14L 3s

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

┌╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║║│║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLsLLLLLsLLLLs sLLLLsLLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	6\17 to 5\14 (423.5 ¢ to 428.6 ¢)
Dark	9\14 to 11\17 (771.4 ¢ to 776.5 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	3L 11s
Sister	3L 14s
Daughters	17L 14s, 14L 17s
Neutralized	11L 6s
2-Flought	31L 3s, 14L 20s
Equal tunings
Equalized (L:s = 1:1)	6\17 (423.5 ¢)
Supersoft (L:s = 4:3)	23\65 (424.6 ¢)
Soft (L:s = 3:2)	17\48 (425.0 ¢)
Semisoft (L:s = 5:3)	28\79 (425.3 ¢)
Basic (L:s = 2:1)	11\31 (425.8 ¢)
Semihard (L:s = 5:2)	27\76 (426.3 ¢)
Hard (L:s = 3:1)	16\45 (426.7 ¢)
Superhard (L:s = 4:1)	21\59 (427.1 ¢)
Collapsed (L:s = 1:0)	5\14 (428.6 ¢)

14L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 3 small steps, repeating every octave. 14L 3s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 423.5 ¢ to 428.6 ¢, or from 771.4 ¢ to 776.5 ¢.

This scale is associated with squares temperament because the number of generators it takes to get to each of the primes 3, 5, and 7 is a square (3 ← −4 generators, 5 ← −16, 7 ← −9).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 14L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
6\17						423.529	776.471	1:1	1.000	Equalized 14L 3s
					35\99	424.242	775.758	6:5	1.200
				29\82		424.390	775.610	5:4	1.250
					52\147	424.490	775.510	9:7	1.286
			23\65			424.615	775.385	4:3	1.333	Supersoft 14L 3s
					63\178	424.719	775.281	11:8	1.375
				40\113		424.779	775.221	7:5	1.400
					57\161	424.845	775.155	10:7	1.429
		17\48				425.000	775.000	3:2	1.500	Soft 14L 3s
					62\175	425.143	774.857	11:7	1.571
				45\127		425.197	774.803	8:5	1.600
					73\206	425.243	774.757	13:8	1.625
			28\79			425.316	774.684	5:3	1.667	Semisoft 14L 3s
					67\189	425.397	774.603	12:7	1.714
				39\110		425.455	774.545	7:4	1.750
					50\141	425.532	774.468	9:5	1.800
	11\31					425.806	774.194	2:1	2.000	Basic 14L 3s Scales with tunings softer than this are proper
					49\138	426.087	773.913	9:4	2.250
				38\107		426.168	773.832	7:3	2.333
					65\183	426.230	773.770	12:5	2.400
			27\76			426.316	773.684	5:2	2.500	Semihard 14L 3s
					70\197	426.396	773.604	13:5	2.600
				43\121		426.446	773.554	8:3	2.667
					59\166	426.506	773.494	11:4	2.750
		16\45				426.667	773.333	3:1	3.000	Hard 14L 3s
					53\149	426.846	773.154	10:3	3.333
				37\104		426.923	773.077	7:2	3.500
					58\163	426.994	773.006	11:3	3.667
			21\59			427.119	772.881	4:1	4.000	Superhard 14L 3s
					47\132	427.273	772.727	9:2	4.500
				26\73		427.397	772.603	5:1	5.000
					31\87	427.586	772.414	6:1	6.000
5\14						428.571	771.429	1:0	→ ∞	Collapsed 14L 3s