I have an 11 course lute where the 11^th course seems to be very
   sensitive and difficult to get in tune. It is gut. No, I do not want to
   use copper or silver wrapped strings.


   So, my question is if there is a relationship between the sensitivity
   of the frequency (pitch) to the tension of the string which would
   indicate that the tension on my string is a bit low.


   I did a chart of this in Mathematica taking the partial derivative of
   the frequency as a function of tension equation (assuming all else
   being equal) and it seems that frequency changes as 1 over the square
   root of the tension. This implies that increasing the tension would
   make the string be less sensitive to changes if frequency due to change
   in tension - i.e. easier to tune.


   Does this make sense to anyone or is it just noise? I am looking to see
   if changing the string will have an effect on tunability and whether it
   indicates a low or high tension change would be good.


   Thanks for listening to the ramblings and any guidance you can provide.
   These are expensive strings (Gut) so just experimenting is a bit
   spendy.

   Regards

   David

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