Direct approximation: Difference between revisions
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Undid the previous edit manually as I realized that "patent interval" and "direct mapping" were entirely the same thing after all |
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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, and as such, it is also called a '''direct mapping'''. It is calculated by [[rounding]] the product of the [[Wikipedia: binary logarithm|binary logarithm]] (''log2'') of the interval ratio (''r'') and the EDO number (''nEdo''). | 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'''. It is 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 00:05, 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. It is 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.