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... From page 214 of "The Physics of Musical Instruments"
2nd ed., the Bessel horn is defined by
x is the geometric distance measured from the reference point
x = 0,
If epsilon = 0 you have a cylindrical horn. If x = 1 you have a
From page 432, applied to a brass instrument the relationship
for a bessel horn can be written
a = b(x + x0)^(-gamma)
where a is the bore radius of the horn and x0 is the small end
of the horn.
b and x0 are chosen to give the correct radii at the small and
large ends of the horn and gamma defines the rate of flare.