2L 3s (3/2-equivalent): Difference between revisions
→Intervals: Added back missing notation, since default is no notation |
CompactStar (talk | contribs) Rework as well as the change of pythium -> meanquad |
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro|Other Names=saturnian}} | {{MOS intro|Other Names=saturnian}} | ||
The name saturnian was coined by [[User:CompactStar|CompactStar]], referring to the sister MOS of [[3L 2s (3/2-equivalent)|uranian]]. | |||
This scale contains 2 diminished triads represented by stacks of the minor third generator.[[Basic]] saturnian is in [[7edf]], a very close approximation of [[12edo]], which allows for playing diatonic music and saturnian music at the same time. 2L 3s⟨3/2⟩ is the parent of the 3/2-repeating [[macrodiatonic and microdiatonic scales|microdiatonic scale]], [[5L 2s (3/2-equivalent)|5L 2s⟨3/2⟩]], and the sister of [[3L 2s (3/2-equivalent)|3L 2s⟨3/2⟩]] (uranian) which is generated by a subminor third rather than a minor third. | |||
== Notation == | == Notation == | ||
The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals. The notation used in this article | The main way of notating the saturnian scale is using a 3/2-repeating notation consisting of 5 naturals. The notation used in this article is the [[diamond MOS notation]]. | ||
=== Intervals === | === Intervals === | ||
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== Theory == | == Theory == | ||
2L 3s⟨3/2⟩ can be interpreted as the [[ | === Temperament interpretations== | ||
From a [[half-prime subgroup]] point of view, 2L 3s⟨3/2⟩ can be interpreted as the [[Sirius B]] temperament, where the minor third generator is represented by ~[[25/21]] and 2 of them make ~[[7/5]]. It may also be interpreted as [[meanquad]] temperament using a period of [[3/2]] rather than [[4/1]], where the minor third generator is represented by [[32/27]]~[[6/5]] (in the CTE tuning, it is exactly 32/27). Both temperaments have very similar generators. | |||
== Modes == | == Modes == | ||
The mode names are based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the [[3L 2s (3/2-equivalent)|uranian scale]]. | The mode names are based on the 6 largest satellites of Saturn, excluding Titan since the "Titanian" name has been used for the [[3L 2s (3/2-equivalent)|uranian scale]]. | ||
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== Scale tree == | == Scale tree == | ||
{{Scale tree|Comments= | {{Scale tree|Comments=11/7: [[CTE tuning]] for Sirius B temperament (293.825¢); 8/5: Pythagorean minor third (294.135¢); }} | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:5-tone scales]] | [[Category:5-tone scales]] | ||
Revision as of 04:40, 8 February 2024
| ↖ 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 ¢.
The name saturnian was coined by CompactStar, referring to the sister MOS of uranian.
This scale contains 2 diminished triads represented by stacks of the minor third generator.Basic saturnian is in 7edf, a very close approximation of 12edo, which allows for playing diatonic 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. The notation used in this article is the diamond MOS notation.
Intervals
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MOS degrees is deprecated. Please use Template:MOS tunings instead. |
| Scale degree | On J | 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) | J | 0 | 0 | 0 | 0 | 0 | 0 | 1/1 (exact) |
| Minor 1-mosdegree | K | 1 | 100.3 | 1 | 78 | 2 | 117 | |
| Major 1-mosdegree | K& | 2 | 200.6 | 3 | 234 | 3 | 175.5 | |
| Diminished 2-mosdegree | L@ | 2 | 200.6 | 2 | 156 | 4 | 234 | |
| Perfect 2-mosdegree | L | 3 | 300.8 | 4 | 312 | 5 | 292.5 | |
| Perfect 3-mosdegree | M | 4 | 401.1 | 5 | 390 | 7 | 409.5 | |
| Augmented 3-mosdegree | M& | 5 | 501.4 | 7 | 546 | 8 | 468 | |
| Minor 4-mosdegree | N@ | 5 | 501.4 | 6 | 468 | 9 | 526.5 | |
| Major 4-mosdegree | N | 6 | 601.7 | 8 | 624 | 10 | 585 | |
| Perfect 5-mosdegree (equave) | J | 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
= Temperament interpretations
From a half-prime subgroup point of view, 2L 3s⟨3/2⟩ can be interpreted as the Sirius B temperament, where the minor third generator is represented by ~25/21 and 2 of them make ~7/5. It may also be interpreted as meanquad temperament using a period of 3/2 rather than 4/1, where the minor third generator is represented by 32/27~6/5 (in the CTE tuning, it is exactly 32/27). Both temperaments have very similar generators.
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 |