String Scaling

[Michael J. Wathen]

I will register my voice in favor of re scaling pianos, Steinways included.
The only pianos I don't feel that are worth re scaling are the Baldwin
grands designed by Conklin, but that is just a hunch. I have never really
checked it out mathematically. 

There are hugh benefits to rescaling in the non bass sections as well.  The
most notable is the result you get when there is even tension through out
the treble.  Most scales have jumps that are really noticeable when the wire
diameter changes.  This  non-uniform distribution would probably cause
unpredictable nodes and boundaries on the vibrating board.  

The modes of vibration on any given board are hardly understood. Having
non-uniform tension is just one element that can be controlled through
proper rescaling.

I once wrote a program in Qbasic to calculate a best treble scale that used
a step function with the string gauge as the variable.  It consisted of a
only a few executing program lines. It tried each gauge of wire starting
with the smallest and it calculated a value for tension for that gauge.
Next, the program asked if this value was within, say, 5 lbs. of 160 lbs. if
not it calculated a new value for tension using the next gauge size up.
When the right gauge was supplied then it was selected and stored in an
array for that note number.  This first gauge value that supplied the
correct tension was also the best choice for "inharmonicity".  In short, the
whole program went for the constant tension while inharmonicity was the
second priority. 

I still have the program somewhere if anyone is interested I can email it as
an attachment.  
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 Michael J. Wathen, RPT			Phone:	513-556-9565
 Piano Technician			Fax:	513-556-3399
 College-Consevatory of Music		Email:  Michael.Wathen@UC.Edu	
 University of Cincinnati
 Cincinnati, OH 45221-0096
 
http://www.uc.edu/~wathenmj/