Tension per cent PR

[baoli liu]

Let me try to do a maths here.We all know the formula
for string frequency,

f=1/2*l(T/u)^1/2, here f is frequency,T is tension,we
can change it to
T=4*l*l*u*f*f,

For note A440,assume the piano is on pitch,

T(440)=4*l*l*u*440*440,

if we raise the pitch by 4 cents(1 HZ),the tension is
going to be

T(441)=4*l*l*u*441*441

T(441):T(440)=1.0045505,that means the tension for
A440 is going to raise 0.455% after 4 cents(1 HZ)
pitch raise.

we can do the same(similar)calculations on all the
strings of a particular piano and all should have the
same results(percentage of tension increase).

Conclusion: the whole tension of a piano will raise by
0.45% after 4 cents(1 HZ for A440) pitch raise.

If i remember correctly,the tension for grand piano
could be more than 15 tons(30,000 pounds),that means
one Hertz pitch raise can change the tension by 135
pounds.

Baoli


--- John Delmore <jodel@kairos.net> wrote:

> Okay, it's mass only.  If someone can give me a
> typical scale description
> (gauges and lengths, including wound strings [with
> total diameter and core
> diameter]), I think I can come up with a general
> figure, per cent pitch
> raise, pretty quickly.
>  
>   _____  
> 
> From: pianotech-bounces@ptg.org
> [mailto:pianotech-bounces@ptg.org] On Behalf
> Of John Delmore
> Sent: Wednesday, December 21, 2005 8:18 AM
> To: 'Pianotech'
> Subject: RE: How to explain a pitch adjustment
>  
> It is an interesting question.  The difference in
> tension needed to cause a
> one cent difference in pitch is going to vary
> according to the mass (and
> possibly the stiffness) of the string (I'll have to
> check my old physics
> books tonight).  So, to get a general value for
> added tension per cent PR,
> you'd have to consider, also, the size of the piano,
> i.e. you'd have
> different values for a spinet, a large upright and a
> large grand.  
> John (finally a bona fide member) Delmore
>  
>   _____  
> 
> From: pianotech-bounces@ptg.org
> [mailto:pianotech-bounces@ptg.org] On Behalf
> Of jonathan stuchell
> Sent: Tuesday, December 20, 2005 9:37 PM
> To: Pianotech
> Subject: Re: How to explain a pitch adjustment
>  
>   Thats good, I want to know the   tension per cent
> . That is a good
> constant, useful for many applications.  
> ----- Original Message ----- 
> From: Geoff Sykes <mailto:thetuner@ivories52.com>  
> To: 'Pianotech' <mailto:pianotech@ptg.org>  
> Sent: Tuesday, December 20, 2005 5:44 PM
> Subject: RE: How to explain a pitch adjustment
>  
> That raises an interesting diversionary question.
> What's the amount of
> tension per cent? How many cents of change, over the
> entire piano, would
> create a ton of tension change?
>  
> -- Geoff
> -----Original Message-----
> From: pianotech-bounces@ptg.org
> [mailto:pianotech-bounces@ptg.org] On Behalf
> Of Cy Shuster
> Sent: Tuesday, December 20, 2005 2:24 PM
> To: Pianotech
> Subject: Re: How to explain a pitch adjustment
> I measure pitch on all the A's before I start, and
> record this for the
> customer on a graph on the invoice.  This gives them
> a great visual about
> what work is needed.  The graph indicates "fine
> tuning" range (+/1 eight
> cents for me).
>  
> The analogy I use is sanding: if wood is very rough,
> you can't start with
> the 1000-grit paper; multiple passes are required. 
> Same thing for painting:
> with regular maintenance, one coat covers, otherwise
> you may need several.
>  
> A description of the forces involved helps: 15 to 20
> tons of tension
> overall; a pitch raise can add a ton of tension
> (right?), yet a fine tuning
> requires < 1% accuracy.  No wonder it doesn't last!
>  
> --Cy--
>  
>  
> 


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