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 ¢)
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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


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

Simple tunings

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
Scale degree	Steps	Cents	Steps	Cents	Steps	Cents	Approx. JI Ratios
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)

Proposed table output for MOS degrees template (not a template)
Degree	Note name	2/1 step ratio (11edo)		3/1 step ratio (15edo)		3/2 step ratio (18edo)
Degree	Note name	Steps	Cents	Steps	Cents	Steps	Cents
Perf. 0-mosstep (unison)	J	0	0¢	0	0¢	0	0¢
Perf. 5-mosstep	O	8	872.7¢	11	880¢	13	866.7¢
Maj. 3-mosstep	M	5	545.5¢	7	560¢	8	533.3¢
Maj. 1-mosstep	K	2	218.2¢	3	240¢	3	200¢
Maj. 6-mosstep	P&	10	1090.9¢	14	1120¢	16	1066.7¢
Maj. 4-mosstep	N&	7	763.6¢	10	800¢	11	733.3¢
Aug. 2-mosstep	L&	4	436.4¢	6	480¢	6	400¢
Aug. 0-mosstep (unison)	J&	1	109.1¢	2	160¢	1	66.7¢
Aug. 5-mosstep	O&	9	981.8¢	13	1040¢	14	933.3¢
Aug. 3-mosstep	M&	6	654.5¢	9	720¢	9	600¢
Aug. 1-mosstep	K&	3	327.3¢	5	400¢	4	266.7¢
Dim. 6-mosstep	P@	8	872.7¢	10	800¢	14	933.3¢
Dim. 4-mosstep	N@	5	545.5¢	6	480¢	9	600¢
Dim. 2-mosstep	L@	2	218.2¢	2	160¢	4	266.7¢
Dim. 7-mosstep (equave)	J@	10	1090.9¢	13	1040¢	17	1133.3¢
Dim. 5-mosstep	O@	7	763.6¢	9	720¢	12	800¢
Min. 3-mosstep	M@	4	436.4¢	5	400¢	7	466.7¢
Min. 1-mosstep	K@	1	109.1¢	1	80¢	2	133.3¢
Min. 6-mosstep	P	9	981.8¢	12	960¢	15	1000¢
Min. 4-mosstep	N	6	654.5¢	8	640¢	10	666.7¢
Perf. 2-mosstep	L	3	327.3¢	4	320¢	5	333.3¢
Perf. 7-mosstep (equave)	(J)	11	1200¢	15	1200¢	18	1200¢

Soft tunings

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

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

Hard tunings

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

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

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