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Verse:Hmøøh/Rewhd Sgutsis: Difference between revisions
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Sgutsitn's best known written work is her treatise, which describes: | Sgutsitn's best known written work is her treatise, which describes: | ||
*Links between the Riemann zeta function and consonance. | *Links between the Riemann zeta function and consonance. | ||
*Various regular temperaments and the equal temperaments supporting them. (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.) | *Various regular temperaments and the equal temperaments supporting them. The equal temperaments supporting a regular temperament also characterize that temperament. | ||
**(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.) | |||
**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... I don't know, Images of constant-structure scales; in addition, MOSes like those found in various world musics. | *Scale-wise... I don't know, Images of constant-structure scales; in addition, MOSes like those found in various world musics. | ||
* | Other stuff: | ||
*Should stay close to equal temperaments whenever possible. That means no wedge products. | |||
*What gets you from a temperament to a "good" period/generator size? | |||
==Compositions== | ==Compositions== | ||