2L 3s (3/2-equivalent): Difference between revisions
CompactStar (talk | contribs) Created page with "{{Infobox MOS}} {{MOS intro|Other Names=saturnian}} Due to its minor third generator, this scale has a wealth of diminished triads. Basic saturnian is in 7edf, an app..." |
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== Intervals == | == Intervals == | ||
{{MOS degrees}} | {{MOS degrees|Step Ratio=2/1; 3/1; 3/2}} | ||
== Genchain == | |||
{|class="wikitable" | |||
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|-4 | |||
|-3 | |||
|-2 | |||
|-1 | |||
|0 | |||
|1 | |||
|2 | |||
|3 | |||
|4 | |||
|- | |||
|d2ms | |||
|m4ms | |||
|m1ms | |||
|P3ms | |||
|P0ms | |||
|P2ms | |||
|M4ms | |||
|M1ms | |||
|A3ms | |||
|} | |||
== Theory == | == Theory == | ||
2L 3s⟨3/2⟩ can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|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). | 2L 3s⟨3/2⟩ can be interpreted as the [[nonoctave]] [[regular temperament]] named [[subgroup temperaments#pythium|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). | ||
Revision as of 04:02, 5 July 2023
| ↖ 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) | 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) | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-mosdegree | 1 | 100.3 | 1 | 78 | 2 | 117 | |
| Major 1-mosdegree | 2 | 200.6 | 3 | 234 | 3 | 175.5 | |
| Diminished 2-mosdegree | 2 | 200.6 | 2 | 156 | 4 | 234 | |
| Perfect 2-mosdegree | 3 | 300.8 | 4 | 312 | 5 | 292.5 | |
| Perfect 3-mosdegree | 4 | 401.1 | 5 | 390 | 7 | 409.5 | |
| Augmented 3-mosdegree | 5 | 501.4 | 7 | 546 | 8 | 468 | |
| Minor 4-mosdegree | 5 | 501.4 | 6 | 468 | 9 | 526.5 | |
| Major 4-mosdegree | 6 | 601.7 | 8 | 624 | 10 | 585 | |
| Perfect 5-mosdegree (equave) | 7 | 702 | 9 | 702 | 12 | 702 | 3/2 (exact) |
Genchain
| 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. 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 |