3L 5s (5/2-equivalent)

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

┌╥┬╥┬┬╥┬┬┐ │║│║││║│││ ││││││││││ └┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLss ssLssLsL
Equave	5/2 (1586.3 ¢)
Period	5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright	5\8 to 2\3 (991.4 ¢ to 1057.5 ¢)
Dark	1\3 to 3\8 (528.8 ¢ to 594.9 ¢)
Related MOS scales
Parent	3L 2s⟨5/2⟩
Sister	5L 3s⟨5/2⟩
Daughters	8L 3s⟨5/2⟩, 3L 8s⟨5/2⟩
Neutralized	6L 2s⟨5/2⟩
2-Flought	11L 5s⟨5/2⟩, 3L 13s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1)	5\8 (991.4 ¢)
Supersoft (L:s = 4:3)	17\27 (998.8 ¢)
Soft (L:s = 3:2)	12\19 (1001.9 ¢)
Semisoft (L:s = 5:3)	19\30 (1004.7 ¢)
Basic (L:s = 2:1)	7\11 (1009.5 ¢)
Semihard (L:s = 5:2)	16\25 (1015.2 ¢)
Hard (L:s = 3:1)	9\14 (1019.8 ¢)
Superhard (L:s = 4:1)	11\17 (1026.4 ¢)
Collapsed (L:s = 1:0)	2\3 (1057.5 ¢)

3L 5s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 3 large steps and 5 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 991.4 ¢ to 1057.5 ¢, or from 528.8 ¢ to 594.9 ¢.

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 3L 5s⟨5/2⟩

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 198.3 ¢
	Major 1-mosstep	M1ms	L	198.3 ¢ to 528.8 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 396.6 ¢
	Major 2-mosstep	M2ms	L + s	396.6 ¢ to 528.8 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	528.8 ¢ to 594.9 ¢
	Augmented 3-mosstep	A3ms	2L + s	594.9 ¢ to 1057.5 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	528.8 ¢ to 793.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	793.2 ¢ to 1057.5 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	528.8 ¢ to 991.4 ¢
	Perfect 5-mosstep	P5ms	2L + 3s	991.4 ¢ to 1057.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	1057.5 ¢ to 1189.7 ¢
	Major 6-mosstep	M6ms	3L + 3s	1189.7 ¢ to 1586.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	1057.5 ¢ to 1388.0 ¢
	Major 7-mosstep	M7ms	3L + 4s	1388.0 ¢ to 1586.3 ¢
8-mosstep	Perfect 8-mosstep	P8ms	3L + 5s	1586.3 ¢

Generator chain

Generator chain of 3L 5s⟨5/2⟩

Bright gens	Scale degree	Abbrev.
10	Augmented 2-mosdegree	A2md
9	Augmented 5-mosdegree	A5md
8	Augmented 0-mosdegree	A0md
7	Augmented 3-mosdegree	A3md
6	Major 6-mosdegree	M6md
5	Major 1-mosdegree	M1md
4	Major 4-mosdegree	M4md
3	Major 7-mosdegree	M7md
2	Major 2-mosdegree	M2md
1	Perfect 5-mosdegree	P5md
0	Perfect 0-mosdegree Perfect 8-mosdegree	P0md P8md
−1	Perfect 3-mosdegree	P3md
−2	Minor 6-mosdegree	m6md
−3	Minor 1-mosdegree	m1md
−4	Minor 4-mosdegree	m4md
−5	Minor 7-mosdegree	m7md
−6	Minor 2-mosdegree	m2md
−7	Diminished 5-mosdegree	d5md
−8	Diminished 8-mosdegree	d8md
−9	Diminished 3-mosdegree	d3md
−10	Diminished 6-mosdegree	d6md

Modes

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

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8
7|0	1	LsLssLss	Perf.	Maj.	Maj.	Aug.	Maj.	Perf.	Maj.	Maj.	Perf.
6|1	6	LssLsLss	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.
5|2	3	LssLssLs	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.	Min.	Maj.	Perf.
4|3	8	sLsLssLs	Perf.	Min.	Maj.	Perf.	Maj.	Perf.	Min.	Maj.	Perf.
3|4	5	sLssLsLs	Perf.	Min.	Maj.	Perf.	Min.	Perf.	Min.	Maj.	Perf.
2|5	2	sLssLssL	Perf.	Min.	Maj.	Perf.	Min.	Perf.	Min.	Min.	Perf.
1|6	7	ssLsLssL	Perf.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Perf.
0|7	4	ssLssLsL	Perf.	Min.	Min.	Perf.	Min.	Dim.	Min.	Min.	Perf.

Scale tree

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

Generator(ed5/2)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\8						991.446	594.868	1:1	1.000	Equalized 3L 5s⟨5/2⟩
					27\43	996.057	590.256	6:5	1.200
				22\35		997.111	589.202	5:4	1.250
					39\62	997.842	588.471	9:7	1.286
			17\27			998.790	587.524	4:3	1.333	Supersoft 3L 5s⟨5/2⟩
					46\73	999.595	586.719	11:8	1.375
				29\46		1000.067	586.246	7:5	1.400
					41\65	1000.598	585.716	10:7	1.429
		12\19				1001.882	584.431	3:2	1.500	Soft 3L 5s⟨5/2⟩
					43\68	1003.110	583.204	11:7	1.571
				31\49		1003.586	582.727	8:5	1.600
					50\79	1003.996	582.318	13:8	1.625
			19\30			1004.665	581.648	5:3	1.667	Semisoft 3L 5s⟨5/2⟩
					45\71	1005.410	580.904	12:7	1.714
				26\41		1005.955	580.359	7:4	1.750
					33\52	1006.699	579.615	9:5	1.800
	7\11					1009.472	576.841	2:1	2.000	Basic 3L 5s⟨5/2⟩ Scales with tunings softer than this are proper
					30\47	1012.541	573.773	9:4	2.250
				23\36		1013.478	572.836	7:3	2.333
					39\61	1014.201	572.113	12:5	2.400
			16\25			1015.241	571.073	5:2	2.500	Semihard 3L 5s⟨5/2⟩
					41\64	1016.232	570.081	13:5	2.600
				25\39		1016.868	569.446	8:3	2.667
					34\53	1017.635	568.679	11:4	2.750
		9\14				1019.773	566.541	3:1	3.000	Hard 3L 5s⟨5/2⟩
					29\45	1022.291	564.023	10:3	3.333
				20\31		1023.428	562.886	7:2	3.500
					31\48	1024.494	561.819	11:3	3.667
			11\17			1026.438	559.875	4:1	4.000	Superhard 3L 5s⟨5/2⟩
					24\37	1028.960	557.353	9:2	4.500
				13\20		1031.104	555.210	5:1	5.000
					15\23	1034.552	551.761	6:1	6.000
2\3						1057.542	528.771	1:0	→ ∞	Collapsed 3L 5s⟨5/2⟩

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