User:Ganaram inukshuk/4L 3s: Difference between revisions

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Line 59: Line 59:
|3\15, 240¢
|3\15, 240¢
|3\18, 200¢
|3\18, 200¢
|-
|-bgcolor="#eaeaff"
|Maj. 6-mosstep
|Maj. 6-mosstep
|P&
|P&
Line 65: Line 65:
|14\15, 1120¢
|14\15, 1120¢
|16\18, 1066.7¢
|16\18, 1066.7¢
|-
|-bgcolor="#eaeaff"
|Maj. 4-mosstep
|Maj. 4-mosstep
|N&
|N&
Line 71: Line 71:
|10\15, 800¢
|10\15, 800¢
|11\18, 733.3¢
|11\18, 733.3¢
|-
|-bgcolor="#eaeaff"
|Aug. 2-mosstep
|Aug. 2-mosstep
|L&
|L&
Line 77: Line 77:
|6\15, 480¢
|6\15, 480¢
|6\18, 400¢
|6\18, 400¢
|-
|-bgcolor="#eaeaff"
|Aug. 0-mosstep (unison)
|Aug. 0-mosstep (unison)
|J&
|J&
Line 83: Line 83:
|2\15, 160¢
|2\15, 160¢
|1\18, 66.7¢
|1\18, 66.7¢
|-
|-bgcolor="#eaeaff"
|Aug. 5-mosstep
|Aug. 5-mosstep
|O&
|O&
Line 89: Line 89:
|13\15, 1040¢
|13\15, 1040¢
|14\18, 933.3¢
|14\18, 933.3¢
|-
|-bgcolor="#eaeaff"
|Aug. 3-mosstep
|Aug. 3-mosstep
|M&
|M&
Line 95: Line 95:
|9\15, 720¢
|9\15, 720¢
|9\18, 600¢
|9\18, 600¢
|-
|-bgcolor="#eaeaff"
|Aug. 1-mosstep
|Aug. 1-mosstep
|K&
|K&
Line 101: Line 101:
|5\15, 400¢
|5\15, 400¢
|4\18, 266.7¢
|4\18, 266.7¢
|-
|-bgcolor="#eaeaff"
|Dim. 6-mosstep
|Dim. 6-mosstep
|P@
|P@
Line 107: Line 107:
|10\15, 800¢
|10\15, 800¢
|14\18, 933.3¢
|14\18, 933.3¢
|-
|-bgcolor="#eaeaff"
|Dim. 4-mosstep
|Dim. 4-mosstep
|N@
|N@
Line 113: Line 113:
|6\15, 480¢
|6\15, 480¢
|9\18, 600¢
|9\18, 600¢
|-
|-bgcolor="#eaeaff"
|Dim. 2-mosstep
|Dim. 2-mosstep
|L@
|L@
Line 119: Line 119:
|2\15, 160¢
|2\15, 160¢
|4\18, 266.7¢
|4\18, 266.7¢
|-
|-bgcolor="#eaeaff"
|Dim. 7-mosstep (equave)
|Dim. 7-mosstep (equave)
|J@
|J@
Line 125: Line 125:
|13\15, 1040¢
|13\15, 1040¢
|17\18, 1133.3¢
|17\18, 1133.3¢
|-
|-bgcolor="#eaeaff"
|Dim. 5-mosstep
|Dim. 5-mosstep
|O@
|O@
Line 131: Line 131:
|9\15, 720¢
|9\15, 720¢
|12\18, 800¢
|12\18, 800¢
|-
|-bgcolor="#eaeaff"
|Min. 3-mosstep
|Min. 3-mosstep
|M@
|M@
Line 137: Line 137:
|5\15, 400¢
|5\15, 400¢
|7\18, 466.7¢
|7\18, 466.7¢
|-
|-bgcolor="#eaeaff"
|Min. 1-mosstep
|Min. 1-mosstep
|K@
|K@

Revision as of 23:01, 22 June 2023

↖ 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 ¢.

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) 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)
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)
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)
Proposed table output for MOS degrees template
Degree Note name 2/1 step ratio

(11edo)

3/1 step ratio

(15edo)

3/2 step ratio

(18edo)

Perf. 0-mosstep (unison) J 0\11, 0¢ 0\15, 0¢ 0\18, 0¢
Perf. 5-mosstep O 8\11, 872.7¢ 11\15, 880¢ 13\18, 866.7¢
Maj. 3-mosstep M 5\11, 545.5¢ 7\15, 560¢ 8\18, 533.3¢
Maj. 1-mosstep K 2\11, 218.2¢ 3\15, 240¢ 3\18, 200¢
Maj. 6-mosstep P& 10\11, 1090.9¢ 14\15, 1120¢ 16\18, 1066.7¢
Maj. 4-mosstep N& 7\11, 763.6¢ 10\15, 800¢ 11\18, 733.3¢
Aug. 2-mosstep L& 4\11, 436.4¢ 6\15, 480¢ 6\18, 400¢
Aug. 0-mosstep (unison) J& 1\11, 109.1¢ 2\15, 160¢ 1\18, 66.7¢
Aug. 5-mosstep O& 9\11, 981.8¢ 13\15, 1040¢ 14\18, 933.3¢
Aug. 3-mosstep M& 6\11, 654.5¢ 9\15, 720¢ 9\18, 600¢
Aug. 1-mosstep K& 3\11, 327.3¢ 5\15, 400¢ 4\18, 266.7¢
Dim. 6-mosstep P@ 8\11, 872.7¢ 10\15, 800¢ 14\18, 933.3¢
Dim. 4-mosstep N@ 5\11, 545.5¢ 6\15, 480¢ 9\18, 600¢
Dim. 2-mosstep L@ 2\11, 218.2¢ 2\15, 160¢ 4\18, 266.7¢
Dim. 7-mosstep (equave) J@ 10\11, 1090.9¢ 13\15, 1040¢ 17\18, 1133.3¢
Dim. 5-mosstep O@ 7\11, 763.6¢ 9\15, 720¢ 12\18, 800¢
Min. 3-mosstep M@ 4\11, 436.4¢ 5\15, 400¢ 7\18, 466.7¢
Min. 1-mosstep K@ 1\11, 109.1¢ 1\15, 80¢ 2\18, 133.3¢
Min. 6-mosstep P 9\11, 981.8¢ 12\15, 960¢ 15\18, 1000¢
Min. 4-mosstep N 6\11, 654.5¢ 8\15, 640¢ 10\18, 666.7¢
Perf. 2-mosstep L 3\11, 327.3¢ 4\15, 320¢ 5\18, 333.3¢
Perf. 7-mosstep (equave) (J) 11\11, 1200¢ 15\15, 1200¢ 18\18, 1200¢

Supersoft

Semisoft

Semihard

Superhard

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
Bright Dark L:s Hardness
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
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