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 == | |||
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|-3 | |||
|-2 | |||
|-1 | |||
|0 | |||
|1 | |||
|2 | |||
|3 | |||
|4 | |||
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|d2ms | |||
|m4ms | |||
|m1ms | |||
|P3ms | |||
|P0ms | |||
|P2ms | |||
|M4ms | |||
|M1ms | |||
|A3ms | |||
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== 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). | ||