The degree to which tubing length effects the repetition frequency (or
rate) of any particular player mechanism is based on two primary fac-
tors.  One is the size of the bleed, the size of the pouch, and the
size of the pouch well.  The second factor is, for lack of a better
term, natural equalization.

Imagine, if you will, any fluid in motion from point A to point B.  If
the motion of the fluid is interrupted at the source (point A), the
degree to which that interruption will have an effect on the flow of
the fluid at point B is determined by the amount of time the fluid has
to equalize the interruption.  At a certain point (X), the interruption
will not be noticed at point B because the differences in pressure (or
flow) have a natural tendency to equalize.  This is where the bleed
size and the size of the pouch and pouch well come into play.

However, first let me digress to make a point.  All fluids, including
air, have no natural boundaries.  On the other hand, solids have very
strict boundaries.  Imagine a straight line of billiard balls that are
all spaced one inch apart.  When you strike the first ball in the line,
it will transfer the energy to the second ball and so forth and so on,
until the energy is reduced to zero from friction.  With moving air,
there are no such boundaries.  So, the pressure differences begin to
equalize immediately.  The degree to which they equalize depends on the
amount of time (or length of the tubing) that exists before the
"change" reaches its destination.

Many years ago, Craig Brougher invented a signal amplifier that can
be installed in-line on a long signal tube that is having difficulty
supplying a strong "on-off" signal to a pouch.  In essence, it's a type
of primary valve found in a double-valve player mechanism.  So, for 
those who are experiencing repetition problems because of long signal
tubes, the signal amplifier is a solution.  They can be purchased at
Player Piano Co.

The real question that remains unanswered is, "How long is too long?"
No doubt there is some formula in physics that would help solve the
question for any particular set of circumstances.  There are a number
of factors that come into play when figuring out how long the tubing
can be.  To name a few, they are: the flexibility and air-tightness of
the pouch and the air-tightness and size of the pouch well.  Then there
is the valve clearance and weight of the valve and valve stem.  Another
consideration is the exact size of the perforation on the music roll.
We all know that hole size varies from manufacturer to manufacturer and
that rolls with larger perforations will play more faithfully than
rolls with smaller perforations, all other things being equal.

I've done a significant number of tests on various valves with respect
to the maximum length of tubing that can be used to get a normal player
valve to operate faithfully.  Without a doubt, the tubing length must
be shorter as the desired repetition rate is increased.  There's also
no doubt that modern Aeolian players, with the mass of tubing that goes
around the action before reaching the valves in the center section,
have a problem with the repetition rate, especially at lower volume
(i.e. vacuum) levels.  My explanation to my customers is, "It's the
nature of the beast."  They can either buy better quality rolls (with
larger perforations) or turn the volume up a bit higher.

In closing, while this posting doesn't truly answer the question that
was initially posed, I hope it sheds enough light on the subject to
help the reader understand that hose length definitely affects the
repetition rate of all player piano valves.  In summary, the longer the
hose, the worse the repetition rate.

Musically,
John A. Tuttle
Player-Care.com
Brick, NJ