2L 16s

2L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 16 small steps, with a period of 1 large step and 8 small steps that repeats every 600.0 ¢, or twice every octave. 2L 16s is related to 2L 8s, expanding it by 8 tones. Generators that produce this scale range from 533.3 ¢ to 600 ¢, or from 0 ¢ to 66.7 ¢.

↖ 1L 15s	↑ 2L 15s	3L 15s ↗
← 1L 16s	2L 16s	3L 16s →
↙ 1L 17s	↓ 2L 17s	3L 17s ↘

Scale structure
Step pattern	LssssssssLssssssss ssssssssLssssssssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	8\18 to 1\2 (533.3 ¢ to 600.0 ¢)
Dark	0\2 to 1\18 (0.0 ¢ to 66.7 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	5:1 to 1:0
Related MOS scales
Parent	2L 14s
Sister	16L 2s
Daughters	18L 2s, 2L 18s
Neutralized	4L 14s
2-Flought	20L 16s, 2L 34s
Equal tunings
Equalized (L:s = 1:1)	8\18 (533.3 ¢)
Supersoft (L:s = 4:3)	25\56 (535.7 ¢)
Soft (L:s = 3:2)	17\38 (536.8 ¢)
Semisoft (L:s = 5:3)	26\58 (537.9 ¢)
Basic (L:s = 2:1)	9\20 (540.0 ¢)
Semihard (L:s = 5:2)	19\42 (542.9 ¢)
Hard (L:s = 3:1)	10\22 (545.5 ¢)
Superhard (L:s = 4:1)	11\24 (550.0 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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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 2L 16s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 66.7 ¢
	Augmented 1-mosstep	A1ms	L	66.7 ¢ to 600.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 133.3 ¢
	Major 2-mosstep	M2ms	L + s	133.3 ¢ to 600.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 200.0 ¢
	Major 3-mosstep	M3ms	L + 2s	200.0 ¢ to 600.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 266.7 ¢
	Major 4-mosstep	M4ms	L + 3s	266.7 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 333.3 ¢
	Major 5-mosstep	M5ms	L + 4s	333.3 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 400.0 ¢
	Major 6-mosstep	M6ms	L + 5s	400.0 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 466.7 ¢
	Major 7-mosstep	M7ms	L + 6s	466.7 ¢ to 600.0 ¢
8-mosstep	Diminished 8-mosstep	d8ms	8s	0.0 ¢ to 533.3 ¢
	Perfect 8-mosstep	P8ms	L + 7s	533.3 ¢ to 600.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	L + 8s	600.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	L + 9s	600.0 ¢ to 666.7 ¢
	Augmented 10-mosstep	A10ms	2L + 8s	666.7 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	600.0 ¢ to 733.3 ¢
	Major 11-mosstep	M11ms	2L + 9s	733.3 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	600.0 ¢ to 800.0 ¢
	Major 12-mosstep	M12ms	2L + 10s	800.0 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0 ¢ to 866.7 ¢
	Major 13-mosstep	M13ms	2L + 11s	866.7 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0 ¢ to 933.3 ¢
	Major 14-mosstep	M14ms	2L + 12s	933.3 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	600.0 ¢ to 1000.0 ¢
	Major 15-mosstep	M15ms	2L + 13s	1000.0 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	600.0 ¢ to 1066.7 ¢
	Major 16-mosstep	M16ms	2L + 14s	1066.7 ¢ to 1200.0 ¢
17-mosstep	Diminished 17-mosstep	d17ms	L + 16s	600.0 ¢ to 1133.3 ¢
	Perfect 17-mosstep	P17ms	2L + 15s	1133.3 ¢ to 1200.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	2L + 16s	1200.0 ¢

