5L 18s

↖ 4L 17s	↑ 5L 17s	6L 17s ↗
← 4L 18s	5L 18s	6L 18s →
↙ 4L 19s	↓ 5L 19s	6L 19s ↘

┌╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║│││║││││║│││║││││║│││││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLssssLsssLssssLssss ssssLssssLsssLssssLsssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	9\23 to 2\5 (469.6¢ to 480.0¢)
Dark	3\5 to 14\23 (720.0¢ to 730.4¢)
TAMNAMS information
Descends from	5L 3s (oneirotonic)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 13s
Sister	18L 5s
Daughters	23L 5s, 5L 23s
Neutralized	10L 13s
2-Flought	28L 18s, 5L 41s
Equal tunings
Equalized (L:s = 1:1)	9\23 (469.6¢)
Supersoft (L:s = 4:3)	29\74 (470.3¢)
Soft (L:s = 3:2)	20\51 (470.6¢)
Semisoft (L:s = 5:3)	31\79 (470.9¢)
Basic (L:s = 2:1)	11\28 (471.4¢)
Semihard (L:s = 5:2)	24\61 (472.1¢)
Hard (L:s = 3:1)	13\33 (472.7¢)
Superhard (L:s = 4:1)	15\38 (473.7¢)
Collapsed (L:s = 1:0)	2\5 (480.0¢)

5L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 18 small steps, repeating every octave. 5L 18s is a great-grandchild scale of 5L 3s, expanding it by 15 tones. Generators that produce this scale range from 469.6¢ to 480¢, or from 720¢ to 730.4¢.

Modes

Modes of 5L 18s

UDP	Cyclic order	Step pattern
22|0	1	LsssLssssLsssLssssLssss
21|1	10	LsssLssssLssssLsssLssss
20|2	19	LssssLsssLssssLsssLssss
19|3	5	LssssLsssLssssLssssLsss
18|4	14	LssssLssssLsssLssssLsss
17|5	23	sLsssLssssLsssLssssLsss
16|6	9	sLsssLssssLssssLsssLsss
15|7	18	sLssssLsssLssssLsssLsss
14|8	4	sLssssLsssLssssLssssLss
13|9	13	sLssssLssssLsssLssssLss
12|10	22	ssLsssLssssLsssLssssLss
11|11	8	ssLsssLssssLssssLsssLss
10|12	17	ssLssssLsssLssssLsssLss
9|13	3	ssLssssLsssLssssLssssLs
8|14	12	ssLssssLssssLsssLssssLs
7|15	21	sssLsssLssssLsssLssssLs
6|16	7	sssLsssLssssLssssLsssLs
5|17	16	sssLssssLsssLssssLsssLs
4|18	2	sssLssssLsssLssssLssssL
3|19	11	sssLssssLssssLsssLssssL
2|20	20	ssssLsssLssssLsssLssssL
1|21	6	ssssLsssLssssLssssLsssL
0|22	15	ssssLssssLsssLssssLsssL

Scale tree

Scale Tree and Tuning Spectrum of 5L 18s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\23						469.565	730.435	1:1	1.000	Equalized 5L 18s
					47\120	470.000	730.000	6:5	1.200
				38\97		470.103	729.897	5:4	1.250
					67\171	470.175	729.825	9:7	1.286
			29\74			470.270	729.730	4:3	1.333	Supersoft 5L 18s
					78\199	470.352	729.648	11:8	1.375
				49\125		470.400	729.600	7:5	1.400
					69\176	470.455	729.545	10:7	1.429
		20\51				470.588	729.412	3:2	1.500	Soft 5L 18s
					71\181	470.718	729.282	11:7	1.571
				51\130		470.769	729.231	8:5	1.600
					82\209	470.813	729.187	13:8	1.625
			31\79			470.886	729.114	5:3	1.667	Semisoft 5L 18s
					73\186	470.968	729.032	12:7	1.714
				42\107		471.028	728.972	7:4	1.750
					53\135	471.111	728.889	9:5	1.800
	11\28					471.429	728.571	2:1	2.000	Basic 5L 18s Scales with tunings softer than this are proper
					46\117	471.795	728.205	9:4	2.250
				35\89		471.910	728.090	7:3	2.333
					59\150	472.000	728.000	12:5	2.400
			24\61			472.131	727.869	5:2	2.500	Semihard 5L 18s
					61\155	472.258	727.742	13:5	2.600
				37\94		472.340	727.660	8:3	2.667
					50\127	472.441	727.559	11:4	2.750
		13\33				472.727	727.273	3:1	3.000	Hard 5L 18s
					41\104	473.077	726.923	10:3	3.333
				28\71		473.239	726.761	7:2	3.500
					43\109	473.394	726.606	11:3	3.667
			15\38			473.684	726.316	4:1	4.000	Superhard 5L 18s
					32\81	474.074	725.926	9:2	4.500
				17\43		474.419	725.581	5:1	5.000
					19\48	475.000	725.000	6:1	6.000
2\5						480.000	720.000	1:0	→ ∞	Collapsed 5L 18s