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 ¢.

4L 3s can be though of as a warped diatonic scale, where one large step of diatonic (5L 2s) is replaced with a small step.

Name

TAMNAMS suggests the name smitonic smy-TON-ik /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.

Notation and intervals

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

Basic tuning

The basic tuning for 4L 3s has large steps that are 2 edosteps and small steps that are 1 edostep, which is supported by 11edo. Raising or lowering any of the nominals by a chroma produces the following scale degrees.

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)

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)		15edo (Hard, L:s = 3:1)		18edo (Soft, L:s = 3:2)		Approx. JI Ratios
	Steps	Cents	Steps	Cents	Steps	Cents
Perfect 0-smidegree (unison)	0	0	0	0	0	0	1/1 (exact)
Minor 1-smidegree	1	109.1	1	80	2	133.3
Major 1-smidegree	2	218.2	3	240	3	200
Perfect 2-smidegree	3	327.3	4	320	5	333.3
Augmented 2-smidegree	4	436.4	6	480	6	400
Minor 3-smidegree	4	436.4	5	400	7	466.7
Major 3-smidegree	5	545.5	7	560	8	533.3
Minor 4-smidegree	6	654.5	8	640	10	666.7
Major 4-smidegree	7	763.6	10	800	11	733.3
Diminished 5-smidegree	7	763.6	9	720	12	800
Perfect 5-smidegree	8	872.7	11	880	13	866.7
Minor 6-smidegree	9	981.8	12	960	15	1000
Major 6-smidegree	10	1090.9	14	1120	16	1066.7
Perfect 7-smidegree (octave)	11	1200	15	1200	18	1200	2/1 (exact)

Soft tunings

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

Scale degree of 4L 3s

Scale degree	18edo (Soft, L:s = 3:2)		25edo (Supersoft, L:s = 4:3)		29edo (Semisoft, L:s = 5:3)		Approx. JI Ratios
	Steps	Cents	Steps	Cents	Steps	Cents
Perfect 0-smidegree (unison)	0	0	0	0	0	0	1/1 (exact)
Minor 1-smidegree	2	133.3	3	144	3	124.1
Major 1-smidegree	3	200	4	192	5	206.9
Perfect 2-smidegree	5	333.3	7	336	8	331
Augmented 2-smidegree	6	400	8	384	10	413.8
Minor 3-smidegree	7	466.7	10	480	11	455.2
Major 3-smidegree	8	533.3	11	528	13	537.9
Minor 4-smidegree	10	666.7	14	672	16	662.1
Major 4-smidegree	11	733.3	15	720	18	744.8
Diminished 5-smidegree	12	800	17	816	19	786.2
Perfect 5-smidegree	13	866.7	18	864	21	869
Minor 6-smidegree	15	1000	21	1008	24	993.1
Major 6-smidegree	16	1066.7	22	1056	26	1075.9
Perfect 7-smidegree (octave)	18	1200	25	1200	29	1200	2/1 (exact)

Hard tunings

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

Scale degree of 4L 3s

Scale degree	15edo (Hard, L:s = 3:1)		19edo (Superhard, L:s = 4:1)		26edo (Semihard, L:s = 5:2)		Approx. JI Ratios
	Steps	Cents	Steps	Cents	Steps	Cents
Perfect 0-smidegree (unison)	0	0	0	0	0	0	1/1 (exact)
Minor 1-smidegree	1	80	1	63.2	2	92.3
Major 1-smidegree	3	240	4	252.6	5	230.8
Perfect 2-smidegree	4	320	5	315.8	7	323.1
Augmented 2-smidegree	6	480	8	505.3	10	461.5
Minor 3-smidegree	5	400	6	378.9	9	415.4
Major 3-smidegree	7	560	9	568.4	12	553.8
Minor 4-smidegree	8	640	10	631.6	14	646.2
Major 4-smidegree	10	800	13	821.1	17	784.6
Diminished 5-smidegree	9	720	11	694.7	16	738.5
Perfect 5-smidegree	11	880	14	884.2	19	876.9
Minor 6-smidegree	12	960	15	947.4	21	969.2
Major 6-smidegree	14	1120	18	1136.8	24	1107.7
Perfect 7-smidegree (octave)	15	1200	19	1200	26	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