13L 9s

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 ¢.

↖ 12L 8s	↑ 13L 8s	14L 8s ↗
← 12L 9s	13L 9s	14L 9s →
↙ 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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Modes

Modes of 13L 9s

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

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

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