Harmonic limit: Difference between revisions
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While harmonic limit encompasses all ratios up to a given prime, '''proper harmonic limit''' classifies JI ratios based only based on the ''highest'' prime they contain in either the numerator or denominator. Equivalently, it is all of the intervals of a prime limit that are not found in a lower prime limit. It has been called '''harmonic class''' or '''HC'''. | While harmonic limit encompasses all ratios up to a given prime, '''proper harmonic limit''' classifies JI ratios based only based on the ''highest'' prime they contain in either the numerator or denominator. Equivalently, it is all of the intervals of a prime limit that are not found in a lower prime limit. It has been called '''harmonic class''' or '''HC'''. | ||
A ratio belongs to the proper ''p''-prime limit if and only if | A ratio belongs to the proper ''p''-prime limit if and only if ''p'' is the highest prime number found in its factorization. For example: | ||
* [[7/4]] is proper 7-limit because 7 is the highest prime in its factorization. | * [[7/4]] is proper 7-limit because 7 is the highest prime in its factorization. | ||
* [[5/4]] is proper 5-limit, not proper 7-limit, even though it's within the 7-limit. | * [[5/4]] is proper 5-limit, not proper 7-limit, even though it's within the 7-limit. | ||