18L 9s

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Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 1\9 (133.3 ¢)
Generator size
Bright 1\27 to 1\18 (44.4 ¢ to 66.7 ¢)
Dark 1\18 to 2\27 (66.7 ¢ to 88.9 ¢)
TAMNAMS information
Related to 9L 9s
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 9L 9s
Sister 9L 18s
Daughters 27L 18s, 18L 27s
Neutralized 9L 18s
2-Flought 45L 9s, 18L 36s
Equal tunings
Equalized (L:s = 1:1) 1\27 (44.4 ¢)
Supersoft (L:s = 4:3) 4\99 (48.5 ¢)
Soft (L:s = 3:2) 3\72 (50.0 ¢)
Semisoft (L:s = 5:3) 5\117 (51.3 ¢)
Basic (L:s = 2:1) 2\45 (53.3 ¢)
Semihard (L:s = 5:2) 5\108 (55.6 ¢)
Hard (L:s = 3:1) 3\63 (57.1 ¢)
Superhard (L:s = 4:1) 4\81 (59.3 ¢)
Collapsed (L:s = 1:0) 1\18 (66.7 ¢)

18L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 9 small steps, with a period of 2 large steps and 1 small step that repeats every 133.3 ¢, or 9 times every octave. 18L 9s is a child scale of 9L 9s, expanding it by 9 tones. Generators that produce this scale range from 44.4 ¢ to 66.7 ¢, or from 66.7 ¢ to 88.9 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

This MOS scale is associated with ennealimmal temperament.

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 18L 9s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 44.4 ¢
Perfect 1-mosstep P1ms L 44.4 ¢ to 66.7 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 66.7 ¢ to 88.9 ¢
Augmented 2-mosstep A2ms 2L 88.9 ¢ to 133.3 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 133.3 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 133.3 ¢ to 177.8 ¢
Perfect 4-mosstep P4ms 3L + s 177.8 ¢ to 200.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 200.0 ¢ to 222.2 ¢
Augmented 5-mosstep A5ms 4L + s 222.2 ¢ to 266.7 ¢
6-mosstep Perfect 6-mosstep P6ms 4L + 2s 266.7 ¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 266.7 ¢ to 311.1 ¢
Perfect 7-mosstep P7ms 5L + 2s 311.1 ¢ to 333.3 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 333.3 ¢ to 355.6 ¢
Augmented 8-mosstep A8ms 6L + 2s 355.6 ¢ to 400.0 ¢
9-mosstep Perfect 9-mosstep P9ms 6L + 3s 400.0 ¢
10-mosstep Diminished 10-mosstep d10ms 6L + 4s 400.0 ¢ to 444.4 ¢
Perfect 10-mosstep P10ms 7L + 3s 444.4 ¢ to 466.7 ¢
11-mosstep Perfect 11-mosstep P11ms 7L + 4s 466.7 ¢ to 488.9 ¢
Augmented 11-mosstep A11ms 8L + 3s 488.9 ¢ to 533.3 ¢
12-mosstep Perfect 12-mosstep P12ms 8L + 4s 533.3 ¢
13-mosstep Diminished 13-mosstep d13ms 8L + 5s 533.3 ¢ to 577.8 ¢
Perfect 13-mosstep P13ms 9L + 4s 577.8 ¢ to 600.0 ¢
14-mosstep Perfect 14-mosstep P14ms 9L + 5s 600.0 ¢ to 622.2 ¢
Augmented 14-mosstep A14ms 10L + 4s 622.2 ¢ to 666.7 ¢
15-mosstep Perfect 15-mosstep P15ms 10L + 5s 666.7 ¢
16-mosstep Diminished 16-mosstep d16ms 10L + 6s 666.7 ¢ to 711.1 ¢
Perfect 16-mosstep P16ms 11L + 5s 711.1 ¢ to 733.3 ¢
17-mosstep Perfect 17-mosstep P17ms 11L + 6s 733.3 ¢ to 755.6 ¢
Augmented 17-mosstep A17ms 12L + 5s 755.6 ¢ to 800.0 ¢
18-mosstep Perfect 18-mosstep P18ms 12L + 6s 800.0 ¢
19-mosstep Diminished 19-mosstep d19ms 12L + 7s 800.0 ¢ to 844.4 ¢
Perfect 19-mosstep P19ms 13L + 6s 844.4 ¢ to 866.7 ¢
20-mosstep Perfect 20-mosstep P20ms 13L + 7s 866.7 ¢ to 888.9 ¢
Augmented 20-mosstep A20ms 14L + 6s 888.9 ¢ to 933.3 ¢
21-mosstep Perfect 21-mosstep P21ms 14L + 7s 933.3 ¢
22-mosstep Diminished 22-mosstep d22ms 14L + 8s 933.3 ¢ to 977.8 ¢
Perfect 22-mosstep P22ms 15L + 7s 977.8 ¢ to 1000.0 ¢
23-mosstep Perfect 23-mosstep P23ms 15L + 8s 1000.0 ¢ to 1022.2 ¢
Augmented 23-mosstep A23ms 16L + 7s 1022.2 ¢ to 1066.7 ¢
24-mosstep Perfect 24-mosstep P24ms 16L + 8s 1066.7 ¢
25-mosstep Diminished 25-mosstep d25ms 16L + 9s 1066.7 ¢ to 1111.1 ¢
Perfect 25-mosstep P25ms 17L + 8s 1111.1 ¢ to 1133.3 ¢
26-mosstep Perfect 26-mosstep P26ms 17L + 9s 1133.3 ¢ to 1155.6 ¢
Augmented 26-mosstep A26ms 18L + 8s 1155.6 ¢ to 1200.0 ¢
27-mosstep Perfect 27-mosstep P27ms 18L + 9s 1200.0 ¢

