3L 14s

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 ¢.

↖ 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
Related to	3L 5s (checkertonic)
With tunings	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 ¢)
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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

Tuning spectrum

Symbolic / Sidi / Smate range

generator										L	s	L/s	gen (cents)	comment
1\3										1	0		400.000
									15\44	10	1	10.000	409.091
								14\41		9	1	9.000	409.756	Hocus
									27\79	17	2	8.500	410.127
							13\38			8	1	8.000	410.526
						12\35				7	1	7.000	411.429
							23\67			13	2	6.500	411.940
					11\32					6	1	6.000	412.500
							32\93			17	3	5.667	412.903
						21\61				11	2	5.500	413.115
							31\90			16	3	5.333	413.333
				10\29						5	1	5.000	413.793
							39\113			19	4	4.750	414.159
						29\84				14	3	4.667	414.286
					19\55					9	2	4.500	414.545	Roman
						28\81				13	3	4.333	414.815
							37\107			17	4	4.250	414.953
			9\26							4	1	4.000	415.385
						35\101				15	4	3.750	415.842
					26\75					11	3	3.667	416.000
				17\49						7	2	3.500	416.327
					25\72					10	3	3.333	416.667	Sqrtphi
						33\95				13	4	3.250	416.842
							41\118			16	5	3.200	416.949
		8\23								3	1	3.000	417.391
						39\112				14	5	2.800	417.857
					31\89					11	4	2.750	417.978
				23\66						8	3	2.667	418.182
					38\109					13	5	2.600	418.349
			15\43							5	2	2.500	418.605
					37\106					12	5	2.400	418.868
				22\63						7	3	2.333	419.048
					29\83					9	4	2.250	419.277
						36\103				11	5	2.200	419.417
	7\20									2	1	2.000	420.000
						41\117				11	6	1.833	420.513
					34\97					9	5	1.800	420.619
				27\77						7	4	1.750	420.779
			20\57							5	3	1.667	421.053
				33\94						8	5	1.600	421.277	Bossier
		13\37								3	2	1.500	421.622
				32\91						7	5	1.400	421.978
			19\54							4	3	1.333	422.222
				25\71						5	4	1.250	422.535
					31\88					6	5	1.200	422.727
						37\105				7	6	1.167	422.857
							43\122			8	7	1.143	422.951
								49\139		9	8	1.125	423.022
									55\156	10	9	1.111	423.077
6\17										1	1	1.000	423.529