11ms 7L + 4s 825.0 ¢ to 933.3 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 800.0 ¢ to 900.0 ¢
Major 12-mosstep M12ms 7L + 5s 900.0 ¢ to 933.3 ¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 933.3 ¢ to 975.0 ¢
Major 13-mosstep M13ms 8L + 5s 975.0 ¢ to 1066.7 ¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 933.3 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 8L + 6s 1050.0 ¢ to 1066.7 ¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 1066.7 ¢ to 1125.0 ¢
Major 15-mosstep M15ms 9L + 6s 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 9L + 7s 1200.0 ¢

Generator chain

Generator chain of 9L 7s
Bright gens Scale degree Abbrev.
24 Augmented 8-mosdegree A8md
23 Augmented 1-mosdegree A1md
22 Augmented 10-mosdegree A10md
21 Augmented 3-mosdegree A3md
20 Augmented 12-mosdegree A12md
19 Augmented 5-mosdegree A5md
18 Augmented 14-mosdegree A14md
17 Augmented 7-mosdegree A7md
16 Augmented 0-mosdegree A0md
15 Augmented 9-mosdegree A9md
14 Major 2-mosdegree M2md
13 Major 11-mosdegree M11md
12 Major 4-mosdegree M4md
11 Major 13-mosdegree M13md
10 Major 6-mosdegree M6md
9 Major 15-mosdegree M15md
8 Major 8-mosdegree M8md
7 Major 1-mosdegree M1md
6 Major 10-mosdegree M10md
5 Major 3-mosdegree M3md
4 Major 12-mosdegree M12md
3 Major 5-mosdegree M5md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 16-mosdegree		 P0md
P16md
−1 Perfect 9-mosdegree P9md
−2 Minor 2-mosdegree m2md
−3 Minor 11-mosdegree m11md
−4 Minor 4-mosdegree m4md
−5 Minor 13-mosdegree m13md
−6 Minor 6-mosdegree m6md
−7 Minor 15-mosdegree m15md
−8 Minor 8-mosdegree m8md
−9 Minor 1-mosdegree m1md
−10 Minor 10-mosdegree m10md
−11 Minor 3-mosdegree m3md
−12 Minor 12-mosdegree m12md
−13 Minor 5-mosdegree m5md
−14 Minor 14-mosdegree m14md
−15 Diminished 7-mosdegree d7md
−16 Diminished 16-mosdegree d16md
−17 Diminished 9-mosdegree d9md
−18 Diminished 2-mosdegree d2md
−19 Diminished 11-mosdegree d11md
−20 Diminished 4-mosdegree d4md
−21 Diminished 13-mosdegree d13md
−22 Diminished 6-mosdegree d6md
−23 Diminished 15-mosdegree d15md
−24 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 9L 7s
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 LLsLsLsLLsLsLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|1 8 LLsLsLsLsLLsLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|2 15 LsLLsLsLsLLsLsLs Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|3 6 LsLLsLsLsLsLLsLs Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf.
11|4 13 LsLsLLsLsLsLLsLs Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf.
10|5 4 LsLsLLsLsLsLsLLs Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf.
9|6 11 LsLsLsLLsLsLsLLs Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf.
8|7 2 LsLsLsLLsLsLsLsL Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
7|8 9 LsLsLsLsLLsLsLsL Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
6|9 16 sLLsLsLsLLsLsLsL Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
5|10 7 sLLsLsLsLsLLsLsL Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf.
4|11 14 sLsLLsLsLsLLsLsL Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf.
3|12 5 sLsLLsLsLsLsLLsL Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf.
2|13 12 sLsLsLLsLsLsLLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf.
1|14 3 sLsLsLLsLsLsLsLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|15 10 sLsLsLsLLsLsLsLL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\16 525.000 675.000 1:1 1.000 Equalized 9L 7s
39\89 525.843 674.157 6:5 1.200
32\73 526.027 673.973 5:4 1.250
57\130 526.154 673.846 9:7 1.286 Armodue is around here
25\57 526.316 673.684 4:3 1.333 Supersoft 9L 7s
68\155 526.452 673.548 11:8 1.375
43\98 526.531 673.469 7:5 1.400 Trismegistus is around here
61\139 526.619 673.381 10:7 1.429
18\41 526.829 673.171 3:2 1.500 Soft 9L 7s
65\148 527.027 672.973 11:7 1.571
47\107 527.103 672.897 8:5 1.600
76\173 527.168 672.832 13:8 1.625
29\66 527.273 672.727 5:3 1.667 Semisoft 9L 7s
69\157 527.389 672.611 12:7 1.714
40\91 527.473 672.527 7:4 1.750
51\116 527.586 672.414 9:5 1.800
11\25 528.000 672.000 2:1 2.000 Basic 9L 7s
Scales with tunings softer than this are proper
48\109 528.440 671.560 9:4 2.250
37\84 528.571 671.429 7:3 2.333
63\143 528.671 671.329 12:5 2.400
26\59 528.814 671.186 5:2 2.500 Semihard 9L 7s
67\152 528.947 671.053 13:5 2.600
41\93 529.032 670.968 8:3 2.667
56\127 529.134 670.866 11:4 2.750
15\34 529.412 670.588 3:1 3.000 Hard 9L 7s
49\111 529.730 670.270 10:3 3.333 Mabila (5-limit) is around here
34\77 529.870 670.130 7:2 3.500
53\120 530.000 670.000 11:3 3.667 Amavil is around here
19\43 530.233 669.767 4:1 4.000 Superhard 9L 7s
42\95 530.526 669.474 9:2 4.500
23\52 530.769 669.231 5:1 5.000
27\61 531.148 668.852 6:1 6.000
4\9 533.333 666.667 1:0 → ∞ Collapsed 9L 7s
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