4L 15s

↖ 3L 14s	↑ 4L 14s	5L 14s ↗
← 3L 15s	4L 15s	5L 15s →
↙ 3L 16s	↓ 4L 16s	5L 16s ↘

Scale structure
Step pattern	LsssLssssLssssLssss ssssLssssLssssLsssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	14\19 to 3\4 (884.2 ¢ to 900.0 ¢)
Dark	1\4 to 5\19 (300.0 ¢ to 315.8 ¢)
TAMNAMS information
Related to	4L 3s (smitonic)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	4L 11s
Sister	15L 4s
Daughters	19L 4s, 4L 19s
Neutralized	8L 11s
2-Flought	23L 15s, 4L 34s
Equal tunings
Equalized (L:s = 1:1)	14\19 (884.2 ¢)
Supersoft (L:s = 4:3)	45\61 (885.2 ¢)
Soft (L:s = 3:2)	31\42 (885.7 ¢)
Semisoft (L:s = 5:3)	48\65 (886.2 ¢)
Basic (L:s = 2:1)	17\23 (887.0 ¢)
Semihard (L:s = 5:2)	37\50 (888.0 ¢)
Hard (L:s = 3:1)	20\27 (888.9 ¢)
Superhard (L:s = 4:1)	23\31 (890.3 ¢)
Collapsed (L:s = 1:0)	3\4 (900.0 ¢)
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4L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 15 small steps, repeating every octave. 4L 15s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 884.2 ¢ to 900 ¢, or from 300 ¢ to 315.8 ¢.

This scale is associated with myna temperament (pronounced /'maɪnə/), where stacking two bright generators and octave-reducing produces 7/5 (~582¢).

Modes

Modes of 4L 15s

UDP	Cyclic order	Step pattern
18|0	1	LsssLssssLssssLssss
17|1	15	LssssLsssLssssLssss
16|2	10	LssssLssssLsssLssss
15|3	5	LssssLssssLssssLsss
14|4	19	sLsssLssssLssssLsss
13|5	14	sLssssLsssLssssLsss
12|6	9	sLssssLssssLsssLsss
11|7	4	sLssssLssssLssssLss
10|8	18	ssLsssLssssLssssLss
9|9	13	ssLssssLsssLssssLss
8|10	8	ssLssssLssssLsssLss
7|11	3	ssLssssLssssLssssLs
6|12	17	sssLsssLssssLssssLs
5|13	12	sssLssssLsssLssssLs
4|14	7	sssLssssLssssLsssLs
3|15	2	sssLssssLssssLssssL
2|16	16	ssssLsssLssssLssssL
1|17	11	ssssLssssLsssLssssL
0|18	6	ssssLssssLssssLsssL

Intervals

Intervals of 4L 15s

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 63.2 ¢
	Major 1-mosstep	M1ms	L	63.2 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 126.3 ¢
	Major 2-mosstep	M2ms	L + s	126.3 ¢ to 300.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 189.5 ¢
	Major 3-mosstep	M3ms	L + 2s	189.5 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 252.6 ¢
	Major 4-mosstep	M4ms	L + 3s	252.6 ¢ to 300.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	300.0 ¢ to 315.8 ¢
	Augmented 5-mosstep	A5ms	2L + 3s	315.8 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 378.9 ¢
	Major 6-mosstep	M6ms	2L + 4s	378.9 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0 ¢ to 442.1 ¢
	Major 7-mosstep	M7ms	2L + 5s	442.1 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0 ¢ to 505.3 ¢
	Major 8-mosstep	M8ms	2L + 6s	505.3 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	300.0 ¢ to 568.4 ¢
	Major 9-mosstep	M9ms	2L + 7s	568.4 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	600.0 ¢ to 631.6 ¢
	Major 10-mosstep	M10ms	3L + 7s	631.6 ¢ to 900.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	600.0 ¢ to 694.7 ¢
	Major 11-mosstep	M11ms	3L + 8s	694.7 ¢ to 900.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0 ¢ to 757.9 ¢
	Major 12-mosstep	M12ms	3L + 9s	757.9 ¢ to 900.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	600.0 ¢ to 821.1 ¢
	Major 13-mosstep	M13ms	3L + 10s	821.1 ¢ to 900.0 ¢
14-mosstep	Diminished 14-mosstep	d14ms	2L + 12s	600.0 ¢ to 884.2 ¢
	Perfect 14-mosstep	P14ms	3L + 11s	884.2 ¢ to 900.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	3L + 12s	900.0 ¢ to 947.4 ¢
	Major 15-mosstep	M15ms	4L + 11s	947.4 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	900.0 ¢ to 1010.5 ¢
	Major 16-mosstep	M16ms	4L + 12s	1010.5 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	900.0 ¢ to 1073.7 ¢
	Major 17-mosstep	M17ms	4L + 13s	1073.7 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	900.0 ¢ to 1136.8 ¢
	Major 18-mosstep	M18ms	4L + 14s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	4L + 15s	1200.0 ¢

Scale tree

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 4L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
14\19						884.211	315.789	1:1	1.000	Equalized 4L 15s
					73\99	884.848	315.152	6:5	1.200
				59\80		885.000	315.000	5:4	1.250
					104\141	885.106	314.894	9:7	1.286
			45\61			885.246	314.754	4:3	1.333	Supersoft 4L 15s
					121\164	885.366	314.634	11:8	1.375
				76\103		885.437	314.563	7:5	1.400
					107\145	885.517	314.483	10:7	1.429
		31\42				885.714	314.286	3:2	1.500	Soft 4L 15s
					110\149	885.906	314.094	11:7	1.571
				79\107		885.981	314.019	8:5	1.600
					127\172	886.047	313.953	13:8	1.625
			48\65			886.154	313.846	5:3	1.667	Semisoft 4L 15s
					113\153	886.275	313.725	12:7	1.714
				65\88		886.364	313.636	7:4	1.750
					82\111	886.486	313.514	9:5	1.800
	17\23					886.957	313.043	2:1	2.000	Basic 4L 15s Scales with tunings softer than this are proper
					71\96	887.500	312.500	9:4	2.250
				54\73		887.671	312.329	7:3	2.333
					91\123	887.805	312.195	12:5	2.400
			37\50			888.000	312.000	5:2	2.500	Semihard 4L 15s
					94\127	888.189	311.811	13:5	2.600
				57\77		888.312	311.688	8:3	2.667
					77\104	888.462	311.538	11:4	2.750
		20\27				888.889	311.111	3:1	3.000	Hard 4L 15s
					63\85	889.412	310.588	10:3	3.333
				43\58		889.655	310.345	7:2	3.500
					66\89	889.888	310.112	11:3	3.667
			23\31			890.323	309.677	4:1	4.000	Superhard 4L 15s
					49\66	890.909	309.091	9:2	4.500
				26\35		891.429	308.571	5:1	5.000
					29\39	892.308	307.692	6:1	6.000
3\4						900.000	300.000	1:0	→ ∞	Collapsed 4L 15s