3L 5s (3/1-equivalent)

↖ 2L 4s⟨3/1⟩ ↑ 3L 4s⟨3/1⟩ 4L 4s⟨3/1⟩ ↗

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

↙ 2L 6s⟨3/1⟩ ↓ 3L 6s⟨3/1⟩ 4L 6s⟨3/1⟩ ↘
	Scale structure
Step pattern	LsLssLss; ssLssLsL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
	Generator size(edt)
Bright	5\8 to 2\3 (1188.7 ¢ to 1268.0 ¢)
Dark	1\3 to 3\8 (634.0 ¢ to 713.2 ¢)
	Related MOS scales
Parent	3L 2s⟨3/1⟩
Sister	5L 3s⟨3/1⟩
Daughters	8L 3s⟨3/1⟩, 3L 8s⟨3/1⟩
Neutralized	6L 2s⟨3/1⟩
2-Flought	11L 5s⟨3/1⟩, 3L 13s⟨3/1⟩
	Equal tunings(edt)
Equalized (L:s = 1:1)	5\8 (1188.7 ¢)
Supersoft (L:s = 4:3)	17\27 (1197.5 ¢)
Soft (L:s = 3:2)	12\19 (1201.2 ¢)
Semisoft (L:s = 5:3)	19\30 (1204.6 ¢)
Basic (L:s = 2:1)	7\11 (1210.3 ¢)
Semihard (L:s = 5:2)	16\25 (1217.3 ¢)
Hard (L:s = 3:1)	9\14 (1222.7 ¢)
Superhard (L:s = 4:1)	11\17 (1230.7 ¢)
Collapsed (L:s = 1:0)	2\3 (1268.0 ¢)
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3L 5s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 5 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1188.7 ¢ to 1268 ¢, or from 634 ¢ to 713.2 ¢. 3L 5s⟨3/1⟩ scale pattern includes the well-known 2L 3s pattern within it.

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 3L 5s⟨3/1⟩
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	Minor 1-mosstep	m1ms	s	0.0 ¢ to 237.7 ¢
1-mosstep	Major 1-mosstep	M1ms	L	237.7 ¢ to 634.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 475.5 ¢
2-mosstep	Major 2-mosstep	M2ms	L + s	475.5 ¢ to 634.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	634.0 ¢ to 713.2 ¢
3-mosstep	Augmented 3-mosstep	A3ms	2L + s	713.2 ¢ to 1268.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	634.0 ¢ to 951.0 ¢
4-mosstep	Major 4-mosstep	M4ms	2L + 2s	951.0 ¢ to 1268.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	634.0 ¢ to 1188.7 ¢
5-mosstep	Perfect 5-mosstep	P5ms	2L + 3s	1188.7 ¢ to 1268.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	1268.0 ¢ to 1426.5 ¢
6-mosstep	Major 6-mosstep	M6ms	3L + 3s	1426.5 ¢ to 1902.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	1268.0 ¢ to 1664.2 ¢
7-mosstep	Major 7-mosstep	M7ms	3L + 4s	1664.2 ¢ to 1902.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	3L + 5s	1902.0 ¢

Generator chain

Generator chain of 3L 5s⟨3/1⟩
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⟨3/1⟩
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	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.

