The sound produced by brass instruments when played at high dynamic levels is characterised by what is known as a "brassy" quality. This quality of sound, however, is not due to the material with which the instruments are made, but rather to their length and geometry, much to the surprise of brass instrument players. Instruments, such as the trombone and trumpet, which include long cylindrical ducts, are capable of sustaining nonlinear steepening as waves propagate in their interior, and shocks may eventually form. The manner in which this mechanism gives rise to the aforementioned brassy sound is explored for progressive, rather than standing waves. Further, skilled players know that it is possible to modify their embouchure in order to produce brassy sound even at moderate dynamic levels. We show that this is due to the shape of the signal produced at the mouthpiece exit, and in particular the maximum value of its time derivative. If shock waves form, schlieren visualisation can then be used to analyse the geometry of the radiated wavefronts. Finally, a finite volume full-wave numerical method is used to study standing waves in cylindrical pipes in the nonlinear regime. Musical examples will be given, and further work involving instrument mutes and prehispanic Mayan wind instruments will be discussed.