Chordal Embeddings Based on Topology of the Tonal Space

Anton Ayzenberg, Maxim Beketov, Aleksandra Burashnikova, German Magai, Anton Polevoi, Ivan Shanin, Konstantin Sorokin

Abstract: In the classical western musical tradition, the mutual simultaneous appearance of two tones in a melody is determined by harmony, i.e. the ratio of their frequencies. To perform NLP-based methods for MIDI file analysis, one needs to construct vector embeddings of chords, taking mutual harmonicity into account. Previous works utilising this idea were based on the notion of Euler’s Tonnetz. Being a beautiful topological model describing consonance relations in music, the classical Tonnetz has a certain disadvantage in that it forgets particular octaves. In this paper, we introduce the mathematical generalisation of Tonnetz taking octaves into account. Based on this model, we introduce several types of metrics on chords and use them to construct chordal embeddings. These embeddings are tested on two types of tasks: the chord estimation task, based on the Harmony Transformer model, and the music generation task, provided on the basis of TonicNet.