2L 3s (3/2-equivalent): Difference between revisions
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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. 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). | 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. 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 == | == Modes == | ||
The mode names are based on the | 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]]. | ||
{{MOS modes|Mode Names= | {{MOS modes|Mode Names=Rhean; Iapetian; Dionian; Tethyian; Enceladean}} | ||
== Scale tree == | == Scale tree == | ||
{{Scale tree|Comments=5/4:Optimal 3/2.4.5.7 pythium around here;8/5:Near-just 32/27, optimal 3/2.4.5 pythium around here;2/1:Augmented 8-mosdegree is nearly an octave;1/0:Degenerate scale with only 2 tones}} | {{Scale tree|Comments=5/4:Optimal 3/2.4.5.7 pythium around here;8/5:Near-just 32/27, optimal 3/2.4.5 pythium around here;2/1:Augmented 8-mosdegree is nearly an octave;1/0:Degenerate scale with only 2 tones}} | ||