Generator chain

Generator chain of 18L 9s
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.
4 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
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 2-mosdegree A2md Augmented 5-mosdegree A5md Augmented 8-mosdegree A8md Augmented 11-mosdegree A11md Augmented 14-mosdegree A14md Augmented 17-mosdegree A17md Augmented 20-mosdegree A20md Augmented 23-mosdegree A23md Augmented 26-mosdegree A26md
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
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 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
−2 Diminished 1-mosdegree d1md Diminished 4-mosdegree d4md Diminished 7-mosdegree d7md Diminished 10-mosdegree d10md Diminished 13-mosdegree d13md Diminished 16-mosdegree d16md Diminished 19-mosdegree d19md Diminished 22-mosdegree d22md Diminished 25-mosdegree d25md
−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
−4 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

Modes

Scale degrees of the modes of 18L 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 17 18 19 20 21 22 23 24 25 26 27
18|0(9) 1 LLsLLsLLsLLsLLsLLsLLsLLsLLs 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. Aug. Perf.
9|9(9) 2 LsLLsLLsLLsLLsLLsLLsLLsLLsL 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) 3 sLLsLLsLLsLLsLLsLLsLLsLLsLL 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. Perf.

Scale tree

Scale tree and tuning spectrum of 18L 9s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\27 44.444 88.889 1:1 1.000 Equalized 18L 9s
6\153 47.059 86.275 6:5 1.200
5\126 47.619 85.714 5:4 1.250
9\225 48.000 85.333 9:7 1.286
4\99 48.485 84.848 4:3 1.333 Supersoft 18L 9s
11\270 48.889 84.444 11:8 1.375
7\171 49.123 84.211 7:5 1.400
10\243 49.383 83.951 10:7 1.429
3\72 50.000 83.333 3:2 1.500 Soft 18L 9s
11\261 50.575 82.759 11:7 1.571
8\189 50.794 82.540 8:5 1.600
13\306 50.980 82.353 13:8 1.625
5\117 51.282 82.051 5:3 1.667 Semisoft 18L 9s
12\279 51.613 81.720 12:7 1.714
7\162 51.852 81.481 7:4 1.750
9\207 52.174 81.159 9:5 1.800
2\45 53.333 80.000 2:1 2.000 Basic 18L 9s
9\198 54.545 78.788 9:4 2.250
7\153 54.902 78.431 7:3 2.333
12\261 55.172 78.161 12:5 2.400
5\108 55.556 77.778 5:2 2.500 Semihard 18L 9s
13\279 55.914 77.419 13:5 2.600
8\171 56.140 77.193 8:3 2.667
11\234 56.410 76.923 11:4 2.750
3\63 57.143 76.190 3:1 3.000 Hard 18L 9s
10\207 57.971 75.362 10:3 3.333
7\144 58.333 75.000 7:2 3.500
11\225 58.667 74.667 11:3 3.667
4\81 59.259 74.074 4:1 4.000 Superhard 18L 9s
9\180 60.000 73.333 9:2 4.500
5\99 60.606 72.727 5:1 5.000
6\117 61.538 71.795 6:1 6.000
1\18 66.667 66.667 1:0 → ∞ Collapsed 18L 9s
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