18L 5s

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↖ 17L 4s ↑ 18L 4s 19L 4s ↗
← 17L 5s 18L 5s 19L 5s →
↙ 17L 6s ↓ 18L 6s 19L 6s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║│║║║║│║║║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLsLLLLsLLLs
sLLLsLLLLsLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 14\23 to 11\18 (730.4¢ to 733.3¢)
Dark 7\18 to 9\23 (466.7¢ to 469.6¢)
TAMNAMS information
Descends from 5L 3s
Ancestor's step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 5L 13s
Sister 5L 18s
Daughters 23L 18s, 18L 23s
Neutralized 13L 10s
2-Flought 41L 5s, 18L 28s
Equal tunings
Equalized (L:s = 1:1) 14\23 (730.4¢)
Supersoft (L:s = 4:3) 53\87 (731.0¢)
Soft (L:s = 3:2) 39\64 (731.2¢)
Semisoft (L:s = 5:3) 64\105 (731.4¢)
Basic (L:s = 2:1) 25\41 (731.7¢)
Semihard (L:s = 5:2) 61\100 (732.0¢)
Hard (L:s = 3:1) 36\59 (732.2¢)
Superhard (L:s = 4:1) 47\77 (732.5¢)
Collapsed (L:s = 1:0) 11\18 (733.3¢)

18L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 5 small steps, repeating every octave. 18L 5s is a great-grandchild scale of 5L 3s, expanding it by 15 tones. Generators that produce this scale range from 730.4¢ to 733.3¢, or from 466.7¢ to 469.6¢.

Modes

Modes of 18L 5s
UDP Cyclic
order		 Step
pattern
22|0 1 LLLLsLLLLsLLLsLLLLsLLLs
21|1 15 LLLLsLLLsLLLLsLLLLsLLLs
20|2 6 LLLLsLLLsLLLLsLLLsLLLLs
19|3 20 LLLsLLLLsLLLLsLLLsLLLLs
18|4 11 LLLsLLLLsLLLsLLLLsLLLLs
17|5 2 LLLsLLLLsLLLsLLLLsLLLsL
16|6 16 LLLsLLLsLLLLsLLLLsLLLsL
15|7 7 LLLsLLLsLLLLsLLLsLLLLsL
14|8 21 LLsLLLLsLLLLsLLLsLLLLsL
13|9 12 LLsLLLLsLLLsLLLLsLLLLsL
12|10 3 LLsLLLLsLLLsLLLLsLLLsLL
11|11 17 LLsLLLsLLLLsLLLLsLLLsLL
10|12 8 LLsLLLsLLLLsLLLsLLLLsLL
9|13 22 LsLLLLsLLLLsLLLsLLLLsLL
8|14 13 LsLLLLsLLLsLLLLsLLLLsLL
7|15 4 LsLLLLsLLLsLLLLsLLLsLLL
6|16 18 LsLLLsLLLLsLLLLsLLLsLLL
5|17 9 LsLLLsLLLLsLLLsLLLLsLLL
4|18 23 sLLLLsLLLLsLLLsLLLLsLLL
3|19 14 sLLLLsLLLsLLLLsLLLLsLLL
2|20 5 sLLLLsLLLsLLLLsLLLsLLLL
1|21 19 sLLLsLLLLsLLLLsLLLsLLLL
0|22 10 sLLLsLLLLsLLLsLLLLsLLLL

