4L 9s

4L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 9 small steps, repeating every octave. 4L 9s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 276.9 ¢ to 300 ¢, or from 900 ¢ to 923.1 ¢.

↖ 3L 8s	↑ 4L 8s	5L 8s ↗
← 3L 9s	4L 9s	5L 9s →
↙ 3L 10s	↓ 4L 10s	5L 10s ↘

Scale structure
Step pattern	LssLssLssLsss sssLssLssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\13 to 1\4 (276.9 ¢ to 300.0 ¢)
Dark	3\4 to 10\13 (900.0 ¢ to 923.1 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 5s
Sister	9L 4s
Daughters	13L 4s, 4L 13s
Neutralized	8L 5s
2-Flought	17L 9s, 4L 22s
Equal tunings
Equalized (L:s = 1:1)	3\13 (276.9 ¢)
Supersoft (L:s = 4:3)	10\43 (279.1 ¢)
Soft (L:s = 3:2)	7\30 (280.0 ¢)
Semisoft (L:s = 5:3)	11\47 (280.9 ¢)
Basic (L:s = 2:1)	4\17 (282.4 ¢)
Semihard (L:s = 5:2)	9\38 (284.2 ¢)
Hard (L:s = 3:1)	5\21 (285.7 ¢)
Superhard (L:s = 4:1)	6\25 (288.0 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
View • Talk • Edit

4L 9s represents chromatic scales of Huxley, Lovecraft, gariberttet, and subklei temperaments. The harmonic entropy minimum for this pattern maps +2, +3, and +5 bright generators to 7/5, 5/3, and 7/3, respectively.

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 4L 9s

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 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	L + s	184.6 ¢ to 300.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 276.9 ¢
	Perfect 3-mosstep	P3ms	L + 2s	276.9 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	300.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	369.2 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	2L + 3s	461.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	2L + 4s	553.8 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	600.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	3L + 4s	646.2 ¢ to 900.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	600.0 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	3L + 5s	738.5 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	600.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	3L + 6s	830.8 ¢ to 900.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	3L + 7s	900.0 ¢ to 923.1 ¢
	Augmented 10-mosstep	A10ms	4L + 6s	923.1 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	900.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	4L + 7s	1015.4 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	900.0 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	4L + 8s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	4L + 9s	1200.0 ¢

Generator chain

Generator chain of 4L 9s

Bright gens	Scale degree	Abbrev.
16	Augmented 9-mosdegree	A9md
15	Augmented 6-mosdegree	A6md
14	Augmented 3-mosdegree	A3md
13	Augmented 0-mosdegree	A0md
12	Augmented 10-mosdegree	A10md
11	Major 7-mosdegree	M7md
10	Major 4-mosdegree	M4md
9	Major 1-mosdegree	M1md
8	Major 11-mosdegree	M11md
7	Major 8-mosdegree	M8md
6	Major 5-mosdegree	M5md
5	Major 2-mosdegree	M2md
4	Major 12-mosdegree	M12md
3	Major 9-mosdegree	M9md
2	Major 6-mosdegree	M6md
1	Perfect 3-mosdegree	P3md
0	Perfect 0-mosdegree Perfect 13-mosdegree	P0md P13md
−1	Perfect 10-mosdegree	P10md
−2	Minor 7-mosdegree	m7md
−3	Minor 4-mosdegree	m4md
−4	Minor 1-mosdegree	m1md
−5	Minor 11-mosdegree	m11md
−6	Minor 8-mosdegree	m8md
−7	Minor 5-mosdegree	m5md
−8	Minor 2-mosdegree	m2md
−9	Minor 12-mosdegree	m12md
−10	Minor 9-mosdegree	m9md
−11	Minor 6-mosdegree	m6md
−12	Diminished 3-mosdegree	d3md
−13	Diminished 13-mosdegree	d13md
−14	Diminished 10-mosdegree	d10md
−15	Diminished 7-mosdegree	d7md
−16	Diminished 4-mosdegree	d4md

Modes

Scale degrees of the modes of 4L 9s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13
12|0	1	LssLssLssLsss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Perf.
11|1	4	LssLssLsssLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
10|2	7	LssLsssLssLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
9|3	10	LsssLssLssLss	Perf.	Maj.	Maj.	Perf.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
8|4	13	sLssLssLssLss	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
7|5	3	sLssLssLsssLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Perf.	Min.	Maj.	Perf.
6|6	6	sLssLsssLssLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
5|7	9	sLsssLssLssLs	Perf.	Min.	Maj.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
4|8	12	ssLssLssLssLs	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
3|9	2	ssLssLssLsssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Maj.	Perf.	Min.	Min.	Perf.
2|10	5	ssLssLsssLssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
1|11	8	ssLsssLssLssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
0|12	11	sssLssLssLssL	Perf.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 4L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\13						276.923	923.077	1:1	1.000	Equalized 4L 9s
					16\69	278.261	921.739	6:5	1.200
				13\56		278.571	921.429	5:4	1.250
					23\99	278.788	921.212	9:7	1.286
			10\43			279.070	920.930	4:3	1.333	Supersoft 4L 9s
					27\116	279.310	920.690	11:8	1.375
				17\73		279.452	920.548	7:5	1.400
					24\103	279.612	920.388	10:7	1.429
		7\30				280.000	920.000	3:2	1.500	Soft 4L 9s
					25\107	280.374	919.626	11:7	1.571
				18\77		280.519	919.481	8:5	1.600
					29\124	280.645	919.355	13:8	1.625
			11\47			280.851	919.149	5:3	1.667	Semisoft 4L 9s
					26\111	281.081	918.919	12:7	1.714
				15\64		281.250	918.750	7:4	1.750
					19\81	281.481	918.519	9:5	1.800
	4\17					282.353	917.647	2:1	2.000	Basic 4L 9s Scales with tunings softer than this are proper
					17\72	283.333	916.667	9:4	2.250
				13\55		283.636	916.364	7:3	2.333
					22\93	283.871	916.129	12:5	2.400
			9\38			284.211	915.789	5:2	2.500	Semihard 4L 9s
					23\97	284.536	915.464	13:5	2.600
				14\59		284.746	915.254	8:3	2.667
					19\80	285.000	915.000	11:4	2.750
		5\21				285.714	914.286	3:1	3.000	Hard 4L 9s
					16\67	286.567	913.433	10:3	3.333
				11\46		286.957	913.043	7:2	3.500
					17\71	287.324	912.676	11:3	3.667
			6\25			288.000	912.000	4:1	4.000	Superhard 4L 9s
					13\54	288.889	911.111	9:2	4.500
				7\29		289.655	910.345	5:1	5.000
					8\33	290.909	909.091	6:1	6.000
1\4						300.000	900.000	1:0	→ ∞	Collapsed 4L 9s