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¢)
Step size ranges
Large	1\17 to 1\16 (70.6¢ to 75.0¢)
Small	0\16 to 1\17 (0.0¢ to 70.6¢)
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)
Related MOS scales
Parent	1L 15s
Sister	1L 16s
Daughters	17L 16s 16L 17s
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 degrees

Scale degree of 16L 1s

Scale degree	33edo (Basic, L:s = 2:1)		Approx. JI Ratios
	Steps	Cents
Perfect 0-mosdegree (unison)	0	0	1/1 (exact)
Diminished 1-mosdegree	1	36.4
Perfect 1-mosdegree	2	72.7
Minor 2-mosdegree	3	109.1
Major 2-mosdegree	4	145.5
Minor 3-mosdegree	5	181.8
Major 3-mosdegree	6	218.2
Minor 4-mosdegree	7	254.5
Major 4-mosdegree	8	290.9
Minor 5-mosdegree	9	327.3
Major 5-mosdegree	10	363.6
Minor 6-mosdegree	11	400
Major 6-mosdegree	12	436.4
Minor 7-mosdegree	13	472.7
Major 7-mosdegree	14	509.1
Minor 8-mosdegree	15	545.5
Major 8-mosdegree	16	581.8
Minor 9-mosdegree	17	618.2
Major 9-mosdegree	18	654.5
Minor 10-mosdegree	19	690.9
Major 10-mosdegree	20	727.3
Minor 11-mosdegree	21	763.6
Major 11-mosdegree	22	800
Minor 12-mosdegree	23	836.4
Major 12-mosdegree	24	872.7
Minor 13-mosdegree	25	909.1
Major 13-mosdegree	26	945.5
Minor 14-mosdegree	27	981.8
Major 14-mosdegree	28	1018.2
Minor 15-mosdegree	29	1054.5
Major 15-mosdegree	30	1090.9
Perfect 16-mosdegree	31	1127.3
Augmented 16-mosdegree	32	1163.6
Perfect 17-mosdegree (octave)	33	1200	2/1 (exact)

Scale tree

Scale tree and tuning spectrum of 16L 1s

Generator (in steps of edo)						Cents		Step ratio		Comments (Every tuning produces a proper scale)
						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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