9L 18s

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↖ 8L 17s ↑ 9L 17s 10L 17s ↗
← 8L 18s 9L 18s 10L 18s →
↙ 8L 19s ↓ 9L 19s 10L 19s ↘ 
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Scale structure
Step pattern LssLssLssLssLssLssLssLssLss
ssLssLssLssLssLssLssLssLssL
Equave 2/1 (1200.0 ¢)
Period 1\9 (133.3 ¢)
Generator size
Bright 2\27 to 1\9 (88.9 ¢ to 133.3 ¢)
Dark 0\9 to 1\27 (0.0 ¢ to 44.4 ¢)
TAMNAMS information
Related to 9L 9s
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 9L 9s
Sister 18L 9s
Daughters 27L 9s, 9L 27s
Neutralized 18L 9s
2-Flought 36L 18s, 9L 45s
Equal tunings
Equalized (L:s = 1:1) 2\27 (88.9 ¢)
Supersoft (L:s = 4:3) 7\90 (93.3 ¢)
Soft (L:s = 3:2) 5\63 (95.2 ¢)
Semisoft (L:s = 5:3) 8\99 (97.0 ¢)
Basic (L:s = 2:1) 3\36 (100.0 ¢)
Semihard (L:s = 5:2) 7\81 (103.7 ¢)
Hard (L:s = 3:1) 4\45 (106.7 ¢)
Superhard (L:s = 4:1) 5\54 (111.1 ¢)
Collapsed (L:s = 1:0) 1\9 (133.3 ¢)

9L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 18 small steps, with a period of 1 large step and 2 small steps that repeats every 133.3 ¢, or 9 times every octave. 9L 18s is a child scale of 9L 9s, expanding it by 9 tones. Generators that produce this scale range from 88.9 ¢ to 133.3 ¢, or from 0 ¢ to 44.4 ¢.

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 18s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 44.4 ¢
Augmented 1-mosstep A1ms L 44.4 ¢ to 133.3 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 88.9 ¢
Perfect 2-mosstep P2ms L + s 88.9 ¢ to 133.3 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 133.3 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 133.3 ¢ to 177.8 ¢
Augmented 4-mosstep A4ms 2L + 2s 177.8 ¢ to 266.7 ¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 133.3 ¢ to 222.2 ¢
Perfect 5-mosstep P5ms 2L + 3s 222.2 ¢ to 266.7 ¢
6-mosstep Perfect 6-mosstep P6ms 2L + 4s 266.7 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 266.7 ¢ to 311.1 ¢
Augmented 7-mosstep A7ms 3L + 4s 311.1 ¢ to 400.0 ¢
8-mosstep Diminished 8-mosstep d8ms 2L + 6s 266.7 ¢ to 355.6 ¢
Perfect 8-mosstep P8ms 3L + 5s 355.6 ¢ to 400.0 ¢
9-mosstep Perfect 9-mosstep P9ms 3L + 6s 400.0 ¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 400.0 ¢ to 444.4 ¢
Augmented 10-mosstep A10ms 4L + 6s 444.4 ¢ to 533.3 ¢
11-mosstep Diminished 11-mosstep d11ms 3L + 8s 400.0 ¢ to 488.9 ¢
Perfect 11-mosstep P11ms 4L + 7s 488.9 ¢ to 533.3 ¢
12-mosstep Perfect 12-mosstep P12ms 4L + 8s 533.3 ¢
13-mosstep Perfect 13-mosstep P13ms 4L + 9s 533.3 ¢ to 577.8 ¢
Augmented 13-mosstep A13ms 5L + 8s 577.8 ¢ to 666.7 ¢
14-mosstep Diminished 14-mosstep d14ms 4L + 10s 533.3 ¢ to 622.2 ¢
Perfect 14-mosstep P14ms 5L + 9s 622.2 ¢ to 666.7 ¢
15-mosstep Perfect 15-mosstep P15ms 5L + 10s 666.7 ¢
16-mosstep Perfect 16-mosstep P16ms 5L + 11s 666.7 ¢ to 711.1 ¢
Augmented 16-mosstep A16ms 6L + 10s 711.1 ¢ to 800.0 ¢
17-mosstep Diminished 17-mosstep d17ms 5L + 12s 666.7 ¢ to 755.6 ¢
Perfect 17-mosstep P17ms 6L + 11s 755.6 ¢ to 800.0 ¢
18-mosstep Perfect 18-mosstep P18ms 6L + 12s 800.0 ¢
19-mosstep Perfect 19-mosstep P19ms 6L + 13s 800.0 ¢ to 844.4 ¢
Augmented 19-mosstep A19ms 7L + 12s 844.4 ¢ to 933.3 ¢
20-mosstep Diminished 20-mosstep d20ms 6L + 14s 800.0 ¢ to 888.9 ¢
Perfect 20-mosstep P20ms 7L + 13s 888.9 ¢ to 933.3 ¢
21-mosstep Perfect 21-mosstep P21ms 7L + 14s 933.3 ¢
22-mosstep Perfect 22-mosstep P22ms 7L + 15s 933.3 ¢ to 977.8 ¢
Augmented 22-mosstep A22ms 8L + 14s 977.8 ¢ to 1066.7 ¢
23-mosstep Diminished 23-mosstep d23ms 7L + 16s 933.3 ¢ to 1022.2 ¢
Perfect 23-mosstep P23ms 8L + 15s 1022.2 ¢ to 1066.7 ¢
24-mosstep Perfect 24-mosstep P24ms 8L + 16s 1066.7 ¢
25-mosstep Perfect 25-mosstep P25ms 8L + 17s 1066.7 ¢ to 1111.1 ¢
Augmented 25-mosstep A25ms 9L + 16s 1111.1 ¢ to 1200.0 ¢
26-mosstep Diminished 26-mosstep d26ms 8L + 18s 1066.7 ¢ to 1155.6 ¢
Perfect 26-mosstep P26ms 9L + 17s 1155.6 ¢ to 1200.0 ¢
27-mosstep Perfect 27-mosstep P27ms 9L + 18s 1200.0 ¢

