5L 1s (3/2-equivalent)

5L 1s⟨3/2⟩ is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 5 large steps and 1 small step, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 117 ¢ to 140.4 ¢, or from 561.6 ¢ to 585 ¢. Scales of this form are always proper because there is only one small step.

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

Scale structure
Step pattern	LLLLLs sLLLLL
Equave	3/2 (702.0 ¢)
Period	3/2 (702.0 ¢)
Generator size(edf)
Bright	1\6 to 1\5 (117.0 ¢ to 140.4 ¢)
Dark	4\5 to 5\6 (561.6 ¢ to 585.0 ¢)
Related MOS scales
Parent	1L 4s⟨3/2⟩
Sister	1L 5s⟨3/2⟩
Daughters	6L 5s⟨3/2⟩, 5L 6s⟨3/2⟩
Neutralized	4L 2s⟨3/2⟩
2-Flought	11L 1s⟨3/2⟩, 5L 7s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1)	1\6 (117.0 ¢)
Supersoft (L:s = 4:3)	4\23 (122.1 ¢)
Soft (L:s = 3:2)	3\17 (123.9 ¢)
Semisoft (L:s = 5:3)	5\28 (125.3 ¢)
Basic (L:s = 2:1)	2\11 (127.6 ¢)
Semihard (L:s = 5:2)	5\27 (130.0 ¢)
Hard (L:s = 3:1)	3\16 (131.6 ¢)
Superhard (L:s = 4:1)	4\21 (133.7 ¢)
Collapsed (L:s = 1:0)	1\5 (140.4 ¢)
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It is most notable as the hexatonic scale of halftone temperament, with the bright generator being a sharp 15/14 and the dark generator being a flat 7/5.

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 1s⟨3/2⟩

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 117.0 ¢
	Perfect 1-mosstep	P1ms	L	117.0 ¢ to 140.4 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	140.4 ¢ to 234.0 ¢
	Major 2-mosstep	M2ms	2L	234.0 ¢ to 280.8 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	280.8 ¢ to 351.0 ¢
	Major 3-mosstep	M3ms	3L	351.0 ¢ to 421.2 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	421.2 ¢ to 468.0 ¢
	Major 4-mosstep	M4ms	4L	468.0 ¢ to 561.6 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	561.6 ¢ to 585.0 ¢
	Augmented 5-mosstep	A5ms	5L	585.0 ¢ to 702.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	702.0 ¢

Generator chain

Generator chain of 5L 1s⟨3/2⟩

Bright gens	Scale degree	Abbrev.
10	Augmented 4-mosdegree	A4md
9	Augmented 3-mosdegree	A3md
8	Augmented 2-mosdegree	A2md
7	Augmented 1-mosdegree	A1md
6	Augmented 0-mosdegree	A0md
5	Augmented 5-mosdegree	A5md
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 6-mosdegree	P0md P6md
−1	Perfect 5-mosdegree	P5md
−2	Minor 4-mosdegree	m4md
−3	Minor 3-mosdegree	m3md
−4	Minor 2-mosdegree	m2md
−5	Diminished 1-mosdegree	d1md
−6	Diminished 6-mosdegree	d6md
−7	Diminished 5-mosdegree	d5md
−8	Diminished 4-mosdegree	d4md
−9	Diminished 3-mosdegree	d3md
−10	Diminished 2-mosdegree	d2md

Modes

Scale degrees of the modes of 5L 1s⟨3/2⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6
5|0	1	LLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Aug.	Perf.
4|1	2	LLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.
3|2	3	LLLsLL	Perf.	Perf.	Maj.	Maj.	Min.	Perf.	Perf.
2|3	4	LLsLLL	Perf.	Perf.	Maj.	Min.	Min.	Perf.	Perf.
1|4	5	LsLLLL	Perf.	Perf.	Min.	Min.	Min.	Perf.	Perf.
0|5	6	sLLLLL	Perf.	Dim.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 5L 1s⟨3/2⟩

Generator(edf)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\6						116.993	584.963	1:1	1.000	Equalized 5L 1s⟨3/2⟩
					6\35	120.335	581.620	6:5	1.200
				5\29		121.027	580.928	5:4	1.250
					9\52	121.492	580.463	9:7	1.286
			4\23			122.079	579.876	4:3	1.333	Supersoft 5L 1s⟨3/2⟩
					11\63	122.564	579.391	11:8	1.375
				7\40		122.842	579.113	7:5	1.400
					10\57	123.150	578.805	10:7	1.429
		3\17				123.874	578.081	3:2	1.500	Soft 5L 1s⟨3/2⟩
					11\62	124.540	577.415	11:7	1.571
				8\45		124.792	577.163	8:5	1.600
					13\73	125.006	576.949	13:8	1.625
			5\28			125.349	576.606	5:3	1.667	Semisoft 5L 1s⟨3/2⟩
					12\67	125.723	576.232	12:7	1.714
				7\39		125.992	575.963	7:4	1.750
					9\50	126.352	575.603	9:5	1.800
	2\11					127.628	574.327	2:1	2.000	Basic 5L 1s⟨3/2⟩
					9\49	128.931	573.024	9:4	2.250
				7\38		129.308	572.648	7:3	2.333
					12\65	129.592	572.363	12:5	2.400
			5\27			129.992	571.963	5:2	2.500	Semihard 5L 1s⟨3/2⟩ Halftone is in this region
					13\70	130.363	571.592	13:5	2.600
				8\43		130.596	571.359	8:3	2.667
					11\59	130.873	571.082	11:4	2.750
		3\16				131.617	570.338	3:1	3.000	Hard 5L 1s⟨3/2⟩
					10\53	132.444	569.511	10:3	3.333
				7\37		132.802	569.153	7:2	3.500
					11\58	133.129	568.826	11:3	3.667
			4\21			133.706	568.249	4:1	4.000	Superhard 5L 1s⟨3/2⟩
					9\47	134.417	567.538	9:2	4.500
				5\26		134.991	566.964	5:1	5.000
					6\31	135.862	566.093	6:1	6.000
1\5						140.391	561.564	1:0	→ ∞	Collapsed 5L 1s⟨3/2⟩