Bill Chapman wrote:

> I recently saw some reed pipes, probably Vox, that had graduated
> boots for resonators, as opposed to the tops of the pipe. ... The
> longest bass was about 3 feet and the shortest was about 8 inches.
> The tops are almost all the same size.  They were made by Wicks ...

These pipes are indeed Vox Humanas.  The actual resonator is the small
piece at the top, beginning with the outward tapered cone topped with
a short cylinder and a cap with several holes.  This is what we call
a fractional length resonator.  Fractional length resonators are tuned
to an upper harmonic, yet they must support the fundamental pitch, an
octave or two below their natural inclination.  It's like getting a
soprano to sing bass.

Since the reed is a switch, sending shaped pulses of air into the
resonator, we wonder why the boot has to be scaled.  The answer is
apparent if we look at the air on both sides of the reed.  When the
shallot closes, creating low pressure on the resonator side, and
pulling back on the air column, a higher pressure builds inside the
boot near the reed opening.

When the shallot opens, creating higher pressure at the base of the
resonator, pushing on the air column, inside the boot there is a
corresponding pressure drop.  This phenomenon, that one side of the
reed tongue exhibits high pressure, when the other exhibits low implies
that somewhere in the vicinity of the shallot opening, there is a node,
which is why reed resonators behave acoustically like stopped pipes.

The fractional length resonator will influence the reed tongue to jump
up to a higher harmonic.  The long boot sets up some complex physics to
keep the tongue happy at a lower pitch.

Those of you who have free-reed pipes, like Welte trumpets or Loesche
clarinets, may have noticed that sometimes the pipe just will not tune
to the correct note.  If it tunes with a good, strong tone about a half
to a quarter step flat, and then dies when brought up to pitch, the
problem is very likely a boot that is too short.  A good set of free-reed
pipes has a very accurately scaled set of boots.

John Nolte