Rear Duplex

[Delwin D Fandrich]

----- Original Message -----
From: Richard Brekne <richardb@c2i.net>
To: PTG <pianotech@ptg.org>
Sent: Saturday, September 25, 1999 11:38 AM
Subject: Rear Duplex


> If it doesnt serve this purpose, why
> is it called by many a "duplex" ??
>
------------------------------------------------------

Most of what I have to say on this subject has already been printed in the
Journal or on this list, but...

This is another area fraught with terminology problems.  Which was why early
on I coined the phrase "back scale" to cover that portion of the string
between the rear bridge pin (or whatever is being used as a bridge
termination device) and the rear counterbearing bar or hitchpin (or whatever
else is being used as the rear termination device.)

The word "duplex" means (1) 'twofold or double,' or (2) 'relating to or
being a single assembly...having two identical units or parts that are
capable of operating simultaneously or independently.'  It is rare that the
speaking length and the back scale of any unison form a true duplex.  Some
pianos are set up such that the back scale length is more-or-less the same
as the speaking length through a few notes in the high treble, but the
increasing length of the speaking portion of the string soon makes this
impractical.  So, in terms of one end of a single unison, the term seems
largely useless.

Another term commonly used is "aliquot."  This is a much more accurate term,
but it, too, has problems.  Aliquot means, "of, relating to, or denoting an
exact divisor or factor of a quantity, especially of an integer."  In
theory, the length of an aliquot string segment should be an "exact divisor
or factor of a quantity."  Again, it is rare that this is actually the case,
although some manufacturers do make an attempt to set up the back scales of
the two treble sections this way.  Steinway provides a continuous casting
for each section which is aligned to the bridge during construction.  In
theory this casting equalizes the back scale string lengths of each unison
and makes their lengths equal to some partial of the speaking length of each
unison.  The variables of manufacturing insure that this goal is rarely, if
ever, actually achieved.  The most precise systems provide some mechanism --
usually by allowing individual back bearing bars to be moved -- for
adjusting the back scale length for each individual tri-chord string set.
The Fazioli comes to mind.  As do a few older US built grands.  Possibly the
current Mason & Hamlin?  I'm afraid I haven't looked recently.  (There is a
device, and a process, being advertised in the Journal that can be used to
accurately adjust these back bearing bars.)  Bearing bars such as those used
on the older Baldwins do not qualify since the individual bars used were
pinned to the plates and were not movable.

So, in practice the word aliquot has come to be used to denote any back
scale string segment that gives even some remote appearance of being
"tuned."  I have encountered pianos that use continuous cast bearing bars
similar in appearance to those used by Steinway that were positioned such
that the back scale string lengths had no discernable mathematical
relationship to the speaking lengths.  While they were advertised as 'tuned
aliquot' scales, in my opinion they were not.  I leave it to others to
decide just where these systems fit into the scheme of things.

And then there is the question of just how these back scale string segments
should be tuned.  Some say that they should be tuned exactly to some partial
of the speaking length, others maintain that they should be tuned slightly
sharp of some partial.

I have no real position in all of this -- I don't believe that tuning the
back scale is of any particular acoustical value, but it probably doesn't
hurt much either -- but the problem of terminology and definitions can cause
much confusion.

So, for whatever it is worth...In my work, I have come to terms with the
following:
    1)  The Back Scale.  That portion of the string segment between the rear
bridge termination device the 'back scale' regardless of its length.
    2)  The Front Scale.  The 'front scale' is that segment of the wire
between the V-bar and the front bearing bar.)

This back scale can be designed in any number of different ways.
    3)  The Aliquot System.  If the back scale is designed such that its
length is just approximately the same, or slightly shorter than, some exact
divisor of the speaking length (i.e., having a frequency close to, or
slightly higher than, the resonant frequency than some exact harmonic) it is
an 'aliquot system.'
    4)  The Tuned Aliquot System.  If the back scale is designed such that
its length is, or can be adjusted to, some exact divisor of the speaking
length, I refer to it as a 'tuned aliquot system.'
    5)  A Duplex System.  A 'duplex' system is one in which both the front
scale and the back scale are aliquot systems.
    6)  A Full Duplex System.  A 'full-duplex' system is one in which both
the front and back scales are aliquot systems and each are 'tuned' to
identical harmonics of the fundamental.

Now, I have no desire to impose these definitions on anyone else.  The above
simply explains how I have come to use them.  They may or may not be
'correct.'  If your definition differs, I'd like to hear what you have come
up with, including your reasons for calling these things whatever it is that
you call them.

Have fun, folks.

Del