Chord complexity: Difference between revisions
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<math>\displaystyle B_s(x_1, x_2, \ldots, x_N) = \frac{(x_1 \cdot x_2 \cdot \ldots \cdot x_N)^{1/N}}{N^{1/s}}</math> | <math>\displaystyle B_s(x_1, x_2, \ldots, x_N) = \frac{(x_1 \cdot x_2 \cdot \ldots \cdot x_N)^{1/N}}{N^{1/s}}</math> | ||
is the "Benedetti" version. The numerator is the geometric mean, and the denominator normalizes by the size of the chord. The logarithmic "Tenney" version is as follows: | |||
<math>\displaystyle T_s(x_1, x_2, \ldots, x_N) = \frac{1}{N} \log(x_1 \cdot x_2 \cdot \ldots \cdot x_N) - \frac{1}{s}\log(N)</math> | <math>\displaystyle T_s(x_1, x_2, \ldots, x_N) = \frac{1}{N} \log(x_1 \cdot x_2 \cdot \ldots \cdot x_N) - \frac{1}{s}\log(N)</math> | ||