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The acoustic impedance Z(f) of the flute has a range of around 70 dB. We report the use of a novel impedance spectrometer to measure the acoustic impedance of the flute with a resolution of +/- 1 1 Hz, a dynamic range of over 80 dB and which makes the measurement in 1 second. We report Z(f) for the standard fingerings over the range C4 to C7, and for selected non-standard fingerings as well. These results explain some of the idiosyncracies of the instrument well known to flutists, and in some cases suggest ways in which these may be overcome.