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.

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 ¢

Generator chain

Generator chain of 9L 4s

Bright gens	Scale degree	Abbrev.
21	Augmented 2-mosdegree	A2md
20	Augmented 5-mosdegree	A5md
19	Augmented 8-mosdegree	A8md
18	Augmented 11-mosdegree	A11md
17	Augmented 1-mosdegree	A1md
16	Augmented 4-mosdegree	A4md
15	Augmented 7-mosdegree	A7md
14	Augmented 10-mosdegree	A10md
13	Augmented 0-mosdegree	A0md
12	Augmented 3-mosdegree	A3md
11	Major 6-mosdegree	M6md
10	Major 9-mosdegree	M9md
9	Major 12-mosdegree	M12md
8	Major 2-mosdegree	M2md
7	Major 5-mosdegree	M5md
6	Major 8-mosdegree	M8md
5	Major 11-mosdegree	M11md
4	Major 1-mosdegree	M1md
3	Major 4-mosdegree	M4md
2	Major 7-mosdegree	M7md
1	Perfect 10-mosdegree	P10md
0	Perfect 0-mosdegree Perfect 13-mosdegree	P0md P13md
−1	Perfect 3-mosdegree	P3md
−2	Minor 6-mosdegree	m6md
−3	Minor 9-mosdegree	m9md
−4	Minor 12-mosdegree	m12md
−5	Minor 2-mosdegree	m2md
−6	Minor 5-mosdegree	m5md
−7	Minor 8-mosdegree	m8md
−8	Minor 11-mosdegree	m11md
−9	Minor 1-mosdegree	m1md
−10	Minor 4-mosdegree	m4md
−11	Minor 7-mosdegree	m7md
−12	Diminished 10-mosdegree	d10md
−13	Diminished 13-mosdegree	d13md
−14	Diminished 3-mosdegree	d3md
−15	Diminished 6-mosdegree	d6md
−16	Diminished 9-mosdegree	d9md
−17	Diminished 12-mosdegree	d12md
−18	Diminished 2-mosdegree	d2md
−19	Diminished 5-mosdegree	d5md
−20	Diminished 8-mosdegree	d8md
−21	Diminished 11-mosdegree	d11md

Modes

Scale degrees of the modes of 9L 4s

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	LLLsLLsLLsLLs	Perf.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
11|1	11	LLsLLLsLLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
10|2	8	LLsLLsLLLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
9|3	5	LLsLLsLLsLLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Perf.
8|4	2	LLsLLsLLsLLsL	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
7|5	12	LsLLLsLLsLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
6|6	9	LsLLsLLLsLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Perf.
5|7	6	LsLLsLLsLLLsL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Perf.
4|8	3	LsLLsLLsLLsLL	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
3|9	13	sLLLsLLsLLsLL	Perf.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
2|10	10	sLLsLLLsLLsLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
1|11	7	sLLsLLsLLLsLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
0|12	4	sLLsLLsLLsLLL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Perf.

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