18L 5s
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Step pattern
LLLLsLLLLsLLLsLLLLsLLLs
sLLLsLLLLsLLLsLLLLsLLLL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
14\23 to 11\18 (730.4 ¢ to 733.3 ¢)
Dark
7\18 to 9\23 (466.7 ¢ to 469.6 ¢)
Related to
5L 3s (oneirotonic)
With tunings
3:1 to 4:1 (parahard)
Parent
5L 13s
Sister
5L 18s
Daughters
23L 18s, 18L 23s
Neutralized
13L 10s
2-Flought
41L 5s, 18L 28s
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 ¢)
| ↖ 17L 4s | ↑ 18L 4s | 19L 4s ↗ |
| ← 17L 5s | 18L 5s | 19L 5s → |
| ↙ 17L 6s | ↓ 18L 6s | 19L 6s ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║║│║║║│║║║║│║║║││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLLsLLLLsLLLsLLLLsLLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 ¢.
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 diatonic interval categories.
Intervals
| 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 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 40 | Augmented 8-mosdegree | A8md |
| 39 | Augmented 17-mosdegree | A17md |
| 38 | Augmented 3-mosdegree | A3md |
| 37 | Augmented 12-mosdegree | A12md |
| 36 | Augmented 21-mosdegree | A21md |
| 35 | Augmented 7-mosdegree | A7md |
| 34 | Augmented 16-mosdegree | A16md |
| 33 | Augmented 2-mosdegree | A2md |
| 32 | Augmented 11-mosdegree | A11md |
| 31 | Augmented 20-mosdegree | A20md |
| 30 | Augmented 6-mosdegree | A6md |
| 29 | Augmented 15-mosdegree | A15md |
| 28 | Augmented 1-mosdegree | A1md |
| 27 | Augmented 10-mosdegree | A10md |
| 26 | Augmented 19-mosdegree | A19md |
| 25 | Augmented 5-mosdegree | A5md |
| 24 | Augmented 14-mosdegree | A14md |
| 23 | Augmented 0-mosdegree | A0md |
| 22 | Augmented 9-mosdegree | A9md |
| 21 | Major 18-mosdegree | M18md |
| 20 | Major 4-mosdegree | M4md |
| 19 | Major 13-mosdegree | M13md |
| 18 | Major 22-mosdegree | M22md |
| 17 | Major 8-mosdegree | M8md |
| 16 | Major 17-mosdegree | M17md |
| 15 | Major 3-mosdegree | M3md |
| 14 | Major 12-mosdegree | M12md |
| 13 | Major 21-mosdegree | M21md |
| 12 | Major 7-mosdegree | M7md |
| 11 | Major 16-mosdegree | M16md |
| 10 | Major 2-mosdegree | M2md |
| 9 | Major 11-mosdegree | M11md |
| 8 | Major 20-mosdegree | M20md |
| 7 | Major 6-mosdegree | M6md |
| 6 | Major 15-mosdegree | M15md |
| 5 | Major 1-mosdegree | M1md |
| 4 | Major 10-mosdegree | M10md |
| 3 | Major 19-mosdegree | M19md |
| 2 | Major 5-mosdegree | M5md |
| 1 | Perfect 14-mosdegree | P14md |
| 0 | Perfect 0-mosdegree Perfect 23-mosdegree |
P0md P23md |
| −1 | Perfect 9-mosdegree | P9md |
| −2 | Minor 18-mosdegree | m18md |
| −3 | Minor 4-mosdegree | m4md |
| −4 | Minor 13-mosdegree | m13md |
| −5 | Minor 22-mosdegree | m22md |
| −6 | Minor 8-mosdegree | m8md |
| −7 | Minor 17-mosdegree | m17md |
| −8 | Minor 3-mosdegree | m3md |
| −9 | Minor 12-mosdegree | m12md |
| −10 | Minor 21-mosdegree | m21md |
| −11 | Minor 7-mosdegree | m7md |
| −12 | Minor 16-mosdegree | m16md |
| −13 | Minor 2-mosdegree | m2md |
| −14 | Minor 11-mosdegree | m11md |
| −15 | Minor 20-mosdegree | m20md |
| −16 | Minor 6-mosdegree | m6md |
| −17 | Minor 15-mosdegree | m15md |
| −18 | Minor 1-mosdegree | m1md |
| −19 | Minor 10-mosdegree | m10md |
| −20 | Minor 19-mosdegree | m19md |
| −21 | Minor 5-mosdegree | m5md |
| −22 | Diminished 14-mosdegree | d14md |
