4L 6s (5/1-equivalent)

↖ 3L 5s⟨5/1⟩	↑ 4L 5s⟨5/1⟩	5L 5s⟨5/1⟩ ↗
← 3L 6s⟨5/1⟩	4L 6s (5/1-equivalent)	5L 6s⟨5/1⟩ →
↙ 3L 7s⟨5/1⟩	↓ 4L 7s⟨5/1⟩	5L 7s⟨5/1⟩ ↘

Scale structure
Step pattern	LsLssLsLss ssLsLssLsL
Equave	5/1 (2786.3 ¢)
Period	1\2 (1393.2 ¢)
Generator size(ed5/1)
Bright	2\10 to 1\4 (557.3 ¢ to 696.6 ¢)
Dark	1\4 to 3\10 (696.6 ¢ to 835.9 ¢)
Related MOS scales
Parent	4L 2s⟨5/1⟩
Sister	6L 4s⟨5/1⟩
Daughters	10L 4s⟨5/1⟩, 4L 10s⟨5/1⟩
Neutralized	8L 2s⟨5/1⟩
2-Flought	14L 6s⟨5/1⟩, 4L 16s⟨5/1⟩
Equal tunings(ed5/1)
Equalized (L:s = 1:1)	2\10 (557.3 ¢)
Supersoft (L:s = 4:3)	7\34 (573.7 ¢)
Soft (L:s = 3:2)	5\24 (580.5 ¢)
Semisoft (L:s = 5:3)	8\38 (586.6 ¢)
Basic (L:s = 2:1)	3\14 (597.1 ¢)
Semihard (L:s = 5:2)	7\32 (609.5 ¢)
Hard (L:s = 3:1)	4\18 (619.2 ¢)
Superhard (L:s = 4:1)	5\22 (633.3 ¢)
Collapsed (L:s = 1:0)	1\4 (696.6 ¢)
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4L 6s⟨5/1⟩ is a 5/1-equivalent (non-octave) moment of symmetry scale containing 4 large steps and 6 small steps, with a period of 2 large steps and 3 small steps that repeats every 1393.2 ¢, or twice every interval of 5/1 (2786.3 ¢). Generators that produce this scale range from 557.3 ¢ to 696.6 ¢, or from 696.6 ¢ to 835.9 ¢.

Theory

The primary temperament interpretation of this scale is as the decatonic scale of the no-twos-or-threes (5.7.11) temperament juggernaut, in which the generator is 7/5 and the half-pentave period is 11/5. This is a very good and low-badness temperament on the 5.7.11 subgroup, although it suffers from a somewhat high error because of the smeary 11/5 at 1393 cents. It can be viewed as a "juggernaut diatonic" since the basic tuning of 14ed5 is the simplest acceptable juggernaut tuning, analogous to 12edo.

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 4L 6s⟨5/1⟩

Generator(ed5/1)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\10						557.263	835.894	1:1	1.000	Equalized 4L 6s⟨5/1⟩
					11\54	567.582	825.574	6:5	1.200
				9\44		569.928	823.229	5:4	1.250
					16\78	571.552	821.605	9:7	1.286
			7\34			573.653	819.504	4:3	1.333	Supersoft 4L 6s⟨5/1⟩
					19\92	575.434	817.723	11:8	1.375
				12\58		576.479	816.678	7:5	1.400
					17\82	577.650	815.506	10:7	1.429
		5\24				580.482	812.675	3:2	1.500	Soft 4L 6s⟨5/1⟩
					18\86	583.182	809.975	11:7	1.571
				13\62		584.227	808.930	8:5	1.600
					21\100	585.126	808.031	13:8	1.625
			8\38			586.592	806.564	5:3	1.667	Semisoft 4L 6s⟨5/1⟩
					19\90	588.222	804.935	12:7	1.714
				11\52		589.413	803.744	7:4	1.750
					14\66	591.036	802.121	9:5	1.800
	3\14					597.067	796.090	2:1	2.000	Basic 4L 6s⟨5/1⟩ Scales with tunings softer than this are proper
					13\60	603.701	789.456	9:4	2.250
				10\46		605.720	787.436	7:3	2.333
					17\78	607.274	785.883	12:5	2.400
			7\32			609.506	783.651	5:2	2.500	Semihard 4L 6s⟨5/1⟩
					18\82	611.630	781.527	13:5	2.600
				11\50		612.989	780.168	8:3	2.667
					15\68	614.628	778.529	11:4	2.750
		4\18				619.181	773.976	3:1	3.000	Hard 4L 6s⟨5/1⟩
					13\58	624.519	768.638	10:3	3.333
				9\40		626.921	766.236	7:2	3.500
					14\62	629.168	763.989	11:3	3.667
			5\22			633.253	759.904	4:1	4.000	Superhard 4L 6s⟨5/1⟩
					11\48	638.530	754.627	9:2	4.500
				6\26		642.995	750.161	5:1	5.000
					7\30	650.140	743.017	6:1	6.000
1\4						696.578	696.578	1:0	→ ∞	Collapsed 4L 6s⟨5/1⟩