  The classical Transfer-Matrix Method (TMM) is often used to calculate the
input impedance of woodwind instruments. However, the TMM ignores the possible
influence of the radiated sound from toneholes on other open holes. In this
paper a method is proposed to account for external tonehole interactions. We
describe the Transfer-Matrix Method with external Interaction (TMMI) and then
compare results using this approach with the Finite Element Method (FEM) and
TMM, as well as with experimental data. It is found that the external tonehole
interactions increase the amount of radiated energy, reduce slightly the lower
resonance frequencies, and modify significantly the response near and above the
tonehole lattice cutoff frequency. In an appendix, a simple perturbation of the
TMM to account for external interactions is investigated, though it is found to
be inadequate at low frequencies and for holes spaced far apart.