Tuning ranges

Simple tunings

Simple Tunings of 3L 5s⟨3/1⟩
Scale degree	Abbrev.	Basic (2:1) 11edt		Hard (3:1) 14edt		Soft (3:2) 19edt
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\11	0.0	0\14	0.0	0\19	0.0
Minor 1-mosdegree	m1md	1\11	172.9	1\14	135.9	2\19	200.2
Major 1-mosdegree	M1md	2\11	345.8	3\14	407.6	3\19	300.3
Minor 2-mosdegree	m2md	2\11	345.8	2\14	271.7	4\19	400.4
Major 2-mosdegree	M2md	3\11	518.7	4\14	543.4	5\19	500.5
Perfect 3-mosdegree	P3md	4\11	691.6	5\14	679.3	7\19	700.7
Augmented 3-mosdegree	A3md	5\11	864.5	7\14	951.0	8\19	800.8
Minor 4-mosdegree	m4md	5\11	864.5	6\14	815.1	9\19	900.9
Major 4-mosdegree	M4md	6\11	1037.4	8\14	1086.8	10\19	1001.0
Diminished 5-mosdegree	d5md	6\11	1037.4	7\14	951.0	11\19	1101.1
Perfect 5-mosdegree	P5md	7\11	1210.3	9\14	1222.7	12\19	1201.2
Minor 6-mosdegree	m6md	8\11	1383.2	10\14	1358.5	14\19	1401.4
Major 6-mosdegree	M6md	9\11	1556.1	12\14	1630.2	15\19	1501.5
Minor 7-mosdegree	m7md	9\11	1556.1	11\14	1494.4	16\19	1601.6
Major 7-mosdegree	M7md	10\11	1729.1	13\14	1766.1	17\19	1701.7
Perfect 8-mosdegree	P8md	11\11	1902.0	14\14	1902.0	19\19	1902.0

Soft-of-basic tunings

Tunings of 3L 5s⟨3/1⟩
Scale degree	Abbrev.	5:4 35edt		Supersoft (4:3) 27edt		Soft (3:2) 19edt		Semisoft (5:3) 30edt
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\35	0.0	0\27	0.0	0\19	0.0	0\30	0.0
Minor 1-mosdegree	m1md	4\35	217.4	3\27	211.3	2\19	200.2	3\30	190.2
Major 1-mosdegree	M1md	5\35	271.7	4\27	281.8	3\19	300.3	5\30	317.0
Minor 2-mosdegree	m2md	8\35	434.7	6\27	422.7	4\19	400.4	6\30	380.4
Major 2-mosdegree	M2md	9\35	489.1	7\27	493.1	5\19	500.5	8\30	507.2
Perfect 3-mosdegree	P3md	13\35	706.4	10\27	704.4	7\19	700.7	11\30	697.4
Augmented 3-mosdegree	A3md	14\35	760.8	11\27	774.9	8\19	800.8	13\30	824.2
Minor 4-mosdegree	m4md	17\35	923.8	13\27	915.8	9\19	900.9	14\30	887.6
Major 4-mosdegree	M4md	18\35	978.1	14\27	986.2	10\19	1001.0	16\30	1014.4
Diminished 5-mosdegree	d5md	21\35	1141.2	16\27	1127.1	11\19	1101.1	17\30	1077.8
Perfect 5-mosdegree	P5md	22\35	1195.5	17\27	1197.5	12\19	1201.2	19\30	1204.6
Minor 6-mosdegree	m6md	26\35	1412.9	20\27	1408.9	14\19	1401.4	22\30	1394.8
Major 6-mosdegree	M6md	27\35	1467.2	21\27	1479.3	15\19	1501.5	24\30	1521.6
Minor 7-mosdegree	m7md	30\35	1630.2	23\27	1620.2	16\19	1601.6	25\30	1585.0
Major 7-mosdegree	M7md	31\35	1684.6	24\27	1690.6	17\19	1701.7	27\30	1711.8
Perfect 8-mosdegree	P8md	35\35	1902.0	27\27	1902.0	19\19	1902.0	30\30	1902.0

