Constrained tuning: Difference between revisions
→Simple Fast Closed-Form Algorithm: formatting |
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where | where | ||
* <math>x</math> is any random | * <math>x</math> is any random generator map giving pure octaves | ||
* <math>B</math> is a matrix whose rows are a basis for the subspace of generator maps with octave coordinate set to 0 | * <math>B</math> is a matrix whose rows are a basis for the subspace of generator maps with octave coordinate set to 0 | ||
* <math>h</math> | * <math>h</math> is a free variable. | ||
Given that, and assuming <math>M</math> is our mapping matrix, <math>W</math> our weighting matrix, and <math>j</math> our JIP, we can solve for the best possible <math>g</math> in closed form: | Given that, and assuming <math>M</math> is our mapping matrix, <math>W</math> our weighting matrix, and <math>j</math> our JIP, we can solve for the best possible <math>g</math> in closed form: | ||