# 2L 3s

(Redirected from Pentic)
 ↖ 1L 2s ↑ 2L 2s 3L 2s ↗ ← 1L 3s 2L 3s 3L 3s → ↙ 1L 4s ↓ 2L 4s 3L 4s ↘
```┌╥┬╥┬┬┐
│║│║│││
│││││││
└┴┴┴┴┴┘```
Scale structure
Step pattern LsLss
ssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 2\5 to 1\2 (480.0¢ to 600.0¢)
Dark 1\2 to 3\5 (600.0¢ to 720.0¢)
Related MOS scales
Parent 2L 1s
Sister 3L 2s
Daughters 5L 2s, 2L 5s
Neutralized 4L 1s
2-Flought 7L 3s, 2L 8s
Equal tunings
Equalized (L:s = 1:1) 2\5 (480.0¢)
Supersoft (L:s = 4:3) 7\17 (494.1¢)
Soft (L:s = 3:2) 5\12 (500.0¢)
Semisoft (L:s = 5:3) 8\19 (505.3¢)
Basic (L:s = 2:1) 3\7 (514.3¢)
Semihard (L:s = 5:2) 7\16 (525.0¢)
Hard (L:s = 3:1) 4\9 (533.3¢)
Superhard (L:s = 4:1) 5\11 (545.5¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)
For the 3/2-equivalent 2L 3s pattern, see 2L 3s (3/2-equivalent).

2L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 480¢ to 600¢, or from 600¢ to 720¢. This scale is the "classic" pentatonic scale, which is perhaps the most common scale in the world.

The meantone pentatonic scale, in which the generator approximates 4/3 but other intervals in the scale approximate 6/5 and 5/4, has by far the lowest harmonic entropy of all 5-note MOS scales, which explains the worldwide popularity of these scales and their very long history of use. It is also strictly proper.

## Names

The TAMNAMS system suggests the name pentic, derived from an informal clipping of "pentatonic" that is sometimes used to refer to this scale.

## Modes

Scale degrees of the modes of 2L 3s
UDP Cyclic
Order
Step
Pattern
Scale Degree (mosdegree)
0 1 2 3 4 5
4|0 1 LsLss Perf. Maj. Perf. Aug. Maj. Perf.
3|1 3 LssLs Perf. Maj. Perf. Perf. Maj. Perf.
2|2 5 sLsLs Perf. Min. Perf. Perf. Maj. Perf.
1|3 2 sLssL Perf. Min. Perf. Perf. Min. Perf.
0|4 4 ssLsL Perf. Min. Dim. Perf. Min. Perf.

## Scale tree

 Todo: expand Add back entries from original scale tree.
Scale Tree and Tuning Spectrum of 2L 3s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
2\5 480.000 720.000 1:1 1.000 Equalized 2L 3s
11\27 488.889 711.111 6:5 1.200
9\22 490.909 709.091 5:4 1.250
16\39 492.308 707.692 9:7 1.286
7\17 494.118 705.882 4:3 1.333 Supersoft 2L 3s
19\46 495.652 704.348 11:8 1.375
12\29 496.552 703.448 7:5 1.400
17\41 497.561 702.439 10:7 1.429
5\12 500.000 700.000 3:2 1.500 Soft 2L 3s
18\43 502.326 697.674 11:7 1.571
13\31 503.226 696.774 8:5 1.600
21\50 504.000 696.000 13:8 1.625
8\19 505.263 694.737 5:3 1.667 Semisoft 2L 3s
19\45 506.667 693.333 12:7 1.714
11\26 507.692 692.308 7:4 1.750
14\33 509.091 690.909 9:5 1.800
3\7 514.286 685.714 2:1 2.000 Basic 2L 3s
Scales with tunings softer than this are proper
13\30 520.000 680.000 9:4 2.250
10\23 521.739 678.261 7:3 2.333
17\39 523.077 676.923 12:5 2.400
7\16 525.000 675.000 5:2 2.500 Semihard 2L 3s
18\41 526.829 673.171 13:5 2.600
11\25 528.000 672.000 8:3 2.667
15\34 529.412 670.588 11:4 2.750
4\9 533.333 666.667 3:1 3.000 Hard 2L 3s
13\29 537.931 662.069 10:3 3.333
9\20 540.000 660.000 7:2 3.500
14\31 541.935 658.065 11:3 3.667
5\11 545.455 654.545 4:1 4.000 Superhard 2L 3s
11\24 550.000 650.000 9:2 4.500
6\13 553.846 646.154 5:1 5.000
7\15 560.000 640.000 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 3s

From a 3-limit perspective, just make a chain of four 4/3's and octave-reduce, and you end up with pentatonic.

From a 5-limit perspective, the most interesting temperaments with this kind of pentatonic scale are meantone and mavila.

There is also the interesting 2.3.7 temperament that tempers out 64/63 (archy, "no-fives dominant").