Direct approximation: Difference between revisions
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m an interval can't be "mostly" just; it either is just or isn't. Perhaps you mean "usually"? |
m more direct language |
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A '''patent interval''' of a (usually just) interval is the number of EDO steps of the | A '''patent interval''' of a (usually 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 [[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 10:34, 18 January 2021
A patent interval of a (usually 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 a representative set of intervals in a given EDO; in fact this set consists of prime intervals.