Helmholtz and Steinway

John Delacour JD@Pianomaker.co.uk
Mon, 19 Nov 2001 21:30:03 +0000


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At 8:05 PM -0800 11/18/01, Delwin D Fandrich wrote:

>This isn't apples and oranges, more like prunes and
>pomegranates. Or prunes and potatoes. Fiber optic cables, and the light
>traveling through them, do bear some resemblance to telegraph wires, and the
>electrical current traveling through them, do bear some resemblance to each
>other but neither is remotely similar to a piano string winding its way
>through a couple of offset bridge pins and across the top of a bridge.

Since I'm no greengrocer I'll have to take your word for it, Del, 
until someone who knows can tell me why a telegraph wire does sing. 
And if there are any geologists about, if I produce a certain 
earpiercing screech with a 3" chalk on a blackboard, what will be the 
relative frequency of the screech when I break an inch off the end of 
it?





Here's a rough monochord I set up to take an objective look at a few 
of the things we've been heating the air with.  Two standard upright 
agraffes driven into a length of 40mm Delignit serve as the end 
points of the speaking length.  The wire is 12.5 gauge.  A 5 mm drill 
bit supports the back length between the hitchpin.

I first rolled the drill to tune the back length by sound only, 
plucking this and the speaking length alternately to get the note.  I 
then checked the tuning of the back length by plucking only the 
speaking length and immediately damping it, aiming for maximum 
resonance of the partial in the back length.  Finally I measured the 
back length, which come to 87 mm. or 1/8 of the speaking length 
sounding 3 octaves above the fundamental.  So far as practical 
measurements can detect, there is no detectable inharmonicity in the 
main length.  The arrangement is not meant to be typical of anything 
and is purely for experimental purposes.

Ron O. mentioned in passing Wayne Stuart's use of silicone rubber in 
his agraffes.  Since I had a sheet of this lying around, I plugged 
these agraffes with a good firm strip of it and it made not a scrap 
of difference to anything.  With or without silicone rubber (which is 
not significant -- I just thought I'd try it), either section of the 
wire, when struck or plucked, sets up oscillations in the other 
section.  The back length gives a frequency of ca. 2088 c/s with 
considerable falseness.  The harmonic induced in the speaking length 
sings with a much slower false beat and continues for longer if the 
back length is not muted.  The volume of the induced wave in the 
speaking length falls markedly as the back length is stopped.

The front section, of length 55 mm, rises directly to the wrestpin 
giving roughly a G#.

THE LENGTHWISE WAVE.
  By pure chance, with this configuration, the pitch of the lengthwise 
wave is also about the same G#.  This wave is set up by stroking the 
wire between finger and thumb using either a rag wetted with lighter 
fuel or powdered resin.  This I take to be Theodore Steinway's 
"whistle".  This whistle is fairly constant and pure at this tension 
(ca. 100 lbf).  Altering the tension makes no difference to the pitch 
of the whistle except that at extremely low tensions, instead of a 
single pitch, it trills about a semitone, like one of those very 
skilled whistling workmen that I like to be a long way off.  It is as 
though there are two distinct pitches available.  The trilling effect 
only happens at very low tension but I have also obtained the two at 
high tension, alternating but not trilling.

If I place a simple bridge under the wire to raise the pitch of the 
speaking length a two or three tones, the frequency of the 
compression wave remains the same.  This would bear out what Stephen 
seems to be saying.  It would seem to mean that when Conklin talks of 
getting the correct relationship between the transverse frequency, he 
means that a meeting point must be found for a given "system", as 
Stephen refers to it, between the required frequency of the partials 
for the given note and the lengthwise frequency of the system that 
will most suitably be used for those partials.  My first impression 
is that this might be easier said than done.  There is no problem 
setting up a routine to seek this goal but the goal might not be 
attainable in view of all the other design factors of the scale. 
Have you, Del, or you Ron O, ever allowed longitudinal wave 
considerations to affect your scale calculations?  I think we should 
be told.

Before any such thing could be attempted, one would need accurate 
data to calculate the frequency of a given "system" in the abstact, 
taking into account, presumably, more than simply the mass of the 
system.  Conklin may give some information in his patent as to how 
the lengthwise frequency is calculated, but he gives no hint of it in 
his lectures.

THE STEINWAY EFFECT
Now I've only just set up this rig, so I've only had a little time to 
play with it and not yet even worked out where to start, but there's 
nothing like a practical experiment for getting through the trees to 
the wood and the main points quickly become obvious.

At the moment I'm doing everything by ear and it will be necessary to 
use electronic recording devices to get the details, but it seems 
that the sense of Steinway's patent becomes clearer to me using my 
set-up.  There is no doubt that there is an optimum position for the 
back length support at which point the discordant clash of certain 
frequencies between 3000 and 5000, close to the lengthwise wave 
frequency, becomes still and more harmonious.  This point does seem 
to be that which gives in the back length the tuned partial of the 
speaking length.  Further than that I won't say because I haven't had 
time enough and haven't any electronic help.  What is clear is that 
certain beats in the very high frequencies, that can jar badly on the 
highly sharpened ear of the experimenter (though probably completely 
unheard by the casual observer) can be brought to heel by proper 
positioning of the back length support (ie. the 5mm drill) and these 
frequencies then amalgamate with the other partials of the note, even 
though perhaps somewhat discordantly.

JD


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