4L 21s

↖ 3L 20s	↑ 4L 20s	5L 20s ↗
← 3L 21s	4L 21s	5L 21s →
↙ 3L 22s	↓ 4L 22s	5L 22s ↘

Scale structure
Step pattern	LsssssLsssssLsssssLssssss ssssssLsssssLsssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	6\25 to 1\4 (288.0 ¢ to 300.0 ¢)
Dark	3\4 to 19\25 (900.0 ¢ to 912.0 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	5:1 to 1:0
Related MOS scales
Parent	4L 17s
Sister	21L 4s
Daughters	25L 4s, 4L 25s
Neutralized	8L 17s
2-Flought	29L 21s, 4L 46s
Equal tunings
Equalized (L:s = 1:1)	6\25 (288.0 ¢)
Supersoft (L:s = 4:3)	19\79 (288.6 ¢)
Soft (L:s = 3:2)	13\54 (288.9 ¢)
Semisoft (L:s = 5:3)	20\83 (289.2 ¢)
Basic (L:s = 2:1)	7\29 (289.7 ¢)
Semihard (L:s = 5:2)	15\62 (290.3 ¢)
Hard (L:s = 3:1)	8\33 (290.9 ¢)
Superhard (L:s = 4:1)	9\37 (291.9 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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4L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 21 small steps, repeating every octave. 4L 21s is related to 4L 5s, expanding it by 16 tones. Generators that produce this scale range from 288 ¢ to 300 ¢, or from 900 ¢ to 912 ¢.

This scale is associated with moulin temperament, which includes a very precise 8:11:13 triad. Eliora proposes the name moulinoid for this pattern.

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.

Template:MOS data is deprecated. Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 4L 21s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
6\25						288.000	912.000	1:1	1.000	Equalized 4L 21s
					31\129	288.372	911.628	6:5	1.200
				25\104		288.462	911.538	5:4	1.250
					44\183	288.525	911.475	9:7	1.286
			19\79			288.608	911.392	4:3	1.333	Supersoft 4L 21s
					51\212	288.679	911.321	11:8	1.375
				32\133		288.722	911.278	7:5	1.400
					45\187	288.770	911.230	10:7	1.429
		13\54				288.889	911.111	3:2	1.500	Soft 4L 21s
					46\191	289.005	910.995	11:7	1.571
				33\137		289.051	910.949	8:5	1.600
					53\220	289.091	910.909	13:8	1.625
			20\83			289.157	910.843	5:3	1.667	Semisoft 4L 21s
					47\195	289.231	910.769	12:7	1.714
				27\112		289.286	910.714	7:4	1.750
					34\141	289.362	910.638	9:5	1.800
	7\29					289.655	910.345	2:1	2.000	Basic 4L 21s Scales with tunings softer than this are proper
					29\120	290.000	910.000	9:4	2.250
				22\91		290.110	909.890	7:3	2.333
					37\153	290.196	909.804	12:5	2.400
			15\62			290.323	909.677	5:2	2.500	Semihard 4L 21s
					38\157	290.446	909.554	13:5	2.600
				23\95		290.526	909.474	8:3	2.667
					31\128	290.625	909.375	11:4	2.750
		8\33				290.909	909.091	3:1	3.000	Hard 4L 21s
					25\103	291.262	908.738	10:3	3.333
				17\70		291.429	908.571	7:2	3.500
					26\107	291.589	908.411	11:3	3.667
			9\37			291.892	908.108	4:1	4.000	Superhard 4L 21s
					19\78	292.308	907.692	9:2	4.500
				10\41		292.683	907.317	5:1	5.000
					11\45	293.333	906.667	6:1	6.000
1\4						300.000	900.000	1:0	→ ∞	Collapsed 4L 21s

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