Direct approximation: Difference between revisions
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A [[patent val]] is the best mapping of a representative set of intervals in a given EDO; | A [[patent val]] is the best mapping of a representative set of intervals in a given EDO; for the ''p''-[[prime limit]] this set consists of [[prime interval]]s. | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Method]] | [[Category:Method]] | ||
[[Category:Val]] | [[Category:Val]] | ||
Revision as of 11:35, 18 January 2021
A patent interval of a (usually but not necessarily just) interval is the number of EDO steps of the best approximation of an interval in a respective EDO. It's calculated by rounding the product of 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 in a given EDO; for the p-prime limit this set consists of prime intervals.