9L 4s

↖ 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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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 ¢.

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¢.

Modes

Modes of 9L 4s

UDP	Cyclic order	Step pattern
12|0	1	LLLsLLsLLsLLs
11|1	11	LLsLLLsLLsLLs
10|2	8	LLsLLsLLLsLLs
9|3	5	LLsLLsLLsLLLs
8|4	2	LLsLLsLLsLLsL
7|5	12	LsLLLsLLsLLsL
6|6	9	LsLLsLLLsLLsL
5|7	6	LsLLsLLsLLLsL
4|8	3	LsLLsLLsLLsLL
3|9	13	sLLLsLLsLLsLL
2|10	10	sLLsLLLsLLsLL
1|11	7	sLLsLLsLLLsLL
0|12	4	sLLsLLsLLsLLL

Intervals

Intervals of 9L 4s

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 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 266.7 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	266.7 ¢ to 276.9 ¢
	Augmented 3-mosstep	A3ms	3L	276.9 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	266.7 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	3L + s	369.2 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	400.0 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	4L + s	461.5 ¢ to 533.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	533.3 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	5L + s	553.8 ¢ to 666.7 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	533.3 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	5L + 2s	646.2 ¢ to 666.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	666.7 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	6L + 2s	738.5 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	800.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	7L + 2s	830.8 ¢ to 933.3 ¢
10-mosstep	Diminished 10-mosstep	d10ms	6L + 4s	800.0 ¢ to 923.1 ¢
	Perfect 10-mosstep	P10ms	7L + 3s	923.1 ¢ to 933.3 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	933.3 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	8L + 3s	1015.4 ¢ to 1066.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	1066.7 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	9L + 3s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	9L + 4s	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 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