2L 3s (3/2-equivalent)
| ↖ 1L 2s⟨3/2⟩ | ↑ 2L 2s⟨3/2⟩ | 3L 2s⟨3/2⟩ ↗ |
| ← 1L 3s⟨3/2⟩ | 2L 3s (3/2-equivalent) | 3L 3s⟨3/2⟩ → |
| ↙ 1L 4s⟨3/2⟩ | ↓ 2L 4s⟨3/2⟩ | 3L 4s⟨3/2⟩ ↘ |
┌╥┬╥┬┬┐ │║│║│││ │││││││ └┴┴┴┴┴┘
ssLsL
2L 3s⟨3/2⟩, also called saturnian, is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 2 large steps and 3 small steps, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 280.8 ¢ to 351 ¢, or from 351 ¢ to 421.2 ¢. Due to its minor third generator, this scale has a wealth of diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time.
Intervals
|
MOS degrees is deprecated. Please use Template:MOS tunings instead. |
| Scale degree | 7edf (Basic, L:s = 2:1) | Approx. JI Ratios | |
|---|---|---|---|
| Steps | Cents | ||
| Perfect 0-mosdegree (unison) | 0 | 0 | 1/1 (exact) |
| Minor 1-mosdegree | 1 | 100.3 | |
| Major 1-mosdegree | 2 | 200.6 | |
| Diminished 2-mosdegree | 2 | 200.6 | |
| Perfect 2-mosdegree | 3 | 300.8 | |
| Perfect 3-mosdegree | 4 | 401.1 | |
| Augmented 3-mosdegree | 5 | 501.4 | |
| Minor 4-mosdegree | 5 | 501.4 | |
| Major 4-mosdegree | 6 | 601.7 | |
| Perfect 5-mosdegree (equave) | 7 | 702 | 3/2 (exact) |
Theory
2L 3s⟨3/2⟩ can be interpreted as the nonoctave regular temperament named pythium by User:CompactStar, tempering out 81/80 in the 3/2.4.5 subgroup. This is the simplest 3/2-equivalent temperament not containing octaves. Because the 3/2-reduced 5th harmonic of 40/27 is conflated with the just perfect fifth, the CTE generator of this temperament is exactly the 32/27 Pythagorean minor third. Although the most accurate tunings use near-32/27 generators, pythium can be tuned with minor thirds as high as that of 11edf's (319 cents).
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 4|0 | 1 | LsLss |
| 3|1 | 3 | LssLs |
| 2|2 | 5 | sLsLs |
| 1|3 | 2 | sLssL |
| 0|4 | 4 | ssLsL |