3L 1s: Difference between revisions

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{{Infobox MOS|name=tetric}}
{{Infobox MOS|name=tetric}}
{{MOS intro}}


'''3L 1s''' is the MOS pattern LLLs, with generators ranging from 1\4 (one step of [[4edo]] = 300¢) to 1\3 (one step of [[3edo]] = 400¢).
== Scale properties ==
{{TAMNAMS use}}


== Modes ==
=== Intervals ===
* 3|0 LLLs
{{MOS intervals}}
* 2|1 LLsL
 
* 1|2 LsLL
=== Generator chain ===
* 0|3 sLLL
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


== Scale tree ==
== Scale tree ==
Generator ranges:
Generator ranges:
* Chroma-positive generator: 300 cents (1\4) to 400 cents (1\3)
* Chroma-positive generator: 300{{c}} (1\4) to 400{{c}} (1\3)
* Chroma-negative generator: 800 cents (2\3) to 900 cents (3\4)
* Chroma-negative generator: 800{{c}} (2\3) to 900{{c}} (3\4)
{{Scale tree|Comments=9/7:[[Hanson]]/[[keemun]];11/8:[[Superkleismic]];10/7:[[Hyperkleismic]];13/8:Golden [[dicot]] (331.672 cents);9/5:Sixix;2/1:Basic 3L 1s;9/4:[[Mohaha]]/[[mohajira]];12/5:[[Hemif]]/[[hemififths]];13/5;Golden suhajira (354.823 cents);11/4:[[Beatles]];9/2:[[Sephiroth]];6/1:[[Magic]]↓}}
{{MOS tuning spectrum
| 9/7 = [[Hanson]]/[[keemun]]
| 11/8 = [[Superkleismic]]
| 10/7 = [[Hyperkleismic]]
| 13/8 = Lucas generator (331.672{{c}})
| 9/5 = [[Sixix]]
| 9/4 = [[Mohaha]]/[[mohajira]]
| 12/5 = [[Hemif]]/[[hemififths]]
| 13/5 = Golden suhajira (354.823{{c}})
| 11/4 = [[Beatles]]
| 9/2 = [[Sephiroth]]
| 6/1 = [[Magic]] ↓
}}
 
[[Category:Tetrad]]
[[Category:Tetrad]]
[[Category:4-tone scales]]
[[Category:4-tone scales]]

Latest revision as of 09:26, 22 June 2025

← 2L 1s 3L 1s 4L 1s →
↙ 2L 2s ↓ 3L 2s 4L 2s ↘ 
┌╥╥╥┬┐
│║║║││
││││││
└┴┴┴┴┘
Scale structure
Step pattern LLLs
sLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\4 to 1\3 (300.0 ¢ to 400.0 ¢)
Dark 2\3 to 3\4 (800.0 ¢ to 900.0 ¢)
Related MOS scales
Parent 1L 2s
Sister 1L 3s
Daughters 4L 3s, 3L 4s
Neutralized 2L 2s
2-Flought 7L 1s, 3L 5s
Equal tunings
Equalized (L:s = 1:1) 1\4 (300.0 ¢)
Supersoft (L:s = 4:3) 4\15 (320.0 ¢)
Soft (L:s = 3:2) 3\11 (327.3 ¢)
Semisoft (L:s = 5:3) 5\18 (333.3 ¢)
Basic (L:s = 2:1) 2\7 (342.9 ¢)
Semihard (L:s = 5:2) 5\17 (352.9 ¢)
Hard (L:s = 3:1) 3\10 (360.0 ¢)
Superhard (L:s = 4:1) 4\13 (369.2 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 300 ¢ to 400 ¢, or from 800 ¢ to 900 ¢. Scales of this form are always proper because there is only one small step.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 3L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 300.0 ¢
Perfect 1-mosstep P1ms L 300.0 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 400.0 ¢ to 600.0 ¢
Major 2-mosstep M2ms 2L 600.0 ¢ to 800.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 800.0 ¢ to 900.0 ¢
Augmented 3-mosstep A3ms 3L 900.0 ¢ to 1200.0 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 1200.0 ¢

Generator chain

Generator chain of 3L 1s
Bright gens Scale degree Abbrev.
6 Augmented 2-mosdegree A2md
5 Augmented 1-mosdegree A1md
4 Augmented 0-mosdegree A0md
3 Augmented 3-mosdegree A3md
2 Major 2-mosdegree M2md
1 Perfect 1-mosdegree P1md
0 Perfect 0-mosdegree
Perfect 4-mosdegree		 P0md
P4md
−1 Perfect 3-mosdegree P3md
−2 Minor 2-mosdegree m2md
−3 Diminished 1-mosdegree d1md
−4 Diminished 4-mosdegree d4md
−5 Diminished 3-mosdegree d3md
−6 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 3L 1s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4
3|0 1 LLLs Perf. Perf. Maj. Aug. Perf.
2|1 2 LLsL Perf. Perf. Maj. Perf. Perf.
1|2 3 LsLL Perf. Perf. Min. Perf. Perf.
0|3 4 sLLL Perf. Dim. Min. Perf. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 300 ¢ (1\4) to 400 ¢ (1\3)
  • Chroma-negative generator: 800 ¢ (2\3) to 900 ¢ (3\4)
Scale tree and tuning spectrum of 3L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\4 300.000 900.000 1:1 1.000 Equalized 3L 1s
6\23 313.043 886.957 6:5 1.200
5\19 315.789 884.211 5:4 1.250
9\34 317.647 882.353 9:7 1.286 Hanson/keemun
4\15 320.000 880.000 4:3 1.333 Supersoft 3L 1s
11\41 321.951 878.049 11:8 1.375 Superkleismic
7\26 323.077 876.923 7:5 1.400
10\37 324.324 875.676 10:7 1.429 Hyperkleismic
3\11 327.273 872.727 3:2 1.500 Soft 3L 1s
11\40 330.000 870.000 11:7 1.571
8\29 331.034 868.966 8:5 1.600
13\47 331.915 868.085 13:8 1.625 Lucas generator (331.672 ¢)
5\18 333.333 866.667 5:3 1.667 Semisoft 3L 1s
12\43 334.884 865.116 12:7 1.714
7\25 336.000 864.000 7:4 1.750
9\32 337.500 862.500 9:5 1.800 Sixix
2\7 342.857 857.143 2:1 2.000 Basic 3L 1s
9\31 348.387 851.613 9:4 2.250 Mohaha/mohajira
7\24 350.000 850.000 7:3 2.333
12\41 351.220 848.780 12:5 2.400 Hemif/hemififths
5\17 352.941 847.059 5:2 2.500 Semihard 3L 1s
13\44 354.545 845.455 13:5 2.600 Golden suhajira (354.823 ¢)
8\27 355.556 844.444 8:3 2.667
11\37 356.757 843.243 11:4 2.750 Beatles
3\10 360.000 840.000 3:1 3.000 Hard 3L 1s
10\33 363.636 836.364 10:3 3.333
7\23 365.217 834.783 7:2 3.500
11\36 366.667 833.333 11:3 3.667
4\13 369.231 830.769 4:1 4.000 Superhard 3L 1s
9\29 372.414 827.586 9:2 4.500 Sephiroth
5\16 375.000 825.000 5:1 5.000
6\19 378.947 821.053 6:1 6.000 Magic ↓
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 1s
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