2L 3s
| ↖ 1L 2s | ↑ 2L 2s | 3L 2s ↗ |
| ← 1L 3s | 2L 3s | 3L 3s → |
| ↙ 1L 4s | ↓ 2L 4s | 3L 4s ↘ |
┌╥┬╥┬┬┐ │║│║│││ │││││││ └┴┴┴┴┴┘
ssLsL
- 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.
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 240.0¢ |
| Major 1-mosstep | M1ms | L | 240.0¢ to 600.0¢ | |
| 2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0¢ to 480.0¢ |
| Perfect 2-mosstep | P2ms | L + s | 480.0¢ to 600.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | L + 2s | 600.0¢ to 720.0¢ |
| Augmented 3-mosstep | A3ms | 2L + s | 720.0¢ to 1200.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 600.0¢ to 960.0¢ |
| Major 4-mosstep | M4ms | 2L + 2s | 960.0¢ to 1200.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 2L + 3s | 1200.0¢ |
Modes
Degrees
| 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. |
Mode names
There are three sets of mode names: descriptive, modal (5 of the 7 heptatonic modes), and traditional Chinese.
| UDP | Cyclic order |
Step pattern |
Descriptive | Modal | Chinese |
|---|---|---|---|---|---|
| 4|0 | 1 | LsLss | Fifthless | Phrygian | Jue |
| 3|1 | 3 | LssLs | Minor | Aeolian | Yu |
| 2|2 | 5 | sLsLs | Thirdless Minor* | Dorian | Shang |
| 1|3 | 2 | sLssL | Thirdless Major* | Mixolydian | Zhi |
| 0|4 | 4 | ssLsL | Major | Ionian | Gong |
* Thirdless Minor/Major is also known as Suspended Minor/Major
Scales
Scale list
- Archy5 – 472edo tuning
- Edson5 – 29edo tuning
- Pythagorean5 – Pythagorean tuning
- Meantone5 – 31edo tuning
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 | Slendro (insofar as it resembles a MOS) would be in this region | |||||
| 9\22 | 490.909 | 709.091 | 5:4 | 1.250 | ||||||
| 16\39 | 492.308 | 707.692 | 9:7 | 1.286 | No-5s superpyth/dominant is around here | |||||
| 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 | Pythagorean pentatonic is around here | |||||
| 5\12 | 500.000 | 700.000 | 3:2 | 1.500 | Soft 2L 3s Familiar 12-equal pentatonic | |||||
| 18\43 | 502.326 | 697.674 | 11:7 | 1.571 | ||||||
| 13\31 | 503.226 | 696.774 | 8:5 | 1.600 | Optimal meantone pentatonic is around here | |||||
| 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 Five-note subset of pelog (insofar as it resembles a MOS) would be in this region | |||||
| 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").