18L 3s

↖ 17L 2s	↑ 18L 2s	19L 2s ↗
← 17L 3s	18L 3s	19L 3s →
↙ 17L 4s	↓ 18L 4s	19L 4s ↘

Scale structure
Step pattern	LLLLLLsLLLLLLsLLLLLLs sLLLLLLsLLLLLLsLLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\21 to 1\18 (57.1 ¢ to 66.7 ¢)
Dark	5\18 to 6\21 (333.3 ¢ to 342.9 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	4:1 to 5:1
Related MOS scales
Parent	3L 15s
Sister	3L 18s
Daughters	21L 18s, 18L 21s
Neutralized	15L 6s
2-Flought	39L 3s, 18L 24s
Equal tunings
Equalized (L:s = 1:1)	1\21 (57.1 ¢)
Supersoft (L:s = 4:3)	4\81 (59.3 ¢)
Soft (L:s = 3:2)	3\60 (60.0 ¢)
Semisoft (L:s = 5:3)	5\99 (60.6 ¢)
Basic (L:s = 2:1)	2\39 (61.5 ¢)
Semihard (L:s = 5:2)	5\96 (62.5 ¢)
Hard (L:s = 3:1)	3\57 (63.2 ¢)
Superhard (L:s = 4:1)	4\75 (64.0 ¢)
Collapsed (L:s = 1:0)	1\18 (66.7 ¢)
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18L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 18 large steps and 3 small steps, with a period of 6 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 18L 3s is related to 3L 6s, expanding it by 12 tones. Generators that produce this scale range from 57.1 ¢ to 66.7 ¢, or from 333.3 ¢ to 342.9 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Tunings of scale degrees

Simple Tunings of 18L 3s

Scale degree	Abbrev.	Basic (2:1) 39edo		Hard (3:1) 57edo		Soft (3:2) 60edo
		Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\39	0.0	0\57	0.0	0\60	0.0
Diminished 1-mosdegree	d1md	1\39	30.8	1\57	21.1	2\60	40.0
Perfect 1-mosdegree	P1md	2\39	61.5	3\57	63.2	3\60	60.0
Minor 2-mosdegree	m2md	3\39	92.3	4\57	84.2	5\60	100.0
Major 2-mosdegree	M2md	4\39	123.1	6\57	126.3	6\60	120.0
Minor 3-mosdegree	m3md	5\39	153.8	7\57	147.4	8\60	160.0
Major 3-mosdegree	M3md	6\39	184.6	9\57	189.5	9\60	180.0
Minor 4-mosdegree	m4md	7\39	215.4	10\57	210.5	11\60	220.0
Major 4-mosdegree	M4md	8\39	246.2	12\57	252.6	12\60	240.0
Minor 5-mosdegree	m5md	9\39	276.9	13\57	273.7	14\60	280.0
Major 5-mosdegree	M5md	10\39	307.7	15\57	315.8	15\60	300.0
Perfect 6-mosdegree	P6md	11\39	338.5	16\57	336.8	17\60	340.0
Augmented 6-mosdegree	A6md	12\39	369.2	18\57	378.9	18\60	360.0
Perfect 7-mosdegree	P7md	13\39	400.0	19\57	400.0	20\60	400.0
Diminished 8-mosdegree	d8md	14\39	430.8	20\57	421.1	22\60	440.0
Perfect 8-mosdegree	P8md	15\39	461.5	22\57	463.2	23\60	460.0
Minor 9-mosdegree	m9md	16\39	492.3	23\57	484.2	25\60	500.0
Major 9-mosdegree	M9md	17\39	523.1	25\57	526.3	26\60	520.0
Minor 10-mosdegree	m10md	18\39	553.8	26\57	547.4	28\60	560.0
Major 10-mosdegree	M10md	19\39	584.6	28\57	589.5	29\60	580.0
Minor 11-mosdegree	m11md	20\39	615.4	29\57	610.5	31\60	620.0
Major 11-mosdegree	M11md	21\39	646.2	31\57	652.6	32\60	640.0
Minor 12-mosdegree	m12md	22\39	676.9	32\57	673.7	34\60	680.0
Major 12-mosdegree	M12md	23\39	707.7	34\57	715.8	35\60	700.0
Perfect 13-mosdegree	P13md	24\39	738.5	35\57	736.8	37\60	740.0
Augmented 13-mosdegree	A13md	25\39	769.2	37\57	778.9	38\60	760.0
Perfect 14-mosdegree	P14md	26\39	800.0	38\57	800.0	40\60	800.0
Diminished 15-mosdegree	d15md	27\39	830.8	39\57	821.1	42\60	840.0
Perfect 15-mosdegree	P15md	28\39	861.5	41\57	863.2	43\60	860.0
Minor 16-mosdegree	m16md	29\39	892.3	42\57	884.2	45\60	900.0
Major 16-mosdegree	M16md	30\39	923.1	44\57	926.3	46\60	920.0
Minor 17-mosdegree	m17md	31\39	953.8	45\57	947.4	48\60	960.0
Major 17-mosdegree	M17md	32\39	984.6	47\57	989.5	49\60	980.0
Minor 18-mosdegree	m18md	33\39	1015.4	48\57	1010.5	51\60	1020.0
Major 18-mosdegree	M18md	34\39	1046.2	50\57	1052.6	52\60	1040.0
Minor 19-mosdegree	m19md	35\39	1076.9	51\57	1073.7	54\60	1080.0
Major 19-mosdegree	M19md	36\39	1107.7	53\57	1115.8	55\60	1100.0
Perfect 20-mosdegree	P20md	37\39	1138.5	54\57	1136.8	57\60	1140.0
Augmented 20-mosdegree	A20md	38\39	1169.2	56\57	1178.9	58\60	1160.0
Perfect 21-mosdegree	P21md	39\39	1200.0	57\57	1200.0	60\60	1200.0

