This study focuses on a particular attribute of trumpet tones, the brightness, and on the physical characteristics of the instrument thought to govern its magnitude. On the one hand, an objective study was carried out with input impedance measurements, and, on the other hand, a subjective study with hearing tests and a panel of subjects. To create a set of different trumpets a variable depth mouthpiece was developed whose depth can be easily and continuously adjusted from "deep" to "shallow." Using this mouthpiece and the same trumpet, several instruments were generated which may be played in three ways: (i) by a musician, (ii) by an artificial mouth, and (iii) using physical modeling simulations. The influence of the depth of the mouthpiece on the perception of the trumpet's tones was investigated, and the ability of a musician, the artificial mouth, or physical modeling simulations to demonstrate perceptively noticeable differences was assessed. Physical characteristics extracted from the impedance curves are finally proposed to explain the brightness of trumpet tones. As a result, the physical modeling simulations now seem to be mature enough to exhibit coherent and subtle perceptual differences between tones. This opens the door to virtual acoustics for instrument makers.