Chord complexity: Difference between revisions
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== Dirichlet Complexity == | == Dirichlet Complexity == | ||
One simple function, which meets both of our simple criteria, is simply to assign the n'th harmonic a weighting which is some power of n, called the '''rolloff''', and then sum together the weights to get a strength for the overall chord. Thus, we have | One simple function, which meets both of our simple criteria, is simply to assign the <math>n</math>'th harmonic a weighting which is some power of <math>1/n</math>, called the '''rolloff''', and then sum together the weights to get a strength for the overall chord. Thus, we have | ||
<math>\displaystyle f_s(x_1, x_2, \ldots, x_N) = \frac{1}{x_1^s} + \frac{1}{x_2^s} + ... + \frac{1}{x_N^s}</math> | <math>\displaystyle f_s(x_1, x_2, \ldots, x_N) = \frac{1}{x_1^s} + \frac{1}{x_2^s} + ... + \frac{1}{x_N^s}</math> | ||