1L 13s

	↑ 1L 12s	2L 12s ↗
	1L 13s	2L 13s →
	↓ 1L 14s	2L 14s ↘

Scale structure
Step pattern	Lsssssssssssss sssssssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\14 to 1\1 (1114.3 ¢ to 1200.0 ¢)
Dark	0\1 to 1\14 (0.0 ¢ to 85.7 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	5:1 to 1:0
Related MOS scales
Parent	1L 12s
Sister	13L 1s
Daughters	14L 1s, 1L 14s
Neutralized	2L 12s
2-Flought	15L 13s, 1L 27s
Equal tunings
Equalized (L:s = 1:1)	13\14 (1114.3 ¢)
Supersoft (L:s = 4:3)	40\43 (1116.3 ¢)
Soft (L:s = 3:2)	27\29 (1117.2 ¢)
Semisoft (L:s = 5:3)	41\44 (1118.2 ¢)
Basic (L:s = 2:1)	14\15 (1120.0 ¢)
Semihard (L:s = 5:2)	29\31 (1122.6 ¢)
Hard (L:s = 3:1)	15\16 (1125.0 ¢)
Superhard (L:s = 4:1)	16\17 (1129.4 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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1L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 13 small steps, repeating every octave. 1L 13s is related to 1L 9s, expanding it by 4 tones. Generators that produce this scale range from 1114.3 ¢ to 1200 ¢, or from 0 ¢ to 85.7 ¢.

Modes

Modes of 1L 13s

UDP	Cyclic order	Step pattern
13|0	1	Lsssssssssssss
12|1	14	sLssssssssssss
11|2	13	ssLsssssssssss
10|3	12	sssLssssssssss
9|4	11	ssssLsssssssss
8|5	10	sssssLssssssss
7|6	9	ssssssLsssssss
6|7	8	sssssssLssssss
5|8	7	ssssssssLsssss
4|9	6	sssssssssLssss
3|10	5	ssssssssssLsss
2|11	4	sssssssssssLss
1|12	3	ssssssssssssLs
0|13	2	sssssssssssssL

Intervals

Intervals of 1L 13s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 85.7 ¢
	Augmented 1-mosstep	A1ms	L	85.7 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	L + s	171.4 ¢ to 1200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 257.1 ¢
	Major 3-mosstep	M3ms	L + 2s	257.1 ¢ to 1200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	L + 3s	342.9 ¢ to 1200.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	L + 4s	428.6 ¢ to 1200.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	L + 5s	514.3 ¢ to 1200.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	L + 6s	600.0 ¢ to 1200.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	L + 7s	685.7 ¢ to 1200.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	L + 8s	771.4 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	10s	0.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	L + 9s	857.1 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	11s	0.0 ¢ to 942.9 ¢
	Major 11-mosstep	M11ms	L + 10s	942.9 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	12s	0.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	L + 11s	1028.6 ¢ to 1200.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	13s	0.0 ¢ to 1114.3 ¢
	Perfect 13-mosstep	P13ms	L + 12s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	L + 13s	1200.0 ¢

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 1L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\14						1114.286	85.714	1:1	1.000	Equalized 1L 13s
					66\71	1115.493	84.507	6:5	1.200
				53\57		1115.789	84.211	5:4	1.250
					93\100	1116.000	84.000	9:7	1.286
			40\43			1116.279	83.721	4:3	1.333	Supersoft 1L 13s
					107\115	1116.522	83.478	11:8	1.375
				67\72		1116.667	83.333	7:5	1.400
					94\101	1116.832	83.168	10:7	1.429
		27\29				1117.241	82.759	3:2	1.500	Soft 1L 13s
					95\102	1117.647	82.353	11:7	1.571
				68\73		1117.808	82.192	8:5	1.600
					109\117	1117.949	82.051	13:8	1.625
			41\44			1118.182	81.818	5:3	1.667	Semisoft 1L 13s
					96\103	1118.447	81.553	12:7	1.714
				55\59		1118.644	81.356	7:4	1.750
					69\74	1118.919	81.081	9:5	1.800
	14\15					1120.000	80.000	2:1	2.000	Basic 1L 13s Scales with tunings softer than this are proper
					57\61	1121.311	78.689	9:4	2.250
				43\46		1121.739	78.261	7:3	2.333
					72\77	1122.078	77.922	12:5	2.400
			29\31			1122.581	77.419	5:2	2.500	Semihard 1L 13s
					73\78	1123.077	76.923	13:5	2.600
				44\47		1123.404	76.596	8:3	2.667
					59\63	1123.810	76.190	11:4	2.750
		15\16				1125.000	75.000	3:1	3.000	Hard 1L 13s
					46\49	1126.531	73.469	10:3	3.333
				31\33		1127.273	72.727	7:2	3.500
					47\50	1128.000	72.000	11:3	3.667
			16\17			1129.412	70.588	4:1	4.000	Superhard 1L 13s
					33\35	1131.429	68.571	9:2	4.500
				17\18		1133.333	66.667	5:1	5.000
					18\19	1136.842	63.158	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 13s

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