Leadpipe or mouthpipe system for trombone or other brass instrument

A leadpipe comprising:

• a sidewall defining an enclosed channel, the sidewall having an upstream end and a downstream end;
• wherein the sidewall is comprised of a plurality of sections including a first tapered section upstream of at least one subsequent section;
• wherein each of the sections extends longitudinally between the upstream end of the sidewall and the downstream end of the sidewall;
• wherein the first tapered section is disposed upstream of the at least one subsequent sections;
• wherein the first tapered section and at least one subsequent section of the sidewall each define a generally frustoconical cavity having an upstream end with an upstream inner diameter Df and a downstream end with a downstream inner diameter Ds;
• wherein the downstream inner diameter of each of the sections is larger than the upstream inner diameter;
• and
• wherein each of the sections has a length L and a taper T, wherein the taper is defined as T=(Ds−Df)/L, wherein the taper of the first tapered section is larger than the taper of each of the subsequent sections, and wherein the taper of each of the subsequent sections is less than the taper of the section immediately upstream.