The Baroque and early Classical flutes have six finger holes that are small enough to be covered by the unaided fingers, and also positioned so as to allow this. They have a partly conical bore, which is narrower than that of the Boehm flute. We compare these instruments in terms of their sound spectra and intonation, and we explain some of the features of these in terms of their acoustic impedance. Because flutes are open at the air jet, the minima in impedance are of greatest interest. The Classical and Baroque instruments have impedance minima whose depths decrease more rapidly with increasing frequency than those of the Boehm flute. This is attributed to the narrower bore and the consequently greater wall losses, and is one reason for the darker timbre of these instruments. In most fingerings, the effect of a series of open holes is to produce a ’cut off filter’, which reduces the depth of higher minima. This occurs at lower frequency for the Classical and Baroque flutes, because of the smaller and fewer tone holes. We also report the effects of cross fingerings, and the effects of the differing hole sizes required by the comfortable placing of tone holes. The frequency dependence of the end effects produced by cross fingering leads to inharmonicities in the impedance minima, which in part explains why notes produced with these fingerings have darker timbre than those produced with simple fingerings.