Generator embedding optimization: Difference between revisions

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Let's just dive into an example.

The example given in the diagrams back in article 3 [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#How_to_choose_the_true_optimum|here]] and article 6 [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_computation#Tie_breaking:_power_limit_method|here]] were a bit silly. The easiest way to break the tie in this case would be to remove the offending target-interval from the set, since with constant damage, it will not aid in preferring one tuning to another. More natural examples of tied tunings — that cannot be resolved so easily — require 3D tuning damage space. So that's what we'll be looking at here.

Suppose we're doing a minimax-U tuning of blackwood temperament, and our target-interval set is <math>\{ \frac21, \frac31, \frac51, \frac65 \}</math>. This is a rank-2 temperament, so we're in 3D tuning damage space. The relevant region of its tuning damage space is visualized below. The yellow hyper-V is the damage graph for <math>\frac21</math>, the blue hyper-V is for <math>\frac31</math>, the green hyper-V is for <math>\frac51</math>, and the red hyper-V is for <math>\frac65</math>.

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 Let's just dive into an example.
+The example given in the diagrams back in article 3 [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_fundamentals#How_to_choose_the_true_optimum|here]] and article 6 [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_tuning_computation#Tie_breaking:_power_limit_method|here]] were a bit silly. The easiest way to break the tie in this case would be to remove the offending target-interval from the set, since with constant damage, it will not aid in preferring one tuning to another. More natural examples of tied tunings — that cannot be resolved so easily — require 3D tuning damage space. So that's what we'll be looking at here.
 Suppose we're doing a minimax-U tuning of blackwood temperament, and our target-interval set is <math>\{ \frac21, \frac31, \frac51, \frac65 \}</math>. This is a rank-2 temperament, so we're in 3D tuning damage space. The relevant region of its tuning damage space is visualized below. The yellow hyper-V is the damage graph for <math>\frac21</math>, the blue hyper-V is for <math>\frac31</math>, the green hyper-V is for <math>\frac51</math>, and the red hyper-V is for <math>\frac65</math>.