13L 4s

↖ 12L 3s	↑ 13L 3s	14L 3s ↗
← 12L 4s	13L 4s	14L 4s →
↙ 12L 5s	↓ 13L 5s	14L 5s ↘

┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║│║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\17 to 10\13 (917.6¢ to 923.1¢)
Dark	3\13 to 4\17 (276.9¢ to 282.4¢)
TAMNAMS information
Descends from	4L 5s (gramitonic)
Ancestor's step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	4L 9s
Sister	4L 13s
Daughters	17L 13s, 13L 17s
Neutralized	9L 8s
2-Flought	30L 4s, 13L 21s
Equal tunings
Equalized (L:s = 1:1)	13\17 (917.6¢)
Supersoft (L:s = 4:3)	49\64 (918.8¢)
Soft (L:s = 3:2)	36\47 (919.1¢)
Semisoft (L:s = 5:3)	59\77 (919.5¢)
Basic (L:s = 2:1)	23\30 (920.0¢)
Semihard (L:s = 5:2)	56\73 (920.5¢)
Hard (L:s = 3:1)	33\43 (920.9¢)
Superhard (L:s = 4:1)	43\56 (921.4¢)
Collapsed (L:s = 1:0)	10\13 (923.1¢)

13L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 4 small steps, repeating every octave. 13L 4s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 917.6¢ to 923.1¢, or from 276.9¢ to 282.4¢.

Modes

Modes of 13L 4s

UDP	Cyclic order	Step pattern
16|0	1	LLLLsLLLsLLLsLLLs
15|1	14	LLLsLLLLsLLLsLLLs
14|2	10	LLLsLLLsLLLLsLLLs
13|3	6	LLLsLLLsLLLsLLLLs
12|4	2	LLLsLLLsLLLsLLLsL
11|5	15	LLsLLLLsLLLsLLLsL
10|6	11	LLsLLLsLLLLsLLLsL
9|7	7	LLsLLLsLLLsLLLLsL
8|8	3	LLsLLLsLLLsLLLsLL
7|9	16	LsLLLLsLLLsLLLsLL
6|10	12	LsLLLsLLLLsLLLsLL
5|11	8	LsLLLsLLLsLLLLsLL
4|12	4	LsLLLsLLLsLLLsLLL
3|13	17	sLLLLsLLLsLLLsLLL
2|14	13	sLLLsLLLLsLLLsLLL
1|15	9	sLLLsLLLsLLLLsLLL
0|16	5	sLLLsLLLsLLLsLLLL

Intervals

Intervals of 13L 4s

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 70.6¢
	Major 1-mosstep	M1ms	L	70.6¢ to 92.3¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3¢ to 141.2¢
	Major 2-mosstep	M2ms	2L	141.2¢ to 184.6¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	184.6¢ to 211.8¢
	Major 3-mosstep	M3ms	3L	211.8¢ to 276.9¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	276.9¢ to 282.4¢
	Augmented 4-mosstep	A4ms	4L	282.4¢ to 369.2¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	276.9¢ to 352.9¢
	Major 5-mosstep	M5ms	4L + s	352.9¢ to 369.2¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	369.2¢ to 423.5¢
	Major 6-mosstep	M6ms	5L + s	423.5¢ to 461.5¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	461.5¢ to 494.1¢
	Major 7-mosstep	M7ms	6L + s	494.1¢ to 553.8¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	553.8¢ to 564.7¢
	Major 8-mosstep	M8ms	7L + s	564.7¢ to 646.2¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	553.8¢ to 635.3¢
	Major 9-mosstep	M9ms	7L + 2s	635.3¢ to 646.2¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	646.2¢ to 705.9¢
	Major 10-mosstep	M10ms	8L + 2s	705.9¢ to 738.5¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	738.5¢ to 776.5¢
	Major 11-mosstep	M11ms	9L + 2s	776.5¢ to 830.8¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	830.8¢ to 847.1¢
	Major 12-mosstep	M12ms	10L + 2s	847.1¢ to 923.1¢
13-mosstep	Diminished 13-mosstep	d13ms	9L + 4s	830.8¢ to 917.6¢
	Perfect 13-mosstep	P13ms	10L + 3s	917.6¢ to 923.1¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	923.1¢ to 988.2¢
	Major 14-mosstep	M14ms	11L + 3s	988.2¢ to 1015.4¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	1015.4¢ to 1058.8¢
	Major 15-mosstep	M15ms	12L + 3s	1058.8¢ to 1107.7¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	1107.7¢ to 1129.4¢
	Major 16-mosstep	M16ms	13L + 3s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	13L + 4s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 13L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\17						917.647	282.353	1:1	1.000	Equalized 13L 4s
					75\98	918.367	281.633	6:5	1.200
				62\81		918.519	281.481	5:4	1.250
					111\145	918.621	281.379	9:7	1.286
			49\64			918.750	281.250	4:3	1.333	Supersoft 13L 4s
					134\175	918.857	281.143	11:8	1.375
				85\111		918.919	281.081	7:5	1.400
					121\158	918.987	281.013	10:7	1.429
		36\47				919.149	280.851	3:2	1.500	Soft 13L 4s
					131\171	919.298	280.702	11:7	1.571
				95\124		919.355	280.645	8:5	1.600
					154\201	919.403	280.597	13:8	1.625
			59\77			919.481	280.519	5:3	1.667	Semisoft 13L 4s
					141\184	919.565	280.435	12:7	1.714
				82\107		919.626	280.374	7:4	1.750
					105\137	919.708	280.292	9:5	1.800
	23\30					920.000	280.000	2:1	2.000	Basic 13L 4s Scales with tunings softer than this are proper
					102\133	920.301	279.699	9:4	2.250
				79\103		920.388	279.612	7:3	2.333
					135\176	920.455	279.545	12:5	2.400
			56\73			920.548	279.452	5:2	2.500	Semihard 13L 4s
					145\189	920.635	279.365	13:5	2.600
				89\116		920.690	279.310	8:3	2.667
					122\159	920.755	279.245	11:4	2.750
		33\43				920.930	279.070	3:1	3.000	Hard 13L 4s
					109\142	921.127	278.873	10:3	3.333
				76\99		921.212	278.788	7:2	3.500
					119\155	921.290	278.710	11:3	3.667
			43\56			921.429	278.571	4:1	4.000	Superhard 13L 4s
					96\125	921.600	278.400	9:2	4.500
				53\69		921.739	278.261	5:1	5.000
					63\82	921.951	278.049	6:1	6.000
10\13						923.077	276.923	1:0	→ ∞	Collapsed 13L 4s

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