Database on tone rows and tropes -- How to input a distance structure

How to input a distance structure

Let f: {1,…,12}→ Z₁₂ be a tone row, then we compute the distances of f(1) and f(2), f(2) and f(3), …, and f(12) and f(1).

Let v_i be the distance of f(i) and f(i+1), 1≤ i≤ 11, and f(12) the distance of f(12) and f(1). They all belong to the set {1,…,6}. The distance structure is the D₁₂-orbit of the vector (v₁,…,v₁₂) where the dihedral group acts on the set of indices in the natural way.

The distance structure is input as a comma-separated list of 12 distances describing the complete distance structure of a tone row.

List of all distance structures which belong to at least two D₁₂ × D₁₂-orbits of tone rows.

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