Musical instruments are complex sound sources that exhibit directivity patterns that not only vary depending on the frequency, but can also change as a function of the played tone. It is yet unclear whether the directivity variation as a function of the played tone leads to a perceptible difference compared to an auralization that uses an averaged directivity pattern. This paper examines the directivity of 38 musical instruments from a publicly available database and then selects three representative instruments among those with similar radiation characteristics (oboe, violin, and trumpet). To evaluate the listeners' ability to perceive a difference between auralizations of virtual environments using tone-dependent and averaged directivities, a listening test was conducted using the directivity patterns of the three selected instruments in both anechoic and reverberant conditions. The results show that, in anechoic conditions, listeners can reliably detect differences between the tone-dependent and averaged directivities for the oboe but not for the violin or the trumpet. Nevertheless, in reverberant conditions, listeners can distinguish tone-dependent directivity from averaged directivity for all instruments under study.