3L 2s

3L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 720 ¢ to 800 ¢, or from 400 ¢ to 480 ¢.

↖ 2L 1s	↑ 3L 1s	4L 1s ↗
← 2L 2s	3L 2s	4L 2s →
↙ 2L 3s	↓ 3L 3s	4L 3s ↘

Scale structure
Step pattern	LLsLs sLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\5 to 2\3 (720.0 ¢ to 800.0 ¢)
Dark	1\3 to 2\5 (400.0 ¢ to 480.0 ¢)
Related MOS scales
Parent	2L 1s
Sister	2L 3s
Daughters	5L 3s, 3L 5s
Neutralized	1L 4s
2-Flought	8L 2s, 3L 7s
Equal tunings
Equalized (L:s = 1:1)	3\5 (720.0 ¢)
Supersoft (L:s = 4:3)	11\18 (733.3 ¢)
Soft (L:s = 3:2)	8\13 (738.5 ¢)
Semisoft (L:s = 5:3)	13\21 (742.9 ¢)
Basic (L:s = 2:1)	5\8 (750.0 ¢)
Semihard (L:s = 5:2)	12\19 (757.9 ¢)
Hard (L:s = 3:1)	7\11 (763.6 ¢)
Superhard (L:s = 4:1)	9\14 (771.4 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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For the 3/2-equivalent 3L 2s pattern, see 3L 2s (fifth-equivalent).

The only notable low-harmonic-entropy scale for this MOS pattern is sensi, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone[5]. It's also improper.

Name

The TAMNAMS system applies the name antipentic as the scale utilizes opposite step sizes to the “classic” pentatonic scale (2L 3s). The name antipentic can be used regardless of the equave.

Intervals

Intervals of 3L 2s

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 240.0 ¢
	Major 1-mosstep	M1ms	L	240.0 ¢ to 400.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	400.0 ¢ to 480.0 ¢
	Augmented 2-mosstep	A2ms	2L	480.0 ¢ to 800.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	400.0 ¢ to 720.0 ¢
	Perfect 3-mosstep	P3ms	2L + s	720.0 ¢ to 800.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	800.0 ¢ to 960.0 ¢
	Major 4-mosstep	M4ms	3L + s	960.0 ¢ to 1200.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	1200.0 ¢

Modes

Scale degrees of the modes of 3L 2s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5
4|0	1	LLsLs	Perf.	Maj.	Aug.	Perf.	Maj.	Perf.
3|1	4	LsLLs	Perf.	Maj.	Perf.	Perf.	Maj.	Perf.
2|2	2	LsLsL	Perf.	Maj.	Perf.	Perf.	Min.	Perf.
1|3	5	sLLsL	Perf.	Min.	Perf.	Perf.	Min.	Perf.
0|4	3	sLsLL	Perf.	Min.	Perf.	Dim.	Min.	Perf.

Scale tree

Generator ranges:

• Chroma-positive generator: 720 ¢ (3\5) to 800 ¢ (2\3)
• Chroma-negative generator: 400 ¢ (1\3) to 480 ¢ (2\5)

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 3L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\5						720.000	480.000	1:1	1.000	Equalized 3L 2s
					17\28	728.571	471.429	6:5	1.200
				14\23		730.435	469.565	5:4	1.250
					25\41	731.707	468.293	9:7	1.286
			11\18			733.333	466.667	4:3	1.333	Supersoft 3L 2s
					30\49	734.694	465.306	11:8	1.375
				19\31		735.484	464.516	7:5	1.400
					27\44	736.364	463.636	10:7	1.429
		8\13				738.462	461.538	3:2	1.500	Soft 3L 2s
					29\47	740.426	459.574	11:7	1.571
				21\34		741.176	458.824	8:5	1.600
					34\55	741.818	458.182	13:8	1.625
			13\21			742.857	457.143	5:3	1.667	Semisoft 3L 2s
					31\50	744.000	456.000	12:7	1.714
				18\29		744.828	455.172	7:4	1.750
					23\37	745.946	454.054	9:5	1.800
	5\8					750.000	450.000	2:1	2.000	Basic 3L 2s Scales with tunings softer than this are proper
					22\35	754.286	445.714	9:4	2.250
				17\27		755.556	444.444	7:3	2.333
					29\46	756.522	443.478	12:5	2.400
			12\19			757.895	442.105	5:2	2.500	Semihard 3L 2s
					31\49	759.184	440.816	13:5	2.600
				19\30		760.000	440.000	8:3	2.667
					26\41	760.976	439.024	11:4	2.750
		7\11				763.636	436.364	3:1	3.000	Hard 3L 2s
					23\36	766.667	433.333	10:3	3.333
				16\25		768.000	432.000	7:2	3.500
					25\39	769.231	430.769	11:3	3.667
			9\14			771.429	428.571	4:1	4.000	Superhard 3L 2s
					20\31	774.194	425.806	9:2	4.500
				11\17		776.471	423.529	5:1	5.000
					13\20	780.000	420.000	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 2s