5L 9s

5L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 9 small steps, repeating every octave. 5L 9s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 942.9 ¢ to 960 ¢, or from 240 ¢ to 257.1 ¢.

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

Scale structure
Step pattern	LsLssLssLssLss ssLssLssLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\14 to 4\5 (942.9 ¢ to 960.0 ¢)
Dark	1\5 to 3\14 (240.0 ¢ to 257.1 ¢)
TAMNAMS information
Related to	5L 4s (semiquartal)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	5L 4s
Sister	9L 5s
Daughters	14L 5s, 5L 14s
Neutralized	10L 4s
2-Flought	19L 9s, 5L 23s
Equal tunings
Equalized (L:s = 1:1)	11\14 (942.9 ¢)
Supersoft (L:s = 4:3)	37\47 (944.7 ¢)
Soft (L:s = 3:2)	26\33 (945.5 ¢)
Semisoft (L:s = 5:3)	41\52 (946.2 ¢)
Basic (L:s = 2:1)	15\19 (947.4 ¢)
Semihard (L:s = 5:2)	34\43 (948.8 ¢)
Hard (L:s = 3:1)	19\24 (950.0 ¢)
Superhard (L:s = 4:1)	23\29 (951.7 ¢)
Collapsed (L:s = 1:0)	4\5 (960.0 ¢)
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The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth.

4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13.

This MOS can be viewed as two parallel diatonic scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a meantone or superpyth 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for barbados subgroup harmonies.

Modes

Modes of 5L 9s

UDP	Cyclic order	Step pattern
13|0	1	LsLssLssLssLss
12|1	12	LssLsLssLssLss
11|2	9	LssLssLsLssLss
10|3	6	LssLssLssLsLss
9|4	3	LssLssLssLssLs
8|5	14	sLsLssLssLssLs
7|6	11	sLssLsLssLssLs
6|7	8	sLssLssLsLssLs
5|8	5	sLssLssLssLsLs
4|9	2	sLssLssLssLssL
3|10	13	ssLsLssLssLssL
2|11	10	ssLssLsLssLssL
1|12	7	ssLssLssLsLssL
0|13	4	ssLssLssLssLsL

Intervals

Intervals of 5L 9s

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 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	L + s	171.4 ¢ to 240.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	240.0 ¢ to 257.1 ¢
	Augmented 3-mosstep	A3ms	2L + s	257.1 ¢ to 480.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	2L + 2s	342.9 ¢ to 480.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	2L + 3s	428.6 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	480.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	3L + 3s	514.3 ¢ to 720.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	480.0 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	3L + 4s	600.0 ¢ to 720.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	480.0 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	3L + 5s	685.7 ¢ to 720.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	720.0 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	4L + 5s	771.4 ¢ to 960.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	720.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	4L + 6s	857.1 ¢ to 960.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	3L + 8s	720.0 ¢ to 942.9 ¢
	Perfect 11-mosstep	P11ms	4L + 7s	942.9 ¢ to 960.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	960.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	5L + 7s	1028.6 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	960.0 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	5L + 8s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	5L + 9s	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 5L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\14						942.857	257.143	1:1	1.000	Equalized 5L 9s
					59\75	944.000	256.000	6:5	1.200
				48\61		944.262	255.738	5:4	1.250
					85\108	944.444	255.556	9:7	1.286
			37\47			944.681	255.319	4:3	1.333	Supersoft 5L 9s
					100\127	944.882	255.118	11:8	1.375
				63\80		945.000	255.000	7:5	1.400
					89\113	945.133	254.867	10:7	1.429
		26\33				945.455	254.545	3:2	1.500	Soft 5L 9s
					93\118	945.763	254.237	11:7	1.571
				67\85		945.882	254.118	8:5	1.600
					108\137	945.985	254.015	13:8	1.625
			41\52			946.154	253.846	5:3	1.667	Semisoft 5L 9s
					97\123	946.341	253.659	12:7	1.714
				56\71		946.479	253.521	7:4	1.750
					71\90	946.667	253.333	9:5	1.800
	15\19					947.368	252.632	2:1	2.000	Basic 5L 9s Scales with tunings softer than this are proper
					64\81	948.148	251.852	9:4	2.250
				49\62		948.387	251.613	7:3	2.333
					83\105	948.571	251.429	12:5	2.400
			34\43			948.837	251.163	5:2	2.500	Semihard 5L 9s
					87\110	949.091	250.909	13:5	2.600
				53\67		949.254	250.746	8:3	2.667
					72\91	949.451	250.549	11:4	2.750
		19\24				950.000	250.000	3:1	3.000	Hard 5L 9s
					61\77	950.649	249.351	10:3	3.333
				42\53		950.943	249.057	7:2	3.500
					65\82	951.220	248.780	11:3	3.667
			23\29			951.724	248.276	4:1	4.000	Superhard 5L 9s
					50\63	952.381	247.619	9:2	4.500
				27\34		952.941	247.059	5:1	5.000
					31\39	953.846	246.154	6:1	6.000
4\5						960.000	240.000	1:0	→ ∞	Collapsed 5L 9s