User:Ganaram inukshuk/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 ¢)

This is a test page. For the main page, see 4L 3s.

4L 3s, named smitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 857.1 ¢ to 900 ¢, or from 300 ¢ to 342.9 ¢.

Notation

Unless otherwise stated, diamond-MOS notation is used in this article, applying unaltered note names JKLMNOP to the mode 3|3 (step pattern LsLsLsL). Alterations by a chroma are denoted using the symbols & (pronounced "am" or "amp", which raises or "amplifies" a pitch by a chroma) and @ (pronounced "at", which rhymes with "flat").

The gamuts for 4L 3s in 11edo, 15edo, and 18edo are shown below.

Step ratio	Gamut
2:1 (11edo)	J, J&/K@, K, L, L&/M@, M, N, N&/O@, O, P, P&/J@, J
3:1 (15edo)	J, K@, J&, K, L, M@, L&, M, N, O@, N&, O, P, J@, P&, J
3:2 (18edo)	J, J&, K@, K, K&/L@, L, L&, M@, M, M&/N@, N, N&, O@, O, O&/P@, P, P&, J@, J

Tunings

Unless otherwise stated, TAMNAMS is used in this article to name 4L 3s step ratio sizes and ranges, and intervals and scale degrees. Intervals and scale degrees are indexed starting at 0 (0-smistep, 1-smistep, etc). 1-indexed terms (smi-1st, smi-2nd, etc) are discouraged for non-diatonic MOS scales.

Simple tunings

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	11edo (Basic, L:s = 2:1)		Approx. JI Ratios
	Steps	Cents
Perfect 0-smidegree (unison)	0	0	1/1 (exact)
Minor 1-smidegree	1	109.1
Major 1-smidegree	2	218.2
Perfect 2-smidegree	3	327.3
Augmented 2-smidegree	4	436.4
Minor 3-smidegree	4	436.4
Major 3-smidegree	5	545.5
Minor 4-smidegree	6	654.5
Major 4-smidegree	7	763.6
Diminished 5-smidegree	7	763.6
Perfect 5-smidegree	8	872.7
Minor 6-smidegree	9	981.8
Major 6-smidegree	10	1090.9
Perfect 7-smidegree (octave)	11	1200	2/1 (exact)

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	15edo (Hard, L:s = 3:1)		Approx. JI Ratios
	Steps	Cents
Perfect 0-smidegree (unison)	0	0	1/1 (exact)
Minor 1-smidegree	1	80
Major 1-smidegree	3	240
Perfect 2-smidegree	4	320
Augmented 2-smidegree	6	480
Minor 3-smidegree	5	400
Major 3-smidegree	7	560
Minor 4-smidegree	8	640
Major 4-smidegree	10	800
Diminished 5-smidegree	9	720
Perfect 5-smidegree	11	880
Minor 6-smidegree	12	960
Major 6-smidegree	14	1120
Perfect 7-smidegree (octave)	15	1200	2/1 (exact)

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.

Scale degree of 4L 3s

Scale degree	18edo (Soft, L:s = 3:2)		Approx. JI Ratios
	Steps	Cents
Perfect 0-smidegree (unison)	0	0	1/1 (exact)
Minor 1-smidegree	2	133.3
Major 1-smidegree	3	200
Perfect 2-smidegree	5	333.3
Augmented 2-smidegree	6	400
Minor 3-smidegree	7	466.7
Major 3-smidegree	8	533.3
Minor 4-smidegree	10	666.7
Major 4-smidegree	11	733.3
Diminished 5-smidegree	12	800
Perfect 5-smidegree	13	866.7
Minor 6-smidegree	15	1000
Major 6-smidegree	16	1066.7
Perfect 7-smidegree (octave)	18	1200	2/1 (exact)

Modes

Modes of 4L 3s

UDP	Cyclic order	Step pattern
6|0	1	LLsLsLs
5|1	6	LsLLsLs
4|2	4	LsLsLLs
3|3	2	LsLsLsL
2|4	7	sLLsLsL
1|5	5	sLsLLsL
0|6	3	sLsLsLL