Intervals

Intervals of 18L 5s
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 52.2¢
Major 1-mosstep M1ms L 52.2¢ to 66.7¢
2-mosstep Minor 2-mosstep m2ms L + s 66.7¢ to 104.3¢
Major 2-mosstep M2ms 2L 104.3¢ to 133.3¢
3-mosstep Minor 3-mosstep m3ms 2L + s 133.3¢ to 156.5¢
Major 3-mosstep M3ms 3L 156.5¢ to 200.0¢
4-mosstep Minor 4-mosstep m4ms 3L + s 200.0¢ to 208.7¢
Major 4-mosstep M4ms 4L 208.7¢ to 266.7¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 200.0¢ to 260.9¢
Major 5-mosstep M5ms 4L + s 260.9¢ to 266.7¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 266.7¢ to 313.0¢
Major 6-mosstep M6ms 5L + s 313.0¢ to 333.3¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 333.3¢ to 365.2¢
Major 7-mosstep M7ms 6L + s 365.2¢ to 400.0¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 400.0¢ to 417.4¢
Major 8-mosstep M8ms 7L + s 417.4¢ to 466.7¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 466.7¢ to 469.6¢
Augmented 9-mosstep A9ms 8L + s 469.6¢ to 533.3¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 466.7¢ to 521.7¢
Major 10-mosstep M10ms 8L + 2s 521.7¢ to 533.3¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 533.3¢ to 573.9¢
Major 11-mosstep M11ms 9L + 2s 573.9¢ to 600.0¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 600.0¢ to 626.1¢
Major 12-mosstep M12ms 10L + 2s 626.1¢ to 666.7¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 666.7¢ to 678.3¢
Major 13-mosstep M13ms 11L + 2s 678.3¢ to 733.3¢
14-mosstep Diminished 14-mosstep d14ms 10L + 4s 666.7¢ to 730.4¢
Perfect 14-mosstep P14ms 11L + 3s 730.4¢ to 733.3¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 733.3¢ to 782.6¢
Major 15-mosstep M15ms 12L + 3s 782.6¢ to 800.0¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 800.0¢ to 834.8¢
Major 16-mosstep M16ms 13L + 3s 834.8¢ to 866.7¢
17-mosstep Minor 17-mosstep m17ms 13L + 4s 866.7¢ to 887.0¢
Major 17-mosstep M17ms 14L + 3s 887.0¢ to 933.3¢
18-mosstep Minor 18-mosstep m18ms 14L + 4s 933.3¢ to 939.1¢
Major 18-mosstep M18ms 15L + 3s 939.1¢ to 1000.0¢
19-mosstep Minor 19-mosstep m19ms 14L + 5s 933.3¢ to 991.3¢
Major 19-mosstep M19ms 15L + 4s 991.3¢ to 1000.0¢
20-mosstep Minor 20-mosstep m20ms 15L + 5s 1000.0¢ to 1043.5¢
Major 20-mosstep M20ms 16L + 4s 1043.5¢ to 1066.7¢
21-mosstep Minor 21-mosstep m21ms 16L + 5s 1066.7¢ to 1095.7¢
Major 21-mosstep M21ms 17L + 4s 1095.7¢ to 1133.3¢
22-mosstep Minor 22-mosstep m22ms 17L + 5s 1133.3¢ to 1147.8¢
Major 22-mosstep M22ms 18L + 4s 1147.8¢ to 1200.0¢
23-mosstep Perfect 23-mosstep P23ms 18L + 5s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 18L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
14\23 730.435 469.565 1:1 1.000 Equalized 18L 5s
81\133 730.827 469.173 6:5 1.200
67\110 730.909 469.091 5:4 1.250
120\197 730.964 469.036 9:7 1.286
53\87 731.034 468.966 4:3 1.333 Supersoft 18L 5s
145\238 731.092 468.908 11:8 1.375
92\151 731.126 468.874 7:5 1.400
131\215 731.163 468.837 10:7 1.429
39\64 731.250 468.750 3:2 1.500 Soft 18L 5s
142\233 731.330 468.670 11:7 1.571
103\169 731.361 468.639 8:5 1.600
167\274 731.387 468.613 13:8 1.625
64\105 731.429 468.571 5:3 1.667 Semisoft 18L 5s
153\251 731.474 468.526 12:7 1.714
89\146 731.507 468.493 7:4 1.750
114\187 731.551 468.449 9:5 1.800
25\41 731.707 468.293 2:1 2.000 Basic 18L 5s
Scales with tunings softer than this are proper
111\182 731.868 468.132 9:4 2.250
86\141 731.915 468.085 7:3 2.333
147\241 731.950 468.050 12:5 2.400
61\100 732.000 468.000 5:2 2.500 Semihard 18L 5s
158\259 732.046 467.954 13:5 2.600
97\159 732.075 467.925 8:3 2.667
133\218 732.110 467.890 11:4 2.750
36\59 732.203 467.797 3:1 3.000 Hard 18L 5s
119\195 732.308 467.692 10:3 3.333
83\136 732.353 467.647 7:2 3.500
130\213 732.394 467.606 11:3 3.667
47\77 732.468 467.532 4:1 4.000 Superhard 18L 5s
105\172 732.558 467.442 9:2 4.500
58\95 732.632 467.368 5:1 5.000
69\113 732.743 467.257 6:1 6.000
11\18 733.333 466.667 1:0 → ∞ Collapsed 18L 5s


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