| −23 | Diminished 23-mosdegree | d23md |
| −24 | Diminished 9-mosdegree | d9md |
| −25 | Diminished 18-mosdegree | d18md |
| −26 | Diminished 4-mosdegree | d4md |
| −27 | Diminished 13-mosdegree | d13md |
| −28 | Diminished 22-mosdegree | d22md |
| −29 | Diminished 8-mosdegree | d8md |
| −30 | Diminished 17-mosdegree | d17md |
| −31 | Diminished 3-mosdegree | d3md |
| −32 | Diminished 12-mosdegree | d12md |
| −33 | Diminished 21-mosdegree | d21md |
| −34 | Diminished 7-mosdegree | d7md |
| −35 | Diminished 16-mosdegree | d16md |
| −36 | Diminished 2-mosdegree | d2md |
| −37 | Diminished 11-mosdegree | d11md |
| −38 | Diminished 20-mosdegree | d20md |
| −39 | Diminished 6-mosdegree | d6md |
| −40 | Diminished 15-mosdegree | d15md |
Modes
| 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 | |||
| 22|0 | 1 | LLLLsLLLLsLLLsLLLLsLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 21|1 | 15 | LLLLsLLLsLLLLsLLLLsLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 20|2 | 6 | LLLLsLLLsLLLLsLLLsLLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 19|3 | 20 | LLLsLLLLsLLLLsLLLsLLLLs | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 18|4 | 11 | LLLsLLLLsLLLsLLLLsLLLLs | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 17|5 | 2 | LLLsLLLLsLLLsLLLLsLLLsL | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Perf. |
| 16|6 | 16 | LLLsLLLsLLLLsLLLLsLLLsL | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Perf. |
| 15|7 | 7 | LLLsLLLsLLLLsLLLsLLLLsL | Perf. | Maj. | Maj. | Maj. | Min. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. |
| 14|8 | 21 | LLsLLLLsLLLLsLLLsLLLLsL | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. |
| 13|9 | 12 | LLsLLLLsLLLsLLLLsLLLLsL | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. |
| 12|10 | 3 | LLsLLLLsLLLsLLLLsLLLsLL | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Maj. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. |
| 11|11 | 17 | LLsLLLsLLLLsLLLLsLLLsLL | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. |
| 10|12 | 8 | LLsLLLsLLLLsLLLsLLLLsLL | Perf. | Maj. | Maj. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. |
| 9|13 | 22 | LsLLLLsLLLLsLLLsLLLLsLL | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. |
| 8|14 | 13 | LsLLLLsLLLsLLLLsLLLLsLL | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. |
| 7|15 | 4 | LsLLLLsLLLsLLLLsLLLsLLL | Perf. | Maj. | Min. | Min. | Min. | Maj. | Maj. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 6|16 | 18 | LsLLLsLLLLsLLLLsLLLsLLL | Perf. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 5|17 | 9 | LsLLLsLLLLsLLLsLLLLsLLL | Perf. | Maj. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 4|18 | 23 | sLLLLsLLLLsLLLsLLLLsLLL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 3|19 | 14 | sLLLLsLLLsLLLLsLLLLsLLL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. |
| 2|20 | 5 | sLLLLsLLLsLLLLsLLLsLLLL | Perf. | Min. | Min. | Min. | Min. | Maj. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 1|21 | 19 | sLLLsLLLLsLLLLsLLLsLLLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|22 | 10 | sLLLsLLLLsLLLsLLLLsLLLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
Scale tree
| 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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