15L 1s


← 14L 1s	15L 1s	16L 1s →
↙ 14L 2s	↓ 15L 2s	16L 2s ↘

┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║║║║║║║││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

1\16 to 1\15 (75.0 ¢ to 80.0 ¢)

Dark

14\15 to 15\16 (1120.0 ¢ to 1125.0 ¢)

TAMNAMS information

Descends from

1L 9s (antisinatonic)

Ancestor's step ratio range

6:1 to 7:1

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

1\16 (75.0 ¢)

Supersoft (L:s = 4:3)

4\63 (76.2 ¢)

3\47 (76.6 ¢)

5\78 (76.9 ¢)

2\31 (77.4 ¢)

5\77 (77.9 ¢)

3\46 (78.3 ¢)

Superhard (L:s = 4:1)

4\61 (78.7 ¢)

Collapsed (L:s = 1:0)

1\15 (80.0 ¢)

15L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 1 small step, repeating every octave. 15L 1s is related to 1L 9s, expanding it by 6 tones. Generators that produce this scale range from 75 ¢ to 80 ¢, or from 1120 ¢ to 1125 ¢. Scales of this form are always proper because there is only one small step.

It is notable for corresponding to valentine[16].

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

Intervals of 15L 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 75.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	L	75.0 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0 ¢ to 150.0 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	150.0 ¢ to 160.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	160.0 ¢ to 225.0 ¢
3-mosstep	Major 3-mosstep	M3ms	3L	225.0 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	240.0 ¢ to 300.0 ¢
4-mosstep	Major 4-mosstep	M4ms	4L	300.0 ¢ to 320.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	320.0 ¢ to 375.0 ¢
5-mosstep	Major 5-mosstep	M5ms	5L	375.0 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	400.0 ¢ to 450.0 ¢
6-mosstep	Major 6-mosstep	M6ms	6L	450.0 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	480.0 ¢ to 525.0 ¢
7-mosstep	Major 7-mosstep	M7ms	7L	525.0 ¢ to 560.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	560.0 ¢ to 600.0 ¢
8-mosstep	Major 8-mosstep	M8ms	8L	600.0 ¢ to 640.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	640.0 ¢ to 675.0 ¢
9-mosstep	Major 9-mosstep	M9ms	9L	675.0 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	720.0 ¢ to 750.0 ¢
10-mosstep	Major 10-mosstep	M10ms	10L	750.0 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	800.0 ¢ to 825.0 ¢
11-mosstep	Major 11-mosstep	M11ms	11L	825.0 ¢ to 880.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	880.0 ¢ to 900.0 ¢
12-mosstep	Major 12-mosstep	M12ms	12L	900.0 ¢ to 960.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	960.0 ¢ to 975.0 ¢
13-mosstep	Major 13-mosstep	M13ms	13L	975.0 ¢ to 1040.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	1040.0 ¢ to 1050.0 ¢
14-mosstep	Major 14-mosstep	M14ms	14L	1050.0 ¢ to 1120.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	14L + s	1120.0 ¢ to 1125.0 ¢
15-mosstep	Augmented 15-mosstep	A15ms	15L	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	15L + s	1200.0 ¢

