The mouthpiece assembly includes an internal thread which engages an external thread of a leadpipe of a brass musical instrument. The internal thread can be placed on the stem of the mouthpiece or on an extension to the leadpipe into which the stem frictionally engages. In either case, the radial gap between the mouthpiece and the leadpipe is substantially eliminated. Additionally, the diameter of the air passageway can be configured to be substantially free of discontinuities. The various pieces of the mouthpiece assembly can be interchanged to vary some characteristics of the mouthpiece while keeping other characteristics constant.