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 ¢)
View • Talk • Edit

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.

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 ¢

Generator chain

Generator chain of 14L 3s

Bright gens	Scale degree	Abbrev.
30	Augmented 10-mosdegree	A10md
29	Augmented 4-mosdegree	A4md
28	Augmented 15-mosdegree	A15md
27	Augmented 9-mosdegree	A9md
26	Augmented 3-mosdegree	A3md
25	Augmented 14-mosdegree	A14md
24	Augmented 8-mosdegree	A8md
23	Augmented 2-mosdegree	A2md
22	Augmented 13-mosdegree	A13md
21	Augmented 7-mosdegree	A7md
20	Augmented 1-mosdegree	A1md
19	Augmented 12-mosdegree	A12md
18	Augmented 6-mosdegree	A6md
17	Augmented 0-mosdegree	A0md
16	Augmented 11-mosdegree	A11md
15	Major 5-mosdegree	M5md
14	Major 16-mosdegree	M16md
13	Major 10-mosdegree	M10md
12	Major 4-mosdegree	M4md
11	Major 15-mosdegree	M15md
10	Major 9-mosdegree	M9md
9	Major 3-mosdegree	M3md
8	Major 14-mosdegree	M14md
7	Major 8-mosdegree	M8md
6	Major 2-mosdegree	M2md
5	Major 13-mosdegree	M13md
4	Major 7-mosdegree	M7md
3	Major 1-mosdegree	M1md
2	Major 12-mosdegree	M12md
1	Perfect 6-mosdegree	P6md
0	Perfect 0-mosdegree Perfect 17-mosdegree	P0md P17md
−1	Perfect 11-mosdegree	P11md
−2	Minor 5-mosdegree	m5md
−3	Minor 16-mosdegree	m16md
−4	Minor 10-mosdegree	m10md
−5	Minor 4-mosdegree	m4md
−6	Minor 15-mosdegree	m15md
−7	Minor 9-mosdegree	m9md
−8	Minor 3-mosdegree	m3md
−9	Minor 14-mosdegree	m14md
−10	Minor 8-mosdegree	m8md
−11	Minor 2-mosdegree	m2md
−12	Minor 13-mosdegree	m13md
−13	Minor 7-mosdegree	m7md
−14	Minor 1-mosdegree	m1md
−15	Minor 12-mosdegree	m12md
−16	Diminished 6-mosdegree	d6md
−17	Diminished 17-mosdegree	d17md
−18	Diminished 11-mosdegree	d11md
−19	Diminished 5-mosdegree	d5md
−20	Diminished 16-mosdegree	d16md
−21	Diminished 10-mosdegree	d10md
−22	Diminished 4-mosdegree	d4md
−23	Diminished 15-mosdegree	d15md
−24	Diminished 9-mosdegree	d9md
−25	Diminished 3-mosdegree	d3md
−26	Diminished 14-mosdegree	d14md
−27	Diminished 8-mosdegree	d8md
−28	Diminished 2-mosdegree	d2md
−29	Diminished 13-mosdegree	d13md
−30	Diminished 7-mosdegree	d7md

Modes

Scale degrees of the modes of 14L 3s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
16|0	1	LLLLLsLLLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
15|1	7	LLLLLsLLLLsLLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
14|2	13	LLLLsLLLLLsLLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
13|3	2	LLLLsLLLLLsLLLLsL	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.
12|4	8	LLLLsLLLLsLLLLLsL	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.
11|5	14	LLLsLLLLLsLLLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.
10|6	3	LLLsLLLLLsLLLLsLL	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.
9|7	9	LLLsLLLLsLLLLLsLL	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.
8|8	15	LLsLLLLLsLLLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.
7|9	4	LLsLLLLLsLLLLsLLL	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.
6|10	10	LLsLLLLsLLLLLsLLL	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.
5|11	16	LsLLLLLsLLLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.
4|12	5	LsLLLLLsLLLLsLLLL	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.
3|13	11	LsLLLLsLLLLLsLLLL	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.
2|14	17	sLLLLLsLLLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.
1|15	6	sLLLLLsLLLLsLLLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.
0|16	12	sLLLLsLLLLLsLLLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.

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