5L 8s

5L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 8 small steps, repeating every octave. 5L 8s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 461.5 ¢ to 480 ¢, or from 720 ¢ to 738.5 ¢.

↖ 4L 7s	↑ 5L 7s	6L 7s ↗
← 4L 8s	5L 8s	6L 8s →
↙ 4L 9s	↓ 5L 9s	6L 9s ↘

Scale structure
Step pattern	LsLssLsLssLss ssLssLsLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\13 to 2\5 (461.5 ¢ to 480.0 ¢)
Dark	3\5 to 8\13 (720.0 ¢ to 738.5 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	5L 3s
Sister	8L 5s
Daughters	13L 5s, 5L 13s
Neutralized	10L 3s
2-Flought	18L 8s, 5L 21s
Equal tunings
Equalized (L:s = 1:1)	5\13 (461.5 ¢)
Supersoft (L:s = 4:3)	17\44 (463.6 ¢)
Soft (L:s = 3:2)	12\31 (464.5 ¢)
Semisoft (L:s = 5:3)	19\49 (465.3 ¢)
Basic (L:s = 2:1)	7\18 (466.7 ¢)
Semihard (L:s = 5:2)	16\41 (468.3 ¢)
Hard (L:s = 3:1)	9\23 (469.6 ¢)
Superhard (L:s = 4:1)	11\28 (471.4 ¢)
Collapsed (L:s = 1:0)	2\5 (480.0 ¢)
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5L 8s represents the chromatic scales of Semisept, A-Team and Vulture temperaments.

Modes

Modes of 5L 8s

UDP	Cyclic order	Step pattern
12|0	1	LsLssLsLssLss
11|1	6	LsLssLssLsLss
10|2	11	LssLsLssLsLss
9|3	3	LssLsLssLssLs
8|4	8	LssLssLsLssLs
7|5	13	sLsLssLsLssLs
6|6	5	sLsLssLssLsLs
5|7	10	sLssLsLssLsLs
4|8	2	sLssLsLssLssL
3|9	7	sLssLssLsLssL
2|10	12	ssLsLssLsLssL
1|11	4	ssLsLssLssLsL
0|12	9	ssLssLsLssLsL

Intervals

Intervals of 5L 8s

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 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	L + s	184.6 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	240.0 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	2L + s	276.9 ¢ to 480.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	240.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	369.2 ¢ to 480.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	240.0 ¢ to 461.5 ¢
	Perfect 5-mosstep	P5ms	2L + 3s	461.5 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	480.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	3L + 3s	553.8 ¢ to 720.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	480.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	3L + 4s	646.2 ¢ to 720.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	3L + 5s	720.0 ¢ to 738.5 ¢
	Augmented 8-mosstep	A8ms	4L + 4s	738.5 ¢ to 960.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	720.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	4L + 5s	830.8 ¢ to 960.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	720.0 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	4L + 6s	923.1 ¢ to 960.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	960.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	5L + 6s	1015.4 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	960.0 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	5L + 7s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	5L + 8s	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 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\13						461.538	738.462	1:1	1.000	Equalized 5L 8s
					27\70	462.857	737.143	6:5	1.200
				22\57		463.158	736.842	5:4	1.250
					39\101	463.366	736.634	9:7	1.286
			17\44			463.636	736.364	4:3	1.333	Supersoft 5L 8s
					46\119	463.866	736.134	11:8	1.375
				29\75		464.000	736.000	7:5	1.400
					41\106	464.151	735.849	10:7	1.429
		12\31				464.516	735.484	3:2	1.500	Soft 5L 8s
					43\111	464.865	735.135	11:7	1.571
				31\80		465.000	735.000	8:5	1.600
					50\129	465.116	734.884	13:8	1.625
			19\49			465.306	734.694	5:3	1.667	Semisoft 5L 8s
					45\116	465.517	734.483	12:7	1.714
				26\67		465.672	734.328	7:4	1.750
					33\85	465.882	734.118	9:5	1.800
	7\18					466.667	733.333	2:1	2.000	Basic 5L 8s Scales with tunings softer than this are proper
					30\77	467.532	732.468	9:4	2.250
				23\59		467.797	732.203	7:3	2.333
					39\100	468.000	732.000	12:5	2.400
			16\41			468.293	731.707	5:2	2.500	Semihard 5L 8s
					41\105	468.571	731.429	13:5	2.600
				25\64		468.750	731.250	8:3	2.667
					34\87	468.966	731.034	11:4	2.750
		9\23				469.565	730.435	3:1	3.000	Hard 5L 8s
					29\74	470.270	729.730	10:3	3.333
				20\51		470.588	729.412	7:2	3.500
					31\79	470.886	729.114	11:3	3.667
			11\28			471.429	728.571	4:1	4.000	Superhard 5L 8s
					24\61	472.131	727.869	9:2	4.500
				13\33		472.727	727.273	5:1	5.000
					15\38	473.684	726.316	6:1	6.000
2\5						480.000	720.000	1:0	→ ∞	Collapsed 5L 8s