Pinedye: Difference between revisions
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'''Pinedye''' (also denoted 1s in [[groundfault]]'s [[aberrismic theory]]) is a quasi-[[diatonic]] [[scale pattern]] with [[step signature]] 5L 2M 1s. The name ''pinedye'' is a blend of ''[[pine]]'' (7L1s) and ''diatonic''. [[20edo]] is the first edo with 5L 2M 1s and hence the first [[edo]] with a quasi-diatonic [[ternary scale]]. | '''Pinedye''' (also denoted 1s in [[groundfault]]'s [[aberrismic theory]]) is a quasi-[[diatonic]] [[scale pattern]] with [[step signature]] 5L 2M 1s. The name ''pinedye'' is a blend of ''[[pine]]'' (7L1s) and ''diatonic''. [[20edo]] is the first edo with 5L 2M 1s and hence the first [[edo]] with a quasi-diatonic [[ternary scale]]. | ||
The step pattern of pinedye is | The step pattern of pinedye is LLmLLmLs (chiral, 1sR), LLmLLsLm (chiral, 1sL), or LLsLLmLm (achiral, 1sC). | ||
The standard untempered 2.3.5 interpretation for pinedye has L = [[10/9]], M = [[27/25]], s = [[81/80]]. Pental pinedye has generator sequence GS(4/3, 4/3, 5/4) or GS(5/4, 4/3, 4/3), or in step vector form GS(2L+M, 2L+M, 2L+s) or GS(2L+s, 2L+M, 2L+M). | The standard untempered 2.3.5 interpretation for pinedye has L = [[10/9]], M = [[27/25]], s = [[81/80]]. Pental pinedye has generator sequence GS(4/3, 4/3, 5/4) (for 1sR), GS(4/3, 5/4, 4/3) (for 1sL), or GS(5/4, 4/3, 4/3) (for 1sC), or in step vector form GS(2L+M, 2L+M, 2L+s) or GS(2L+s, 2L+M, 2L+M). | ||
[[Category:Rank-3 scales]] | [[Category:Rank-3 scales]] | ||
[[Category:Aberrismic theory]] | [[Category:Aberrismic theory]] | ||
Revision as of 03:41, 30 November 2024
Pinedye (also denoted 1s in groundfault's aberrismic theory) is a quasi-diatonic scale pattern with step signature 5L 2M 1s. The name pinedye is a blend of pine (7L1s) and diatonic. 20edo is the first edo with 5L 2M 1s and hence the first edo with a quasi-diatonic ternary scale.
The step pattern of pinedye is LLmLLmLs (chiral, 1sR), LLmLLsLm (chiral, 1sL), or LLsLLmLm (achiral, 1sC).
The standard untempered 2.3.5 interpretation for pinedye has L = 10/9, M = 27/25, s = 81/80. Pental pinedye has generator sequence GS(4/3, 4/3, 5/4) (for 1sR), GS(4/3, 5/4, 4/3) (for 1sL), or GS(5/4, 4/3, 4/3) (for 1sC), or in step vector form GS(2L+M, 2L+M, 2L+s) or GS(2L+s, 2L+M, 2L+M).