[Dixielandjazz] Slide trombones

Edgerton, Paul A paul.edgerton at eds.com
Mon Mar 21 12:22:13 PST 2005

Time for another DJML science lesson: today's word is "parabola."

A parabola is a conic section. That is, one can take a cone standing on its
circular base -- a trombone will do nicely -- and slice it parallel to the
axis of the cone.  The resulting curve is called a parabola.  Anybody who
has seen the Gateway Arch in St. Louis or watched a perfectly thrown "Hail
Mary" pass has seen what I'm describing.  (Kids! If you try this experiment
at home, use a sharp band saw -- but ask permission first!)

The mathematically significant feature of a parabola is that it has a focal
point.  In the case of a trombonist, the focal point is typically seated at
the bar in a short skirt.

When a parabola is rotated through space about its axis, it forms a
paraboloid.  One common paraboloid is a satellite dish antenna. Another is
the reflective surface of an old-style automotive headlamp.  If a trombonist
is rotated about his axis, he gets dizzy.  The same effect is generated when
he sits at the bar next to the skirt.

The purpose of a horn is to couple an acoustic radiator with the focal
point, so it isn't correct to say a brass instrument's bore is parabolic.
Now that you have now been properly educated, you can avoid making
embarrassing mistakes like this in conversation with the skirts at the bar. 

All brass instruments have bores that are conical, and most contain
cylindrical sections to accommodate things like tuning slides.  The trumpet
and trombone, in particular, have a bore that is predominantly cylindrical
with the conical sections being mainly in the lead pipe and bell.

Wait a minute, I have just received new information that the primary
definition of the word "parabolic" is "Of or similar to a parable."

Ahem, please forget I ever mentioned the skirt at the bar.

-- Paul Edgerton

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