3L 2s

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↖ 2L 1s ↑3L 1s 4L 1s ↗
← 2L 2s3L 2s 4L 2s →
↙ 2L 3s ↓3L 3s 4L 3s ↘
┌╥╥┬╥┬┐
│║║│║││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LLsLs
sLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\5 to 2\3 (720.0¢ to 800.0¢)
Dark 1\3 to 2\5 (400.0¢ to 480.0¢)
Related MOS scales
Parent 2L 1s
Sister 2L 3s
Daughters 5L 3s, 3L 5s
Neutralized 1L 4s
Equal tunings
Equalized (L:s = 1:1) 3\5 (720.0¢)
Supersoft (L:s = 4:3) 11\18 (733.3¢)
Soft (L:s = 3:2) 8\13 (738.5¢)
Semisoft (L:s = 5:3) 13\21 (742.9¢)
Basic (L:s = 2:1) 5\8 (750.0¢)
Semihard (L:s = 5:2) 12\19 (757.9¢)
Hard (L:s = 3:1) 7\11 (763.6¢)
Superhard (L:s = 4:1) 9\14 (771.4¢)
Collapsed (L:s = 1:0) 2\3 (800.0¢)
For the 3/2-equivalent 3L 2s pattern, see 3L 2s (fifth-equivalent).

3L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 720¢ to 800¢, or from 400¢ to 480¢. The only notable low-harmonic-entropy scale for this MOS pattern is sensi, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

Name

The TAMNAMS system applies the name antipentic as the scale utilizes opposite step sizes to the “classic” pentatonic scale (2L 3s). The name antipentic can be used regardless of the equave.

Modes

  • 4|0 LLsLs
  • 3|1 LsLLs
  • 2|2 LsLsL
  • 1|3 sLLsL
  • 0|4 sLsLL

Scale tree

Generator ranges:

  • Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
  • Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)
Generator Cents L s L/s Comments
3\5 720.000 1 1 1.000
17\28 728.571 6 5 1.200
14\23 730.435 5 4 1.250
25\41 731.707 9 7 1.286
11\18 733.333 4 3 1.333
30\49 734.694 11 8 1.375 Semisept
19\31 735.484 7 5 1.400
27\44 736.364 10 7 1.429
8\13 738.462 3 2 1.500
29\47 740.426 11 7 1.571
21\34 741.176 8 5 1.600
34\55 741.818 13 8 1.625 Golden father/petritri/aurora (741.6408¢)
13\21 742.857 5 3 1.667
31\50 744.000 12 7 1.714
18\29 744.828 7 4 1.750
23\37 745.946 9 5 1.800
5\8 750.000 2 1 2.000 Basic antipentic
(Generators smaller than this are proper)
22\35 754.286 9 4 2.250
17\27 755.556 7 3 2.333
29\46 756.522 12 5 2.400 Sensi
12\19 757.895 5 2 2.500
31\49 759.184 13 5 2.600 Golden sentry (759.4078¢)
19\30 760.000 8 3 2.667
26\41 760.976 11 4 2.750
7\11 763.636 3 1 3.000
23\36 766.667 10 3 3.333
16\25 768.000 7 2 3.500
25\39 769.231 11 3 3.667
9\14 771.429 4 1 4.000
20\31 774.194 9 2 4.500 Squares/skwares
11\17 776.471 5 1 5.000
13\20 780.000 6 1 6.000
2\3 800.000 1 0 → inf