BOP tuning: Difference between revisions

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 This property is particularly important for infinite-limit generalized patent vals, where it can be shown that regardless of whether ratios are mapped "consistently" via the prime mapping, or "inconsistently" to the nearest EDO-step, the same BOP tuning is optimal for all rational numbers.
-= Applications Of The Above =
-The above is an important result because it tells us, as the prime limit goes to infinity, that the same BOP tuning minimizes the max <math>1/(nd)^s</math>-weighted error on all intervals regardless of whether the mappings used are entirely prime-based and consistent, entirely "direct" and inconsistent, an amalgamation of direct and indirect mappings, etc. No matter how you do it, the worst Tenney-weighted error can never be worse than that of the worst prime.
 As a simpler example, this guarantees that the BOP tuning for 2.3.5.9 16-EDO, with the inconsistent mapping of 57 steps on the 9/1, is the same as the 2.3.5 tuning for 16-EDO.