6L 16s

6L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 16 small steps, with a period of 3 large steps and 8 small steps that repeats every 600.0 ¢, or twice every octave. 6L 16s is a grandchild scale of 6L 4s, expanding it by 12 tones. Generators that produce this scale range from 381.8 ¢ to 400 ¢, or from 200 ¢ to 218.2 ¢.

↖ 5L 15s	↑ 6L 15s	7L 15s ↗
← 5L 16s	6L 16s	7L 16s →
↙ 5L 17s	↓ 6L 17s	7L 17s ↘

Scale structure
Step pattern	LssLsssLsssLssLsssLsss sssLsssLssLsssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	7\22 to 2\6 (381.8 ¢ to 400.0 ¢)
Dark	1\6 to 4\22 (200.0 ¢ to 218.2 ¢)
TAMNAMS information
Related to	6L 4s (lemon)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	6L 10s
Sister	16L 6s
Daughters	22L 6s, 6L 22s
Neutralized	12L 10s
2-Flought	28L 16s, 6L 38s
Equal tunings
Equalized (L:s = 1:1)	7\22 (381.8 ¢)
Supersoft (L:s = 4:3)	23\72 (383.3 ¢)
Soft (L:s = 3:2)	16\50 (384.0 ¢)
Semisoft (L:s = 5:3)	25\78 (384.6 ¢)
Basic (L:s = 2:1)	9\28 (385.7 ¢)
Semihard (L:s = 5:2)	20\62 (387.1 ¢)
Hard (L:s = 3:1)	11\34 (388.2 ¢)
Superhard (L:s = 4:1)	13\40 (390.0 ¢)
Collapsed (L:s = 1:0)	2\6 (400.0 ¢)
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It has a small major third as a generator instead of the medium to large major third which generates 3L 8s. With the half-octave equivalence, the third inverts to a 'diatonic' whole tone of no more than 4/22edo (218.182 cents).

Modes

Modes of 6L 16s

UDP	Cyclic order	Step pattern
20|0(2)	1	LssLsssLsssLssLsssLsss
18|2(2)	8	LsssLssLsssLsssLssLsss
16|4(2)	4	LsssLsssLssLsssLsssLss
14|6(2)	11	sLssLsssLsssLssLsssLss
12|8(2)	7	sLsssLssLsssLsssLssLss
10|10(2)	3	sLsssLsssLssLsssLsssLs
8|12(2)	10	ssLssLsssLsssLssLsssLs
6|14(2)	6	ssLsssLssLsssLsssLssLs
4|16(2)	2	ssLsssLsssLssLsssLsssL
2|18(2)	9	sssLssLsssLsssLssLsssL
0|20(2)	5	sssLsssLssLsssLsssLssL

Intervals

Intervals of 6L 16s

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 200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 109.1 ¢
	Major 2-mosstep	M2ms	L + s	109.1 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	L + 2s	163.6 ¢ to 200.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	200.0 ¢ to 218.2 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	218.2 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	200.0 ¢ to 272.7 ¢
	Major 5-mosstep	M5ms	2L + 3s	272.7 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	200.0 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	327.3 ¢ to 400.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	200.0 ¢ to 381.8 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	381.8 ¢ to 400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	400.0 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	3L + 5s	436.4 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	400.0 ¢ to 490.9 ¢
	Major 9-mosstep	M9ms	3L + 6s	490.9 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	400.0 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	3L + 7s	545.5 ¢ to 600.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	600.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	600.0 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	4L + 8s	654.5 ¢ to 800.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	600.0 ¢ to 709.1 ¢
	Major 13-mosstep	M13ms	4L + 9s	709.1 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	600.0 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	4L + 10s	763.6 ¢ to 800.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	4L + 11s	800.0 ¢ to 818.2 ¢
	Augmented 15-mosstep	A15ms	5L + 10s	818.2 ¢ to 1000.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	800.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	5L + 11s	872.7 ¢ to 1000.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	4L + 13s	800.0 ¢ to 927.3 ¢
	Major 17-mosstep	M17ms	5L + 12s	927.3 ¢ to 1000.0 ¢
18-mosstep	Diminished 18-mosstep	d18ms	4L + 14s	800.0 ¢ to 981.8 ¢
	Perfect 18-mosstep	P18ms	5L + 13s	981.8 ¢ to 1000.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	5L + 14s	1000.0 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	6L + 13s	1036.4 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	5L + 15s	1000.0 ¢ to 1090.9 ¢
	Major 20-mosstep	M20ms	6L + 14s	1090.9 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	5L + 16s	1000.0 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	6L + 15s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	6L + 16s	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 6L 16s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\22						381.818	218.182	1:1	1.000	Equalized 6L 16s
					37\116	382.759	217.241	6:5	1.200
				30\94		382.979	217.021	5:4	1.250
					53\166	383.133	216.867	9:7	1.286
			23\72			383.333	216.667	4:3	1.333	Supersoft 6L 16s
					62\194	383.505	216.495	11:8	1.375
				39\122		383.607	216.393	7:5	1.400
					55\172	383.721	216.279	10:7	1.429
		16\50				384.000	216.000	3:2	1.500	Soft 6L 16s
					57\178	384.270	215.730	11:7	1.571
				41\128		384.375	215.625	8:5	1.600
					66\206	384.466	215.534	13:8	1.625
			25\78			384.615	215.385	5:3	1.667	Semisoft 6L 16s
					59\184	384.783	215.217	12:7	1.714
				34\106		384.906	215.094	7:4	1.750
					43\134	385.075	214.925	9:5	1.800
	9\28					385.714	214.286	2:1	2.000	Basic 6L 16s Scales with tunings softer than this are proper
					38\118	386.441	213.559	9:4	2.250
				29\90		386.667	213.333	7:3	2.333
					49\152	386.842	213.158	12:5	2.400
			20\62			387.097	212.903	5:2	2.500	Semihard 6L 16s
					51\158	387.342	212.658	13:5	2.600
				31\96		387.500	212.500	8:3	2.667
					42\130	387.692	212.308	11:4	2.750
		11\34				388.235	211.765	3:1	3.000	Hard 6L 16s
					35\108	388.889	211.111	10:3	3.333
				24\74		389.189	210.811	7:2	3.500
					37\114	389.474	210.526	11:3	3.667
			13\40			390.000	210.000	4:1	4.000	Superhard 6L 16s
					28\86	390.698	209.302	9:2	4.500
				15\46		391.304	208.696	5:1	5.000
					17\52	392.308	207.692	6:1	6.000
2\6						400.000	200.000	1:0	→ ∞	Collapsed 6L 16s