18L 3s

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.

↖ 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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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