Database on tone rows and tropes -- Number of k-chords in an n-scale

Number of k-chords in an n-scale

It is possible to enumerate orbits of k-chords in an n-scale with respect to certain group actions. Choose the action of a suitable group from dihedral group D_n, cyclic group C_n, linear affine group Aff ₁(Z_n), identity group which contains only the identity id on Z_n, or an arbitrary group, which can be determined by a set of generators.

The result is a polynomial in x with integer coefficients. The coefficient of x^k is the number of orbits of k-chords, 0≤ k≤ n.

Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019