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 ¢)
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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.

Template:MOS data is deprecated. Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

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