13L 9s

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↙ 12L 10s	↓ 13L 10s	14L 10s ↘

Scale structure
Step pattern	LLsLsLLsLsLLsLsLLsLsLs sLsLsLLsLsLLsLsLLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\22 to 3\13 (272.7 ¢ to 276.9 ¢)
Dark	10\13 to 17\22 (923.1 ¢ to 927.3 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	9L 4s
Sister	9L 13s
Daughters	22L 13s, 13L 22s
Neutralized	4L 18s
2-Flought	35L 9s, 13L 31s
Equal tunings
Equalized (L:s = 1:1)	5\22 (272.7 ¢)
Supersoft (L:s = 4:3)	18\79 (273.4 ¢)
Soft (L:s = 3:2)	13\57 (273.7 ¢)
Semisoft (L:s = 5:3)	21\92 (273.9 ¢)
Basic (L:s = 2:1)	8\35 (274.3 ¢)
Semihard (L:s = 5:2)	19\83 (274.7 ¢)
Hard (L:s = 3:1)	11\48 (275.0 ¢)
Superhard (L:s = 4:1)	14\61 (275.4 ¢)
Collapsed (L:s = 1:0)	3\13 (276.9 ¢)
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13L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 9 small steps, repeating every octave. 13L 9s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 272.7 ¢ to 276.9 ¢, or from 923.1 ¢ to 927.3 ¢.

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 interval regions.

Intervals

Intervals of 13L 9s

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 54.5 ¢
	Major 1-mosstep	M1ms	L	54.5 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 109.1 ¢
	Major 2-mosstep	M2ms	2L	109.1 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	92.3 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	2L + s	163.6 ¢ to 184.6 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	184.6 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	3L + s	218.2 ¢ to 276.9 ¢
5-mosstep	Diminished 5-mosstep	d5ms	2L + 3s	184.6 ¢ to 272.7 ¢
	Perfect 5-mosstep	P5ms	3L + 2s	272.7 ¢ to 276.9 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	276.9 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	4L + 2s	327.3 ¢ to 369.2 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	369.2 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	5L + 2s	381.8 ¢ to 461.5 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	369.2 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	5L + 3s	436.4 ¢ to 461.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	461.5 ¢ to 490.9 ¢
	Major 9-mosstep	M9ms	6L + 3s	490.9 ¢ to 553.8 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	461.5 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	6L + 4s	545.5 ¢ to 553.8 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	553.8 ¢ to 600.0 ¢
	Major 11-mosstep	M11ms	7L + 4s	600.0 ¢ to 646.2 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	646.2 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	8L + 4s	654.5 ¢ to 738.5 ¢
13-mosstep	Minor 13-mosstep	m13ms	7L + 6s	646.2 ¢ to 709.1 ¢
	Major 13-mosstep	M13ms	8L + 5s	709.1 ¢ to 738.5 ¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	738.5 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	9L + 5s	763.6 ¢ to 830.8 ¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	738.5 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	9L + 6s	818.2 ¢ to 830.8 ¢
16-mosstep	Minor 16-mosstep	m16ms	9L + 7s	830.8 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	10L + 6s	872.7 ¢ to 923.1 ¢
17-mosstep	Perfect 17-mosstep	P17ms	10L + 7s	923.1 ¢ to 927.3 ¢
	Augmented 17-mosstep	A17ms	11L + 6s	927.3 ¢ to 1015.4 ¢
18-mosstep	Minor 18-mosstep	m18ms	10L + 8s	923.1 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	11L + 7s	981.8 ¢ to 1015.4 ¢
19-mosstep	Minor 19-mosstep	m19ms	11L + 8s	1015.4 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	12L + 7s	1036.4 ¢ to 1107.7 ¢
20-mosstep	Minor 20-mosstep	m20ms	11L + 9s	1015.4 ¢ to 1090.9 ¢
	Major 20-mosstep	M20ms	12L + 8s	1090.9 ¢ to 1107.7 ¢
21-mosstep	Minor 21-mosstep	m21ms	12L + 9s	1107.7 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	13L + 8s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	13L + 9s	1200.0 ¢

