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

Related to

1L 9s (antisinatonic)

With tunings

4:1 to 5:1

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

1\14 (85.7 ¢)

Supersoft (L:s = 4:3)

4\55 (87.3 ¢)

3\41 (87.8 ¢)

5\68 (88.2 ¢)

2\27 (88.9 ¢)

5\67 (89.6 ¢)

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 properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

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

Generator chain

Generator chain of 13L 1s
Bright gens	Scale degree	Abbrev.
26	Augmented 12-mosdegree	A12md
25	Augmented 11-mosdegree	A11md
24	Augmented 10-mosdegree	A10md
23	Augmented 9-mosdegree	A9md
22	Augmented 8-mosdegree	A8md
21	Augmented 7-mosdegree	A7md
20	Augmented 6-mosdegree	A6md
19	Augmented 5-mosdegree	A5md
18	Augmented 4-mosdegree	A4md
17	Augmented 3-mosdegree	A3md
16	Augmented 2-mosdegree	A2md
15	Augmented 1-mosdegree	A1md
14	Augmented 0-mosdegree	A0md
13	Augmented 13-mosdegree	A13md
12	Major 12-mosdegree	M12md
11	Major 11-mosdegree	M11md
10	Major 10-mosdegree	M10md
9	Major 9-mosdegree	M9md
8	Major 8-mosdegree	M8md
7	Major 7-mosdegree	M7md
6	Major 6-mosdegree	M6md
5	Major 5-mosdegree	M5md
4	Major 4-mosdegree	M4md
3	Major 3-mosdegree	M3md
2	Major 2-mosdegree	M2md
1	Perfect 1-mosdegree	P1md
0	Perfect 0-mosdegree Perfect 14-mosdegree	P0md P14md
−1	Perfect 13-mosdegree	P13md
−2	Minor 12-mosdegree	m12md
−3	Minor 11-mosdegree	m11md
−4	Minor 10-mosdegree	m10md
−5	Minor 9-mosdegree	m9md
−6	Minor 8-mosdegree	m8md
−7	Minor 7-mosdegree	m7md
−8	Minor 6-mosdegree	m6md
−9	Minor 5-mosdegree	m5md
−10	Minor 4-mosdegree	m4md
−11	Minor 3-mosdegree	m3md
−12	Minor 2-mosdegree	m2md
−13	Diminished 1-mosdegree	d1md
−14	Diminished 14-mosdegree	d14md
−15	Diminished 13-mosdegree	d13md
−16	Diminished 12-mosdegree	d12md
−17	Diminished 11-mosdegree	d11md
−18	Diminished 10-mosdegree	d10md
−19	Diminished 9-mosdegree	d9md
−20	Diminished 8-mosdegree	d8md
−21	Diminished 7-mosdegree	d7md
−22	Diminished 6-mosdegree	d6md
−23	Diminished 5-mosdegree	d5md
−24	Diminished 4-mosdegree	d4md
−25	Diminished 3-mosdegree	d3md
−26	Diminished 2-mosdegree	d2md

Modes

Scale degrees of the modes of 13L 1s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
13\|0	1	LLLLLLLLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
12\|1	2	LLLLLLLLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
11\|2	3	LLLLLLLLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
10\|3	4	LLLLLLLLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
9\|4	5	LLLLLLLLLsLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
8\|5	6	LLLLLLLLsLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
7\|6	7	LLLLLLLsLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
6\|7	8	LLLLLLsLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
5\|8	9	LLLLLsLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
4\|9	10	LLLLsLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
3\|10	11	LLLsLLLLLLLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
2\|11	12	LLsLLLLLLLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
1\|12	13	LsLLLLLLLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|13	14	sLLLLLLLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 13L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
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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13L 1s

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

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