Direct approximation: Difference between revisions
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A '''patent interval''' of a (usually but not necessarily just) interval is the number of | 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''). | ||
round(log2(r)*nEdo) | round(log2(r)*nEdo) | ||
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A [[patent val]] is the best mapping of a representative set of intervals in a given | 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 11:46, 18 January 2021
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 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.