Diasem: Difference between revisions

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'''Diasem''' (also known as 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.

Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]]. This interpretation or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].

Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].

"Diasem" is a name given by [[groundfault]] (though others have discussed the scale before her). The name is a portmanteau of "diatonic" and "semiquartal" (or "[[Semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.

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 '''Diasem''' (also known as 2s in [[groundfault]]'s [[aberrismic theory]]) is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. [[21edo]] is the smallest edo to support a non-degenerate diasem.
-Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]]. This interpretation or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].
+Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]]. This interpretation, or more generally the series of [[generator sequence]] scales generated by GS(7/6, 8/7) or GS(8/7, 7/6), has been named '''Tas''' (from Archytas) by [[Scott Dakota]].
 "Diasem" is a name given by [[groundfault]] (though others have discussed the scale before her). The name is a portmanteau of "diatonic" and "semiquartal" (or "[[Semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.