Direct approximation: Difference between revisions

@@ Line 1: / Line 1: @@
-A '''patent interval''' is the "best" mapping of an interval in a given EDO, it's calculated by rounding the EDO's "best" mapping of that interval.
+A '''patent interval''' of a (mostly just) interval is the number of EDO steps of the "best" mapping of an interval in a respective 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 val]] is the best mapping a representative set of intervals in a given EDO.
+ round(log2(r)*nEdo)
+; Some Examples
+{| class="wikitable center-all"
+! \
+! 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 a representative set of intervals in a given EDO; in fact this set consists of [[prime interval]]s.
 [[Category:Interval]]
 [[Category:Method]]