Constrained tuning: Difference between revisions

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 ==== Method of Lagrange multipliers ====
-It can also be solved analytically using the {{w|Lagrange multipliers|method of Lagrange multipliers}}. The solution is given by:
+It can also be solved analytically using the method of {{w|Lagrange multipliers}}. The solution is given by:
 <math>\displaystyle
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 where
-* <math>x</math> is any random generator map giving pure octaves
+* ''x'' 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
+* ''B'' is a matrix whose rows are a basis for the subspace of generator maps with octave coordinate set to 0
-* <math>h</math> is a free variable.
+* ''h'' 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 ''M'' is our mapping matrix, ''W'' our weighting matrix, and ''j'' our JIP, we can solve for the best possible ''g'' in closed form:
 $$