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 contains 2 diminished triads. Basic saturnian is in 7edf, an approximation of 12edo, which allows for playing regular music and saturnian music at the same time. 2L 3s⟨3/2⟩ is the parent of the 3/2-repeating microdiatonic scale, 5L 2s⟨3/2⟩, and the sister of 3L 2s⟨3/2⟩ (uranian) which is generated by a subminor third rather than a minor third.
Notation
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals (e.g. A-E for the 2|2 mode).
Intervals
|
MOS degrees is deprecated. Please use Template:MOS tunings instead. |
| Scale degree | On A | 7edf (Basic, L:s = 2:1) | 9edf (Hard, L:s = 3:1) | 12edf (Soft, L:s = 3:2) | Approx. JI Ratios | |||
|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | |||
| Perfect 0-mosdegree (unison) | A | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-mosdegree | B | 1 | 100.3 | 1 | 78 | 2 | 117 | |
| Major 1-mosdegree | B# | 2 | 200.6 | 3 | 234 | 3 | 175.5 | |
| Diminished 2-mosdegree | Cb | 2 | 200.6 | 2 | 156 | 4 | 234 | |
| Perfect 2-mosdegree | C | 3 | 300.8 | 4 | 312 | 5 | 292.5 | |
| Perfect 3-mosdegree | D | 4 | 401.1 | 5 | 390 | 7 | 409.5 | |
| Augmented 3-mosdegree | D# | 5 | 501.4 | 7 | 546 | 8 | 468 | |
| Minor 4-mosdegree | Eb | 5 | 501.4 | 6 | 468 | 9 | 526.5 | |
| Major 4-mosdegree | E | 6 | 601.7 | 8 | 624 | 10 | 585 | |
| Perfect 5-mosdegree (equave) | A | 7 | 702 | 9 | 702 | 12 | 702 | 3/2 (exact) |
Genchain
| -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
| d2ms | m4ms | m1ms | P3ms | P0ms | P2ms | M4ms | M1ms | A3ms |
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. The best extension of pythium to the 3/2.4.5.7 subgroup adds 64/63 to the comma list, making the CTE generator slightly flatter than 32/27, about 286 cents. Although the most accurate pythium generators are near 32/27, pythium can be tuned with minor thirds as sharp as that of 11edf's (319 cents).
Modes
The mode names are based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the uranian scale.
| 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 |