Verse:Hmøøh/Rewhd Sgutsis: Difference between revisions
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**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. | ||
**The great thing about equal temperaments might really be that they provide a way of categorizing intervals | |||
*Equal temperaments with "good" (highly composite) divisions of the fifth. | *Equal temperaments with "good" (highly composite) divisions of the fifth. | ||
*The appendix gives the mathematical details behind the theory. E.g. proofs that the algorithms she uses work; links between the Riemann zeta function and "good" equal temperaments. 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. | *The appendix gives the mathematical details behind the theory. E.g. proofs that the algorithms she uses work; links between the Riemann zeta function and "good" equal temperaments. 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. | ||