9L 5s

Todo: confirm Verify temperaments that correspond with 9L 5s

9L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 5 small steps, repeating every octave. 9L 5s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 257.1 ¢ to 266.7 ¢, or from 933.3 ¢ to 942.9 ¢. The generator can be said to approximate 7/6, but just 7/6 is larger than 2\9edo, so it cannot be used as a generator. The simplest just interval that works as a generator is 36/31. Two generators are said to create a fourth like Godzilla, but in reality it is closer to 27/20, if that is considered a consonance. 9L5s is third smallest MOS of Semiphore.

↖ 8L 4s	↑ 9L 4s	10L 4s ↗
← 8L 5s	9L 5s	10L 5s →
↙ 8L 6s	↓ 9L 6s	10L 6s ↘

Scale structure
Step pattern	LLsLLsLLsLLsLs sLsLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\14 to 2\9 (257.1 ¢ to 266.7 ¢)
Dark	7\9 to 11\14 (933.3 ¢ to 942.9 ¢)
TAMNAMS information
Related to	5L 4s (semiquartal)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 4s
Sister	5L 9s
Daughters	14L 9s, 9L 14s
Neutralized	4L 10s
2-Flought	23L 5s, 9L 19s
Equal tunings
Equalized (L:s = 1:1)	3\14 (257.1 ¢)
Supersoft (L:s = 4:3)	11\51 (258.8 ¢)
Soft (L:s = 3:2)	8\37 (259.5 ¢)
Semisoft (L:s = 5:3)	13\60 (260.0 ¢)
Basic (L:s = 2:1)	5\23 (260.9 ¢)
Semihard (L:s = 5:2)	12\55 (261.8 ¢)
Hard (L:s = 3:1)	7\32 (262.5 ¢)
Superhard (L:s = 4:1)	9\41 (263.4 ¢)
Collapsed (L:s = 1:0)	2\9 (266.7 ¢)
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Modes

Modes of 9L 5s

UDP	Cyclic order	Step pattern
13|0	1	LLsLLsLLsLLsLs
12|1	4	LLsLLsLLsLsLLs
11|2	7	LLsLLsLsLLsLLs
10|3	10	LLsLsLLsLLsLLs
9|4	13	LsLLsLLsLLsLLs
8|5	2	LsLLsLLsLLsLsL
7|6	5	LsLLsLLsLsLLsL
6|7	8	LsLLsLsLLsLLsL
5|8	11	LsLsLLsLLsLLsL
4|9	14	sLLsLLsLLsLLsL
3|10	3	sLLsLLsLLsLsLL
2|11	6	sLLsLLsLsLLsLL
1|12	9	sLLsLsLLsLLsLL
0|13	12	sLsLLsLLsLLsLL

Intervals

Intervals of 9L 5s

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 85.7 ¢
	Major 1-mosstep	M1ms	L	85.7 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	2L	171.4 ¢ to 266.7 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	133.3 ¢ to 257.1 ¢
	Perfect 3-mosstep	P3ms	2L + s	257.1 ¢ to 266.7 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	266.7 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	3L + s	342.9 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	400.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	4L + s	428.6 ¢ to 533.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	400.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	4L + 2s	514.3 ¢ to 533.3 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	533.3 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	5L + 2s	600.0 ¢ to 666.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	666.7 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	6L + 2s	685.7 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	666.7 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	6L + 3s	771.4 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	800.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	7L + 3s	857.1 ¢ to 933.3 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	933.3 ¢ to 942.9 ¢
	Augmented 11-mosstep	A11ms	8L + 3s	942.9 ¢ to 1066.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	933.3 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	8L + 4s	1028.6 ¢ to 1066.7 ¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	1066.7 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	9L + 4s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	9L + 5s	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 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\14						257.143	942.857	1:1	1.000	Equalized 9L 5s
					17\79	258.228	941.772	6:5	1.200
				14\65		258.462	941.538	5:4	1.250
					25\116	258.621	941.379	9:7	1.286
			11\51			258.824	941.176	4:3	1.333	Supersoft 9L 5s
					30\139	258.993	941.007	11:8	1.375
				19\88		259.091	940.909	7:5	1.400
					27\125	259.200	940.800	10:7	1.429
		8\37				259.459	940.541	3:2	1.500	Soft 9L 5s
					29\134	259.701	940.299	11:7	1.571
				21\97		259.794	940.206	8:5	1.600
					34\157	259.873	940.127	13:8	1.625
			13\60			260.000	940.000	5:3	1.667	Semisoft 9L 5s
					31\143	260.140	939.860	12:7	1.714
				18\83		260.241	939.759	7:4	1.750
					23\106	260.377	939.623	9:5	1.800
	5\23					260.870	939.130	2:1	2.000	Basic 9L 5s Scales with tunings softer than this are proper
					22\101	261.386	938.614	9:4	2.250
				17\78		261.538	938.462	7:3	2.333
					29\133	261.654	938.346	12:5	2.400
			12\55			261.818	938.182	5:2	2.500	Semihard 9L 5s
					31\142	261.972	938.028	13:5	2.600
				19\87		262.069	937.931	8:3	2.667
					26\119	262.185	937.815	11:4	2.750
		7\32				262.500	937.500	3:1	3.000	Hard 9L 5s
					23\105	262.857	937.143	10:3	3.333
				16\73		263.014	936.986	7:2	3.500
					25\114	263.158	936.842	11:3	3.667
			9\41			263.415	936.585	4:1	4.000	Superhard 9L 5s
					20\91	263.736	936.264	9:2	4.500
				11\50		264.000	936.000	5:1	5.000
					13\59	264.407	935.593	6:1	6.000
2\9						266.667	933.333	1:0	→ ∞	Collapsed 9L 5s