4L 13s

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

┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║│││║│││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLsssLsssLssss ssssLsssLsssLsssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	4\17 to 1\4 (282.4¢ to 300.0¢)
Dark	3\4 to 13\17 (900.0¢ to 917.6¢)
TAMNAMS information
Descends from	4L 5s (gramitonic)
Ancestor's step ratio range	3:1 to 1:0 (hard)
Related MOS scales
Parent	4L 9s
Sister	13L 4s
Daughters	17L 4s, 4L 17s
Neutralized	8L 9s
2-Flought	21L 13s, 4L 30s
Equal tunings
Equalized (L:s = 1:1)	4\17 (282.4¢)
Supersoft (L:s = 4:3)	13\55 (283.6¢)
Soft (L:s = 3:2)	9\38 (284.2¢)
Semisoft (L:s = 5:3)	14\59 (284.7¢)
Basic (L:s = 2:1)	5\21 (285.7¢)
Semihard (L:s = 5:2)	11\46 (287.0¢)
Hard (L:s = 3:1)	6\25 (288.0¢)
Superhard (L:s = 4:1)	7\29 (289.7¢)
Collapsed (L:s = 1:0)	1\4 (300.0¢)

4L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 13 small steps, repeating every octave. 4L 13s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 282.4¢ to 300¢, or from 900¢ to 917.6¢.

Modes

Modes of 4L 13s

UDP	Cyclic order	Step pattern
16|0	1	LsssLsssLsssLssss
15|1	5	LsssLsssLssssLsss
14|2	9	LsssLssssLsssLsss
13|3	13	LssssLsssLsssLsss
12|4	17	sLsssLsssLsssLsss
11|5	4	sLsssLsssLssssLss
10|6	8	sLsssLssssLsssLss
9|7	12	sLssssLsssLsssLss
8|8	16	ssLsssLsssLsssLss
7|9	3	ssLsssLsssLssssLs
6|10	7	ssLsssLssssLsssLs
5|11	11	ssLssssLsssLsssLs
4|12	15	sssLsssLsssLsssLs
3|13	2	sssLsssLsssLssssL
2|14	6	sssLsssLssssLsssL
1|15	10	sssLssssLsssLsssL
0|16	14	ssssLsssLsssLsssL

Intervals

Intervals of 4L 13s

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 300.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 141.2¢
	Major 2-mosstep	M2ms	L + s	141.2¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 211.8¢
	Major 3-mosstep	M3ms	L + 2s	211.8¢ to 300.0¢
4-mosstep	Diminished 4-mosstep	d4ms	4s	0.0¢ to 282.4¢
	Perfect 4-mosstep	P4ms	L + 3s	282.4¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0¢ to 352.9¢
	Major 5-mosstep	M5ms	2L + 3s	352.9¢ to 600.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0¢ to 423.5¢
	Major 6-mosstep	M6ms	2L + 4s	423.5¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0¢ to 494.1¢
	Major 7-mosstep	M7ms	2L + 5s	494.1¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0¢ to 564.7¢
	Major 8-mosstep	M8ms	2L + 6s	564.7¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	600.0¢ to 635.3¢
	Major 9-mosstep	M9ms	3L + 6s	635.3¢ to 900.0¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	600.0¢ to 705.9¢
	Major 10-mosstep	M10ms	3L + 7s	705.9¢ to 900.0¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	600.0¢ to 776.5¢
	Major 11-mosstep	M11ms	3L + 8s	776.5¢ to 900.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0¢ to 847.1¢
	Major 12-mosstep	M12ms	3L + 9s	847.1¢ to 900.0¢
13-mosstep	Perfect 13-mosstep	P13ms	3L + 10s	900.0¢ to 917.6¢
	Augmented 13-mosstep	A13ms	4L + 9s	917.6¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	900.0¢ to 988.2¢
	Major 14-mosstep	M14ms	4L + 10s	988.2¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	3L + 12s	900.0¢ to 1058.8¢
	Major 15-mosstep	M15ms	4L + 11s	1058.8¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	900.0¢ to 1129.4¢
	Major 16-mosstep	M16ms	4L + 12s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	4L + 13s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\17						282.353	917.647	1:1	1.000	Equalized 4L 13s
					21\89	283.146	916.854	6:5	1.200
				17\72		283.333	916.667	5:4	1.250
					30\127	283.465	916.535	9:7	1.286
			13\55			283.636	916.364	4:3	1.333	Supersoft 4L 13s
					35\148	283.784	916.216	11:8	1.375
				22\93		283.871	916.129	7:5	1.400
					31\131	283.969	916.031	10:7	1.429
		9\38				284.211	915.789	3:2	1.500	Soft 4L 13s
					32\135	284.444	915.556	11:7	1.571
				23\97		284.536	915.464	8:5	1.600
					37\156	284.615	915.385	13:8	1.625
			14\59			284.746	915.254	5:3	1.667	Semisoft 4L 13s
					33\139	284.892	915.108	12:7	1.714
				19\80		285.000	915.000	7:4	1.750
					24\101	285.149	914.851	9:5	1.800
	5\21					285.714	914.286	2:1	2.000	Basic 4L 13s Scales with tunings softer than this are proper
					21\88	286.364	913.636	9:4	2.250
				16\67		286.567	913.433	7:3	2.333
					27\113	286.726	913.274	12:5	2.400
			11\46			286.957	913.043	5:2	2.500	Semihard 4L 13s
					28\117	287.179	912.821	13:5	2.600
				17\71		287.324	912.676	8:3	2.667
					23\96	287.500	912.500	11:4	2.750
		6\25				288.000	912.000	3:1	3.000	Hard 4L 13s
					19\79	288.608	911.392	10:3	3.333
				13\54		288.889	911.111	7:2	3.500
					20\83	289.157	910.843	11:3	3.667
			7\29			289.655	910.345	4:1	4.000	Superhard 4L 13s
					15\62	290.323	909.677	9:2	4.500
				8\33		290.909	909.091	5:1	5.000
					9\37	291.892	908.108	6:1	6.000
1\4						300.000	900.000	1:0	→ ∞	Collapsed 4L 13s

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