4L 2s

↖ 3L 1s	↑ 4L 1s	5L 1s ↗
← 3L 2s	4L 2s	5L 2s →
↙ 3L 3s	↓ 4L 3s	5L 3s ↘

┌╥╥┬╥╥┬┐ │║║│║║││ ││││││││ └┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLs sLLsLL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	1\6 to 1\4 (200.0 ¢ to 300.0 ¢)
Dark	1\4 to 2\6 (300.0 ¢ to 400.0 ¢)
TAMNAMS information
Name	citric
Prefix	citro-
Abbrev.	cit
Related MOS scales
Parent	2L 2s
Sister	2L 4s
Daughters	6L 4s, 4L 6s
Neutralized	2L 4s
2-Flought	10L 2s, 4L 8s
Equal tunings
Equalized (L:s = 1:1)	1\6 (200.0 ¢)
Supersoft (L:s = 4:3)	4\22 (218.2 ¢)
Soft (L:s = 3:2)	3\16 (225.0 ¢)
Semisoft (L:s = 5:3)	5\26 (230.8 ¢)
Basic (L:s = 2:1)	2\10 (240.0 ¢)
Semihard (L:s = 5:2)	5\24 (250.0 ¢)
Hard (L:s = 3:1)	3\14 (257.1 ¢)
Superhard (L:s = 4:1)	4\18 (266.7 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)

4L 2s, named citric in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 2 small steps, with a period of 2 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 200 ¢ to 300 ¢, or from 300 ¢ to 400 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. This MOS resembles 5L 2s, but with one large step removed.

There are three scales with this MOS pattern that are significant minima of harmonic entropy. The first is antikythera, or no-3's srutal/pajara, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.

The second is decimal, in which two generators make a 4/3, and the third is Doublewide, in which the generator is 7/6 so the period minus the generator is 6/5.

In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).

Modes

Modes of 4L 2s

UDP	Cyclic order	Step pattern
4|0(2)	1	LLsLLs
2|2(2)	2	LsLLsL
0|4(2)	3	sLLsLL

Scale tree

Generator											Cents	Comments
1\6											200
					6\34						211.76
				5\28							214.29	Antikythera is around here
			4\22								218.18
		3\16									225
											227.56
				8\42							228.57
											600/(1+phi)	Golden lemba
					13\68						229.41
			5\26								230.77
											232.8
				7\36							233.33	Lemba is around here
	2\10										240	Boundary of propriety for near-MOS Optimum rank range (L/s=2/1) for MOS
			5\24								250	Decimal is around here
											251.89
				8\38							252.63
											253.39	L/s = e
		3\14									257.14	L/s = 3
											258.81	L/s = pi
			4\18								266.67	L/s = 4
				5\22							272.73
					6\26						276.92	Doublewide is around here
						7\30					280
							8\34				282.35
								9\38			284.21
									10\42		285.71
										11\46	286.96
1\4											300