13L 2s

↖ 12L 1s	↑ 13L 1s	14L 1s ↗
← 12L 2s	13L 2s	14L 2s →
↙ 12L 3s	↓ 13L 3s	14L 3s ↘

Scale structure
Step pattern	LLLLLLLsLLLLLLs sLLLLLLsLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\15 to 7\13 (640.0 ¢ to 646.2 ¢)
Dark	6\13 to 7\15 (553.8 ¢ to 560.0 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	2L 11s
Sister	2L 13s
Daughters	15L 13s, 13L 15s
Neutralized	11L 4s
2-Flought	28L 2s, 13L 17s
Equal tunings
Equalized (L:s = 1:1)	8\15 (640.0 ¢)
Supersoft (L:s = 4:3)	31\58 (641.4 ¢)
Soft (L:s = 3:2)	23\43 (641.9 ¢)
Semisoft (L:s = 5:3)	38\71 (642.3 ¢)
Basic (L:s = 2:1)	15\28 (642.9 ¢)
Semihard (L:s = 5:2)	37\69 (643.5 ¢)
Hard (L:s = 3:1)	22\41 (643.9 ¢)
Superhard (L:s = 4:1)	29\54 (644.4 ¢)
Collapsed (L:s = 1:0)	7\13 (646.2 ¢)
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13L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every octave. 13L 2s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 640 ¢ to 646.2 ¢, or from 553.8 ¢ to 560 ¢.

The dark generator for this scale corresponds to a superfourth (interval sharper than 4/3). This generator has almost no sensible interpretation except to be taken as 11/8, meaning the MOS is an 11+-limit scale.

Modes

Modes of 13L 2s

UDP	Cyclic order	Step pattern
14|0	1	LLLLLLLsLLLLLLs
13|1	9	LLLLLLsLLLLLLLs
12|2	2	LLLLLLsLLLLLLsL
11|3	10	LLLLLsLLLLLLLsL
10|4	3	LLLLLsLLLLLLsLL
9|5	11	LLLLsLLLLLLLsLL
8|6	4	LLLLsLLLLLLsLLL
7|7	12	LLLsLLLLLLLsLLL
6|8	5	LLLsLLLLLLsLLLL
5|9	13	LLsLLLLLLLsLLLL
4|10	6	LLsLLLLLLsLLLLL
3|11	14	LsLLLLLLLsLLLLL
2|12	7	LsLLLLLLsLLLLLL
1|13	15	sLLLLLLLsLLLLLL
0|14	8	sLLLLLLsLLLLLLL

Intervals

Intervals of 13L 2s

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 80.0 ¢
	Major 1-mosstep	M1ms	L	80.0 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	2L	160.0 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	184.6 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	3L	240.0 ¢ to 276.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	276.9 ¢ to 320.0 ¢
	Major 4-mosstep	M4ms	4L	320.0 ¢ to 369.2 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	369.2 ¢ to 400.0 ¢
	Major 5-mosstep	M5ms	5L	400.0 ¢ to 461.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	461.5 ¢ to 480.0 ¢
	Major 6-mosstep	M6ms	6L	480.0 ¢ to 553.8 ¢
7-mosstep	Perfect 7-mosstep	P7ms	6L + s	553.8 ¢ to 560.0 ¢
	Augmented 7-mosstep	A7ms	7L	560.0 ¢ to 646.2 ¢
8-mosstep	Diminished 8-mosstep	d8ms	6L + 2s	553.8 ¢ to 640.0 ¢
	Perfect 8-mosstep	P8ms	7L + s	640.0 ¢ to 646.2 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	646.2 ¢ to 720.0 ¢
	Major 9-mosstep	M9ms	8L + s	720.0 ¢ to 738.5 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	738.5 ¢ to 800.0 ¢
	Major 10-mosstep	M10ms	9L + s	800.0 ¢ to 830.8 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	830.8 ¢ to 880.0 ¢
	Major 11-mosstep	M11ms	10L + s	880.0 ¢ to 923.1 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	923.1 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	11L + s	960.0 ¢ to 1015.4 ¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	1015.4 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	12L + s	1040.0 ¢ to 1107.7 ¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	1107.7 ¢ to 1120.0 ¢
	Major 14-mosstep	M14ms	13L + s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	13L + 2s	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 13L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\15						640.000	560.000	1:1	1.000	Equalized 13L 2s
					47\88	640.909	559.091	6:5	1.200
				39\73		641.096	558.904	5:4	1.250
					70\131	641.221	558.779	9:7	1.286
			31\58			641.379	558.621	4:3	1.333	Supersoft 13L 2s
					85\159	641.509	558.491	11:8	1.375
				54\101		641.584	558.416	7:5	1.400
					77\144	641.667	558.333	10:7	1.429
		23\43				641.860	558.140	3:2	1.500	Soft 13L 2s
					84\157	642.038	557.962	11:7	1.571
				61\114		642.105	557.895	8:5	1.600
					99\185	642.162	557.838	13:8	1.625
			38\71			642.254	557.746	5:3	1.667	Semisoft 13L 2s
					91\170	642.353	557.647	12:7	1.714
				53\99		642.424	557.576	7:4	1.750
					68\127	642.520	557.480	9:5	1.800
	15\28					642.857	557.143	2:1	2.000	Basic 13L 2s Scales with tunings softer than this are proper
					67\125	643.200	556.800	9:4	2.250
				52\97		643.299	556.701	7:3	2.333
					89\166	643.373	556.627	12:5	2.400
			37\69			643.478	556.522	5:2	2.500	Semihard 13L 2s
					96\179	643.575	556.425	13:5	2.600
				59\110		643.636	556.364	8:3	2.667
					81\151	643.709	556.291	11:4	2.750
		22\41				643.902	556.098	3:1	3.000	Hard 13L 2s
					73\136	644.118	555.882	10:3	3.333
				51\95		644.211	555.789	7:2	3.500
					80\149	644.295	555.705	11:3	3.667
			29\54			644.444	555.556	4:1	4.000	Superhard 13L 2s
					65\121	644.628	555.372	9:2	4.500
				36\67		644.776	555.224	5:1	5.000
					43\80	645.000	555.000	6:1	6.000
7\13						646.154	553.846	1:0	→ ∞	Collapsed 13L 2s