A brass instrument has three major parts: an input segment, a cylindrical or conical central segment, and a bell. (The latter two are often treated together.) It is conceptually useful to isolate the input segment from the rest of the air column and study the acoustical behavior of that complete segment rather than its components. Features in time- and frequency-domain plots can be correlated very easily with each other and with the physical structure. Combining the input segment's time-domain behavior with that for the rest of the air column yields some novel impulse responses for use with any model of the lip reed [R. D. Ayers, J. Acoust. Soc. Am. 100, 1190--1198 (1996)]. In the frequency domain, effective lengths for the input segment and the rest of the air column can be combined to give a useful indicator for the degree of harmonic alignment among the input impedance peaks [R. D. Ayers, J. Acoust. Soc. Am. 98, 81--87 (1995)]. Specific examples in both domains will be discussed.