Scale tree

Scale tree and tuning spectrum of 18L 3s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\21						57.143	342.857	1:1	1.000	Equalized 18L 3s
					6\123	58.537	341.463	6:5	1.200
				5\102		58.824	341.176	5:4	1.250
					9\183	59.016	340.984	9:7	1.286
			4\81			59.259	340.741	4:3	1.333	Supersoft 18L 3s
					11\222	59.459	340.541	11:8	1.375
				7\141		59.574	340.426	7:5	1.400
					10\201	59.701	340.299	10:7	1.429
		3\60				60.000	340.000	3:2	1.500	Soft 18L 3s
					11\219	60.274	339.726	11:7	1.571
				8\159		60.377	339.623	8:5	1.600
					13\258	60.465	339.535	13:8	1.625
			5\99			60.606	339.394	5:3	1.667	Semisoft 18L 3s
					12\237	60.759	339.241	12:7	1.714
				7\138		60.870	339.130	7:4	1.750
					9\177	61.017	338.983	9:5	1.800
	2\39					61.538	338.462	2:1	2.000	Basic 18L 3s
					9\174	62.069	337.931	9:4	2.250
				7\135		62.222	337.778	7:3	2.333
					12\231	62.338	337.662	12:5	2.400
			5\96			62.500	337.500	5:2	2.500	Semihard 18L 3s
					13\249	62.651	337.349	13:5	2.600
				8\153		62.745	337.255	8:3	2.667
					11\210	62.857	337.143	11:4	2.750
		3\57				63.158	336.842	3:1	3.000	Hard 18L 3s
					10\189	63.492	336.508	10:3	3.333
				7\132		63.636	336.364	7:2	3.500
					11\207	63.768	336.232	11:3	3.667
			4\75			64.000	336.000	4:1	4.000	Superhard 18L 3s
					9\168	64.286	335.714	9:2	4.500
				5\93		64.516	335.484	5:1	5.000
					6\111	64.865	335.135	6:1	6.000
1\18						66.667	333.333	1:0	→ ∞	Collapsed 18L 3s