User:Zeta Function/Half-cubic limit: Difference between revisions

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== Generalization ==
== Generalization ==
In general, the (p, q, a)-half-cubic limit is the set of octave-reduced intervals in the p-prime limit and a-odd limit whose numerators and denominators do not contain more than q prime factors (including multiplicity). Thus, the previously defined limit would correspond to a (p, 2, {{math|∞}})-half cubic limit. This generalization is designed to give more flexibility during composing than the first framework. A good example of such a limit might be the (13, 2, 65)-half cubic limit, which is suited to 13-limit composing.  
In general, the (p, q, a)-half-cubic limit is the set of octave-reduced intervals in the p-prime limit and a-odd limit whose numerators and denominators do not contain more than q prime factors (including multiplicity). Thus, the previously defined limit would correspond to a (p, 2, )-half cubic limit. This generalization is designed to give more flexibility during composing than the first framework. A good example of such a limit might be the (13, 2, 65)-half cubic limit, which is suited to 13-limit composing.  
[[Category:Limit]]
[[Category:Limit]]