Direct approximation
A patent interval or direct mapping of a (usually but not necessarily just) interval in a given edo is the number of edo steps of the best approximation of an interval in that edo. It's 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.