16L 3s

↖ 15L 2s	↑ 16L 2s	17L 2s ↗
← 15L 3s	16L 3s	17L 3s →
↙ 15L 4s	↓ 16L 4s	17L 4s ↘

┌╥╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║│║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLsLLLLLsLLLLLs sLLLLLsLLLLLsLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\19 to 11\16 (821.1¢ to 825.0¢)
Dark	5\16 to 6\19 (375.0¢ to 378.9¢)
TAMNAMS information
Descends from	3L 7s
Ancestor's step ratio range	3:1 to 4:1 (parahard)
Related MOS scales
Parent	3L 13s
Sister	3L 16s
Daughters	19L 16s, 16L 19s
Neutralized	13L 6s
2-Flought	35L 3s, 16L 22s
Equal tunings
Equalized (L:s = 1:1)	13\19 (821.1¢)
Supersoft (L:s = 4:3)	50\73 (821.9¢)
Soft (L:s = 3:2)	37\54 (822.2¢)
Semisoft (L:s = 5:3)	61\89 (822.5¢)
Basic (L:s = 2:1)	24\35 (822.9¢)
Semihard (L:s = 5:2)	59\86 (823.3¢)
Hard (L:s = 3:1)	35\51 (823.5¢)
Superhard (L:s = 4:1)	46\67 (823.9¢)
Collapsed (L:s = 1:0)	11\16 (825.0¢)

16L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 3 small steps, repeating every octave. 16L 3s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 821.1¢ to 825¢, or from 375¢ to 378.9¢.

Modes

Modes of 16L 3s

UDP	Cyclic order	Step pattern
18|0	1	LLLLLLsLLLLLsLLLLLs
17|1	14	LLLLLsLLLLLLsLLLLLs
16|2	8	LLLLLsLLLLLsLLLLLLs
15|3	2	LLLLLsLLLLLsLLLLLsL
14|4	15	LLLLsLLLLLLsLLLLLsL
13|5	9	LLLLsLLLLLsLLLLLLsL
12|6	3	LLLLsLLLLLsLLLLLsLL
11|7	16	LLLsLLLLLLsLLLLLsLL
10|8	10	LLLsLLLLLsLLLLLLsLL
9|9	4	LLLsLLLLLsLLLLLsLLL
8|10	17	LLsLLLLLLsLLLLLsLLL
7|11	11	LLsLLLLLsLLLLLLsLLL
6|12	5	LLsLLLLLsLLLLLsLLLL
5|13	18	LsLLLLLLsLLLLLsLLLL
4|14	12	LsLLLLLsLLLLLLsLLLL
3|15	6	LsLLLLLsLLLLLsLLLLL
2|16	19	sLLLLLLsLLLLLsLLLLL
1|17	13	sLLLLLsLLLLLLsLLLLL
0|18	7	sLLLLLsLLLLLsLLLLLL

Intervals

Intervals of 16L 3s

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 63.2¢
	Major 1-mosstep	M1ms	L	63.2¢ to 75.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0¢ to 126.3¢
	Major 2-mosstep	M2ms	2L	126.3¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0¢ to 189.5¢
	Major 3-mosstep	M3ms	3L	189.5¢ to 225.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	225.0¢ to 252.6¢
	Major 4-mosstep	M4ms	4L	252.6¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	300.0¢ to 315.8¢
	Major 5-mosstep	M5ms	5L	315.8¢ to 375.0¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	375.0¢ to 378.9¢
	Augmented 6-mosstep	A6ms	6L	378.9¢ to 450.0¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	375.0¢ to 442.1¢
	Major 7-mosstep	M7ms	6L + s	442.1¢ to 450.0¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	450.0¢ to 505.3¢
	Major 8-mosstep	M8ms	7L + s	505.3¢ to 525.0¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	525.0¢ to 568.4¢
	Major 9-mosstep	M9ms	8L + s	568.4¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	600.0¢ to 631.6¢
	Major 10-mosstep	M10ms	9L + s	631.6¢ to 675.0¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	675.0¢ to 694.7¢
	Major 11-mosstep	M11ms	10L + s	694.7¢ to 750.0¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	750.0¢ to 757.9¢
	Major 12-mosstep	M12ms	11L + s	757.9¢ to 825.0¢
13-mosstep	Diminished 13-mosstep	d13ms	10L + 3s	750.0¢ to 821.1¢
	Perfect 13-mosstep	P13ms	11L + 2s	821.1¢ to 825.0¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	825.0¢ to 884.2¢
	Major 14-mosstep	M14ms	12L + 2s	884.2¢ to 900.0¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	900.0¢ to 947.4¢
	Major 15-mosstep	M15ms	13L + 2s	947.4¢ to 975.0¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	975.0¢ to 1010.5¢
	Major 16-mosstep	M16ms	14L + 2s	1010.5¢ to 1050.0¢
17-mosstep	Minor 17-mosstep	m17ms	14L + 3s	1050.0¢ to 1073.7¢
	Major 17-mosstep	M17ms	15L + 2s	1073.7¢ to 1125.0¢
18-mosstep	Minor 18-mosstep	m18ms	15L + 3s	1125.0¢ to 1136.8¢
	Major 18-mosstep	M18ms	16L + 2s	1136.8¢ to 1200.0¢
19-mosstep	Perfect 19-mosstep	P19ms	16L + 3s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 16L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\19						821.053	378.947	1:1	1.000	Equalized 16L 3s
					76\111	821.622	378.378	6:5	1.200
				63\92		821.739	378.261	5:4	1.250
					113\165	821.818	378.182	9:7	1.286
			50\73			821.918	378.082	4:3	1.333	Supersoft 16L 3s
					137\200	822.000	378.000	11:8	1.375
				87\127		822.047	377.953	7:5	1.400
					124\181	822.099	377.901	10:7	1.429
		37\54				822.222	377.778	3:2	1.500	Soft 16L 3s
					135\197	822.335	377.665	11:7	1.571
				98\143		822.378	377.622	8:5	1.600
					159\232	822.414	377.586	13:8	1.625
			61\89			822.472	377.528	5:3	1.667	Semisoft 16L 3s
					146\213	822.535	377.465	12:7	1.714
				85\124		822.581	377.419	7:4	1.750
					109\159	822.642	377.358	9:5	1.800
	24\35					822.857	377.143	2:1	2.000	Basic 16L 3s Scales with tunings softer than this are proper
					107\156	823.077	376.923	9:4	2.250
				83\121		823.140	376.860	7:3	2.333
					142\207	823.188	376.812	12:5	2.400
			59\86			823.256	376.744	5:2	2.500	Semihard 16L 3s
					153\223	823.318	376.682	13:5	2.600
				94\137		823.358	376.642	8:3	2.667
					129\188	823.404	376.596	11:4	2.750
		35\51				823.529	376.471	3:1	3.000	Hard 16L 3s
					116\169	823.669	376.331	10:3	3.333
				81\118		823.729	376.271	7:2	3.500
					127\185	823.784	376.216	11:3	3.667
			46\67			823.881	376.119	4:1	4.000	Superhard 16L 3s
					103\150	824.000	376.000	9:2	4.500
				57\83		824.096	375.904	5:1	5.000
					68\99	824.242	375.758	6:1	6.000
11\16						825.000	375.000	1:0	→ ∞	Collapsed 16L 3s

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