2L 3s
| ↖1L 2s | ↑2L 2s | 3L 2s↗ |
| ←1L 3s | 2L 3s | 3L 3s→ |
| ↙1L 4s | ↓2L 4s | 3L 4s↘ |
┌╥┬╥┬┬┐ │║│║│││ │││││││ └┴┴┴┴┴┘
ssLsL
2L 5s
- 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. 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
- 4|0 LsLss
- 3|1 LssLs
- 2|2 sLsLs
- 1|3 sLssL
- 0|4 ssLsL
Scales
- Archy5 – 472edo tuning
- Edson5 – 29edo tuning
- Pythagorean5 – Pythagorean tuning
- Meantone5 – 31edo tuning
Scale tree
Todo: expand
Add back entries from original scale tree.
| 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").