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Fantastic, Bob!  Thank you.  I had been thinking about sympathetic 
resonance of the reed and air column - that it's not one or the other 
independently, but a resultant of how they work together (duh).  I 
need to dig out my old Systems Analysis notes and see if I can draw a 
schematic :)

This reverts back to a question I remember coming up a while back 
asking why reeds are designed the way they are.  The answer really 
is "because that is what works".  Some derivations are emperical - 
not necessarily scientific.

If reeds were designed differently, so would facings ;)

--- In MouthpieceWork@yahoogroups.com, "Bob Phillips" 
<rwphillipsidaho@...> wrote:
>
> The reed and the air column have separate vibration 
characteristics.  The
> air column "throbs" at its resonance frequencies (fundamental and
> harmonics).  The reed has a "flapping"  frequency that is much 
higher than
> the horn's tone.
> 
> The air pressure on the back of the reed is driven by the pressure 
waves
> running up and down the horn's air column.  This oscillating 
pressure brings
> the reed in synchronism with the horn (or else, it squeaks --the 
reed gets
> away from the horn).
> 
> The coupling between the reed and the air column is actually a 
compromise
> --the resulting pitch is someplace between the reed's natural 
vibration
> frequency and that of the horn.  The major input to the horn comes 
from the
> air pulses modulated by the reed that is influenced (greatly) by the
> pressure from the horn.
> 
> BUT, the overall pitch --the vibration frequency "agreed to" 
between the
> reed and the vibrating air column is affected by the reed.
> 
> Now, an old, reed is waterlogged (heavier) and its fibers are 
broken down
> (softer), so its natural frequency of vibration is lower than a 
new, dry,
> stiff reed.  The result is that the soft reed combines with the air 
column
> to play flat.
> 
> This coupling is also the reason that a stiff reed makes it easier 
to drive
> the horn into its altissimo range.  The reed can work fast enough 
to keep up
> with the high frequencies the horn needs.
> 
> Bob Phillips
>