3L 8s

3L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 8 small steps, repeating every octave. 3L 8s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 763.6 ¢ to 800 ¢, or from 400 ¢ to 436.4 ¢.

↖ 2L 7s	↑ 3L 7s	4L 7s ↗
← 2L 8s	3L 8s	4L 8s →
↙ 2L 9s	↓ 3L 9s	4L 9s ↘

Scale structure
Step pattern	LssLsssLsss sssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\11 to 2\3 (763.6 ¢ to 800.0 ¢)
Dark	1\3 to 4\11 (400.0 ¢ to 436.4 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	3L 5s
Sister	8L 3s
Daughters	11L 3s, 3L 11s
Neutralized	6L 5s
2-Flought	14L 8s, 3L 19s
Equal tunings
Equalized (L:s = 1:1)	7\11 (763.6 ¢)
Supersoft (L:s = 4:3)	23\36 (766.7 ¢)
Soft (L:s = 3:2)	16\25 (768.0 ¢)
Semisoft (L:s = 5:3)	25\39 (769.2 ¢)
Basic (L:s = 2:1)	9\14 (771.4 ¢)
Semihard (L:s = 5:2)	20\31 (774.2 ¢)
Hard (L:s = 3:1)	11\17 (776.5 ¢)
Superhard (L:s = 4:1)	13\20 (780.0 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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This scale has versions relating to ditonic/coditone, roman, bossier, sqrtphi and squares.

Modes

Modes of 3L 8s

UDP	Cyclic order	Step pattern
10|0	1	LssLsssLsss
9|1	8	LsssLssLsss
8|2	4	LsssLsssLss
7|3	11	sLssLsssLss
6|4	7	sLsssLssLss
5|5	3	sLsssLsssLs
4|6	10	ssLssLsssLs
3|7	6	ssLsssLssLs
2|8	2	ssLsssLsssL
1|9	9	sssLssLsssL
0|10	5	sssLsssLssL

Intervals

Intervals of 3L 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 109.1 ¢
	Major 1-mosstep	M1ms	L	109.1 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 218.2 ¢
	Major 2-mosstep	M2ms	L + s	218.2 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 327.3 ¢
	Major 3-mosstep	M3ms	L + 2s	327.3 ¢ to 400.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	400.0 ¢ to 436.4 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	436.4 ¢ to 800.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	400.0 ¢ to 545.5 ¢
	Major 5-mosstep	M5ms	2L + 3s	545.5 ¢ to 800.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	400.0 ¢ to 654.5 ¢
	Major 6-mosstep	M6ms	2L + 4s	654.5 ¢ to 800.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	400.0 ¢ to 763.6 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	763.6 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	800.0 ¢ to 872.7 ¢
	Major 8-mosstep	M8ms	3L + 5s	872.7 ¢ to 1200.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	800.0 ¢ to 981.8 ¢
	Major 9-mosstep	M9ms	3L + 6s	981.8 ¢ to 1200.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	800.0 ¢ to 1090.9 ¢
	Major 10-mosstep	M10ms	3L + 7s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 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 3L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\11						763.636	436.364	1:1	1.000	Equalized 3L 8s
					37\58	765.517	434.483	6:5	1.200
				30\47		765.957	434.043	5:4	1.250
					53\83	766.265	433.735	9:7	1.286
			23\36			766.667	433.333	4:3	1.333	Supersoft 3L 8s
					62\97	767.010	432.990	11:8	1.375
				39\61		767.213	432.787	7:5	1.400
					55\86	767.442	432.558	10:7	1.429
		16\25				768.000	432.000	3:2	1.500	Soft 3L 8s
					57\89	768.539	431.461	11:7	1.571
				41\64		768.750	431.250	8:5	1.600
					66\103	768.932	431.068	13:8	1.625
			25\39			769.231	430.769	5:3	1.667	Semisoft 3L 8s
					59\92	769.565	430.435	12:7	1.714
				34\53		769.811	430.189	7:4	1.750
					43\67	770.149	429.851	9:5	1.800
	9\14					771.429	428.571	2:1	2.000	Basic 3L 8s Scales with tunings softer than this are proper
					38\59	772.881	427.119	9:4	2.250
				29\45		773.333	426.667	7:3	2.333
					49\76	773.684	426.316	12:5	2.400
			20\31			774.194	425.806	5:2	2.500	Semihard 3L 8s
					51\79	774.684	425.316	13:5	2.600
				31\48		775.000	425.000	8:3	2.667
					42\65	775.385	424.615	11:4	2.750
		11\17				776.471	423.529	3:1	3.000	Hard 3L 8s
					35\54	777.778	422.222	10:3	3.333
				24\37		778.378	421.622	7:2	3.500
					37\57	778.947	421.053	11:3	3.667
			13\20			780.000	420.000	4:1	4.000	Superhard 3L 8s
					28\43	781.395	418.605	9:2	4.500
				15\23		782.609	417.391	5:1	5.000
					17\26	784.615	415.385	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 8s