8L 14s

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↙ 7L 15s	↓ 8L 15s	9L 15s ↘

Scale structure
Step pattern	LsLssLssLssLsLssLssLss ssLssLssLsLssLssLssLsL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	8\22 to 3\8 (436.4 ¢ to 450.0 ¢)
Dark	1\8 to 3\22 (150.0 ¢ to 163.6 ¢)
TAMNAMS information
Related to	6L 2s (ekic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 6s
Sister	14L 8s
Daughters	22L 8s, 8L 22s
Neutralized	16L 6s
2-Flought	30L 14s, 8L 36s
Equal tunings
Equalized (L:s = 1:1)	8\22 (436.4 ¢)
Supersoft (L:s = 4:3)	27\74 (437.8 ¢)
Soft (L:s = 3:2)	19\52 (438.5 ¢)
Semisoft (L:s = 5:3)	30\82 (439.0 ¢)
Basic (L:s = 2:1)	11\30 (440.0 ¢)
Semihard (L:s = 5:2)	25\68 (441.2 ¢)
Hard (L:s = 3:1)	14\38 (442.1 ¢)
Superhard (L:s = 4:1)	17\46 (443.5 ¢)
Collapsed (L:s = 1:0)	3\8 (450.0 ¢)
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8L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 14 small steps, with a period of 4 large steps and 7 small steps that repeats every 600.0 ¢, or twice every octave. 8L 14s is a grandchild scale of 6L 2s, expanding it by 14 tones. Generators that produce this scale range from 436.4 ¢ to 450 ¢, or from 150 ¢ to 163.6 ¢.

Modes

Modes of 8L 14s

UDP	Cyclic order	Step pattern
20|0(2)	1	LsLssLssLssLsLssLssLss
18|2(2)	9	LssLsLssLssLssLsLssLss
16|4(2)	6	LssLssLsLssLssLssLsLss
14|6(2)	3	LssLssLssLsLssLssLssLs
12|8(2)	11	sLsLssLssLssLsLssLssLs
10|10(2)	8	sLssLsLssLssLssLsLssLs
8|12(2)	5	sLssLssLsLssLssLssLsLs
6|14(2)	2	sLssLssLssLsLssLssLssL
4|16(2)	10	ssLsLssLssLssLsLssLssL
2|18(2)	7	ssLssLsLssLssLssLsLssL
0|20(2)	4	ssLssLssLsLssLssLssLsL

Intervals

Intervals of 8L 14s

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 54.5 ¢
	Major 1-mosstep	M1ms	L	54.5 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 109.1 ¢
	Major 2-mosstep	M2ms	L + s	109.1 ¢ to 150.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	150.0 ¢ to 163.6 ¢
	Augmented 3-mosstep	A3ms	2L + s	163.6 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	150.0 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	218.2 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	150.0 ¢ to 272.7 ¢
	Major 5-mosstep	M5ms	2L + 3s	272.7 ¢ to 300.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	300.0 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	3L + 3s	327.3 ¢ to 450.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	300.0 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	3L + 4s	381.8 ¢ to 450.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	300.0 ¢ to 436.4 ¢
	Perfect 8-mosstep	P8ms	3L + 5s	436.4 ¢ to 450.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	450.0 ¢ to 490.9 ¢
	Major 9-mosstep	M9ms	4L + 5s	490.9 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	450.0 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	4L + 6s	545.5 ¢ to 600.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	4L + 7s	600.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	600.0 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	5L + 7s	654.5 ¢ to 750.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	600.0 ¢ to 709.1 ¢
	Major 13-mosstep	M13ms	5L + 8s	709.1 ¢ to 750.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	5L + 9s	750.0 ¢ to 763.6 ¢
	Augmented 14-mosstep	A14ms	6L + 8s	763.6 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	750.0 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	6L + 9s	818.2 ¢ to 900.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	5L + 11s	750.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	6L + 10s	872.7 ¢ to 900.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	6L + 11s	900.0 ¢ to 927.3 ¢
	Major 17-mosstep	M17ms	7L + 10s	927.3 ¢ to 1050.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	6L + 12s	900.0 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	7L + 11s	981.8 ¢ to 1050.0 ¢
19-mosstep	Diminished 19-mosstep	d19ms	6L + 13s	900.0 ¢ to 1036.4 ¢
	Perfect 19-mosstep	P19ms	7L + 12s	1036.4 ¢ to 1050.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	7L + 13s	1050.0 ¢ to 1090.9 ¢
	Major 20-mosstep	M20ms	8L + 12s	1090.9 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	7L + 14s	1050.0 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	8L + 13s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	8L + 14s	1200.0 ¢

Scale tree

16L 2s is generated by two noteworthy temperaments.

The first is the 22&96 temperament which occurs in the zeta edos 22edo and 118edo, as well as 96edo which was important in the early microtonal movement.

The second is the 46&84 temperament which occurs in the zeta edos 46edo and 130edo, as well as 84edo which also well approximates JI unusually well.

Scale tree and tuning spectrum of 8L 14s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\22						436.364	163.636	1:1	1.000	Equalized 8L 14s
					43\118	437.288	162.712	6:5	1.200
				35\96		437.500	162.500	5:4	1.250
					62\170	437.647	162.353	9:7	1.286
			27\74			437.838	162.162	4:3	1.333	Supersoft 8L 14s
					73\200	438.000	162.000	11:8	1.375
				46\126		438.095	161.905	7:5	1.400
					65\178	438.202	161.798	10:7	1.429
		19\52				438.462	161.538	3:2	1.500	Soft 8L 14s
					68\186	438.710	161.290	11:7	1.571
				49\134		438.806	161.194	8:5	1.600
					79\216	438.889	161.111	13:8	1.625
			30\82			439.024	160.976	5:3	1.667	Semisoft 8L 14s
					71\194	439.175	160.825	12:7	1.714
				41\112		439.286	160.714	7:4	1.750
					52\142	439.437	160.563	9:5	1.800
	11\30					440.000	160.000	2:1	2.000	Basic 8L 14s Scales with tunings softer than this are proper
					47\128	440.625	159.375	9:4	2.250
				36\98		440.816	159.184	7:3	2.333
					61\166	440.964	159.036	12:5	2.400
			25\68			441.176	158.824	5:2	2.500	Semihard 8L 14s
					64\174	441.379	158.621	13:5	2.600
				39\106		441.509	158.491	8:3	2.667
					53\144	441.667	158.333	11:4	2.750
		14\38				442.105	157.895	3:1	3.000	Hard 8L 14s
					45\122	442.623	157.377	10:3	3.333
				31\84		442.857	157.143	7:2	3.500
					48\130	443.077	156.923	11:3	3.667
			17\46			443.478	156.522	4:1	4.000	Superhard 8L 14s
					37\100	444.000	156.000	9:2	4.500
				20\54		444.444	155.556	5:1	5.000
					23\62	445.161	154.839	6:1	6.000
3\8						450.000	150.000	1:0	→ ∞	Collapsed 8L 14s