Trumpets are cylindrical brass instruments. The tubing is 2/3 cylindrical, and 1/3 conical. The conical equivalent of the trumpet is the cornet, being 2/3 conical, and 1/3 cylindrical.
The only other version of the horn is the mellophone, a cylindrical marching horn used in American marching bands, and a section of these were used in the Stan Kenton Big Band for many years. Wagner invented the Wagner tuba, really a larger horn and not a tuba at all, and it is played by horn players. Many other classical composers have written for this instrument, including Strauss and Bruckner.
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