5L 9s

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← 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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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 and [math]\displaystyle{ \sqrt{\frac{4}{3}} }[/math] where it is ideal for barbados subgroup harmonies.

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 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 ¢

Generator chain

Generator chain of 5L 9s

Bright gens	Scale degree	Abbrev.
18	Augmented 2-mosdegree	A2md
17	Augmented 5-mosdegree	A5md
16	Augmented 8-mosdegree	A8md
15	Augmented 11-mosdegree	A11md
14	Augmented 0-mosdegree	A0md
13	Augmented 3-mosdegree	A3md
12	Major 6-mosdegree	M6md
11	Major 9-mosdegree	M9md
10	Major 12-mosdegree	M12md
9	Major 1-mosdegree	M1md
8	Major 4-mosdegree	M4md
7	Major 7-mosdegree	M7md
6	Major 10-mosdegree	M10md
5	Major 13-mosdegree	M13md
4	Major 2-mosdegree	M2md
3	Major 5-mosdegree	M5md
2	Major 8-mosdegree	M8md
1	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 14-mosdegree	P0md P14md
−1	Perfect 3-mosdegree	P3md
−2	Minor 6-mosdegree	m6md
−3	Minor 9-mosdegree	m9md
−4	Minor 12-mosdegree	m12md
−5	Minor 1-mosdegree	m1md
−6	Minor 4-mosdegree	m4md
−7	Minor 7-mosdegree	m7md
−8	Minor 10-mosdegree	m10md
−9	Minor 13-mosdegree	m13md
−10	Minor 2-mosdegree	m2md
−11	Minor 5-mosdegree	m5md
−12	Minor 8-mosdegree	m8md
−13	Diminished 11-mosdegree	d11md
−14	Diminished 14-mosdegree	d14md
−15	Diminished 3-mosdegree	d3md
−16	Diminished 6-mosdegree	d6md
−17	Diminished 9-mosdegree	d9md
−18	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 5L 9s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14
13|0	1	LsLssLssLssLss	Perf.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
12|1	12	LssLsLssLssLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
11|2	9	LssLssLsLssLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.
10|3	6	LssLssLssLsLss	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Maj.	Perf.
9|4	3	LssLssLssLssLs	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
8|5	14	sLsLssLssLssLs	Perf.	Min.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
7|6	11	sLssLsLssLssLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
6|7	8	sLssLssLsLssLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Maj.	Perf.
5|8	5	sLssLssLssLsLs	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Maj.	Perf.
4|9	2	sLssLssLssLssL	Perf.	Min.	Maj.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
3|10	13	ssLsLssLssLssL	Perf.	Min.	Min.	Perf.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
2|11	10	ssLssLsLssLssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Perf.
1|12	7	ssLssLssLsLssL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Perf.
0|13	4	ssLssLssLssLsL	Perf.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Perf.

Scale tree

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