Generator chain

Generator chain of 15L 1s
Bright gens	Scale degree	Abbrev.
30	Augmented 14-mosdegree	A14md
29	Augmented 13-mosdegree	A13md
28	Augmented 12-mosdegree	A12md
27	Augmented 11-mosdegree	A11md
26	Augmented 10-mosdegree	A10md
25	Augmented 9-mosdegree	A9md
24	Augmented 8-mosdegree	A8md
23	Augmented 7-mosdegree	A7md
22	Augmented 6-mosdegree	A6md
21	Augmented 5-mosdegree	A5md
20	Augmented 4-mosdegree	A4md
19	Augmented 3-mosdegree	A3md
18	Augmented 2-mosdegree	A2md
17	Augmented 1-mosdegree	A1md
16	Augmented 0-mosdegree	A0md
15	Augmented 15-mosdegree	A15md
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 16-mosdegree	P0md P16md
−1	Perfect 15-mosdegree	P15md
−2	Minor 14-mosdegree	m14md
−3	Minor 13-mosdegree	m13md
−4	Minor 12-mosdegree	m12md
−5	Minor 11-mosdegree	m11md
−6	Minor 10-mosdegree	m10md
−7	Minor 9-mosdegree	m9md
−8	Minor 8-mosdegree	m8md
−9	Minor 7-mosdegree	m7md
−10	Minor 6-mosdegree	m6md
−11	Minor 5-mosdegree	m5md
−12	Minor 4-mosdegree	m4md
−13	Minor 3-mosdegree	m3md
−14	Minor 2-mosdegree	m2md
−15	Diminished 1-mosdegree	d1md
−16	Diminished 16-mosdegree	d16md
−17	Diminished 15-mosdegree	d15md
−18	Diminished 14-mosdegree	d14md
−19	Diminished 13-mosdegree	d13md
−20	Diminished 12-mosdegree	d12md
−21	Diminished 11-mosdegree	d11md
−22	Diminished 10-mosdegree	d10md
−23	Diminished 9-mosdegree	d9md
−24	Diminished 8-mosdegree	d8md
−25	Diminished 7-mosdegree	d7md
−26	Diminished 6-mosdegree	d6md
−27	Diminished 5-mosdegree	d5md
−28	Diminished 4-mosdegree	d4md
−29	Diminished 3-mosdegree	d3md
−30	Diminished 2-mosdegree	d2md

Modes

Scale degrees of the modes of 15L 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
15\|0	1	LLLLLLLLLLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
14\|1	2	LLLLLLLLLLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
13\|2	3	LLLLLLLLLLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
12\|3	4	LLLLLLLLLLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
11\|4	5	LLLLLLLLLLLsLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
10\|5	6	LLLLLLLLLLsLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
9\|6	7	LLLLLLLLLsLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
8\|7	8	LLLLLLLLsLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
7\|8	9	LLLLLLLsLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
6\|9	10	LLLLLLsLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
5\|10	11	LLLLLsLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
4\|11	12	LLLLsLLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
3\|12	13	LLLsLLLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
2\|13	14	LLsLLLLLLLLLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
1\|14	15	LsLLLLLLLLLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|15	16	sLLLLLLLLLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 15L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
1\16						75.000	1125.000	1:1	1.000	Equalized 15L 1s
					6\95	75.789	1124.211	6:5	1.200
				5\79		75.949	1124.051	5:4	1.250
					9\142	76.056	1123.944	9:7	1.286
			4\63			76.190	1123.810	4:3	1.333	Supersoft 15L 1s
					11\173	76.301	1123.699	11:8	1.375
				7\110		76.364	1123.636	7:5	1.400
					10\157	76.433	1123.567	10:7	1.429
		3\47				76.596	1123.404	3:2	1.500	Soft 15L 1s
					11\172	76.744	1123.256	11:7	1.571
				8\125		76.800	1123.200	8:5	1.600
					13\203	76.847	1123.153	13:8	1.625
			5\78			76.923	1123.077	5:3	1.667	Semisoft 15L 1s
					12\187	77.005	1122.995	12:7	1.714
				7\109		77.064	1122.936	7:4	1.750
					9\140	77.143	1122.857	9:5	1.800	Tertia / Tertiaseptal
	2\31					77.419	1122.581	2:1	2.000	Basic 15L 1s
					9\139	77.698	1122.302	9:4	2.250
				7\108		77.778	1122.222	7:3	2.333
					12\185	77.838	1122.162	12:5	2.400
			5\77			77.922	1122.078	5:2	2.500	Semihard 15L 1s
					13\200	78.000	1122.000	13:5	2.600
				8\123		78.049	1121.951	8:3	2.667	Valentine
					11\169	78.107	1121.893	11:4	2.750
		3\46				78.261	1121.739	3:1	3.000	Hard 15L 1s
					10\153	78.431	1121.569	10:3	3.333
				7\107		78.505	1121.495	7:2	3.500
					11\168	78.571	1121.429	11:3	3.667
			4\61			78.689	1121.311	4:1	4.000	Superhard 15L 1s
					9\137	78.832	1121.168	9:2	4.500
				5\76		78.947	1121.053	5:1	5.000
					6\91	79.121	1120.879	6:1	6.000
1\15						80.000	1120.000	1:0	→ ∞	Collapsed 15L 1s

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15L 1s

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

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