Just intonation subgroup: Difference between revisions

TallKite (talk | contribs)
added the 3 categories of subgroups, and a bit of explanation
Inthar (talk | contribs)
definition should be intro
Line 6: Line 6:
}}
}}
{{Todo|add introduction|comment=introduction needed that helps musicians/composers understand that this is relevant to them|inline=1}}
{{Todo|add introduction|comment=introduction needed that helps musicians/composers understand that this is relevant to them|inline=1}}
== Definition ==
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.
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.