Hi John, Sorry for the confusion. "u" is the mass per length, or (m/L). Yes, four cents per hertz is only valid around A440.If the original pitch is not way off A440, the tension change should be about 0.45% for each hertz. For curiosity, we may do a math of 20 Hertz pitch correction, that is probably the maximum pitch correction we usually see. This time, we use the formula you mentioned and raise the pitch from A420 to A440, Original tension for note A420, T (420)=4*L*m*420*420, after raise the pitch by 20 Hertz, the tension becomes, T(440)=4*L*m*440*440. T (440): T (420) =1.0975, that means the tension raised by(about)9.75% after 20Hz pitch correction. We divide 9.75% by 20Hz, we get 0.48% for each HZ--very close to 0.45%. For different note, such as A220, A880 or any notes on the keyboard, we can do a similar calculation and get the same results for each string. The whole tension for a piano is simply added up by each string's tension. So it is easy to conclude that the whole tension of a piano will increase 4.5% for each 4 cents pitch raise,if the piano is not originally way out of tune. Please correct me if I am wrong. Thanks! Baoli --- John Delmore <jodel@kairos.net> wrote: > I'm sorry, Baoli, I don't follow your math. Is "u" > the mass of the string? > Also, isn't the formula f=((T/(m/L))^1/2)/2L? I'm > just working from > "internet formulas", haven't consulted my physics > texts. > > Also, four cents per hertz is only valid around > A440. > John > > -----Original Message----- > From: pianotech-bounces@ptg.org > [mailto:pianotech-bounces@ptg.org] On Behalf > Of baoli liu > Sent: Wednesday, December 21, 2005 12:30 PM > To: Pianotech > Subject: Re: Tension per cent PR > > 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-- > > > > > > > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam > protection around > http://mail.yahoo.com > _______________________________________________ > pianotech list info: > https://www.moypiano.com/resources/#archives > > > > _______________________________________________ > pianotech list info: > https://www.moypiano.com/resources/#archives > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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