5L 9s

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

Scale structure
Step pattern	LsLssLssLssLss
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size ranges
Large	1\14 to 1\5 (85.7¢ to 240.0¢)
Small	0\5 to 1\14 (0.0¢ to 85.7¢)
Generator ranges
Bright	11\14 to 4\5 (942.9¢ to 960.0¢)
Dark	1\5 to 3\14 (240.0¢ to 257.1¢)
TAMNAMS information
Descends from	5L 4s (semiquartal)
Related scales
Parent	5L 4s
Sister	9L 5s
Daughters	14L 5s 5L 14s
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¢)

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¢.

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.

Scale tree

Scale tree and tuning spectrum of 5L 9s

Generator (in steps of 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