3L 8s

↖ 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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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 ¢. 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

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
						44\69	765.217	434.783	7:6	1.167
					37\58		765.517	434.483	6:5	1.200
						67\105	765.714	434.286	11:9	1.222
				30\47			765.957	434.043	5:4	1.250
						83\130	766.154	433.846	14:11	1.273
					53\83		766.265	433.735	9:7	1.286
						76\119	766.387	433.613	13:10	1.300
			23\36				766.667	433.333	4:3	1.333	Supersoft 3L 8s
						85\133	766.917	433.083	15:11	1.364
					62\97		767.010	432.990	11:8	1.375
						101\158	767.089	432.911	18:13	1.385
				39\61			767.213	432.787	7:5	1.400
						94\147	767.347	432.653	17:12	1.417
					55\86		767.442	432.558	10:7	1.429
						71\111	767.568	432.432	13:9	1.444
		16\25					768.000	432.000	3:2	1.500	Soft 3L 8s
						73\114	768.421	431.579	14:9	1.556
					57\89		768.539	431.461	11:7	1.571
						98\153	768.627	431.373	19:12	1.583
				41\64			768.750	431.250	8:5	1.600
						107\167	768.862	431.138	21:13	1.615
					66\103		768.932	431.068	13:8	1.625
						91\142	769.014	430.986	18:11	1.636
			25\39				769.231	430.769	5:3	1.667	Semisoft 3L 8s
						84\131	769.466	430.534	17:10	1.700
					59\92		769.565	430.435	12:7	1.714
						93\145	769.655	430.345	19:11	1.727
				34\53			769.811	430.189	7:4	1.750
						77\120	770.000	430.000	16:9	1.778
					43\67		770.149	429.851	9:5	1.800
						52\81	770.370	429.630	11:6	1.833
	9\14						771.429	428.571	2:1	2.000	Basic 3L 8s Scales with tunings softer than this are proper
						47\73	772.603	427.397	11:5	2.200
					38\59		772.881	427.119	9:4	2.250
						67\104	773.077	426.923	16:7	2.286
				29\45			773.333	426.667	7:3	2.333
						78\121	773.554	426.446	19:8	2.375
					49\76		773.684	426.316	12:5	2.400
						69\107	773.832	426.168	17:7	2.429
			20\31				774.194	425.806	5:2	2.500	Semihard 3L 8s
						71\110	774.545	425.455	18:7	2.571
					51\79		774.684	425.316	13:5	2.600
						82\127	774.803	425.197	21:8	2.625
				31\48			775.000	425.000	8:3	2.667
						73\113	775.221	424.779	19:7	2.714
					42\65		775.385	424.615	11:4	2.750
						53\82	775.610	424.390	14:5	2.800
		11\17					776.471	423.529	3:1	3.000	Hard 3L 8s
						46\71	777.465	422.535	13:4	3.250
					35\54		777.778	422.222	10:3	3.333
						59\91	778.022	421.978	17:5	3.400
				24\37			778.378	421.622	7:2	3.500
						61\94	778.723	421.277	18:5	3.600
					37\57		778.947	421.053	11:3	3.667
						50\77	779.221	420.779	15:4	3.750
			13\20				780.000	420.000	4:1	4.000	Superhard 3L 8s
						41\63	780.952	419.048	13:3	4.333
					28\43		781.395	418.605	9:2	4.500
						43\66	781.818	418.182	14:3	4.667
				15\23			782.609	417.391	5:1	5.000
						32\49	783.673	416.327	11:2	5.500
					17\26		784.615	415.385	6:1	6.000
						19\29	786.207	413.793	7:1	7.000
2\3							800.000	400.000	1:0	→ ∞	Collapsed 3L 8s