3L 14s

↖ 2L 13s	↑ 3L 13s	4L 13s ↗
← 2L 14s	3L 14s	4L 14s →
↙ 2L 15s	↓ 3L 15s	4L 15s ↘

┌╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║││││║│││││║││││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLsssssLsssss sssssLsssssLssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	11\17 to 2\3 (776.5¢ to 800.0¢)
Dark	1\3 to 6\17 (400.0¢ to 423.5¢)
TAMNAMS information
Descends from	3L 5s (checkertonic)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 11s
Sister	14L 3s
Daughters	17L 3s, 3L 17s
Neutralized	6L 11s
2-Flought	20L 14s, 3L 31s
Equal tunings
Equalized (L:s = 1:1)	11\17 (776.5¢)
Supersoft (L:s = 4:3)	35\54 (777.8¢)
Soft (L:s = 3:2)	24\37 (778.4¢)
Semisoft (L:s = 5:3)	37\57 (778.9¢)
Basic (L:s = 2:1)	13\20 (780.0¢)
Semihard (L:s = 5:2)	28\43 (781.4¢)
Hard (L:s = 3:1)	15\23 (782.6¢)
Superhard (L:s = 4:1)	17\26 (784.6¢)
Collapsed (L:s = 1:0)	2\3 (800.0¢)

3L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 14 small steps, repeating every octave. 3L 14s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 776.5¢ to 800¢, or from 400¢ to 423.5¢.

Modes

Modes of 3L 14s

UDP	Cyclic order	Step pattern
16|0	1	LssssLsssssLsssss
15|1	12	LsssssLssssLsssss
14|2	6	LsssssLsssssLssss
13|3	17	sLssssLsssssLssss
12|4	11	sLsssssLssssLssss
11|5	5	sLsssssLsssssLsss
10|6	16	ssLssssLsssssLsss
9|7	10	ssLsssssLssssLsss
8|8	4	ssLsssssLsssssLss
7|9	15	sssLssssLsssssLss
6|10	9	sssLsssssLssssLss
5|11	3	sssLsssssLsssssLs
4|12	14	ssssLssssLsssssLs
3|13	8	ssssLsssssLssssLs
2|14	2	ssssLsssssLsssssL
1|15	13	sssssLssssLsssssL
0|16	7	sssssLsssssLssssL

Intervals

Intervals of 3L 14s

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 70.6¢
	Major 1-mosstep	M1ms	L	70.6¢ to 400.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 141.2¢
	Major 2-mosstep	M2ms	L + s	141.2¢ to 400.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 211.8¢
	Major 3-mosstep	M3ms	L + 2s	211.8¢ to 400.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 282.4¢
	Major 4-mosstep	M4ms	L + 3s	282.4¢ to 400.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 352.9¢
	Major 5-mosstep	M5ms	L + 4s	352.9¢ to 400.0¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	400.0¢ to 423.5¢
	Augmented 6-mosstep	A6ms	2L + 4s	423.5¢ to 800.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	400.0¢ to 494.1¢
	Major 7-mosstep	M7ms	2L + 5s	494.1¢ to 800.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0¢ to 564.7¢
	Major 8-mosstep	M8ms	2L + 6s	564.7¢ to 800.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0¢ to 635.3¢
	Major 9-mosstep	M9ms	2L + 7s	635.3¢ to 800.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0¢ to 705.9¢
	Major 10-mosstep	M10ms	2L + 8s	705.9¢ to 800.0¢
11-mosstep	Diminished 11-mosstep	d11ms	L + 10s	400.0¢ to 776.5¢
	Perfect 11-mosstep	P11ms	2L + 9s	776.5¢ to 800.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	800.0¢ to 847.1¢
	Major 12-mosstep	M12ms	3L + 9s	847.1¢ to 1200.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	800.0¢ to 917.6¢
	Major 13-mosstep	M13ms	3L + 10s	917.6¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	800.0¢ to 988.2¢
	Major 14-mosstep	M14ms	3L + 11s	988.2¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	800.0¢ to 1058.8¢
	Major 15-mosstep	M15ms	3L + 12s	1058.8¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0¢ to 1129.4¢
	Major 16-mosstep	M16ms	3L + 13s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	3L + 14s	1200.0¢

Tuning spectrum

Todo: review Review entries from past page revision and enter them into the scale tree.

Symbolic / Sidi / Smate range

Scale Tree and Tuning Spectrum of 3L 14s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\17						776.471	423.529	1:1	1.000	Equalized 3L 14s
					57\88	777.273	422.727	6:5	1.200
				46\71		777.465	422.535	5:4	1.250
					81\125	777.600	422.400	9:7	1.286
			35\54			777.778	422.222	4:3	1.333	Supersoft 3L 14s
					94\145	777.931	422.069	11:8	1.375
				59\91		778.022	421.978	7:5	1.400
					83\128	778.125	421.875	10:7	1.429
		24\37				778.378	421.622	3:2	1.500	Soft 3L 14s
					85\131	778.626	421.374	11:7	1.571
				61\94		778.723	421.277	8:5	1.600
					98\151	778.808	421.192	13:8	1.625
			37\57			778.947	421.053	5:3	1.667	Semisoft 3L 14s
					87\134	779.104	420.896	12:7	1.714
				50\77		779.221	420.779	7:4	1.750
					63\97	779.381	420.619	9:5	1.800
	13\20					780.000	420.000	2:1	2.000	Basic 3L 14s Scales with tunings softer than this are proper
					54\83	780.723	419.277	9:4	2.250
				41\63		780.952	419.048	7:3	2.333
					69\106	781.132	418.868	12:5	2.400
			28\43			781.395	418.605	5:2	2.500	Semihard 3L 14s
					71\109	781.651	418.349	13:5	2.600
				43\66		781.818	418.182	8:3	2.667
					58\89	782.022	417.978	11:4	2.750
		15\23				782.609	417.391	3:1	3.000	Hard 3L 14s
					47\72	783.333	416.667	10:3	3.333
				32\49		783.673	416.327	7:2	3.500
					49\75	784.000	416.000	11:3	3.667
			17\26			784.615	415.385	4:1	4.000	Superhard 3L 14s
					36\55	785.455	414.545	9:2	4.500
				19\29		786.207	413.793	5:1	5.000
					21\32	787.500	412.500	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 14s

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