  This paper presents a web application for visualizing the tonality of a piece
of music -- the organization of its chords and scales -- at a high level of
abstraction and with coordinated playback. The application applies the discrete
Fourier transform to the pitch-class domain of a user-specified segmentation of
a MIDI file and visualizes the Fourier coefficients' trajectories. Since the
coefficients indicate different musical properties, such as harmonic function,
triadicity, and diatonicity, the application isolates aspects of a piece's
tonality and shows their development in time. The aim of the application is to
bridge a gap between mathematical music theory, musicology, and the general
public by making the discrete Fourier transform as applied to the pitch-class
domain accessible without requiring advanced mathematical knowledge or
programming skills up front.
