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

Equal tunings

Equalized (L:s = 1:1)

1\17 (70.6 ¢)

Supersoft (L:s = 4:3)

4\67 (71.6 ¢)

3\50 (72.0 ¢)

5\83 (72.3 ¢)

2\33 (72.7 ¢)

5\82 (73.2 ¢)

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.

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 diatonic interval categories.

Intervals

The intervals of 16L 1s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 17-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

Intervals of 16L 1s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 70.6 ¢
1-mosstep	Perfect 1-mosstep	P1ms	L	70.6 ¢ to 75.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	75.0 ¢ to 141.2 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	141.2 ¢ to 150.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	150.0 ¢ to 211.8 ¢
3-mosstep	Major 3-mosstep	M3ms	3L	211.8 ¢ to 225.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	225.0 ¢ to 282.4 ¢
4-mosstep	Major 4-mosstep	M4ms	4L	282.4 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	300.0 ¢ to 352.9 ¢
5-mosstep	Major 5-mosstep	M5ms	5L	352.9 ¢ to 375.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	375.0 ¢ to 423.5 ¢
6-mosstep	Major 6-mosstep	M6ms	6L	423.5 ¢ to 450.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	450.0 ¢ to 494.1 ¢
7-mosstep	Major 7-mosstep	M7ms	7L	494.1 ¢ to 525.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	525.0 ¢ to 564.7 ¢
8-mosstep	Major 8-mosstep	M8ms	8L	564.7 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	600.0 ¢ to 635.3 ¢
9-mosstep	Major 9-mosstep	M9ms	9L	635.3 ¢ to 675.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	675.0 ¢ to 705.9 ¢
10-mosstep	Major 10-mosstep	M10ms	10L	705.9 ¢ to 750.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	750.0 ¢ to 776.5 ¢
11-mosstep	Major 11-mosstep	M11ms	11L	776.5 ¢ to 825.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	825.0 ¢ to 847.1 ¢
12-mosstep	Major 12-mosstep	M12ms	12L	847.1 ¢ to 900.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	900.0 ¢ to 917.6 ¢
13-mosstep	Major 13-mosstep	M13ms	13L	917.6 ¢ to 975.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	975.0 ¢ to 988.2 ¢
14-mosstep	Major 14-mosstep	M14ms	14L	988.2 ¢ to 1050.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	14L + s	1050.0 ¢ to 1058.8 ¢
15-mosstep	Major 15-mosstep	M15ms	15L	1058.8 ¢ to 1125.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	15L + s	1125.0 ¢ to 1129.4 ¢
16-mosstep	Augmented 16-mosstep	A16ms	16L	1129.4 ¢ to 1200.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	16L + s	1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 1-mosstep, produces the following scale degrees. A chain of 17 bright generators contains the scale degrees of one of the modes of 16L 1s. Expanding the chain to 33 scale degrees produces the modes of either 17L 16s (for soft-of-basic tunings) or 16L 17s (for hard-of-basic tunings).

Generator chain of 16L 1s
Bright gens	Scale degree	Abbrev.
32	Augmented 15-mosdegree	A15md
31	Augmented 14-mosdegree	A14md
30	Augmented 13-mosdegree	A13md
29	Augmented 12-mosdegree	A12md
28	Augmented 11-mosdegree	A11md
27	Augmented 10-mosdegree	A10md
26	Augmented 9-mosdegree	A9md
25	Augmented 8-mosdegree	A8md
24	Augmented 7-mosdegree	A7md
23	Augmented 6-mosdegree	A6md
22	Augmented 5-mosdegree	A5md
21	Augmented 4-mosdegree	A4md
20	Augmented 3-mosdegree	A3md
19	Augmented 2-mosdegree	A2md
18	Augmented 1-mosdegree	A1md
17	Augmented 0-mosdegree	A0md
16	Augmented 16-mosdegree	A16md
15	Major 15-mosdegree	M15md
14	Major 14-mosdegree	M14md
13	Major 13-mosdegree	M13md
12	Major 12-mosdegree	M12md
11	Major 11-mosdegree	M11md
10	Major 10-mosdegree	M10md
9	Major 9-mosdegree	M9md
8	Major 8-mosdegree	M8md
7	Major 7-mosdegree	M7md
6	Major 6-mosdegree	M6md
5	Major 5-mosdegree	M5md
4	Major 4-mosdegree	M4md
3	Major 3-mosdegree	M3md
2	Major 2-mosdegree	M2md
1	Perfect 1-mosdegree	P1md
0	Perfect 0-mosdegree Perfect 17-mosdegree	P0md P17md
−1	Perfect 16-mosdegree	P16md
−2	Minor 15-mosdegree	m15md
−3	Minor 14-mosdegree	m14md
−4	Minor 13-mosdegree	m13md
−5	Minor 12-mosdegree	m12md
−6	Minor 11-mosdegree	m11md
−7	Minor 10-mosdegree	m10md
−8	Minor 9-mosdegree	m9md
−9	Minor 8-mosdegree	m8md
−10	Minor 7-mosdegree	m7md
−11	Minor 6-mosdegree	m6md
−12	Minor 5-mosdegree	m5md
−13	Minor 4-mosdegree	m4md
−14	Minor 3-mosdegree	m3md
−15	Minor 2-mosdegree	m2md
−16	Diminished 1-mosdegree	d1md
−17	Diminished 17-mosdegree	d17md
−18	Diminished 16-mosdegree	d16md
−19	Diminished 15-mosdegree	d15md
−20	Diminished 14-mosdegree	d14md
−21	Diminished 13-mosdegree	d13md
−22	Diminished 12-mosdegree	d12md
−23	Diminished 11-mosdegree	d11md
−24	Diminished 10-mosdegree	d10md
−25	Diminished 9-mosdegree	d9md
−26	Diminished 8-mosdegree	d8md
−27	Diminished 7-mosdegree	d7md
−28	Diminished 6-mosdegree	d6md
−29	Diminished 5-mosdegree	d5md
−30	Diminished 4-mosdegree	d4md
−31	Diminished 3-mosdegree	d3md
−32	Diminished 2-mosdegree	d2md

Modes

Scale degrees of the modes of 16L 1s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
16\|0	1	LLLLLLLLLLLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
15\|1	2	LLLLLLLLLLLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
14\|2	3	LLLLLLLLLLLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
13\|3	4	LLLLLLLLLLLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
12\|4	5	LLLLLLLLLLLLsLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
11\|5	6	LLLLLLLLLLLsLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
10\|6	7	LLLLLLLLLLsLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
9\|7	8	LLLLLLLLLsLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
8\|8	9	LLLLLLLLsLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
7\|9	10	LLLLLLLsLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
6\|10	11	LLLLLLsLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
5\|11	12	LLLLLsLLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
4\|12	13	LLLLsLLLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
3\|13	14	LLLsLLLLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
2\|14	15	LLsLLLLLLLLLLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
1\|15	16	LsLLLLLLLLLLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|16	17	sLLLLLLLLLLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 16L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
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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16L 1s

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

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