Just intonation subgroup: Difference between revisions

Cmloegcmluin (talk | contribs)
added a necessary disclaimer now that the normal lists page has changed so that the canonical form is the default normal interval list (which it still should be in the most typical context of comma bases)
A more relevant intro
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{{Todo|add introduction|comment=introduction needed that helps musicians/composers understand that this is relevant to them|inline=1}}
A '''just intonation subgroup''' is a [[Wikipedia: Free abelian group|group]] generated by a finite set of positive rational numbers via arbitrary multiplications and divisions. Using subgroups implies a way to organize [[just intonation]] intervals such that they form a lattice. Therefore it is closely related to [[regular temperament theory]].  
A '''just intonation subgroup''' is a [[Wikipedia: Free abelian group|group]] generated by a finite set of positive rational numbers via arbitrary multiplications and divisions. Any such group will be contained in a [[Harmonic limit|''p''-limit]] group for some minimal choice of prime ''p'', which is the prime limit of the subgroup.


There are three categories of subgroups:
There are three categories of subgroups: