Optimization: Difference between revisions

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 === Weight ===
-The weight determines the importance of each formal prime. For instance, the Tenney weight is represented by the transformation matrix
+The weight, represented by a diagonal transformation matrix, determines the importance of each formal prime. Since the tuning space and the interval space are [[Wikipedia:Dual (mathematics)|dual]] to each other, rating of importance in the tuning space is equivalent to rating of complexity in the interval space. The Tenney weight is the most common weight:
 <math>\displaystyle W = \operatorname {diag} (1/\log_2 (Q)) </math>
-which indicates that the prime harmonic ''q'' in Q = {{val| 2 3 5 … }} has the importance of 1/log<sub>2</sub>(''q''). Since the tuning space and the interval space are [[Wikipedia:Dual (mathematics)|dual]] to each other, such a rating of importance in the tuning space has the dual effect in the interval space: the prime harmonic ''q'' has the complexity log<sub>2</sub>(''q''). The more complex an interval is, the more error will be allowed for it.
+which indicates that the prime harmonic ''q'' in Q = {{val| 2 3 5 … }} has the importance of 1/log<sub>2</sub>(''q''). Its dual states that ''q'' has the complexity of log<sub>2</sub>(''q'').
 === Skew ===