Direct approximation: Difference between revisions
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Hopefully made the relationship between a patent interval and a direct mapping more clear |
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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 in that EDO, and as such, it is also called a '''direct mapping'''. | 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, and as such, it is also called a '''direct mapping'''. However, the term "direct mapping" can also refer to the mathematical procedure used to calculate patent intervals. Patent intervals are calculated by [[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) | ||
Revision as of 00:02, 19 January 2021
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, and as such, it is also called a direct mapping. However, the term "direct mapping" can also refer to the mathematical procedure used to calculate patent intervals. Patent intervals are calculated by rounding the product of the binary logarithm (log2) of the interval ratio (r) and the EDO number (nEdo).
round(log2(r)*nEdo)
- Some Examples
| \ | 12edo | 17edo | 19edo | 26edo |
|---|---|---|---|---|
| 3/2 | 7 | 10 | 11 | 15 |
| 5/4 | 4 | 5 | 6 | 8 |
| 6/5 | 3 | 4 | 5 | 7 |
| 7/4 | 10 | 14 | 15 | 21 |
A patent val is the best mapping of a representative set of intervals (taken to be generators for a JI subgroup) in a given EDO; for the p-prime limit this set consists of prime intervals.