10L 4s

↖ 9L 3s	↑ 10L 3s	11L 3s ↗
← 9L 4s	10L 4s	11L 4s →
↙ 9L 5s	↓ 10L 5s	11L 5s ↘

┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║│║║║│║║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLsLLsLLLsLLs
sLLsLLLsLLsLLL

Equave

2/1 (1200.0 ¢)

Period

1\2 (600.0 ¢)

Generator size

Bright

4\14 to 3\10 (342.9 ¢ to 360.0 ¢)

Dark

2\10 to 3\14 (240.0 ¢ to 257.1 ¢)

TAMNAMS information

Related to

4L 6s (lime)

With tunings

1:1 to 2:1 (soft-of-basic)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

4\14 (342.9 ¢)

Supersoft (L:s = 4:3)

15\52 (346.2 ¢)

11\38 (347.4 ¢)

18\62 (348.4 ¢)

7\24 (350.0 ¢)

17\58 (351.7 ¢)

10\34 (352.9 ¢)

Superhard (L:s = 4:1)

13\44 (354.5 ¢)

Collapsed (L:s = 1:0)

3\10 (360.0 ¢)

10L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 4 small steps, with a period of 5 large steps and 2 small steps that repeats every 600.0 ¢, or twice every octave. 10L 4s is a child scale of 4L 6s, expanding it by 4 tones. Generators that produce this scale range from 342.9 ¢ to 360 ¢, or from 240 ¢ to 257.1 ¢.

10L 4s is significant as the "diatonic scale" of hemipythagorean tuning, and contains the intervals of diatonic alongside neutral intervals.

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 10L 4s
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 85.7 ¢
1-mosstep	Major 1-mosstep	M1ms	L	85.7 ¢ to 120.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	120.0 ¢ to 171.4 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	171.4 ¢ to 240.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	240.0 ¢ to 257.1 ¢
3-mosstep	Augmented 3-mosstep	A3ms	3L	257.1 ¢ to 360.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	240.0 ¢ to 342.9 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	342.9 ¢ to 360.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	360.0 ¢ to 428.6 ¢
5-mosstep	Major 5-mosstep	M5ms	4L + s	428.6 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	480.0 ¢ to 514.3 ¢
6-mosstep	Major 6-mosstep	M6ms	5L + s	514.3 ¢ to 600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	600.0 ¢ to 685.7 ¢
8-mosstep	Major 8-mosstep	M8ms	6L + 2s	685.7 ¢ to 720.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	720.0 ¢ to 771.4 ¢
9-mosstep	Major 9-mosstep	M9ms	7L + 2s	771.4 ¢ to 840.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	7L + 3s	840.0 ¢ to 857.1 ¢
10-mosstep	Augmented 10-mosstep	A10ms	8L + 2s	857.1 ¢ to 960.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	7L + 4s	840.0 ¢ to 942.9 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	942.9 ¢ to 960.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	960.0 ¢ to 1028.6 ¢
12-mosstep	Major 12-mosstep	M12ms	9L + 3s	1028.6 ¢ to 1080.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	1080.0 ¢ to 1114.3 ¢
13-mosstep	Major 13-mosstep	M13ms	10L + 3s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	10L + 4s	1200.0 ¢