Hard-of-basic tunings

Tunings of 3L 5s⟨3/1⟩
Scale degree	Abbrev.	Semihard (5:2) 25edt		Hard (3:1) 14edt		Superhard (4:1) 17edt		5:1 20edt
Scale degree	Abbrev.	Steps	¢	Steps	¢	Steps	¢	Steps	¢
Perfect 0-mosdegree	P0md	0\25	0.0	0\14	0.0	0\17	0.0	0\20	0.0
Minor 1-mosdegree	m1md	2\25	152.2	1\14	135.9	1\17	111.9	1\20	95.1
Major 1-mosdegree	M1md	5\25	380.4	3\14	407.6	4\17	447.5	5\20	475.5
Minor 2-mosdegree	m2md	4\25	304.3	2\14	271.7	2\17	223.8	2\20	190.2
Major 2-mosdegree	M2md	7\25	532.5	4\14	543.4	5\17	559.4	6\20	570.6
Perfect 3-mosdegree	P3md	9\25	684.7	5\14	679.3	6\17	671.3	7\20	665.7
Augmented 3-mosdegree	A3md	12\25	912.9	7\14	951.0	9\17	1006.9	11\20	1046.1
Minor 4-mosdegree	m4md	11\25	836.9	6\14	815.1	7\17	783.2	8\20	760.8
Major 4-mosdegree	M4md	14\25	1065.1	8\14	1086.8	10\17	1118.8	12\20	1141.2
Diminished 5-mosdegree	d5md	13\25	989.0	7\14	951.0	8\17	895.0	9\20	855.9
Perfect 5-mosdegree	P5md	16\25	1217.3	9\14	1222.7	11\17	1230.7	13\20	1236.3
Minor 6-mosdegree	m6md	18\25	1369.4	10\14	1358.5	12\17	1342.6	14\20	1331.4
Major 6-mosdegree	M6md	21\25	1597.6	12\14	1630.2	15\17	1678.2	18\20	1711.8
Minor 7-mosdegree	m7md	20\25	1521.6	11\14	1494.4	13\17	1454.4	15\20	1426.5
Major 7-mosdegree	M7md	23\25	1749.8	13\14	1766.1	16\17	1790.1	19\20	1806.9
Perfect 8-mosdegree	P8md	25\25	1902.0	14\14	1902.0	17\17	1902.0	20\20	1902.0

Scale tree

Scale tree and tuning spectrum of 3L 5s⟨3/1⟩
Generator^(edt)						Cents		Step ratio		Comments
Generator^(edt)						Bright	Dark	L:s	Hardness	Comments
5\8						1188.722	713.233	1:1	1.000	Equalized 3L 5s⟨3/1⟩
					27\43	1194.251	707.704	6:5	1.200
				22\35		1195.515	706.440	5:4	1.250
					39\62	1196.391	705.564	9:7	1.286
			17\27			1197.527	704.428	4:3	1.333	Supersoft 3L 5s⟨3/1⟩
					46\73	1198.492	703.463	11:8	1.375
				29\46		1199.059	702.896	7:5	1.400
					41\65	1199.695	702.260	10:7	1.429
		12\19				1201.235	700.720	3:2	1.500	Soft 3L 5s⟨3/1⟩
					43\68	1202.707	699.248	11:7	1.571
				31\49		1203.278	698.677	8:5	1.600
					50\79	1203.769	698.186	13:8	1.625
			19\30			1204.572	697.384	5:3	1.667	Semisoft 3L 5s⟨3/1⟩
					45\71	1205.464	696.491	12:7	1.714
				26\41		1206.118	695.837	7:4	1.750
					33\52	1207.010	694.945	9:5	1.800
	7\11					1210.335	691.620	2:1	2.000	Basic 3L 5s⟨3/1⟩ Scales with tunings softer than this are proper
					30\47	1214.014	687.941	9:4	2.250
				23\36		1215.138	686.817	7:3	2.333
					39\61	1216.004	685.951	12:5	2.400
			16\25			1217.251	684.704	5:2	2.500	Semihard 3L 5s⟨3/1⟩
					41\64	1218.440	683.515	13:5	2.600
				25\39		1219.202	682.753	8:3	2.667
					34\53	1220.122	681.833	11:4	2.750
		9\14				1222.685	679.270	3:1	3.000	Hard 3L 5s⟨3/1⟩
					29\45	1225.704	676.251	10:3	3.333
				20\31		1227.068	674.887	7:2	3.500
					31\48	1228.346	673.609	11:3	3.667
			11\17			1230.677	671.278	4:1	4.000	Superhard 3L 5s⟨3/1⟩
					24\37	1233.701	668.254	9:2	4.500
				13\20		1236.271	665.684	5:1	5.000
					15\23	1240.405	661.550	6:1	6.000
2\3						1267.970	633.985	1:0	→ ∞	Collapsed 3L 5s⟨3/1⟩