Domain basis: Difference between revisions
Cmloegcmluin (talk | contribs) note about non-JI |
Cmloegcmluin (talk | contribs) move section later |
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For some advanced mathematical information about non-standard just intonation (JI) interval subspaces, as well as a gateway to browse temperaments within popular interval subspaces of this sort, see [[Just intonation subgroup|this page]]. | For some advanced mathematical information about non-standard just intonation (JI) interval subspaces, as well as a gateway to browse temperaments within popular interval subspaces of this sort, see [[Just intonation subgroup|this page]]. | ||
= Interval subspaces as subspaces of other interval subspaces = | = Interval subspaces as subspaces of other interval subspaces = | ||
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Functions for finding interval rebases have been implemented in the [[RTT_library_in_Wolfram_Language]] as <code>getRforM</code> and <code>getRforC</code>. Although it also simply contains <code>changeB</code> which you can use directly on any temperament and it will do this step under the hood for you. | Functions for finding interval rebases have been implemented in the [[RTT_library_in_Wolfram_Language]] as <code>getRforM</code> and <code>getRforC</code>. Although it also simply contains <code>changeB</code> which you can use directly on any temperament and it will do this step under the hood for you. | ||
= Non-JI interval subspaces = | |||
The behavior of these are not yet well-described. For, for instance, is best to represent them as matrices? If a formal prime is <math>π/ɸ</math>, does the vinculum allow us to treat the two irrational numbers as separate basis elements? Perhaps, but as far as this author understands, this hasn't been pinned down yet. And so, for example, irrational numbers are not supported yet in the RTT library in Wolfram Language. | |||
= Terminology: interval basis vs. subgroup = | = Terminology: interval basis vs. subgroup = | ||