2L 3s
| Pattern | LsLss | |
| Period | 2/1 | |
| Generator range | 2\5 (480.0¢) to 1\2 (600.0¢) | |
| Parent MOS | 2L 1s | |
| Daughter MOSes | 5L 2s, 2L 5s | |
| Sister MOS | 3L 2s | |
| TAMNAMS name | pentic | |
| Equal tunings | ||
| 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¢) | |
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
Scale Tree
Generator ranges:
- Chroma-positive generator: 480 cents (2\5) to 600 cents (1\2)
- Chroma-negative generator: 600 cents (1\2) to 720 cents (3\5)
| Generator | Cents | s | L-s | |L-2s| | Scale steps | Trichord | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2\5 | 480 | 240 | 0 | 240 | 1 1 1 1 1 | 1 1 | ||||||
| 11\27 | 488.89 | 222.22 | 44.44 | 177.78 | 6 5 5 6 5 | 6 5 | Slendro (insofar as it resembles a MOS)
would be in this region | |||||
| 9\22 | 490.91 | 218.18 | 54.545 | 163.64 | 5 4 4 5 4 | 5 4 | ||||||
| 16\39 | 492.31 | 215.38 | 61.54 | 153.85 | 9 7 7 9 7 | 9 7 | No-5's superpyth/dominant is around here | |||||
| 7\17 | 494.12 | 211.76 | 70.59 | 141.18 | 4 3 3 4 3 | 4 3 | ||||||
| 19\46 | 495.65 | 208.7 | 78.26 | 130.435 | 11 8 8 11 8 | 11 8 | ||||||
| 12\29 | 496.55 | 206.9 | 82.76 | 124.14 | 7 5 5 7 5 | 7 5 | ||||||
| 17\41 | 497.56 | 204.88 | 87.8 | 117.07 | 10 7 7 10 7 | 10 7 | Pythagorean pentatonic is around here | |||||
| 5\12 | 500 | 200 | 100 | 100 | 3 2 2 3 2 | 3 2 | Familiar 12-equal pentatonic
(also optimum rank range: L/s=3/2) | |||||
| 502.305 | 195.39 | 111.53 | 83.86 | pi 2 pi 2 2 | pi 2 | |||||||
| 18\43 | 502.33 | 195.35 | 111.63 | 83.72 | 11 7 7 11 7 | 11 7 | ||||||
| 13\31 | 503.23 | 193.55 | 116.13 | 77.42 | 8 5 5 8 5 | 8 5 | Optimal meantone pentatonic
is around here | |||||
| 1200/(4-phi) | 192.43 | 118.93 | 73.50 | phi 1 1 phi 1 | phi 1 | Golden meantone | ||||||
| 21\50 | 504 | 192 | 120 | 72 | 13 8 8 13 8 | 13 8 | ||||||
| 8\19 | 505.26 | 189.47 | 126.32 | 63.16 | 5 3 3 5 3 | 5 3 | ||||||
| 19\45 | 506.67 | 186.67 | 133.33 | 53.33 | 12 7 7 12 7 | 12 7 | ||||||
| 507.18 | 185.64 | 135.9 | 49.74 | √3 1 √3 1 1 | √3 1 | |||||||
| 11\26 | 507.69 | 184.615 | 138.46 | 46.15 | 7 4 4 7 4 | 7 4 | ||||||
| 14\33 | 509.09 | 181.82 | 145.455 | 36.36 | 9 5 5 9 5 | 9 5 | ||||||
| 3\7 | 514.29 | 171.43 | 171.43 | 0 | 2 1 1 2 1 | 2 1 | (Boundary of propriety: smaller
generators than this are strictly proper) | |||||
| 13\30 | 520 | 160 | 200 | 40 | 9 4 4 9 4 | 9 4 | ||||||
| 10\23 | 521.74 | 156.52 | 208.7 | 52.17 | 7 3 3 7 3 | 7 3 | ||||||
| 17\39 | 523.08 | 153.84 | 215.385 | 61.54 | 12 5 5 12 5 | 12 5 | ||||||
| 7\16 | 525 | 150 | 225 | 75 | 5 2 2 5 2 | 5 2 | 5-note subset of pelog (insofar as it
resembles a MOS) would be in this region | |||||
| 18\41 | 526.83 | 146.34 | 234.15 | 87.8 | 13 5 5 13 5 | 13 5 | ||||||
| 600(25+√5)/31 | 145.7 | 235.75 | 90.05 | phi+1 1 1 phi+1 1 | phi+1 1 | |||||||
| 11\25 | 528 | 144 | 240 | 96 | 8 3 3 8 3 | 8 3 | ||||||
| 528.88 | 142.24 | 244.405 | 102.17 | e 1 e 1 1 | e 1 | L/s = e | ||||||
| 15\34 | 529.41 | 141.18 | 247.06 | 105.88 | 11 4 4 11 4 | 11 4 | ||||||
| 4\9 | 533.33 | 133.33 | 266.67 | 133.33 | 3 1 1 3 1 | 3 1 | L/s = 3 | |||||
| 535.36 | 129.26 | 276.835 | 147.57 | pi 1 pi 1 1 | pi 1 | L/s = pi | ||||||
| 13\29 | 537.93 | 124.14 | 289.655 | 165.52 | 10 3 3 10 3 | 10 3 | ||||||
| 9\20 | 540 | 120 | 240 | 180 | 7 2 2 7 2 | 7 2 | ||||||
| 14\31 | 541.935 | 116.13 | 309.68 | 193.55 | 11 3 3 11 3 | 11 3 | ||||||
| 5\11 | 545.45 | 109.09 | 327.27 | 218.18 | 4 1 1 4 1 | 4 1 | L/s = 4 | |||||
| 11\24 | 550 | 100 | 350 | 250 | 9 2 2 9 2 | 9 2 | ||||||
| 6\13 | 553.85 | 92.31 | 369.23 | 276.92 | 5 1 1 5 1 | 5 1 | ||||||
| 7\15 | 560 | 80 | 480 | 400 | 6 1 1 6 1 | 6 1 | ||||||
| 1\2 | 600 | 0 | 600 | 600 | 1 0 0 1 0 | 1 0 | a degenerated pentatonic scale with only 2 different steps | |||||
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").