4L 18s

↖ 3L 17s	↑ 4L 17s	5L 17s ↗
← 3L 18s	4L 18s	5L 18s →
↙ 3L 19s	↓ 4L 19s	5L 19s ↘

┌╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║│││││║││││║││││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLsssssLssssLsssss sssssLssssLsssssLssssL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	5\22 to 1\4 (272.7¢ to 300.0¢)
Dark	1\4 to 6\22 (300.0¢ to 327.3¢)
TAMNAMS information
Descends from	4L 6s
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	4L 14s
Sister	18L 4s
Daughters	22L 4s, 4L 22s
Neutralized	8L 14s
2-Flought	26L 18s, 4L 40s
Equal tunings
Equalized (L:s = 1:1)	5\22 (272.7¢)
Supersoft (L:s = 4:3)	16\70 (274.3¢)
Soft (L:s = 3:2)	11\48 (275.0¢)
Semisoft (L:s = 5:3)	17\74 (275.7¢)
Basic (L:s = 2:1)	6\26 (276.9¢)
Semihard (L:s = 5:2)	13\56 (278.6¢)
Hard (L:s = 3:1)	7\30 (280.0¢)
Superhard (L:s = 4:1)	8\34 (282.4¢)
Collapsed (L:s = 1:0)	1\4 (300.0¢)

4L 18s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 18 small steps, with a period of 2 large steps and 9 small steps that repeats every 600.0¢, or twice every octave. 4L 18s is a great-grandchild scale of 4L 6s, expanding it by 12 tones. Generators that produce this scale range from 272.7¢ to 300¢, or from 300¢ to 327.3¢.

Modes

Modes of 4L 18s

UDP	Cyclic order	Step pattern
20|0(2)	1	LssssLsssssLssssLsssss
18|2(2)	6	LsssssLssssLsssssLssss
16|4(2)	11	sLssssLsssssLssssLssss
14|6(2)	5	sLsssssLssssLsssssLsss
12|8(2)	10	ssLssssLsssssLssssLsss
10|10(2)	4	ssLsssssLssssLsssssLss
8|12(2)	9	sssLssssLsssssLssssLss
6|14(2)	3	sssLsssssLssssLsssssLs
4|16(2)	8	ssssLssssLsssssLssssLs
2|18(2)	2	ssssLsssssLssssLsssssL
0|20(2)	7	sssssLssssLsssssLssssL

Intervals

Intervals of 4L 18s

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 54.5¢
	Major 1-mosstep	M1ms	L	54.5¢ to 300.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 109.1¢
	Major 2-mosstep	M2ms	L + s	109.1¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 163.6¢
	Major 3-mosstep	M3ms	L + 2s	163.6¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 218.2¢
	Major 4-mosstep	M4ms	L + 3s	218.2¢ to 300.0¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0¢ to 272.7¢
	Perfect 5-mosstep	P5ms	L + 4s	272.7¢ to 300.0¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	300.0¢ to 327.3¢
	Augmented 6-mosstep	A6ms	2L + 4s	327.3¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0¢ to 381.8¢
	Major 7-mosstep	M7ms	2L + 5s	381.8¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0¢ to 436.4¢
	Major 8-mosstep	M8ms	2L + 6s	436.4¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	300.0¢ to 490.9¢
	Major 9-mosstep	M9ms	2L + 7s	490.9¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	300.0¢ to 545.5¢
	Major 10-mosstep	M10ms	2L + 8s	545.5¢ to 600.0¢
11-mosstep	Perfect 11-mosstep	P11ms	2L + 9s	600.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0¢ to 654.5¢
	Major 12-mosstep	M12ms	3L + 9s	654.5¢ to 900.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	600.0¢ to 709.1¢
	Major 13-mosstep	M13ms	3L + 10s	709.1¢ to 900.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	600.0¢ to 763.6¢
	Major 14-mosstep	M14ms	3L + 11s	763.6¢ to 900.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	600.0¢ to 818.2¢
	Major 15-mosstep	M15ms	3L + 12s	818.2¢ to 900.0¢
16-mosstep	Diminished 16-mosstep	d16ms	2L + 14s	600.0¢ to 872.7¢
	Perfect 16-mosstep	P16ms	3L + 13s	872.7¢ to 900.0¢
17-mosstep	Perfect 17-mosstep	P17ms	3L + 14s	900.0¢ to 927.3¢
	Augmented 17-mosstep	A17ms	4L + 13s	927.3¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	900.0¢ to 981.8¢
	Major 18-mosstep	M18ms	4L + 14s	981.8¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	3L + 16s	900.0¢ to 1036.4¢
	Major 19-mosstep	M19ms	4L + 15s	1036.4¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	900.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	4L + 16s	1090.9¢ to 1200.0¢
21-mosstep	Minor 21-mosstep	m21ms	3L + 18s	900.0¢ to 1145.5¢
	Major 21-mosstep	M21ms	4L + 17s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	4L + 18s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 18s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\22						272.727	327.273	1:1	1.000	Equalized 4L 18s
					26\114	273.684	326.316	6:5	1.200
				21\92		273.913	326.087	5:4	1.250
					37\162	274.074	325.926	9:7	1.286
			16\70			274.286	325.714	4:3	1.333	Supersoft 4L 18s
					43\188	274.468	325.532	11:8	1.375
				27\118		274.576	325.424	7:5	1.400
					38\166	274.699	325.301	10:7	1.429
		11\48				275.000	325.000	3:2	1.500	Soft 4L 18s
					39\170	275.294	324.706	11:7	1.571
				28\122		275.410	324.590	8:5	1.600
					45\196	275.510	324.490	13:8	1.625
			17\74			275.676	324.324	5:3	1.667	Semisoft 4L 18s
					40\174	275.862	324.138	12:7	1.714
				23\100		276.000	324.000	7:4	1.750
					29\126	276.190	323.810	9:5	1.800
	6\26					276.923	323.077	2:1	2.000	Basic 4L 18s Scales with tunings softer than this are proper
					25\108	277.778	322.222	9:4	2.250
				19\82		278.049	321.951	7:3	2.333
					32\138	278.261	321.739	12:5	2.400
			13\56			278.571	321.429	5:2	2.500	Semihard 4L 18s
					33\142	278.873	321.127	13:5	2.600
				20\86		279.070	320.930	8:3	2.667
					27\116	279.310	320.690	11:4	2.750
		7\30				280.000	320.000	3:1	3.000	Hard 4L 18s
					22\94	280.851	319.149	10:3	3.333
				15\64		281.250	318.750	7:2	3.500
					23\98	281.633	318.367	11:3	3.667
			8\34			282.353	317.647	4:1	4.000	Superhard 4L 18s
					17\72	283.333	316.667	9:2	4.500
				9\38		284.211	315.789	5:1	5.000
					10\42	285.714	314.286	6:1	6.000
1\4						300.000	300.000	1:0	→ ∞	Collapsed 4L 18s

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