Instruments in the flute family, unlike most wind instruments, are played with the input of the instrument open to the atmosphere. Consequently, they operate at minima in the spectrum of acoustic input impedance. Detailed examination of these minima requires measurements with large dynamic range, which is why the flute has not been hitherto investigated in detail. We report the application of a technique with high precision and large dynamic range to measurements of the impedance spectra of flutes. We compare the acoustical impedance spectra of two examples of the modern orchestral flute and an example of the classical flute. For each instrument, we measured several dozen of the most commonly used different acoustic configurations or fingerings. The results are used to explain features of the spectra of the sound produced, to explain performance features and difficulties of the instruments, and to explain the differences between the performances of the classical and modern instruments. Some hundreds of spectra and sound files are given in JSV+ to allow further examination.