Direct approximation: Difference between revisions
Noted that the term "direct mapping" can refer to patent intervals themselves via analogy with the relationship between "nearest edomapping" and "patent vals". |
Trying to make sure the text reads well, though I don't know if I'm succeeding at this or not. |
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A '''patent interval''' in a given [[EDO]] is the number of EDO steps needed to reach the best approximation of a given interval – usually, but not necessarily just – in that EDO. The method for calculating patent intervals | A '''patent interval''' in a given [[EDO]] is the number of EDO steps needed to reach the best approximation of a given interval – usually, but not necessarily just – in that EDO. The method for calculating patent intervals is referred to as '''direct mapping''', and it involves [[rounding]] the product of the [[Wikipedia: binary logarithm|binary logarithm]] (''log2'') of the interval ratio (''r'') and the EDO number (''nEdo''). | ||
round(log2(r)*nEdo) | round(log2(r)*nEdo) | ||
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A [[patent val]] is the best mapping of a representative set of intervals (taken to be [[generator]]s for a [[JI subgroup]]) in a given EDO; for the ''p''-[[prime limit]] this set consists of [[prime interval]]s. | A [[patent val]] is the best mapping of a representative set of intervals (taken to be [[generator]]s for a [[JI subgroup]]) in a given EDO; for the ''p''-[[prime limit]] this set consists of [[prime interval]]s. Just as the patent val itself can be referred to as the "nearest edomapping", so a patent interval can be referred to as a "direct mapping". | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Method]] | [[Category:Method]] | ||
[[Category:Val]] | [[Category:Val]] | ||