9L 4s

9L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 4 small steps, repeating every octave. 9L 4s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 923.1 ¢ to 933.3 ¢, or from 266.7 ¢ to 276.9 ¢.

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

Scale structure
Step pattern	LLLsLLsLLsLLs sLLsLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	10\13 to 7\9 (923.1 ¢ to 933.3 ¢)
Dark	2\9 to 3\13 (266.7 ¢ to 276.9 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	4L 5s
Sister	4L 9s
Daughters	13L 9s, 9L 13s
Neutralized	5L 8s
2-Flought	22L 4s, 9L 17s
Equal tunings
Equalized (L:s = 1:1)	10\13 (923.1 ¢)
Supersoft (L:s = 4:3)	37\48 (925.0 ¢)
Soft (L:s = 3:2)	27\35 (925.7 ¢)
Semisoft (L:s = 5:3)	44\57 (926.3 ¢)
Basic (L:s = 2:1)	17\22 (927.3 ¢)
Semihard (L:s = 5:2)	41\53 (928.3 ¢)
Hard (L:s = 3:1)	24\31 (929.0 ¢)
Superhard (L:s = 4:1)	31\40 (930.0 ¢)
Collapsed (L:s = 1:0)	7\9 (933.3 ¢)
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It is the chromatic scale of Orwell temperament. The harmonic entropy minimum for this scale has three dark generators map to 8/5 (~813.6 ¢), where the generator is ~271.2 ¢.

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 9L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
10\13						923.077	276.923	1:1	1.000	Equalized 9L 4s
					57\74	924.324	275.676	6:5	1.200
				47\61		924.590	275.410	5:4	1.250
					84\109	924.771	275.229	9:7	1.286
			37\48			925.000	275.000	4:3	1.333	Supersoft 9L 4s
					101\131	925.191	274.809	11:8	1.375
				64\83		925.301	274.699	7:5	1.400
					91\118	925.424	274.576	10:7	1.429
		27\35				925.714	274.286	3:2	1.500	Soft 9L 4s
					98\127	925.984	274.016	11:7	1.571
				71\92		926.087	273.913	8:5	1.600
					115\149	926.174	273.826	13:8	1.625
			44\57			926.316	273.684	5:3	1.667	Semisoft 9L 4s
					105\136	926.471	273.529	12:7	1.714
				61\79		926.582	273.418	7:4	1.750
					78\101	926.733	273.267	9:5	1.800
	17\22					927.273	272.727	2:1	2.000	Basic 9L 4s Scales with tunings softer than this are proper
					75\97	927.835	272.165	9:4	2.250
				58\75		928.000	272.000	7:3	2.333
					99\128	928.125	271.875	12:5	2.400
			41\53			928.302	271.698	5:2	2.500	Semihard 9L 4s
					106\137	928.467	271.533	13:5	2.600
				65\84		928.571	271.429	8:3	2.667
					89\115	928.696	271.304	11:4	2.750
		24\31				929.032	270.968	3:1	3.000	Hard 9L 4s
					79\102	929.412	270.588	10:3	3.333
				55\71		929.577	270.423	7:2	3.500
					86\111	929.730	270.270	11:3	3.667
			31\40			930.000	270.000	4:1	4.000	Superhard 9L 4s
					69\89	930.337	269.663	9:2	4.500
				38\49		930.612	269.388	5:1	5.000
					45\58	931.034	268.966	6:1	6.000
7\9						933.333	266.667	1:0	→ ∞	Collapsed 9L 4s