Generator chain

Generator chain of 10L 4s
Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
11	Augmented 2-mosdegree	A2md	Augmented 9-mosdegree	A9md
10	Augmented 5-mosdegree	A5md	Augmented 12-mosdegree	A12md
9	Augmented 1-mosdegree	A1md	Augmented 8-mosdegree	A8md
8	Augmented 4-mosdegree	A4md	Augmented 11-mosdegree	A11md
7	Augmented 0-mosdegree	A0md	Augmented 7-mosdegree	A7md
6	Augmented 3-mosdegree	A3md	Augmented 10-mosdegree	A10md
5	Major 6-mosdegree	M6md	Major 13-mosdegree	M13md
4	Major 2-mosdegree	M2md	Major 9-mosdegree	M9md
3	Major 5-mosdegree	M5md	Major 12-mosdegree	M12md
2	Major 1-mosdegree	M1md	Major 8-mosdegree	M8md
1	Perfect 4-mosdegree	P4md	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 7-mosdegree	P0md P7md	Perfect 7-mosdegree Perfect 14-mosdegree	P7md P14md
−1	Perfect 3-mosdegree	P3md	Perfect 10-mosdegree	P10md
−2	Minor 6-mosdegree	m6md	Minor 13-mosdegree	m13md
−3	Minor 2-mosdegree	m2md	Minor 9-mosdegree	m9md
−4	Minor 5-mosdegree	m5md	Minor 12-mosdegree	m12md
−5	Minor 1-mosdegree	m1md	Minor 8-mosdegree	m8md
−6	Diminished 4-mosdegree	d4md	Diminished 11-mosdegree	d11md
−7	Diminished 7-mosdegree	d7md	Diminished 14-mosdegree	d14md
−8	Diminished 3-mosdegree	d3md	Diminished 10-mosdegree	d10md
−9	Diminished 6-mosdegree	d6md	Diminished 13-mosdegree	d13md
−10	Diminished 2-mosdegree	d2md	Diminished 9-mosdegree	d9md
−11	Diminished 5-mosdegree	d5md	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 10L 4s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
12\|0(2)	1	LLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Perf.
10\|2(2)	5	LLsLLLsLLsLLLs	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Perf.
8\|4(2)	2	LLsLLsLLLsLLsL	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.	Maj.	Maj.	Perf.	Perf.	Maj.	Min.	Perf.
6\|6(2)	6	LsLLLsLLsLLLsL	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Perf.
4\|8(2)	3	LsLLsLLLsLLsLL	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.	Maj.	Min.	Perf.	Perf.	Min.	Min.	Perf.
2\|10(2)	7	sLLLsLLsLLLsLL	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.	Min.	Min.	Perf.	Perf.	Min.	Min.	Perf.
0\|12(2)	4	sLLsLLLsLLsLLL	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.	Min.	Min.	Perf.	Dim.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 10L 4s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
4\14						342.857	257.143	1:1	1.000	Equalized 10L 4s
					23\80	345.000	255.000	6:5	1.200
				19\66		345.455	254.545	5:4	1.250
					34\118	345.763	254.237	9:7	1.286
			15\52			346.154	253.846	4:3	1.333	Supersoft 10L 4s
					41\142	346.479	253.521	11:8	1.375
				26\90		346.667	253.333	7:5	1.400
					37\128	346.875	253.125	10:7	1.429
		11\38				347.368	252.632	3:2	1.500	Soft 10L 4s
					40\138	347.826	252.174	11:7	1.571
				29\100		348.000	252.000	8:5	1.600
					47\162	348.148	251.852	13:8	1.625
			18\62			348.387	251.613	5:3	1.667	Semisoft 10L 4s
					43\148	348.649	251.351	12:7	1.714
				25\86		348.837	251.163	7:4	1.750
					32\110	349.091	250.909	9:5	1.800
	7\24					350.000	250.000	2:1	2.000	Basic 10L 4s Scales with tunings softer than this are proper
					31\106	350.943	249.057	9:4	2.250
				24\82		351.220	248.780	7:3	2.333
					41\140	351.429	248.571	12:5	2.400	Semihemi
			17\58			351.724	248.276	5:2	2.500	Semihard 10L 4s Sruti, anguirus
					44\150	352.000	248.000	13:5	2.600
				27\92		352.174	247.826	8:3	2.667
					37\126	352.381	247.619	11:4	2.750
		10\34				352.941	247.059	3:1	3.000	Hard 10L 4s Hemifourths
					33\112	353.571	246.429	10:3	3.333
				23\78		353.846	246.154	7:2	3.500
					36\122	354.098	245.902	11:3	3.667
			13\44			354.545	245.455	4:1	4.000	Superhard 10L 4s
					29\98	355.102	244.898	9:2	4.500
				16\54		355.556	244.444	5:1	5.000
					19\64	356.250	243.750	6:1	6.000	↓ Semiseptiquarter
3\10						360.000	240.000	1:0	→ ∞	Collapsed 10L 4s

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