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
Related to	4L 5s (gramitonic)
With tunings	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 ¢)
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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

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 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