14L 2s

14L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 2 small steps, with a period of 7 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. 14L 2s is a great-grandchild scale of 2L 8s, expanding it by 6 tones. Generators that produce this scale range from 75 ¢ to 85.7 ¢, or from 514.3 ¢ to 525 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 13L 1s	↑ 14L 1s	15L 1s ↗
← 13L 2s	14L 2s	15L 2s →
↙ 13L 3s	↓ 14L 3s	15L 3s ↘

Scale structure
Step pattern	LLLLLLLsLLLLLLLs sLLLLLLLsLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	1\16 to 1\14 (75.0 ¢ to 85.7 ¢)
Dark	6\14 to 7\16 (514.3 ¢ to 525.0 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	2L 12s
Sister	2L 14s
Daughters	16L 14s, 14L 16s
Neutralized	12L 4s
2-Flought	30L 2s, 14L 18s
Equal tunings
Equalized (L:s = 1:1)	1\16 (75.0 ¢)
Supersoft (L:s = 4:3)	4\62 (77.4 ¢)
Soft (L:s = 3:2)	3\46 (78.3 ¢)
Semisoft (L:s = 5:3)	5\76 (78.9 ¢)
Basic (L:s = 2:1)	2\30 (80.0 ¢)
Semihard (L:s = 5:2)	5\74 (81.1 ¢)
Hard (L:s = 3:1)	3\44 (81.8 ¢)
Superhard (L:s = 4:1)	4\58 (82.8 ¢)
Collapsed (L:s = 1:0)	1\14 (85.7 ¢)
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Modes

Modes of 14L 2s

UDP	Cyclic order	Step pattern
14|0(2)	1	LLLLLLLsLLLLLLLs
12|2(2)	2	LLLLLLsLLLLLLLsL
10|4(2)	3	LLLLLsLLLLLLLsLL
8|6(2)	4	LLLLsLLLLLLLsLLL
6|8(2)	5	LLLsLLLLLLLsLLLL
4|10(2)	6	LLsLLLLLLLsLLLLL
2|12(2)	7	LsLLLLLLLsLLLLLL
0|14(2)	8	sLLLLLLLsLLLLLLL

Intervals

Intervals of 14L 2s

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 75.0 ¢
	Perfect 1-mosstep	P1ms	L	75.0 ¢ to 85.7 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	85.7 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 171.4 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	171.4 ¢ to 225.0 ¢
	Major 3-mosstep	M3ms	3L	225.0 ¢ to 257.1 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	257.1 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	4L	300.0 ¢ to 342.9 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	342.9 ¢ to 375.0 ¢
	Major 5-mosstep	M5ms	5L	375.0 ¢ to 428.6 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	428.6 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	6L	450.0 ¢ to 514.3 ¢
7-mosstep	Perfect 7-mosstep	P7ms	6L + s	514.3 ¢ to 525.0 ¢
	Augmented 7-mosstep	A7ms	7L	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	7L + s	600.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	7L + 2s	600.0 ¢ to 675.0 ¢
	Perfect 9-mosstep	P9ms	8L + s	675.0 ¢ to 685.7 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	685.7 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	9L + s	750.0 ¢ to 771.4 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	771.4 ¢ to 825.0 ¢
	Major 11-mosstep	M11ms	10L + s	825.0 ¢ to 857.1 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	857.1 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	11L + s	900.0 ¢ to 942.9 ¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	942.9 ¢ to 975.0 ¢
	Major 13-mosstep	M13ms	12L + s	975.0 ¢ to 1028.6 ¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	1028.6 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	13L + s	1050.0 ¢ to 1114.3 ¢
15-mosstep	Perfect 15-mosstep	P15ms	13L + 2s	1114.3 ¢ to 1125.0 ¢
	Augmented 15-mosstep	A15ms	14L + s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	14L + 2s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 14L 2s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\16						75.000	525.000	1:1	1.000	Equalized 14L 2s
					6\94	76.596	523.404	6:5	1.200
				5\78		76.923	523.077	5:4	1.250
					9\140	77.143	522.857	9:7	1.286
			4\62			77.419	522.581	4:3	1.333	Supersoft 14L 2s
					11\170	77.647	522.353	11:8	1.375
				7\108		77.778	522.222	7:5	1.400
					10\154	77.922	522.078	10:7	1.429
		3\46				78.261	521.739	3:2	1.500	Soft 14L 2s
					11\168	78.571	521.429	11:7	1.571
				8\122		78.689	521.311	8:5	1.600
					13\198	78.788	521.212	13:8	1.625
			5\76			78.947	521.053	5:3	1.667	Semisoft 14L 2s
					12\182	79.121	520.879	12:7	1.714
				7\106		79.245	520.755	7:4	1.750
					9\136	79.412	520.588	9:5	1.800
	2\30					80.000	520.000	2:1	2.000	Basic 14L 2s
					9\134	80.597	519.403	9:4	2.250
				7\104		80.769	519.231	7:3	2.333
					12\178	80.899	519.101	12:5	2.400
			5\74			81.081	518.919	5:2	2.500	Semihard 14L 2s
					13\192	81.250	518.750	13:5	2.600
				8\118		81.356	518.644	8:3	2.667
					11\162	81.481	518.519	11:4	2.750
		3\44				81.818	518.182	3:1	3.000	Hard 14L 2s
					10\146	82.192	517.808	10:3	3.333
				7\102		82.353	517.647	7:2	3.500
					11\160	82.500	517.500	11:3	3.667
			4\58			82.759	517.241	4:1	4.000	Superhard 14L 2s
					9\130	83.077	516.923	9:2	4.500
				5\72		83.333	516.667	5:1	5.000
					6\86	83.721	516.279	6:1	6.000
1\14						85.714	514.286	1:0	→ ∞	Collapsed 14L 2s

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