Generator chain

Generator chain of 13L 9s

Bright gens	Scale degree	Abbrev.
34	Augmented 16-mosdegree	A16md
33	Augmented 11-mosdegree	A11md
32	Augmented 6-mosdegree	A6md
31	Augmented 1-mosdegree	A1md
30	Augmented 18-mosdegree	A18md
29	Augmented 13-mosdegree	A13md
28	Augmented 8-mosdegree	A8md
27	Augmented 3-mosdegree	A3md
26	Augmented 20-mosdegree	A20md
25	Augmented 15-mosdegree	A15md
24	Augmented 10-mosdegree	A10md
23	Augmented 5-mosdegree	A5md
22	Augmented 0-mosdegree	A0md
21	Augmented 17-mosdegree	A17md
20	Major 12-mosdegree	M12md
19	Major 7-mosdegree	M7md
18	Major 2-mosdegree	M2md
17	Major 19-mosdegree	M19md
16	Major 14-mosdegree	M14md
15	Major 9-mosdegree	M9md
14	Major 4-mosdegree	M4md
13	Major 21-mosdegree	M21md
12	Major 16-mosdegree	M16md
11	Major 11-mosdegree	M11md
10	Major 6-mosdegree	M6md
9	Major 1-mosdegree	M1md
8	Major 18-mosdegree	M18md
7	Major 13-mosdegree	M13md
6	Major 8-mosdegree	M8md
5	Major 3-mosdegree	M3md
4	Major 20-mosdegree	M20md
3	Major 15-mosdegree	M15md
2	Major 10-mosdegree	M10md
1	Perfect 5-mosdegree	P5md
0	Perfect 0-mosdegree Perfect 22-mosdegree	P0md P22md
−1	Perfect 17-mosdegree	P17md
−2	Minor 12-mosdegree	m12md
−3	Minor 7-mosdegree	m7md
−4	Minor 2-mosdegree	m2md
−5	Minor 19-mosdegree	m19md
−6	Minor 14-mosdegree	m14md
−7	Minor 9-mosdegree	m9md
−8	Minor 4-mosdegree	m4md
−9	Minor 21-mosdegree	m21md
−10	Minor 16-mosdegree	m16md
−11	Minor 11-mosdegree	m11md
−12	Minor 6-mosdegree	m6md
−13	Minor 1-mosdegree	m1md
−14	Minor 18-mosdegree	m18md
−15	Minor 13-mosdegree	m13md
−16	Minor 8-mosdegree	m8md
−17	Minor 3-mosdegree	m3md
−18	Minor 20-mosdegree	m20md
−19	Minor 15-mosdegree	m15md
−20	Minor 10-mosdegree	m10md
−21	Diminished 5-mosdegree	d5md
−22	Diminished 22-mosdegree	d22md
−23	Diminished 17-mosdegree	d17md
−24	Diminished 12-mosdegree	d12md
−25	Diminished 7-mosdegree	d7md
−26	Diminished 2-mosdegree	d2md
−27	Diminished 19-mosdegree	d19md
−28	Diminished 14-mosdegree	d14md
−29	Diminished 9-mosdegree	d9md
−30	Diminished 4-mosdegree	d4md
−31	Diminished 21-mosdegree	d21md
−32	Diminished 16-mosdegree	d16md
−33	Diminished 11-mosdegree	d11md
−34	Diminished 6-mosdegree	d6md

Modes

Scale degrees of the modes of 13L 9s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
21|0	1	LLsLsLLsLsLLsLsLLsLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.
20|1	6	LLsLsLLsLsLLsLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
19|2	11	LLsLsLLsLsLsLLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
18|3	16	LLsLsLsLLsLsLLsLsLLsLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
17|4	21	LsLLsLsLLsLsLLsLsLLsLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
16|5	4	LsLLsLsLLsLsLLsLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
15|6	9	LsLLsLsLLsLsLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
14|7	14	LsLLsLsLsLLsLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
13|8	19	LsLsLLsLsLLsLsLLsLsLLs	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Perf.
12|9	2	LsLsLLsLsLLsLsLLsLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
11|10	7	LsLsLLsLsLLsLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
10|11	12	LsLsLLsLsLsLLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
9|12	17	LsLsLsLLsLsLLsLsLLsLsL	Perf.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
8|13	22	sLLsLsLLsLsLLsLsLLsLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Perf.
7|14	5	sLLsLsLLsLsLLsLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
6|15	10	sLLsLsLLsLsLsLLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
5|16	15	sLLsLsLsLLsLsLLsLsLLsL	Perf.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
4|17	20	sLsLLsLsLLsLsLLsLsLLsL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Maj.	Min.	Perf.
3|18	3	sLsLLsLsLLsLsLLsLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
2|19	8	sLsLLsLsLLsLsLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
1|20	13	sLsLLsLsLsLLsLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0|21	18	sLsLsLLsLsLLsLsLLsLsLL	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 13L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\22						272.727	927.273	1:1	1.000	Equalized 13L 9s
					28\123	273.171	926.829	6:5	1.200
				23\101		273.267	926.733	5:4	1.250
					41\180	273.333	926.667	9:7	1.286
			18\79			273.418	926.582	4:3	1.333	Supersoft 13L 9s
					49\215	273.488	926.512	11:8	1.375
				31\136		273.529	926.471	7:5	1.400
					44\193	273.575	926.425	10:7	1.429
		13\57				273.684	926.316	3:2	1.500	Soft 13L 9s
					47\206	273.786	926.214	11:7	1.571
				34\149		273.826	926.174	8:5	1.600
					55\241	273.859	926.141	13:8	1.625
			21\92			273.913	926.087	5:3	1.667	Semisoft 13L 9s
					50\219	273.973	926.027	12:7	1.714
				29\127		274.016	925.984	7:4	1.750
					37\162	274.074	925.926	9:5	1.800
	8\35					274.286	925.714	2:1	2.000	Basic 13L 9s Scales with tunings softer than this are proper
					35\153	274.510	925.490	9:4	2.250
				27\118		274.576	925.424	7:3	2.333
					46\201	274.627	925.373	12:5	2.400
			19\83			274.699	925.301	5:2	2.500	Semihard 13L 9s
					49\214	274.766	925.234	13:5	2.600
				30\131		274.809	925.191	8:3	2.667
					41\179	274.860	925.140	11:4	2.750
		11\48				275.000	925.000	3:1	3.000	Hard 13L 9s
					36\157	275.159	924.841	10:3	3.333
				25\109		275.229	924.771	7:2	3.500
					39\170	275.294	924.706	11:3	3.667
			14\61			275.410	924.590	4:1	4.000	Superhard 13L 9s
					31\135	275.556	924.444	9:2	4.500
				17\74		275.676	924.324	5:1	5.000
					20\87	275.862	924.138	6:1	6.000
3\13						276.923	923.077	1:0	→ ∞	Collapsed 13L 9s

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