Historical cup‐mouthpiece instruments, especially those from the Renaissance and Baroque periods, have the reputation of being harder to play in tune than modern brass instruments. This paper considers what is meant by ‘‘playing in tune’’ from both acoustical and musical standpoints, and surveys acoustical features of some early cup‐mouthpiece instruments which may have contributed to their reputation for uncertain intonation. Three different classes of instruments are distinguished. The first includes instruments of fixed acoustical length, such as the natural trumpet; the second includes instruments in which the acoustical length may be lengthened by moving a slide or depressing valves, as on the trombone and the valved trumpet; the third includes cup‐mouthpiece instruments in which the acoustical length can be decreased by opening fingerholes, such as the cornetto and the serpent. Different considerations affect intonation in each class of instrument. Experimentally derived input impedance curves, frequency spectra of played notes, and threshold pressure measurements using artificial lips are presented and discussed in the context of intonation sensitivity.