9L 3s

↖ 8L 2s	↑ 9L 2s	10L 2s ↗
← 8L 3s	9L 3s	10L 3s →
↙ 8L 4s	↓ 9L 4s	10L 4s ↘

┌╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLLsLLLs sLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\12 to 1\9 (100.0 ¢ to 133.3 ¢)
Dark	2\9 to 3\12 (266.7 ¢ to 300.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	3L 6s
Sister	3L 9s
Daughters	12L 9s, 9L 12s
Neutralized	6L 6s
2-Flought	21L 3s, 9L 15s
Equal tunings
Equalized (L:s = 1:1)	1\12 (100.0 ¢)
Supersoft (L:s = 4:3)	4\45 (106.7 ¢)
Soft (L:s = 3:2)	3\33 (109.1 ¢)
Semisoft (L:s = 5:3)	5\54 (111.1 ¢)
Basic (L:s = 2:1)	2\21 (114.3 ¢)
Semihard (L:s = 5:2)	5\51 (117.6 ¢)
Hard (L:s = 3:1)	3\30 (120.0 ¢)
Superhard (L:s = 4:1)	4\39 (123.1 ¢)
Collapsed (L:s = 1:0)	1\9 (133.3 ¢)

9L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 3 small steps, with a period of 3 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 9L 3s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 100 ¢ to 133.3 ¢, or from 266.7 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

9L 3s represents the chromatic scale of August temperament and its higher-limit extensions.

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.

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

Scale tree

Scale tree and tuning spectrum of 9L 3s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\12						100.000	300.000	1:1	1.000	Equalized 9L 3s
					6\69	104.348	295.652	6:5	1.200
				5\57		105.263	294.737	5:4	1.250
					9\102	105.882	294.118	9:7	1.286
			4\45			106.667	293.333	4:3	1.333	Supersoft 9L 3s
					11\123	107.317	292.683	11:8	1.375
				7\78		107.692	292.308	7:5	1.400	August
					10\111	108.108	291.892	10:7	1.429
		3\33				109.091	290.909	3:2	1.500	Soft 9L 3s
					11\120	110.000	290.000	11:7	1.571
				8\87		110.345	289.655	8:5	1.600
					13\141	110.638	289.362	13:8	1.625
			5\54			111.111	288.889	5:3	1.667	Semisoft 9L 3s
					12\129	111.628	288.372	12:7	1.714
				7\75		112.000	288.000	7:4	1.750
					9\96	112.500	287.500	9:5	1.800	11-limit August
	2\21					114.286	285.714	2:1	2.000	Basic 9L 3s 13-limit August
					9\93	116.129	283.871	9:4	2.250
				7\72		116.667	283.333	7:3	2.333
					12\123	117.073	282.927	12:5	2.400
			5\51			117.647	282.353	5:2	2.500	Semihard 9L 3s
					13\132	118.182	281.818	13:5	2.600
				8\81		118.519	281.481	8:3	2.667
					11\111	118.919	281.081	11:4	2.750
		3\30				120.000	280.000	3:1	3.000	Hard 9L 3s
					10\99	121.212	278.788	10:3	3.333
				7\69		121.739	278.261	7:2	3.500
					11\108	122.222	277.778	11:3	3.667
			4\39			123.077	276.923	4:1	4.000	Superhard 9L 3s
					9\87	124.138	275.862	9:2	4.500
				5\48		125.000	275.000	5:1	5.000
					6\57	126.316	273.684	6:1	6.000
1\9						133.333	266.667	1:0	→ ∞	Collapsed 9L 3s

This page is a stub. You can help the Xenharmonic Wiki by expanding it.