18L 5s

↖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 (oneirotonic)
Required 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
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	Rotational 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

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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