Chord complexity: Difference between revisions

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=== Generalized Tenney Height ===
=== Generalized Tenney Height ===
In general, we will derive the following expressions for the '''Generalized Benedetti Height''' or '''Generalized Tenney Height''' of any chord, in such a way that chords can be reasonably compared of different sizes:
In general, we will derive the following expressions for the '''Generalized Benedetti Height''' or '''Generalized Tenney Height''' of any chord, in such a way that chords of different sizes can be reasonably compared:


<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>