Generator chain

Generator chain of 2L 16s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
9	Augmented 0-mosdegree	A0md	Augmented 9-mosdegree	A9md
8	Augmented 1-mosdegree	A1md	Augmented 10-mosdegree	A10md
7	Major 2-mosdegree	M2md	Major 11-mosdegree	M11md
6	Major 3-mosdegree	M3md	Major 12-mosdegree	M12md
5	Major 4-mosdegree	M4md	Major 13-mosdegree	M13md
4	Major 5-mosdegree	M5md	Major 14-mosdegree	M14md
3	Major 6-mosdegree	M6md	Major 15-mosdegree	M15md
2	Major 7-mosdegree	M7md	Major 16-mosdegree	M16md
1	Perfect 8-mosdegree	P8md	Perfect 17-mosdegree	P17md
0	Perfect 0-mosdegree Perfect 9-mosdegree	P0md P9md	Perfect 9-mosdegree Perfect 18-mosdegree	P9md P18md
−1	Perfect 1-mosdegree	P1md	Perfect 10-mosdegree	P10md
−2	Minor 2-mosdegree	m2md	Minor 11-mosdegree	m11md
−3	Minor 3-mosdegree	m3md	Minor 12-mosdegree	m12md
−4	Minor 4-mosdegree	m4md	Minor 13-mosdegree	m13md
−5	Minor 5-mosdegree	m5md	Minor 14-mosdegree	m14md
−6	Minor 6-mosdegree	m6md	Minor 15-mosdegree	m15md
−7	Minor 7-mosdegree	m7md	Minor 16-mosdegree	m16md
−8	Diminished 8-mosdegree	d8md	Diminished 17-mosdegree	d17md
−9	Diminished 9-mosdegree	d9md	Diminished 18-mosdegree	d18md

Modes

Scale degrees of the modes of 2L 16s

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	18
16|0(2)	1	LssssssssLssssssss	Perf.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
14|2(2)	9	sLssssssssLsssssss	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
12|4(2)	8	ssLssssssssLssssss	Perf.	Perf.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Perf.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
10|6(2)	7	sssLssssssssLsssss	Perf.	Perf.	Min.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Perf.	Min.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
8|8(2)	6	ssssLssssssssLssss	Perf.	Perf.	Min.	Min.	Min.	Maj.	Maj.	Maj.	Perf.	Perf.	Perf.	Min.	Min.	Min.	Maj.	Maj.	Maj.	Perf.	Perf.
6|10(2)	5	sssssLssssssssLsss	Perf.	Perf.	Min.	Min.	Min.	Min.	Maj.	Maj.	Perf.	Perf.	Perf.	Min.	Min.	Min.	Min.	Maj.	Maj.	Perf.	Perf.
4|12(2)	4	ssssssLssssssssLss	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Maj.	Perf.	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Maj.	Perf.	Perf.
2|14(2)	3	sssssssLssssssssLs	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0|16(2)	2	ssssssssLssssssssL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Perf.

Scale tree

Scale tree and tuning spectrum of 2L 16s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\18						533.333	66.667	1:1	1.000	Equalized 2L 16s
					41\92	534.783	65.217	6:5	1.200
				33\74		535.135	64.865	5:4	1.250
					58\130	535.385	64.615	9:7	1.286
			25\56			535.714	64.286	4:3	1.333	Supersoft 2L 16s
					67\150	536.000	64.000	11:8	1.375
				42\94		536.170	63.830	7:5	1.400
					59\132	536.364	63.636	10:7	1.429
		17\38				536.842	63.158	3:2	1.500	Soft 2L 16s
					60\134	537.313	62.687	11:7	1.571
				43\96		537.500	62.500	8:5	1.600
					69\154	537.662	62.338	13:8	1.625
			26\58			537.931	62.069	5:3	1.667	Semisoft 2L 16s
					61\136	538.235	61.765	12:7	1.714
				35\78		538.462	61.538	7:4	1.750
					44\98	538.776	61.224	9:5	1.800
	9\20					540.000	60.000	2:1	2.000	Basic 2L 16s Scales with tunings softer than this are proper
					37\82	541.463	58.537	9:4	2.250
				28\62		541.935	58.065	7:3	2.333
					47\104	542.308	57.692	12:5	2.400
			19\42			542.857	57.143	5:2	2.500	Semihard 2L 16s
					48\106	543.396	56.604	13:5	2.600
				29\64		543.750	56.250	8:3	2.667
					39\86	544.186	55.814	11:4	2.750
		10\22				545.455	54.545	3:1	3.000	Hard 2L 16s
					31\68	547.059	52.941	10:3	3.333
				21\46		547.826	52.174	7:2	3.500
					32\70	548.571	51.429	11:3	3.667
			11\24			550.000	50.000	4:1	4.000	Superhard 2L 16s
					23\50	552.000	48.000	9:2	4.500
				12\26		553.846	46.154	5:1	5.000
					13\28	557.143	42.857	6:1	6.000
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 16s