Implementation of melodic morphing based on generative theory of tonal music

This paper proposes a new morphing method to generate a melody, given two melodies represented by time-span trees obtained from the generative theory of tonal music (GTTM). In this paper, we define a feature structure based on a time-span tree and the distance between two structures. Next, we construct a lattice of subsumption relations among these structures and define three algebraic operations: reduction, meet, and join. First, we conduct these operations in the pure algebraic domain and a new melody is as an interpolation in the lattice; thereafter, we render the obtained tree into a music melody, assigning a priority order among candidate branches. We confirmed that our morphing algorithm generated new variations with satisfactory quality.