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The Virtual Flute is a web service that provides many thousands of machine-predicted alternative fingerings. Alternative fingerings can offer variations in intonation and timbre, and can be easier to play in different musical contexts. Many play multiphonics. An advanced fingering guide is invaluable when exotic effects and demanding passages are required of the player. The Virtual Flute uses an expert system that predicts musical properties from acoustic impedance spectra. Impedance spectra for the 39,744 acoustic configurations of the flute are generated by a physical model of the instrument, some parameters of which are machine-learned. We report the construction and use of The Virtual Flute (http://www.phys.unsw.edu.au/music/flute/virtual/).