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. | ||
== | == Five-limit srutal (aka diaschismic) == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Badness: 0.017063 | Badness: 0.017063 | ||
=== Srutaloo === | ==== Srutaloo ==== | ||
Srutaloo adds 576/575, 736/729 or 208/207, rhymes with [[Skidoo]]. | Srutaloo adds 576/575, 736/729 or 208/207, rhymes with [[Skidoo]]. | ||
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Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255 | Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255 | ||
Mapping: [{{val| 2 0 11 -42 -28 -18 5 -55 -10}}, {{val| 0 1 -2 15 11 8 1 20 6}}] | Mapping: [{{val| 2 0 11 -42 -28 -18 5 -55 -10 }}, {{val| 0 1 -2 15 11 8 1 20 6 }}] | ||
POTE generator: ~3/2 = 704.899 | |||
Optimal GPV sequence: {{Val list| 34dh, 46, 80, 206cd }} | Optimal GPV sequence: {{Val list| 34dh, 46, 80, 206cd }} | ||
Badness: 0.013555 | |||
===== 29-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19.23.29 | |||
Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255 | |||
Mapping: [{{val| 2 0 11 -42 -28 -18 5 -55 -10 -76 }}, {{val| 0 1 -2 15 11 8 1 20 6 27 }}] | |||
POTE generator: ~3/2 = 704.906 | |||
Optimal GPV sequence: {{Val list| 34dhj, 46, 80, 206cd }} | |||
Badness: 0.013203 | |||
== Pajara == | == Pajara == | ||