The taper and size of the leadpipe and tail section and bell flare do
greatly affect the sound, centering and other general characteristics of the
horn sound. Unless there has been a new breakthrough in mathematics, these
characteristics cannot be completely described using mathematics. I once ha
While my answer will not have the panache of a Cabbage answer, another point of
view can help.
The horn, like all brass instruments can only produce the harmonic series with
the help of the bell shape and any lead pipe taper. Otherwise it would play
only odd harmonics, like a garden hose. That is,
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