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
Related to	5L 3s (oneirotonic)
With tunings	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 ¢)
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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

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

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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