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Created page with "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 val is the be..." |
corrected, formula and some examples added |
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A '''patent interval''' is the "best" mapping of an interval in a | 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:Interval]] | ||
[[Category:Method]] | [[Category:Method]] | ||
Revision as of 10:56, 20 November 2020
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 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.