4L 3s

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

Scale structure
Step pattern	LLsLsLs sLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\7 to 3\4 (857.1 ¢ to 900.0 ¢)
Dark	1\4 to 2\7 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Name	smitonic
Prefix	smi-
Abbrev.	smi
Related MOS scales
Parent	3L 1s
Sister	3L 4s
Daughters	7L 4s, 4L 7s
Neutralized	1L 6s
2-Flought	11L 3s, 4L 10s
Equal tunings
Equalized (L:s = 1:1)	5\7 (857.1 ¢)
Supersoft (L:s = 4:3)	18\25 (864.0 ¢)
Soft (L:s = 3:2)	13\18 (866.7 ¢)
Semisoft (L:s = 5:3)	21\29 (869.0 ¢)
Basic (L:s = 2:1)	8\11 (872.7 ¢)
Semihard (L:s = 5:2)	19\26 (876.9 ¢)
Hard (L:s = 3:1)	11\15 (880.0 ¢)
Superhard (L:s = 4:1)	14\19 (884.2 ¢)
Collapsed (L:s = 1:0)	3\4 (900.0 ¢)
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4L 3s refers to the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 2\7edo (two degrees of 7edo, or approx. 342.857¢). The name smitonic smy-TON-ik /smaɪˈtɒnɪk/ has been proposed (derived from 'sharp minor third', taking sharp to mean sharp of the 12edo minor third).

4L 3s is a distorted diatonic, because it has one large step of diatonic (5L 2s, LLsLLLs) replaced with a small step (yielding LLsLsLs).

Notation

The notation used in this article is LsLsLsL = JKLMNOPJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)

Thus the 11edo gamut is as follows:

J/Q& J&/K@ K/L@ L/K& L&/M@ M/N@ N/M& N&/O@ O/P@ P/O@ P&/J@ J

Scale tree

The spectrum looks like this:

Generator								Tetrachord	g in cents	2g	3g	4g	Comments
1\4								1 0 1	300	600	900	0
							9\35	8 1 8	308.571	617.143	925.714	34.286
						8\31		7 1 7	309.677	619.355	929.023	38.71
					7\27			6 1 6	311.111	622.222	933.333	44.444
				6\23				5 1 5	313.043	626.087	939.13	52.174
			5\19					4 1 4	315.789	631.579	947.368	63.158
				9\34				7 2 7	317.647	634.294	951.941	70.588
		4\15						3 1 3	320	640	960	80	L/s = 3.
				11\41				8 3 8	321.951	643.902	965.854	87.805
						29\108		21 8 21	322.222	644.444	966.667	88.889
					18\67			13 5 13	322.388	644.776	967.364	89.522
			7\26					5 2 5	323.077	646.154	969.231	92.308
							31/115	22 9 22	323.478	646.956	970.434	93.913
								2.44 1 2.44	323.501	647.002	970.003	94.004
						24/89		17 7 17	323.595	647.191	970.786	94.382
					17/63			12 5 12	323.809	647.619	971.428	95.238
				10/37				7 3 7	324.324	648.648	972.972	97.297
	3\11							2 1 2	327.273	654.545	981.818	109.091	Boundary of propriety (generators larger than this are proper)
			8\29					5 3 5	331.034	662.069	993.013	124.138
					21\76			13 8 13	331.579	663.158	994.739	126.316
							34\123	21 13 21	331.707	663.415	995.122	126.829	Golden smitonic
				13\47				8 5 8	331.915	663.83	995.745	127.66
		5\18						3 2 3	333.333	666.667	1000	133.333	Optimum rank range (L/s=3/2)
			7\25					4 3 4	336	672	1008	144
				9\32				5 4 5	337.5	675	1012.5	150
					11\39			6 5 6	338.462	676.923	1015.385	153.846
						13\46		7 6 7	339.13	678.261	1017.391	156.522
							15\53	8 7 8	339.623	679.245	1018.868	158.491
2\7								1 1 1	342.857	685.714	1028.571	171.429

Intervals

Generators	Notation (1/1 = J)	Heptatonic interval category name	Generators	Notation of 2/1 inverse	Heptatonic interval category name
The 7-note MOS has the following intervals (from some root):
0	J	perfect unison	0	J	octave
1	L	perfect smithird	-1	O	perfect smisixth
2	N	minor smififth (aka minor fifth)	-2	M	major smifourth (aka major fourth)
3	P	minor smiseventh	-3	K	major smisecond
4	K@	minor smisecond	-4	Q&	major smiseventh
5	M@	minor smifourth (aka minor fourth)	-5	N&	major smififth (aka major fifth)
6	O@	diminished smisixth	-6	L&	augmented smithird
The chromatic 11-note MOS (either 7L 4s or 4L 7s) also has the following intervals (from some root):
7	J@	diminished octave	-7	J&	augmented unison
8	L@	diminished smithird	-8	O&	augmented smisixth
9	N@	diminished smififth	-9	M&	augmented smifourth
10	P@	diminished smiseventh	-10	K&	augmented smisecond

Samples

A fugue in 18edo (WIP)