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
Descends from	3L 5s (checkertonic)
Ancestor's step ratio range	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).

Modes

Modes of 14L 3s

UDP	Cyclic order	Step pattern
16|0	1	LLLLLsLLLLLsLLLLs
15|1	7	LLLLLsLLLLsLLLLLs
14|2	13	LLLLsLLLLLsLLLLLs
13|3	2	LLLLsLLLLLsLLLLsL
12|4	8	LLLLsLLLLsLLLLLsL
11|5	14	LLLsLLLLLsLLLLLsL
10|6	3	LLLsLLLLLsLLLLsLL
9|7	9	LLLsLLLLsLLLLLsLL
8|8	15	LLsLLLLLsLLLLLsLL
7|9	4	LLsLLLLLsLLLLsLLL
6|10	10	LLsLLLLsLLLLLsLLL
5|11	16	LsLLLLLsLLLLLsLLL
4|12	5	LsLLLLLsLLLLsLLLL
3|13	11	LsLLLLsLLLLLsLLLL
2|14	17	sLLLLLsLLLLLsLLLL
1|15	6	sLLLLLsLLLLsLLLLL
0|16	12	sLLLLsLLLLLsLLLLL

Intervals

Intervals of 14L 3s

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 85.7¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	85.7¢ to 141.2¢
	Major 2-mosstep	M2ms	2L	141.2¢ to 171.4¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	171.4¢ to 211.8¢
	Major 3-mosstep	M3ms	3L	211.8¢ to 257.1¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	257.1¢ to 282.4¢
	Major 4-mosstep	M4ms	4L	282.4¢ to 342.9¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	342.9¢ to 352.9¢
	Major 5-mosstep	M5ms	5L	352.9¢ to 428.6¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	342.9¢ to 423.5¢
	Perfect 6-mosstep	P6ms	5L + s	423.5¢ to 428.6¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	428.6¢ to 494.1¢
	Major 7-mosstep	M7ms	6L + s	494.1¢ to 514.3¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	514.3¢ to 564.7¢
	Major 8-mosstep	M8ms	7L + s	564.7¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	600.0¢ to 635.3¢
	Major 9-mosstep	M9ms	8L + s	635.3¢ to 685.7¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	685.7¢ to 705.9¢
	Major 10-mosstep	M10ms	9L + s	705.9¢ to 771.4¢
11-mosstep	Perfect 11-mosstep	P11ms	9L + 2s	771.4¢ to 776.5¢
	Augmented 11-mosstep	A11ms	10L + s	776.5¢ to 857.1¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	771.4¢ to 847.1¢
	Major 12-mosstep	M12ms	10L + 2s	847.1¢ to 857.1¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	857.1¢ to 917.6¢
	Major 13-mosstep	M13ms	11L + 2s	917.6¢ to 942.9¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	942.9¢ to 988.2¢
	Major 14-mosstep	M14ms	12L + 2s	988.2¢ to 1028.6¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	1028.6¢ to 1058.8¢
	Major 15-mosstep	M15ms	13L + 2s	1058.8¢ to 1114.3¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	1114.3¢ to 1129.4¢
	Major 16-mosstep	M16ms	14L + 2s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	14L + 3s	1200.0¢

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