14L 1s

← 13L 1s	14L 1s	15L 1s →
↙ 13L 2s	↓ 14L 2s	15L 2s ↘

Scale structure
Step pattern	LLLLLLLLLLLLLLs sLLLLLLLLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\15 to 1\14 (80.0 ¢ to 85.7 ¢)
Dark	13\14 to 14\15 (1114.3 ¢ to 1120.0 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	5:1 to 6:1
Related MOS scales
Parent	1L 13s
Sister	1L 14s
Daughters	15L 14s, 14L 15s
Neutralized	13L 2s
2-Flought	29L 1s, 14L 16s
Equal tunings
Equalized (L:s = 1:1)	1\15 (80.0 ¢)
Supersoft (L:s = 4:3)	4\59 (81.4 ¢)
Soft (L:s = 3:2)	3\44 (81.8 ¢)
Semisoft (L:s = 5:3)	5\73 (82.2 ¢)
Basic (L:s = 2:1)	2\29 (82.8 ¢)
Semihard (L:s = 5:2)	5\72 (83.3 ¢)
Hard (L:s = 3:1)	3\43 (83.7 ¢)
Superhard (L:s = 4:1)	4\57 (84.2 ¢)
Collapsed (L:s = 1:0)	1\14 (85.7 ¢)
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14L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 1 small step, repeating every octave. 14L 1s is related to 1L 9s, expanding it by 5 tones. Generators that produce this scale range from 80 ¢ to 85.7 ¢, or from 1114.3 ¢ to 1120 ¢. Scales of this form are always proper because there is only one small step.

This scale is notable for corresponding to 15-note scales of temperaments like nautilus and sextilififths. 6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.

Modes

Modes of 14L 1s

UDP	Cyclic order	Step pattern
14|0	1	LLLLLLLLLLLLLLs
13|1	2	LLLLLLLLLLLLLsL
12|2	3	LLLLLLLLLLLLsLL
11|3	4	LLLLLLLLLLLsLLL
10|4	5	LLLLLLLLLLsLLLL
9|5	6	LLLLLLLLLsLLLLL
8|6	7	LLLLLLLLsLLLLLL
7|7	8	LLLLLLLsLLLLLLL
6|8	9	LLLLLLsLLLLLLLL
5|9	10	LLLLLsLLLLLLLLL
4|10	11	LLLLsLLLLLLLLLL
3|11	12	LLLsLLLLLLLLLLL
2|12	13	LLsLLLLLLLLLLLL
1|13	14	LsLLLLLLLLLLLLL
0|14	15	sLLLLLLLLLLLLLL

Intervals

Intervals of 14L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 80.0 ¢
	Perfect 1-mosstep	P1ms	L	80.0 ¢ to 85.7 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	85.7 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	2L	160.0 ¢ to 171.4 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	171.4 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	3L	240.0 ¢ to 257.1 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	257.1 ¢ to 320.0 ¢
	Major 4-mosstep	M4ms	4L	320.0 ¢ to 342.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	342.9 ¢ to 400.0 ¢
	Major 5-mosstep	M5ms	5L	400.0 ¢ to 428.6 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	428.6 ¢ to 480.0 ¢
	Major 6-mosstep	M6ms	6L	480.0 ¢ to 514.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	514.3 ¢ to 560.0 ¢
	Major 7-mosstep	M7ms	7L	560.0 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	600.0 ¢ to 640.0 ¢
	Major 8-mosstep	M8ms	8L	640.0 ¢ to 685.7 ¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	685.7 ¢ to 720.0 ¢
	Major 9-mosstep	M9ms	9L	720.0 ¢ to 771.4 ¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	771.4 ¢ to 800.0 ¢
	Major 10-mosstep	M10ms	10L	800.0 ¢ to 857.1 ¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	857.1 ¢ to 880.0 ¢
	Major 11-mosstep	M11ms	11L	880.0 ¢ to 942.9 ¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	942.9 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	12L	960.0 ¢ to 1028.6 ¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	1028.6 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	13L	1040.0 ¢ to 1114.3 ¢
14-mosstep	Perfect 14-mosstep	P14ms	13L + s	1114.3 ¢ to 1120.0 ¢
	Augmented 14-mosstep	A14ms	14L	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	14L + s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 14L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\15						80.000	1120.000	1:1	1.000	Equalized 14L 1s
					6\89	80.899	1119.101	6:5	1.200
				5\74		81.081	1118.919	5:4	1.250
					9\133	81.203	1118.797	9:7	1.286
			4\59			81.356	1118.644	4:3	1.333	Supersoft 14L 1s
					11\162	81.481	1118.519	11:8	1.375
				7\103		81.553	1118.447	7:5	1.400
					10\147	81.633	1118.367	10:7	1.429
		3\44				81.818	1118.182	3:2	1.500	Soft 14L 1s
					11\161	81.988	1118.012	11:7	1.571
				8\117		82.051	1117.949	8:5	1.600
					13\190	82.105	1117.895	13:8	1.625
			5\73			82.192	1117.808	5:3	1.667	Semisoft 14L 1s
					12\175	82.286	1117.714	12:7	1.714
				7\102		82.353	1117.647	7:4	1.750
					9\131	82.443	1117.557	9:5	1.800
	2\29					82.759	1117.241	2:1	2.000	Basic 14L 1s
					9\130	83.077	1116.923	9:4	2.250
				7\101		83.168	1116.832	7:3	2.333
					12\173	83.237	1116.763	12:5	2.400
			5\72			83.333	1116.667	5:2	2.500	Semihard 14L 1s
					13\187	83.422	1116.578	13:5	2.600
				8\115		83.478	1116.522	8:3	2.667
					11\158	83.544	1116.456	11:4	2.750
		3\43				83.721	1116.279	3:1	3.000	Hard 14L 1s
					10\143	83.916	1116.084	10:3	3.333
				7\100		84.000	1116.000	7:2	3.500
					11\157	84.076	1115.924	11:3	3.667
			4\57			84.211	1115.789	4:1	4.000	Superhard 14L 1s
					9\128	84.375	1115.625	9:2	4.500
				5\71		84.507	1115.493	5:1	5.000
					6\85	84.706	1115.294	6:1	6.000
1\14						85.714	1114.286	1:0	→ ∞	Collapsed 14L 1s