14L 4s

↖ 13L 3s	↑ 14L 3s	15L 3s ↗
← 13L 4s	14L 4s	15L 4s →
↙ 13L 5s	↓ 14L 5s	15L 5s ↘

┌╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║║│║║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLsLLLLsLLLs sLLLsLLLLsLLLsLLLL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	5\18 to 4\14 (333.3¢ to 342.9¢)
Dark	3\14 to 4\18 (257.1¢ to 266.7¢)
TAMNAMS information
Descends from	4L 6s (lime)
Ancestor's step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	4L 10s
Sister	4L 14s
Daughters	18L 14s, 14L 18s
Neutralized	10L 8s
2-Flought	32L 4s, 14L 22s
Equal tunings
Equalized (L:s = 1:1)	5\18 (333.3¢)
Supersoft (L:s = 4:3)	19\68 (335.3¢)
Soft (L:s = 3:2)	14\50 (336.0¢)
Semisoft (L:s = 5:3)	23\82 (336.6¢)
Basic (L:s = 2:1)	9\32 (337.5¢)
Semihard (L:s = 5:2)	22\78 (338.5¢)
Hard (L:s = 3:1)	13\46 (339.1¢)
Superhard (L:s = 4:1)	17\60 (340.0¢)
Collapsed (L:s = 1:0)	4\14 (342.9¢)

14L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 4 small steps, with a period of 7 large steps and 2 small steps that repeats every 600.0¢, or twice every octave. 14L 4s is a grandchild scale of 4L 6s, expanding it by 8 tones. Generators that produce this scale range from 333.3¢ to 342.9¢, or from 257.1¢ to 266.7¢.

Modes

Modes of 14L 4s

UDP	Cyclic order	Step pattern
16|0(2)	1	LLLLsLLLsLLLLsLLLs
14|2(2)	6	LLLsLLLLsLLLsLLLLs
12|4(2)	2	LLLsLLLsLLLLsLLLsL
10|6(2)	7	LLsLLLLsLLLsLLLLsL
8|8(2)	3	LLsLLLsLLLLsLLLsLL
6|10(2)	8	LsLLLLsLLLsLLLLsLL
4|12(2)	4	LsLLLsLLLLsLLLsLLL
2|14(2)	9	sLLLLsLLLsLLLLsLLL
0|16(2)	5	sLLLsLLLLsLLLsLLLL

Intervals

Intervals of 14L 4s

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 66.7¢
	Major 1-mosstep	M1ms	L	66.7¢ to 85.7¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	85.7¢ to 133.3¢
	Major 2-mosstep	M2ms	2L	133.3¢ to 171.4¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	171.4¢ to 200.0¢
	Major 3-mosstep	M3ms	3L	200.0¢ to 257.1¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	257.1¢ to 266.7¢
	Augmented 4-mosstep	A4ms	4L	266.7¢ to 342.9¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	257.1¢ to 333.3¢
	Perfect 5-mosstep	P5ms	4L + s	333.3¢ to 342.9¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	342.9¢ to 400.0¢
	Major 6-mosstep	M6ms	5L + s	400.0¢ to 428.6¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	428.6¢ to 466.7¢
	Major 7-mosstep	M7ms	6L + s	466.7¢ to 514.3¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	514.3¢ to 533.3¢
	Major 8-mosstep	M8ms	7L + s	533.3¢ to 600.0¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	600.0¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	600.0¢ to 666.7¢
	Major 10-mosstep	M10ms	8L + 2s	666.7¢ to 685.7¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	685.7¢ to 733.3¢
	Major 11-mosstep	M11ms	9L + 2s	733.3¢ to 771.4¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	771.4¢ to 800.0¢
	Major 12-mosstep	M12ms	10L + 2s	800.0¢ to 857.1¢
13-mosstep	Perfect 13-mosstep	P13ms	10L + 3s	857.1¢ to 866.7¢
	Augmented 13-mosstep	A13ms	11L + 2s	866.7¢ to 942.9¢
14-mosstep	Diminished 14-mosstep	d14ms	10L + 4s	857.1¢ to 933.3¢
	Perfect 14-mosstep	P14ms	11L + 3s	933.3¢ to 942.9¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	942.9¢ to 1000.0¢
	Major 15-mosstep	M15ms	12L + 3s	1000.0¢ to 1028.6¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	1028.6¢ to 1066.7¢
	Major 16-mosstep	M16ms	13L + 3s	1066.7¢ to 1114.3¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	1114.3¢ to 1133.3¢
	Major 17-mosstep	M17ms	14L + 3s	1133.3¢ to 1200.0¢
18-mosstep	Perfect 18-mosstep	P18ms	14L + 4s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 14L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\18						333.333	266.667	1:1	1.000	Equalized 14L 4s
					29\104	334.615	265.385	6:5	1.200
				24\86		334.884	265.116	5:4	1.250
					43\154	335.065	264.935	9:7	1.286
			19\68			335.294	264.706	4:3	1.333	Supersoft 14L 4s
					52\186	335.484	264.516	11:8	1.375
				33\118		335.593	264.407	7:5	1.400
					47\168	335.714	264.286	10:7	1.429
		14\50				336.000	264.000	3:2	1.500	Soft 14L 4s
					51\182	336.264	263.736	11:7	1.571
				37\132		336.364	263.636	8:5	1.600
					60\214	336.449	263.551	13:8	1.625
			23\82			336.585	263.415	5:3	1.667	Semisoft 14L 4s
					55\196	336.735	263.265	12:7	1.714
				32\114		336.842	263.158	7:4	1.750
					41\146	336.986	263.014	9:5	1.800
	9\32					337.500	262.500	2:1	2.000	Basic 14L 4s Scales with tunings softer than this are proper
					40\142	338.028	261.972	9:4	2.250
				31\110		338.182	261.818	7:3	2.333
					53\188	338.298	261.702	12:5	2.400
			22\78			338.462	261.538	5:2	2.500	Semihard 14L 4s
					57\202	338.614	261.386	13:5	2.600
				35\124		338.710	261.290	8:3	2.667
					48\170	338.824	261.176	11:4	2.750
		13\46				339.130	260.870	3:1	3.000	Hard 14L 4s
					43\152	339.474	260.526	10:3	3.333
				30\106		339.623	260.377	7:2	3.500
					47\166	339.759	260.241	11:3	3.667
			17\60			340.000	260.000	4:1	4.000	Superhard 14L 4s
					38\134	340.299	259.701	9:2	4.500
				21\74		340.541	259.459	5:1	5.000
					25\88	340.909	259.091	6:1	6.000
4\14						342.857	257.143	1:0	→ ∞	Collapsed 14L 4s

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