[pianotech] Tuning the duplex sections

[John Delacour]

A new aquisition has roused my curiosity.  This is a Brinsmead 
concert grand 9 feet long from about 1870-75 (Pierce's numbers from 
around this time are apparently unreliable).

This piano has 88 keys, full all-over iron frame (cupola 
construction), 'duplex' scaling back and front and a sostenuto 
mechanism.  Steinway's patent for the duplex scale 
<http://tinyurl.com/67lb6m3> is from 1872, the cupola construction 
from 1872 and the sostenuto patent from 1874.

What interests me is not whether Brinsmead copied Steinway or vice 
versa (I've never heard of any litigation) but rather what Steinway 
claims for the duplex scaling, and that is that it brings the 
_longitudinal_ vibrations of the front and back sections into harmony 
with the _longitudinal_ vibrations of the speaking length and gets 
rid of the whistling.

He doesn't make any mention of the fact that the "whistling" of the 
longitudinal wave is most unlikely to be in harmony with the 
transverse vibrations of the speaking length in the first place, 
which seems odd, and Conklin at Baldwin's did some interesting 
experiments aimed at getting rid of this discordancy, and so I don't 
quite see the point of bringing the duplex whistles into harmony with 
the main whistle, which is already likely to be discordant with the 
transverse harmonics of the string, but let that be ...

I'd always supposed that the purpose of the duplex sections was to 
produce _transverse_ vibrations in harmony with the speaking length 
and to reinforce certain partials adding brilliance to the tone.  If 
this were the was, then it would be necessary to have the duplex 
sections not only the proper length but also at the proper tension, 
in other words tuned to the frequency of the partial in question. 
Now I think I'm right in saying that longitudinal vibrations are 
independent of the tension of the wire, in other words that a wire of 
length l at tension t will produce the same longitudinal frequency as 
the same wire at tension 2t or any t.

If this is the case, then according to Theodor Steinway's theory the 
precise tuning of the duplex sections ( though this would follow 
nturally if the tuning is done extremely carefully) will produce no 
benefit tonally.

I'd be interested to hear what people think, or even better know, about this.

JD