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 ¢)
	View • Talk • Edit

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 ¢.

Name

Theory

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.


Edo	Gamut
11edo	J, J&/K@, K, L, L&/M@, M, N, N&/O@, O, P, P&/J@, J
15edo	J, K@, J&, K, L, M@, L&, M, N, O@, N&, O, P, J@, P&, J
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.

Interval/degree tables for various tunings are then shown here, starting with the simple tunings of 2:1, 3:1, and 3:2, followed by the semi/super tunings. These can be in their own sections, or grouped into a broader

Simple tunings

Supersoft

Semisoft

Semihard

Superhard

Modes

A description of the mos's modes and mode names, if any, are written here. Also included are the interval qualities of each mode.

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

Tuning spectrum

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter:

{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}

The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 4L 3s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
5\7						857.143	342.857	1:1	1.000	Equalized 4L 3s
					28\39	861.538	338.462	6:5	1.200
				23\32		862.500	337.500	5:4	1.250
					41\57	863.158	336.842	9:7	1.286
			18\25			864.000	336.000	4:3	1.333	Supersoft 4L 3s
					49\68	864.706	335.294	11:8	1.375
				31\43		865.116	334.884	7:5	1.400
					44\61	865.574	334.426	10:7	1.429
		13\18				866.667	333.333	3:2	1.500	Soft 4L 3s
					47\65	867.692	332.308	11:7	1.571
				34\47		868.085	331.915	8:5	1.600
					55\76	868.421	331.579	13:8	1.625
			21\29			868.966	331.034	5:3	1.667	Semisoft 4L 3s
					50\69	869.565	330.435	12:7	1.714
				29\40		870.000	330.000	7:4	1.750
					37\51	870.588	329.412	9:5	1.800
	8\11					872.727	327.273	2:1	2.000	Basic 4L 3s Scales with tunings softer than this are proper
					35\48	875.000	325.000	9:4	2.250
				27\37		875.676	324.324	7:3	2.333
					46\63	876.190	323.810	12:5	2.400
			19\26			876.923	323.077	5:2	2.500	Semihard 4L 3s
					49\67	877.612	322.388	13:5	2.600
				30\41		878.049	321.951	8:3	2.667
					41\56	878.571	321.429	11:4	2.750
		11\15				880.000	320.000	3:1	3.000	Hard 4L 3s
					36\49	881.633	318.367	10:3	3.333
				25\34		882.353	317.647	7:2	3.500
					39\53	883.019	316.981	11:3	3.667
			14\19			884.211	315.789	4:1	4.000	Superhard 4L 3s
					31\42	885.714	314.286	9:2	4.500
				17\23		886.957	313.043	5:1	5.000
					20\27	888.889	311.111	6:1	6.000
3\4						900.000	300.000	1:0	→ ∞	Collapsed 4L 3s

Scales

Related scales include parent and child/daughter mosses (or subset and superset mosses) and modmosses. Temperament-specific scales can be added here.