Tension Increase(limited English)

[Richard Moody]

Baoli wrote...
> Conclusion is : the tension increase is 0.122 times the lower tension.

I agree.  If frequency increases by a factor of 1.059 per semitone and
tension increases by a factor of  F squared, then 1.059^2 = 1.122.  this
is the factor T increases  since 	T = f^2   * 1--- when(L^2*d^2*.002303)
doesn't change.  

 Baoli....
> If we raise the note A37 by one semitone (from 415.30hz to 440hz),the
>frequency of higher pitch should be 2^(1/12)or  {1.05946} times that of
> the lower pitch. The higher tension should be 1.05946^2 times the lower
>tension,or T(hi) : T(lo)=1.05946^2=1.122
> The amount of higher tension is 1.122 times of  the amount of lower
>tension.The same is true with other string(s),


ric...
So if tension of lower string is 150 then 150 times 1.122 should give
tension if it is raised one semitone which equals 168.4  
Checking using T(150) = f^2*L^2*d^2*(.002303) gives 168.373 when f is 
raised a semitone 

If total tension is 150 times 200   equals   30,000     (assuming 200
strings)
or  if                      168.373 times 200  equals   33,674.6
with your factor    30,000 times 1.122    equals    33,660..........very
close
with 1.1224620 gets even closer.....                       33,674
Therefore your ratio 1.122 for the total tension of one semitone higher is
close enough....    Using .122 gives the  net increase, or how much the
tension changed, or 3660 lbs. 

A lot easier than using  	T = f^2*L^2*d^2*(.002303)

 ---ric 


----------
> From: Baoli Liu <lianqii@pub.ln.cninfo.net>
> To: pianotech@ptg.org
> Subject: Re: Tension Increase(limited English)
> Date: Thursday, January 06, 2000 4:45 AM
> 
> It's hard to say the exact amount of Tension Increase because the
tension is so different between the upright and grand piano,what we could
know exactly is the increase ratio(or time).
> 
> If we raise the note A37 by one semitone(from 415.30hz to 440hz),the
frequency of higher pitch should be 2^(1/12) times that of the lower
pitch,or
> F(hi) : F(lo)=440/415.30=2^(1/12)=1.05946
> 
> the higher tension should be 1.05946^2 times the lower tension,or
> T(hi) : T(lo)=1.05946^2=1.122
> The amount of higher tension is 1.122 times of  the amount of lower
tension.The same is true with other string(s),so the
> 
> Conclusion is : the tension increase is 0.122 times the lower tension.
> 
> Assume that the tension of  one upright piano is 9 tons,if we raise
pitch by semitone,the Tension Increase should be 9*0.122=1.098 tons,assume
that the tension of one grand piano is 15 tons,the tension increase should
be 15*0.122=1.83 tons.
> 
> 
> Thank you for your attention!
> 
> Baoli Liu 
> Shenyang Conservatory of Music
> China