3L 1s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS|name=tetric}}
| Periods = 1
{{MOS intro}}
| nLargeSteps = 3
 
| nSmallSteps = 1
== Names ==
| Equalized = 1
TAMNAMS suggests the temperament-agnostic name tetric for this MOS pattern. [[User:MisterShafXen]] calls this scale quasi-tritonic, as this scale has 3 large steps and only a single small step.
| Paucitonic = 1
 
| Pattern = LLLs
== Scale properties ==
}}
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}


'''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¢).
=== Modes ===
{{MOS mode degrees}}


== Modes ==
== Trivia ==
* 3|0 LLLs
This scale can be considered the neutral analogue to pentatonic, as the hard descendants of this scale include neutral[7] {3L 4s) and dicot[10] (dicoid/3L 7s).
* 2|1 LLsL
* 1|2 LsLL
* 0|3 sLLL


== 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)
 
{{MOS tuning spectrum
{| class="wikitable center-all"
| 9/7 = [[Hanson]]/[[keemun]]
! colspan="6" | Generator
| 11/8 = [[Superkleismic]]
! Cents
| 10/7 = [[Hyperkleismic]]
! L
| 13/8 = Lucas generator (331.672{{c}})
! s
| 9/5 = [[Sixix]]
! L/s
| 9/4 = [[Mohaha]]/[[mohajira]]
! Comments
| 12/5 = [[Hemif]]/[[hemififths]]
|-
| 13/5 = Golden suhajira (354.823{{c}})
| 1\4 || || || || || || 300.000 || 1 || 1 || 1.000 ||
| 11/4 = [[Beatles]]
|-
| 9/2 = [[Sephiroth]]
| || || || || || 6\23 || 313.043 || 6 || 5 || 1.200 ||
| 6/1 = [[Magic]] ↓
|-
}}
| || || || || 5\19 || || 315.789 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\34 || 317.647 || 9 || 7 || 1.286 || [[Hanson]]/[[keemun]]
|-
| || || || 4\15 || || || 320.000 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\41 || 321.951 || 11 || 8 || 1.375 || [[Superkleismic]]
|-
| || || || || 7\26 || || 323.077 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\37 || 324.324 || 10 || 7 || 1.429 || [[Hyperkleismic]]
|-
| || || 3\11 || || || || 327.273 || 3 || 2 || 1.500 ||
|-
| || || || || || 11\40 || 330.000 || 11 || 7 || 1.571 ||
|-
| || || || || 8\29 || || 331.034 || 8 || 5 || 1.600 ||
|-
| || || || || || 13\47 || 331.915 || 13 || 8 || 1.625 || Golden [[dicot]] (331.6718¢)
|-
| || || || 5\18 || || || 333.333 || 5 || 3 || 1.667 ||
|-
| || || || || || 12\43 || 334.884 || 12 || 7 || 1.714 ||
|-
| || || || || 7\25 || || 336.000 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\32 || 337.500 || 9 || 5 || 1.800 || [[Sixix]]
|-
| || 2\7 || || || || || 342.857 || 2 || 1 || 2.000 || Basic 3L 1s
|-
| || || || || || 9\31 || 348.387 || 9 || 4 || 2.250 || [[Mohaha]]/[[mohajira]]
|-
| || || || || 7\24 || || 350.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\41 || 351.220 || 12 || 5 || 2.400 || [[Hemif]]/[[hemififths]]
|-
| || || || 5\17 || || || 352.941 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\44 || 354.545 || 13 || 5 || 2.600 || Golden suhajira (354.8232¢)
|-
| || || || || 8\27 || || 355.556 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\37 || 356.757 || 11 || 4 || 2.750 || [[Beatles]]
|-
| || || 3\10 || || || || 360.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 10\33 || 363.636 || 10 || 3 || 3.333 ||
|-
| || || || || 7\23 || || 365.217 || 7 || 2 || 3.500 ||
|-
| || || || || || 11\36 || 366.667 || 11 || 3 || 3.667 ||
|-
| || || || 4\13 || || || 369.231 || 4 || 1 || 4.000 ||
|-
| || || || || || 9\29 || 372.414 || 9 || 2 || 4.500 || [[Sephiroth]]
|-
| || || || || 5\16 || || 375.000 || 5 || 1 || 5.000 ||
|-
| || || || || || 6\19 || 378.947 || 6 || 1 || 6.000 || [[Magic]]↓
|-
| 1\3 || || || || || || 400.000 || 1 || 0 || → inf ||
|}


[[Category:Tetrad]]
[[Category:Tetrad]]
[[Category:4-tone scales]]

Latest revision as of 19:19, 5 May 2026

← 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 ¢)
View • Talk • Edit

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.

Names

TAMNAMS suggests the temperament-agnostic name tetric for this MOS pattern. User:MisterShafXen calls this scale quasi-tritonic, as this scale has 3 large steps and only a single 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.

Trivia

This scale can be considered the neutral analogue to pentatonic, as the hard descendants of this scale include neutral[7] {3L 4s) and dicot[10] (dicoid/3L 7s).

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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