16L 1s

← 15L 1s	16L 1s	17L 1s →
↙ 15L 2s	↓ 16L 2s	17L 2s ↘

┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLLLLLLLLs sLLLLLLLLLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	1\17 to 1\16 (70.6¢ to 75.0¢)
Dark	15\16 to 16\17 (1125.0¢ to 1129.4¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Ancestor's step ratio range	7:1 to 8:1
Related MOS scales
Parent	1L 15s
Sister	1L 16s
Daughters	17L 16s, 16L 17s
Neutralized	15L 2s
2-Flought	33L 1s, 16L 18s
Equal tunings
Equalized (L:s = 1:1)	1\17 (70.6¢)
Supersoft (L:s = 4:3)	4\67 (71.6¢)
Soft (L:s = 3:2)	3\50 (72.0¢)
Semisoft (L:s = 5:3)	5\83 (72.3¢)
Basic (L:s = 2:1)	2\33 (72.7¢)
Semihard (L:s = 5:2)	5\82 (73.2¢)
Hard (L:s = 3:1)	3\49 (73.5¢)
Superhard (L:s = 4:1)	4\65 (73.8¢)
Collapsed (L:s = 1:0)	1\16 (75.0¢)

16L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 1 small step, repeating every octave. 16L 1s is related to 1L 9s, expanding it by 7 tones. Generators that produce this scale range from 70.6¢ to 75¢, or from 1125¢ to 1129.4¢. Scales of this form are always proper because there is only one small step.

MOS intervals

Intervals of 16L 1s

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 70.6¢
	Perfect 1-mosstep	P1ms	L	70.6¢ to 75.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0¢ to 141.2¢
	Major 2-mosstep	M2ms	2L	141.2¢ to 150.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0¢ to 211.8¢
	Major 3-mosstep	M3ms	3L	211.8¢ to 225.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	225.0¢ to 282.4¢
	Major 4-mosstep	M4ms	4L	282.4¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	300.0¢ to 352.9¢
	Major 5-mosstep	M5ms	5L	352.9¢ to 375.0¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	375.0¢ to 423.5¢
	Major 6-mosstep	M6ms	6L	423.5¢ to 450.0¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	450.0¢ to 494.1¢
	Major 7-mosstep	M7ms	7L	494.1¢ to 525.0¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	525.0¢ to 564.7¢
	Major 8-mosstep	M8ms	8L	564.7¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	600.0¢ to 635.3¢
	Major 9-mosstep	M9ms	9L	635.3¢ to 675.0¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	675.0¢ to 705.9¢
	Major 10-mosstep	M10ms	10L	705.9¢ to 750.0¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	750.0¢ to 776.5¢
	Major 11-mosstep	M11ms	11L	776.5¢ to 825.0¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	825.0¢ to 847.1¢
	Major 12-mosstep	M12ms	12L	847.1¢ to 900.0¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	900.0¢ to 917.6¢
	Major 13-mosstep	M13ms	13L	917.6¢ to 975.0¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	975.0¢ to 988.2¢
	Major 14-mosstep	M14ms	14L	988.2¢ to 1050.0¢
15-mosstep	Minor 15-mosstep	m15ms	14L + s	1050.0¢ to 1058.8¢
	Major 15-mosstep	M15ms	15L	1058.8¢ to 1125.0¢
16-mosstep	Perfect 16-mosstep	P16ms	15L + s	1125.0¢ to 1129.4¢
	Augmented 16-mosstep	A16ms	16L	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	16L + s	1200.0¢

Modes

Modes of 16L 1s

UDP	Cyclic order	Step pattern
16|0	1	LLLLLLLLLLLLLLLLs
15|1	2	LLLLLLLLLLLLLLLsL
14|2	3	LLLLLLLLLLLLLLsLL
13|3	4	LLLLLLLLLLLLLsLLL
12|4	5	LLLLLLLLLLLLsLLLL
11|5	6	LLLLLLLLLLLsLLLLL
10|6	7	LLLLLLLLLLsLLLLLL
9|7	8	LLLLLLLLLsLLLLLLL
8|8	9	LLLLLLLLsLLLLLLLL
7|9	10	LLLLLLLsLLLLLLLLL
6|10	11	LLLLLLsLLLLLLLLLL
5|11	12	LLLLLsLLLLLLLLLLL
4|12	13	LLLLsLLLLLLLLLLLL
3|13	14	LLLsLLLLLLLLLLLLL
2|14	15	LLsLLLLLLLLLLLLLL
1|15	16	LsLLLLLLLLLLLLLLL
0|16	17	sLLLLLLLLLLLLLLLL

Scale tree

Scale Tree and Tuning Spectrum of 16L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\17						70.588	1129.412	1:1	1.000	Equalized 16L 1s
					6\101	71.287	1128.713	6:5	1.200
				5\84		71.429	1128.571	5:4	1.250
					9\151	71.523	1128.477	9:7	1.286
			4\67			71.642	1128.358	4:3	1.333	Supersoft 16L 1s
					11\184	71.739	1128.261	11:8	1.375
				7\117		71.795	1128.205	7:5	1.400
					10\167	71.856	1128.144	10:7	1.429
		3\50				72.000	1128.000	3:2	1.500	Soft 16L 1s
					11\183	72.131	1127.869	11:7	1.571
				8\133		72.180	1127.820	8:5	1.600
					13\216	72.222	1127.778	13:8	1.625
			5\83			72.289	1127.711	5:3	1.667	Semisoft 16L 1s
					12\199	72.362	1127.638	12:7	1.714
				7\116		72.414	1127.586	7:4	1.750
					9\149	72.483	1127.517	9:5	1.800
	2\33					72.727	1127.273	2:1	2.000	Basic 16L 1s
					9\148	72.973	1127.027	9:4	2.250
				7\115		73.043	1126.957	7:3	2.333
					12\197	73.096	1126.904	12:5	2.400
			5\82			73.171	1126.829	5:2	2.500	Semihard 16L 1s
					13\213	73.239	1126.761	13:5	2.600
				8\131		73.282	1126.718	8:3	2.667
					11\180	73.333	1126.667	11:4	2.750
		3\49				73.469	1126.531	3:1	3.000	Hard 16L 1s
					10\163	73.620	1126.380	10:3	3.333
				7\114		73.684	1126.316	7:2	3.500
					11\179	73.743	1126.257	11:3	3.667
			4\65			73.846	1126.154	4:1	4.000	Superhard 16L 1s
					9\146	73.973	1126.027	9:2	4.500
				5\81		74.074	1125.926	5:1	5.000
					6\97	74.227	1125.773	6:1	6.000
1\16						75.000	1125.000	1:0	→ ∞	Collapsed 16L 1s

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