Harmonic Maps – Interactive Visualization Of 3-Note Chord Spaces Based on Spectral Structures

We present Harmonic Maps, a visualization of three-note chord spaces and an interactive application that allows users to explore in real-time the connection between the visualization and its mapped sounds. While typical harmonic analysis is based only on notes or on an audio signal, our analysis takes a hybrid approach by quantifying different types of interactions between the spectra of notes. These quantifications, which we call Harmonic Descriptors, are derived from acoustic or perceptual models. Three such descriptors are defined and mapped: concordance, third order concordance and roughness. Harmonic analysis based on spectral structures opens new possibilities beyond traditional note-only or signal-only approaches. They can be applied to a continuum of frequencies, independent of the tuning system, as well as historical and stylistic constraints. Harmonic Maps based on spectral structures can be especially relevant to study the relationship between timbre and harmony. Our interactive exploration of harmonic spaces can have applications for analytical, compositional and educational purposes