Diasem: Difference between revisions

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'''Diasem''' (also known as '''Tas''', from Archytas) 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. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.

'''Diasem''' (also known as '''Tas''', from Archytas, or 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. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[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]].

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-'''Diasem''' (also known as '''Tas''', from Archytas) 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. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.
+'''Diasem''' (also known as '''Tas''', from Archytas, or 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. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[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]].