3L 5s

↖ 2L 4s	↑ 3L 4s	4L 4s ↗
← 2L 5s	3L 5s	4L 5s →
↙ 2L 6s	↓ 3L 6s	4L 6s ↘

┌╥┬╥┬┬╥┬┬┐ │║│║││║│││ ││││││││││ └┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLss ssLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\8 to 2\3 (750.0 ¢ to 800.0 ¢)
Dark	1\3 to 3\8 (400.0 ¢ to 450.0 ¢)
TAMNAMS information
Name	checkertonic
Prefix	check-
Abbrev.	chk
Related MOS scales
Parent	3L 2s
Sister	5L 3s
Daughters	8L 3s, 3L 8s
Neutralized	6L 2s
2-Flought	11L 5s, 3L 13s
Equal tunings
Equalized (L:s = 1:1)	5\8 (750.0 ¢)
Supersoft (L:s = 4:3)	17\27 (755.6 ¢)
Soft (L:s = 3:2)	12\19 (757.9 ¢)
Semisoft (L:s = 5:3)	19\30 (760.0 ¢)
Basic (L:s = 2:1)	7\11 (763.6 ¢)
Semihard (L:s = 5:2)	16\25 (768.0 ¢)
Hard (L:s = 3:1)	9\14 (771.4 ¢)
Superhard (L:s = 4:1)	11\17 (776.5 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)

3L 5s or antioneirotonic (/oʊnaɪrəˈtɒnɪk/ oh-ny-rə-TON-ik or /ənaɪrə-/ ə-ny-rə-) refers to the structure of octave-equivalent MOS scales with generators ranging from 1\3 (one degrees of 3edo = 400¢) to 3\8 (three degrees of 8edo = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is named antioneirotonic because it is the oneirotonic (5L 3s) MOS pattern with large and small steps switched.

There are two significant harmonic entropy minima with this MOS pattern. Sensi, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. Squares, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.

Generator						Cents	Comments
1\3						400
					8\23	417.39
				7\20		420
			6\17			423.53	L/s = 4
					17\48	425	Squares is around here
				11\31		425.81
						427.73	L/s = pi
		5\14				428.57	L/s = 3
						430.41	L/s = e
				14\39		430.77
					23\64	431.25
			9\25			432
	4\11					436.36	Boundary of propriety: generators larger than this are proper
						439.23
			11\30			440
					29\79	440.51	Golden antioneirotonic
				18\49		440.82
						441.185
		7\19				442.11	Optimum rank range (L/s=3/2) sensi
				17\46		443.48	Sensi is around here
			10\27			444.44
				13\35		445.71
					16\43	446.51
3\8						450