[CAUT] pre-stretching new string?

[Richard Brekne]

David,

No.. you can not calculate for a variable with two unknowns.  If you 
want to solve for pitch as you suggested in your earlier post.. you 
first have to have all the other variables in any equation you use to do 
so. Rewritting the tension formula still includes both tension and 
length, and when you change length you change tension, resulting in two 
unknowns, both of which must be known before you can solve for pitch.

The equation for solving for this accompanying change in tension has 
been posted several times. I post it again for your edification.

http://www.pianostemmer.no/files/stringdeflection/brekne.doc

If you have a formula for arriving at change in pitch for change in 
length directly without solving for the change in tension first... 
please share it with us. 

Cheers
RicB


    Of course you can.  The pitch (frequency) at which a string vibrates
    is a
    function of length, diameter and tension.  A change in length will
    result in
    a change in tension which will result in a change in pitch.  It's a
    complex
    equation but it's not trigonometry, it's algebra.  You can certainly
    rewrite
    the formula to isolate pitch, or tension, or length, or diameter. 
    That's
    the beauty of Algebra.  The miraculous is simply the unexplained. 

     

    A strings vibration period (I assume you mean frequency) will not be
    altered
    by the soundboard.  The string continues to vibrate at its given
    frequency
    until it stops no matter what the soundboard does (though it does
    influence
    how long it will vibrate for).   

     

    David Love
    davidlovepianos at comcast.net
    www

    You can not solve for change in pitch directly by re-writting /
    re-arranging
    the formula for string tension. You can not because any given change in
    length automatically carries with it a change in tension i.e. you
    have two
    unknowns.... tension and length.  Length change is easy to calculate
    with
    the simple trig talked about. But that leaves you with an unknown
    change in
    tension still. You could measure pitch of course and calculate the new
    tension that the new length resulted in...... but aside from being
    the long
    way around... we are solving for pitch.  Its easy enough to do... just
    calculate the change in length, and then the resultant change in
    tension.
    Then you have all the variables you need to calculate for resultant
    pitch.

    Thats.... for a string whose vibration period is truly reflected by the
    soundboard... and not altered significantly due to any stiffness
    issues...
    which just came up and of course sheds a different perspective on
    everything
    to the degree that thought ends up being significant itself.

    Cheers
    RicB




    David Love
    davidlovepianos at comcast.net
    www.davidlovepianos.com

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