5L 2s (5/3-equivalent)

5L 2s⟨5/3⟩ is a 5/3-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 5/3 (884.4 ¢). Generators that produce this scale range from 505.3 ¢ to 530.6 ¢, or from 353.7 ¢ to 379 ¢.

↖ 4L 1s⟨5/3⟩	↑ 5L 1s⟨5/3⟩	6L 1s⟨5/3⟩ ↗
← 4L 2s⟨5/3⟩	5L 2s (5/3-equivalent)	6L 2s⟨5/3⟩ →
↙ 4L 3s⟨5/3⟩	↓ 5L 3s⟨5/3⟩	6L 3s⟨5/3⟩ ↘

Scale structure
Step pattern	LLLsLLs sLLsLLL
Equave	5/3 (884.4 ¢)
Period	5/3 (884.4 ¢)
Generator size(ed5/3)
Bright	4\7 to 3\5 (505.3 ¢ to 530.6 ¢)
Dark	2\5 to 3\7 (353.7 ¢ to 379.0 ¢)
Related MOS scales
Parent	2L 3s⟨5/3⟩
Sister	2L 5s⟨5/3⟩
Daughters	7L 5s⟨5/3⟩, 5L 7s⟨5/3⟩
Neutralized	3L 4s⟨5/3⟩
2-Flought	12L 2s⟨5/3⟩, 5L 9s⟨5/3⟩
Equal tunings(ed5/3)
Equalized (L:s = 1:1)	4\7 (505.3 ¢)
Supersoft (L:s = 4:3)	15\26 (510.2 ¢)
Soft (L:s = 3:2)	11\19 (512.0 ¢)
Semisoft (L:s = 5:3)	18\31 (513.5 ¢)
Basic (L:s = 2:1)	7\12 (515.9 ¢)
Semihard (L:s = 5:2)	17\29 (518.4 ¢)
Hard (L:s = 3:1)	10\17 (520.2 ¢)
Superhard (L:s = 4:1)	13\22 (522.6 ¢)
Collapsed (L:s = 1:0)	3\5 (530.6 ¢)
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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 interval regions.

Intervals

Intervals of 5L 2s⟨5/3⟩

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 126.3 ¢
	Major 1-mosstep	M1ms	L	126.3 ¢ to 176.9 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	176.9 ¢ to 252.7 ¢
	Major 2-mosstep	M2ms	2L	252.7 ¢ to 353.7 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	353.7 ¢ to 379.0 ¢
	Augmented 3-mosstep	A3ms	3L	379.0 ¢ to 530.6 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	353.7 ¢ to 505.3 ¢
	Perfect 4-mosstep	P4ms	3L + s	505.3 ¢ to 530.6 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	530.6 ¢ to 631.7 ¢
	Major 5-mosstep	M5ms	4L + s	631.7 ¢ to 707.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	707.5 ¢ to 758.0 ¢
	Major 6-mosstep	M6ms	5L + s	758.0 ¢ to 884.4 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	884.4 ¢

Generator chain

Generator chain of 5L 2s⟨5/3⟩

Bright gens	Scale degree	Abbrev.
11	Augmented 2-mosdegree	A2md
10	Augmented 5-mosdegree	A5md
9	Augmented 1-mosdegree	A1md
8	Augmented 4-mosdegree	A4md
7	Augmented 0-mosdegree	A0md
6	Augmented 3-mosdegree	A3md
5	Major 6-mosdegree	M6md
4	Major 2-mosdegree	M2md
3	Major 5-mosdegree	M5md
2	Major 1-mosdegree	M1md
1	Perfect 4-mosdegree	P4md
0	Perfect 0-mosdegree Perfect 7-mosdegree	P0md P7md
−1	Perfect 3-mosdegree	P3md
−2	Minor 6-mosdegree	m6md
−3	Minor 2-mosdegree	m2md
−4	Minor 5-mosdegree	m5md
−5	Minor 1-mosdegree	m1md
−6	Diminished 4-mosdegree	d4md
−7	Diminished 7-mosdegree	d7md
−8	Diminished 3-mosdegree	d3md
−9	Diminished 6-mosdegree	d6md
−10	Diminished 2-mosdegree	d2md
−11	Diminished 5-mosdegree	d5md

Modes

Scale degrees of the modes of 5L 2s⟨5/3⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7
6|0	1	LLLsLLs	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
5|1	5	LLsLLLs	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
4|2	2	LLsLLsL	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
3|3	6	LsLLLsL	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
2|4	3	LsLLsLL	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.
1|5	7	sLLLsLL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0|6	4	sLLsLLL	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 5L 2s⟨5/3⟩

Generator(ed5/3)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\7						505.348	379.011	1:1	1.000	Equalized 5L 2s⟨5/3⟩
					23\40	508.506	375.852	6:5	1.200
				19\33		509.176	375.182	5:4	1.250
					34\59	509.630	374.728	9:7	1.286
			15\26			510.207	374.152	4:3	1.333	Supersoft 5L 2s⟨5/3⟩
					41\71	510.686	373.673	11:8	1.375
				26\45		510.963	373.396	7:5	1.400
					37\64	511.270	373.089	10:7	1.429
		11\19				511.997	372.362	3:2	1.500	Soft 5L 2s⟨5/3⟩
					40\69	512.672	371.687	11:7	1.571
				29\50		512.928	371.431	8:5	1.600
					47\81	513.146	371.212	13:8	1.625
			18\31			513.499	370.860	5:3	1.667	Semisoft 5L 2s⟨5/3⟩
					43\74	513.884	370.475	12:7	1.714
				25\43		514.162	370.197	7:4	1.750
					32\55	514.536	369.823	9:5	1.800
	7\12					515.876	368.483	2:1	2.000	Basic 5L 2s⟨5/3⟩ Scales with tunings softer than this are proper
					31\53	517.266	367.092	9:4	2.250
				24\41		517.673	366.685	7:3	2.333
					41\70	517.982	366.377	12:5	2.400
			17\29			518.417	365.942	5:2	2.500	Semihard 5L 2s⟨5/3⟩
					44\75	518.824	365.535	13:5	2.600
				27\46		519.080	365.279	8:3	2.667
					37\63	519.385	364.973	11:4	2.750
		10\17				520.211	364.148	3:1	3.000	Hard 5L 2s⟨5/3⟩
					33\56	521.140	363.219	10:3	3.333
				23\39		521.545	362.814	7:2	3.500
					36\61	521.917	362.442	11:3	3.667
			13\22			522.576	361.783	4:1	4.000	Superhard 5L 2s⟨5/3⟩
					29\49	523.396	360.963	9:2	4.500
				16\27		524.064	360.294	5:1	5.000
					19\32	525.088	359.271	6:1	6.000
3\5						530.615	353.743	1:0	→ ∞	Collapsed 5L 2s⟨5/3⟩

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