13L 1s

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].

← 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
Related to	1L 9s (antisinatonic)
With tunings	4:1 to 5:1
Related MOS scales
Parent	1L 12s
Sister	1L 13s
Daughters	14L 13s, 13L 14s
Neutralized	12L 2s
2-Flought	27L 1s, 13L 15s
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 ¢)
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Modes

Modes of 13L 1s

UDP	Cyclic order	Step pattern
13|0	1	LLLLLLLLLLLLLs
12|1	2	LLLLLLLLLLLLsL
11|2	3	LLLLLLLLLLLsLL
10|3	4	LLLLLLLLLLsLLL
9|4	5	LLLLLLLLLsLLLL
8|5	6	LLLLLLLLsLLLLL
7|6	7	LLLLLLLsLLLLLL
6|7	8	LLLLLLsLLLLLLL
5|8	9	LLLLLsLLLLLLLL
4|9	10	LLLLsLLLLLLLLL
3|10	11	LLLsLLLLLLLLLL
2|11	12	LLsLLLLLLLLLLL
1|12	13	LsLLLLLLLLLLLL
0|13	14	sLLLLLLLLLLLLL

Intervals

Intervals of 13L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 85.7 ¢
	Perfect 1-mosstep	P1ms	L	85.7 ¢ to 92.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	92.3 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	2L	171.4 ¢ to 184.6 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	184.6 ¢ to 257.1 ¢
	Major 3-mosstep	M3ms	3L	257.1 ¢ to 276.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	276.9 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	4L	342.9 ¢ to 369.2 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	369.2 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	5L	428.6 ¢ to 461.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	461.5 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	6L	514.3 ¢ to 553.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	553.8 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	7L	600.0 ¢ to 646.2 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	646.2 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	8L	685.7 ¢ to 738.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	738.5 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	9L	771.4 ¢ to 830.8 ¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	830.8 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	10L	857.1 ¢ to 923.1 ¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	923.1 ¢ to 942.9 ¢
	Major 11-mosstep	M11ms	11L	942.9 ¢ to 1015.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	1015.4 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	12L	1028.6 ¢ to 1107.7 ¢
13-mosstep	Perfect 13-mosstep	P13ms	12L + s	1107.7 ¢ to 1114.3 ¢
	Augmented 13-mosstep	A13ms	13L	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	13L + s	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 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						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

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