13L 1s

←12L 1s	13L 1s	14L 1s→
↙12L 2s	↓13L 2s	14L 2s↘

┌╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLLLLLs sLLLLLLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	1\14 to 1\13 (85.7¢ to 92.3¢)
Dark	12\13 to 13\14 (1107.7¢ to 1114.3¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Related MOS scales
Parent	1L 12s
Sister	1L 13s
Daughters	14L 13s 13L 14s
Equal tunings
Equalized (L:s = 1:1)	1\14 (85.7¢)
Supersoft (L:s = 4:3)	4\55 (87.3¢)
Soft (L:s = 3:2)	3\41 (87.8¢)
Semisoft (L:s = 5:3)	5\68 (88.2¢)
Basic (L:s = 2:1)	2\27 (88.9¢)
Semihard (L:s = 5:2)	5\67 (89.6¢)
Hard (L:s = 3:1)	3\40 (90.0¢)
Superhard (L:s = 4:1)	4\53 (90.6¢)
Collapsed (L:s = 1:0)	1\13 (92.3¢)

13L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 1 small step, repeating every octave. 13L 1s is related to 1L 9s, expanding it by 4 tones. Generators that produce this scale range from 85.7¢ to 92.3¢, or from 1107.7¢ to 1114.3¢. Scales of this form are always proper because there is only one small step.

This scale is notable for corresponding to octacot[14].

Scale tree

Scale tree and tuning spectrum of 13L 1s

Generator (in steps of edo)						Cents		Step ratio		Comments (Every tuning produces a proper scale)
						Bright	Dark	L:s	Hardness
1\14						85.714	1114.286	1:1	1.000	Equalized 13L 1s
					6\83	86.747	1113.253	6:5	1.200
				5\69		86.957	1113.043	5:4	1.250
					9\124	87.097	1112.903	9:7	1.286
			4\55			87.273	1112.727	4:3	1.333	Supersoft 13L 1s
					11\151	87.417	1112.583	11:8	1.375
				7\96		87.500	1112.500	7:5	1.400
					10\137	87.591	1112.409	10:7	1.429
		3\41				87.805	1112.195	3:2	1.500	Soft 13L 1s
					11\150	88.000	1112.000	11:7	1.571	↕ Octacot
				8\109		88.073	1111.927	8:5	1.600
					13\177	88.136	1111.864	13:8	1.625
			5\68			88.235	1111.765	5:3	1.667	Semisoft 13L 1s
					12\163	88.344	1111.656	12:7	1.714
				7\95		88.421	1111.579	7:4	1.750
					9\122	88.525	1111.475	9:5	1.800
	2\27					88.889	1111.111	2:1	2.000	Basic 13L 1s
					9\121	89.256	1110.744	9:4	2.250
				7\94		89.362	1110.638	7:3	2.333
					12\161	89.441	1110.559	12:5	2.400
			5\67			89.552	1110.448	5:2	2.500	Semihard 13L 1s
					13\174	89.655	1110.345	13:5	2.600
				8\107		89.720	1110.280	8:3	2.667
					11\147	89.796	1110.204	11:4	2.750
		3\40				90.000	1110.000	3:1	3.000	Hard 13L 1s
					10\133	90.226	1109.774	10:3	3.333
				7\93		90.323	1109.677	7:2	3.500
					11\146	90.411	1109.589	11:3	3.667
			4\53			90.566	1109.434	4:1	4.000	Superhard 13L 1s
					9\119	90.756	1109.244	9:2	4.500
				5\66		90.909	1109.091	5:1	5.000
					6\79	91.139	1108.861	6:1	6.000
1\13						92.308	1107.692	1:0	→ ∞	Collapsed 13L 1s