Formulae for String Calculations

[John Delacour]

At 10:10 am -0600 3/10/06, Cy Shuster wrote:

>David Sanderson told us that the bare length is critical to 
>inharmonicity. Mismatched bare lengths on wound bichords is a real 
>tuning problem.

I suppose you are talking about what we call the "copper line".  I 
don't know how they do things in America but in England we work from 
a rubbing made by the technician-customer -- see 
<http://pianomaker.co.uk/rubbing.html>.  If the rubbing is too badly 
done, we ask the customer to send another one.  With a satisfactory 
rubbing it is possible to achieve a copper line with no more than a 
millimetre variation, and that is what we do all the time.  We also 
aim for a perfectly even copper line at the top bridge by taking into 
account the amount by which each string will stretch when it is up to 
tension, so the print-out of the scale shows also the stretch in mm. 
and the copper line is drawn on the rubbing accordingly.

What tuning problems an uneven copper line introduces I have no idea 
but it looks awful and is a sign of shoddy workmanship.  The only 
reason I set up the string-making factory 20 years ago was that the 
standard of work of the long-established string-makers was so abysmal 
and most of them would have considered a job excellent if they broke 
off the copper within 1/4" of the mark, which itself was also made to 
pretty wide tolerances.  Speed was the only criterion and the copper 
was broken off with a sharp tug as it came near the mark, with the 
machine running at full speed.  Very impressive, but no way to 
produce a good copper line.

JD