Math/Physics Problem: degrees of rotation of tuning pin = how much pitch change

[John Delacour]

At 13:04 -0500 29/3/08, kurt baxter wrote:

>The know factors would be:
>
>string length
>string thickness
>tuning pin diameter (and therefore radius)
>
>With those factors known, is it possible to calculate the exact 
>rotational movement (in fractions of a degree) required to make a 
>pitch change of say, 1 hertz at the note middle C?

Well, if the pin is 7.00 mm. and the string is 1 mm in diameter, you 
will stretch the string 1 mm for every 14.32 degrees rotation of the 
pin.  You then need to know the modulus of elasticity of the wire, 
since softer wires will stretch more for a given increase in tension. 
You would then use the usual formulas to work out the change in pitch 
for a given extension.  On another day and in a different mood I 
might be inclined to work out the full answer, but it's been a long 
day.

JD