8L 3s

↖ 7L 2s	↑ 8L 2s	9L 2s ↗
← 7L 3s	8L 3s	9L 3s →
↙ 7L 4s	↓ 8L 4s	9L 4s ↘

Scale structure
Step pattern	LLLsLLLsLLs sLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	4\11 to 3\8 (436.4 ¢ to 450.0 ¢)
Dark	5\8 to 7\11 (750.0 ¢ to 763.6 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	3L 5s
Sister	3L 8s
Daughters	11L 8s, 8L 11s
Neutralized	5L 6s
2-Flought	19L 3s, 8L 14s
Equal tunings
Equalized (L:s = 1:1)	4\11 (436.4 ¢)
Supersoft (L:s = 4:3)	15\41 (439.0 ¢)
Soft (L:s = 3:2)	11\30 (440.0 ¢)
Semisoft (L:s = 5:3)	18\49 (440.8 ¢)
Basic (L:s = 2:1)	7\19 (442.1 ¢)
Semihard (L:s = 5:2)	17\46 (443.5 ¢)
Hard (L:s = 3:1)	10\27 (444.4 ¢)
Superhard (L:s = 4:1)	13\35 (445.7 ¢)
Collapsed (L:s = 1:0)	3\8 (450.0 ¢)
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8L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 3 small steps, repeating every octave. 8L 3s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 436.4 ¢ to 450 ¢, or from 750 ¢ to 763.6 ¢. The only significant harmonic entropy minimum with this MOS pattern is sensi, in which the generator is 9/7 and two of them make a 5/3.

Modes

Modes of 8L 3s

UDP	Cyclic order	Step pattern
10|0	1	LLLsLLLsLLs
9|1	5	LLLsLLsLLLs
8|2	9	LLsLLLsLLLs
7|3	2	LLsLLLsLLsL
6|4	6	LLsLLsLLLsL
5|5	10	LsLLLsLLLsL
4|6	3	LsLLLsLLsLL
3|7	7	LsLLsLLLsLL
2|8	11	sLLLsLLLsLL
1|9	4	sLLLsLLsLLL
0|10	8	sLLsLLLsLLL

Scale tree

Generator						Cents	Pentachord steps	Comments
4\11						436.364	1 1 1 1
					23\63	438.095	6 6 6 5
				19\52		438.462	5 5 5 4
			15\41			439.024	4 4 4 3
		11\30				440	3 3 3 2	Optimum rank range (L/s=3/2)
						440.364	pi pi pi 2
				29\79		440.506	8 8 8 5
						440.592	phi phi phi 1
					47\128	440.625	13 13 13 8	Unnamed golden temperament
			18\49			440.816	5 5 5 3
						441.101	√3 √3 √3 1
				25\68		441.176	7 7 7 4
	7\19					442.105	2 2 2 1	Boundary of propriety: generators smaller than this are proper
				24\65		443.077	7 7 7 3
			17\46			443.478	5 5 5 2	Sensi is about here
					44\119	443.6975	13 13 13 5	Golden Sensi
						443.7355	phi+1 phi+1 phi+1 1
				27\73		443.836	8 8 8 3
						443.9385	e e e 1
		10\27				444.444	3 3 3 1
						444.668	pi pi pi 1
			13\35			445.714	4 4 4 1
				16\43		446.512	5 5 5 1
					19\51	447.059	6 6 6 1
3\8						450	1 1 1 0