Reverse crown was agraffe bridges

[Duplexdan@AOL.COM]

Del Fandrich's Statement

That all pianos have both front and rear duplexes. The question is how long 
they are, what the string deflection angle is, ( at the front) and whether or 
not they are tuned.....

is, in my opinion, (take it for what it's worth)  the most provocatively 
productive statement from an academically incisive positive point of view. It 
imposes a categorical imperative on the description of duplex scales.

This imperative, I believe has to be modified to some extent, in this way.

It is a matter of fact that no pianos have their speaking length termination 
nodes at the agraffe and the bridge pins.  All strings in all pianos do 
absolutely extend beyond the bridge to the hitch pin and beyond the agraffe 
to the tuning pin. These extensions are the main issue. How to deal with 
them. How long to make them, and whether or not to superimpose a secondary 
bridge between their nodes that create a secondary scale of specific relation 
to the speaking length. 

Whereas Del is absolutely correct that all pianos do have segments that 
extend past the nodes of the speaking length, the appelation of duplex scale 
to these segments I believe must be modified.

The duplex scale name I believe must be restricted to those pianos whose 
scale designers have devised a system whereby the extended portions of the 
string  are capable of producing a tone  which is in particular harmonic 
relationship with the speaking length and who have provided a means whereby 
to achieve this objective.

I feel it is incorrect to label all non seaking lengths of strings duplex 
scales because they do not "do the duplex". i.e. they do not reflect a 
partial of the speaking length. The Duplex Scale is, I believe a term that 
must be categorically restricted to those piano scale designs that have non 
speaking portions of the string whose fundamental corresponds to a partial of 
the speaking length.

But all my theory, and all Del's theory, and S's patents and HH"s physics and 
all our colleagues insights will never convince any RPT worth his weight in 
tuning by themselves. You've got to try it , and hear it yourself. And why 
keep nipping at the hands that feed us? Our great forbears gave us the duplex 
scale, before you knock it , try it. 99 to 1 you'll like it. Especially the 
part when you get paid for tuning it.

Duplexdan