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 name flanatonic has been proposed by Inthar, for "flat naiadic".

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.

Scale properties

Template:MOS data is deprecated.

Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Proposed mode names

R-4981 has proposed names based on shogi pieces.

Modes of 8L 3s
UDP	Cyclic order	Step pattern	Shogi-based names^[proposed]
10\|0	1	LLLsLLLsLLs	Ōshō (王将)
9\|1	5	LLLsLLsLLLs	Ryūō (竜王)
8\|2	9	LLsLLLsLLLs	Ryūma (竜馬)
7\|3	2	LLsLLLsLLsL	Hisha (飛車)
6\|4	6	LLsLLsLLLsL	Kaku (角)
5\|5	10	LsLLLsLLLsL	Kin (金)
4\|6	3	LsLLLsLLsLL	Gin (銀)
3\|7	7	LsLLsLLLsLL	Keima (桂馬)
2\|8	11	sLLLsLLLsLL	Kyo (香)
1\|9	4	sLLLsLLsLLL	Tokin (と金)
0\|10	8	sLLsLLLsLLL	Fuhyo (歩兵)

Scale tree

Scale tree and tuning spectrum of 8L 3s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
4\11						436.364	763.636	1:1	1.000	Equalized 8L 3s
					23\63	438.095	761.905	6:5	1.200
				19\52		438.462	761.538	5:4	1.250
					34\93	438.710	761.290	9:7	1.286
			15\41			439.024	760.976	4:3	1.333	Supersoft 8L 3s
					41\112	439.286	760.714	11:8	1.375
				26\71		439.437	760.563	7:5	1.400
					37\101	439.604	760.396	10:7	1.429
		11\30				440.000	760.000	3:2	1.500	Soft 8L 3s
					40\109	440.367	759.633	11:7	1.571
				29\79		440.506	759.494	8:5	1.600
					47\128	440.625	759.375	13:8	1.625	Golden sentry (440.5922 ¢)
			18\49			440.816	759.184	5:3	1.667	Semisoft 8L 3s
					43\117	441.026	758.974	12:7	1.714
				25\68		441.176	758.824	7:4	1.750
					32\87	441.379	758.621	9:5	1.800	Clyde
	7\19					442.105	757.895	2:1	2.000	Basic 8L 3s Scales with tunings softer than this are proper
					31\84	442.857	757.143	9:4	2.250	Sensei
				24\65		443.077	756.923	7:3	2.333
					41\111	443.243	756.757	12:5	2.400	Warrior
			17\46			443.478	756.522	5:2	2.500	Semihard 8L 3s Sensi (optimal around here)
					44\119	443.697	756.303	13:5	2.600	Golden sensi
				27\73		443.836	756.164	8:3	2.667
					37\100	444.000	756.000	11:4	2.750
		10\27				444.444	755.556	3:1	3.000	Hard 8L 3s
					33\89	444.944	755.056	10:3	3.333
				23\62		445.161	754.839	7:2	3.500
					36\97	445.361	754.639	11:3	3.667
			13\35			445.714	754.286	4:1	4.000	Superhard 8L 3s
					29\78	446.154	753.846	9:2	4.500
				16\43		446.512	753.488	5:1	5.000
					19\51	447.059	752.941	6:1	6.000
3\8						450.000	750.000	1:0	→ ∞	Collapsed 8L 3s

Todo: review

Make pentachordal analysis its own section (see history of this section)?