Diaschismic family: Difference between revisions
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The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 11 -4 -2 }}, and flipping that yields {{multival| 2 -4 -11 }} for the wedgie for 5-limit '''diaschismic''', or '''srutal''', temperament. This tells us the period is half an octave, the [[Wikipedia: Greatest common divisor|GCD]] of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities. | The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. Its monzo is {{monzo| 11 -4 -2 }}, and flipping that yields {{multival| 2 -4 -11 }} for the wedgie for 5-limit '''diaschismic''', or '''srutal''', temperament. This tells us the period is half an octave, the [[Wikipedia: Greatest common divisor|GCD]] of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]] or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities. | ||
= Srutal aka diaschismic = | = Srutal (12&34, aka diaschismic) = | ||
[[Comma list]]: 2048/2025 | [[Comma list]]: 2048/2025 | ||
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[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* valid range: [600.000 to 720.000] (2 to | * valid range: ~3/2 = [600.000 to 720.000] (1\2 to 6\10) | ||
* nice range: [701.955, 706.843] | * nice range: ~3/2 = [701.955, 706.843] | ||
* strict range: [701.955, 706.843] | * strict range: ~3/2 = [701.955, 706.843] | ||
{{Val list|legend=1| 12, 34, 46, 80, 206c, 286bc }} | {{Val list|legend=1| 10, 12, 22, 34, 46, 80, 206c, 286bc }} | ||
[[Badness]]: 0. | [[Badness]]: 0.019915 | ||
== Seven limit extensions == | == Seven limit extensions == | ||