Direct approximation: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
m another term used on this wiki |
||
| Line 1: | Line 1: | ||
A '''patent interval''' 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 [[Wikipedia: binary logarithm| binary logarithm]] (''log2'') of the interval ratio (''r'') and the edo number (''nEdo''). | 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 [[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 17:19, 18 January 2021
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 in a given edo; for the p-prime limit this set consists of prime intervals.