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Verse:Hmøøh/Rewhd Sgutsis: Difference between revisions
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Sgutsitn's best known written work is her treatise on equal temperaments, which describes: | Sgutsitn's best known written work is her treatise on equal temperaments, which describes: | ||
*Various regular temperaments and the equal temperaments supporting them. The equal temperaments supporting a regular temperament also characterize that temperament. | *Various regular temperaments and the equal temperaments supporting them. The equal temperaments supporting a regular temperament also characterize that temperament. | ||
**She describes a temperament as a span of unison vectors/commas (Note: The commas generate the kernel characterizing a regular temperament relative to the JI space. There are multiple valid generating sets that generate the same kernel, thus multiple comma-sets that characterizes a temperament.) | **She describes a temperament as a span of unison vectors/commas (Note: The commas generate the kernel characterizing a regular temperament relative to the JI space. There are multiple valid generating sets that generate the same kernel, thus multiple comma-sets that characterizes a temperament.) | ||
*Scale-wise... images of constant-structure scales; in addition, MOSes like those found in various world musics. | *Scale-wise... images of constant-structure scales; in addition, MOSes like those found in various world musics. | ||
*Equal temperaments with "good" (highly composite) divisions of the fifth. | *Equal temperaments with "good" (highly composite) divisions of the fifth. | ||
*The appendix gives proofs that the algorithms she uses work; however she didn't have the modern algebraic language to describe what in effect she was doing, making the treatment mathematically less clean than it could have been. Also in the appendix: Links between the Riemann zeta function and "good" equal temperaments. | |||
Other stuff: | Other stuff: | ||