13L 9s

↖ 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
Descends from	4L 5s (gramitonic)
Ancestor's step ratio range	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¢)

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¢.

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

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¢

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

This page is a stub. You can help the Xenharmonic Wiki by expanding it.