Generator chain

Generator chain of 9L 18s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
3 Augmented 0-mosdegree A0md Augmented 3-mosdegree A3md Augmented 6-mosdegree A6md Augmented 9-mosdegree A9md Augmented 12-mosdegree A12md Augmented 15-mosdegree A15md Augmented 18-mosdegree A18md Augmented 21-mosdegree A21md Augmented 24-mosdegree A24md
2 Augmented 1-mosdegree A1md Augmented 4-mosdegree A4md Augmented 7-mosdegree A7md Augmented 10-mosdegree A10md Augmented 13-mosdegree A13md Augmented 16-mosdegree A16md Augmented 19-mosdegree A19md Augmented 22-mosdegree A22md Augmented 25-mosdegree A25md
1 Perfect 2-mosdegree P2md Perfect 5-mosdegree P5md Perfect 8-mosdegree P8md Perfect 11-mosdegree P11md Perfect 14-mosdegree P14md Perfect 17-mosdegree P17md Perfect 20-mosdegree P20md Perfect 23-mosdegree P23md Perfect 26-mosdegree P26md
0 Perfect 0-mosdegree
Perfect 3-mosdegree		 P0md
P3md		 Perfect 3-mosdegree
Perfect 6-mosdegree		 P3md
P6md		 Perfect 6-mosdegree
Perfect 9-mosdegree		 P6md
P9md		 Perfect 9-mosdegree
Perfect 12-mosdegree		 P9md
P12md		 Perfect 12-mosdegree
Perfect 15-mosdegree		 P12md
P15md		 Perfect 15-mosdegree
Perfect 18-mosdegree		 P15md
P18md		 Perfect 18-mosdegree
Perfect 21-mosdegree		 P18md
P21md		 Perfect 21-mosdegree
Perfect 24-mosdegree		 P21md
P24md		 Perfect 24-mosdegree
Perfect 27-mosdegree		 P24md
P27md
−1 Perfect 1-mosdegree P1md Perfect 4-mosdegree P4md Perfect 7-mosdegree P7md Perfect 10-mosdegree P10md Perfect 13-mosdegree P13md Perfect 16-mosdegree P16md Perfect 19-mosdegree P19md Perfect 22-mosdegree P22md Perfect 25-mosdegree P25md
−2 Diminished 2-mosdegree d2md Diminished 5-mosdegree d5md Diminished 8-mosdegree d8md Diminished 11-mosdegree d11md Diminished 14-mosdegree d14md Diminished 17-mosdegree d17md Diminished 20-mosdegree d20md Diminished 23-mosdegree d23md Diminished 26-mosdegree d26md
−3 Diminished 3-mosdegree d3md Diminished 6-mosdegree d6md Diminished 9-mosdegree d9md Diminished 12-mosdegree d12md Diminished 15-mosdegree d15md Diminished 18-mosdegree d18md Diminished 21-mosdegree d21md Diminished 24-mosdegree d24md Diminished 27-mosdegree d27md

Modes

Scale degrees of the modes of 9L 18s
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 18 19 20 21 22 23 24 25 26 27
18|0(9) 1 LssLssLssLssLssLssLssLssLss Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf.
9|9(9) 3 sLssLssLssLssLssLssLssLssLs Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|18(9) 2 ssLssLssLssLssLssLssLssLssL Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 18s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\27 88.889 44.444 1:1 1.000 Equalized 9L 18s
11\144 91.667 41.667 6:5 1.200
9\117 92.308 41.026 5:4 1.250
16\207 92.754 40.580 9:7 1.286
7\90 93.333 40.000 4:3 1.333 Supersoft 9L 18s
19\243 93.827 39.506 11:8 1.375
12\153 94.118 39.216 7:5 1.400
17\216 94.444 38.889 10:7 1.429
5\63 95.238 38.095 3:2 1.500 Soft 9L 18s
18\225 96.000 37.333 11:7 1.571
13\162 96.296 37.037 8:5 1.600
21\261 96.552 36.782 13:8 1.625
8\99 96.970 36.364 5:3 1.667 Semisoft 9L 18s
19\234 97.436 35.897 12:7 1.714
11\135 97.778 35.556 7:4 1.750
14\171 98.246 35.088 9:5 1.800
3\36 100.000 33.333 2:1 2.000 Basic 9L 18s
Scales with tunings softer than this are proper
13\153 101.961 31.373 9:4 2.250
10\117 102.564 30.769 7:3 2.333
17\198 103.030 30.303 12:5 2.400
7\81 103.704 29.630 5:2 2.500 Semihard 9L 18s
18\207 104.348 28.986 13:5 2.600
11\126 104.762 28.571 8:3 2.667
15\171 105.263 28.070 11:4 2.750
4\45 106.667 26.667 3:1 3.000 Hard 9L 18s
13\144 108.333 25.000 10:3 3.333
9\99 109.091 24.242 7:2 3.500
14\153 109.804 23.529 11:3 3.667
5\54 111.111 22.222 4:1 4.000 Superhard 9L 18s
11\117 112.821 20.513 9:2 4.500
6\63 114.286 19.048 5:1 5.000
7\72 116.667 16.667 6:1 6.000
1\9 133.333 0.000 1:0 → ∞ Collapsed 9L 18s
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