Tension Increase(limited English)

[Baoli Liu]

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


----- Original Message ----- 
From: Ron Nossaman <RNossaman@KSCABLE.com>
To: <pianotech@ptg.org>
Sent: Wednesday, January 05, 2000 4:19 AM
Subject: Re: Tension Increase


> >If one raises pitch 1/2 tone to A440, how much tension is added to the 
> >frame, either in percentage or pounds?
> >
> >I successfully carried this out yesterday on a Dominion (circa 1910) which 
> >showed signs of structural weakness with the treble pin block having pulled 
> >slightly forward.
> >
> >Just wondered how much extra stress I had caused. Tuning is scheduled in 
> >four weeks.
> >
> >John Lillico, RPT,
> >Oakville, ON
> 
> 
> Hi John,
> Here are some figures from the original scale of a grand I rescaled. 
> Total Tension:
> @A=440=37555lb  at pitch
> @A=428=35535lb  1/2 <> semitone down
> @A=415=33409lb  1 semitone down
> The figures on your piano would be different, of course, but this should
> give you some place to start. 
> 
> Scary, ain't it? Now go back and fix that pinblock separation. 8^)
> 
> Ron N
>