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Scientific discovery can arise by many means. Results can be obtained from meticulous methodological rigor and carefully plannedthrough experiments, but oftentimes insights are also gained through spontaneous associations of previously unrelated facts or exploratory work. In particular for the latter mode of discovery, a stimulating environment is quintessential in order to allow creativity to flow [4,9]. Collaborative inter-and transdisciplinary research for which knowledge and expertise from different fields is brought into interaction, is especially likely to provide such environments. Interdisciplinary work can, however, be impeded by specialized expert knowledge that is difficult to communicate to researchers with different backgrounds. In such situations, appropriately designed tools may help to build bridges between different research traditions and provide interfaces to otherwise restricted knowledge.Here, we report an instance of scientific discovery made possible through interactive exploration using an online interface for music visualization. We document how the discovery of phantom curves,

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.