Hi David, could you please tell me which gauges are you using? and
   vibrating string length, too. Maybe that could help to understand your
   issue.
   Regards.

   2013/12/18 Sean Smith <[1][email protected]>

     Dear David,
     I'm kind of slow in the math department but in my experience low
     tensions strings _are_ more difficult to tune. When you get close to
     the breaking point - ok, and just a bit shy of almost there - they
     find that sweet spot rather nicely and you get a fine action around
     the tuning peg, too. eg, a quarter turn will yield fewer cents of
     change than at lower tension. That's just my experience. The higher
     tension around the peg also helps your control of turning so having
     pegs nicely fitted (and doped tho I almost never use it) will also
     help. That sweet spot/tension gives a better tone and I think more
     consistent. At lower than ideal tension the ring starts off higher
     and tapers lower according to my tricorder.
     Making sure your nut is well lubricated helps, too. Graphite is
     popular but I like beeswax for less mark up.
     The toughest time I ever had was a roped gut bass on a 4-course
     guitar that was short to begin with (~40cm) and then tuning it down
     a tone for one piece.
     Sean

   On Dec 17, 2013, at 5:59 PM, David Smith wrote:
     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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