[CAUT] pre-stretching new string?

[David Love]

I believe you are the one confused.  Did you do the problem as I outlined?
For BPP to change between two notes targeting the same frequency, the
speaking lengths must be different.  To see whether a change in frequency
between two strings will be different with a change in length as a function
of BPP you must start with two strings that have a different BPP.  If the
strings are equal speaking length then no matter how you change the string
diameter altering the tension and hold the frequency constant, the BPPs will
change together.  A change in length will not result in a difference in the
change in frequency between the two.  However, if you start with two strings
of unequal speaking length with the same starting frequency, the tension (a
in the first example) will be different, but the BPP's will not be equal.
Now when you impose a similar change in length there will be a difference in
the change in frequency between the two. 

 

The more complicated calculation comes because we comparing just two
different notes on the same piano.  You then must do the calculations and
convert the change on each note to cents deviation so that you can see
whether as the percentage of a semitone, one changes more than the other.
In other words, does the high bass go "out of tune" more or less than the
low tenor.  The relative BPPs of the respective notes will give an
indication of which will go out of tune more and it is the one with the
lower BPP that will go out of tune more.  Namely, the BPP of the low tenor
on a Steinway B, for example is around 22%.  The first note of the high bass
is around 60%.   I have my own spreadsheet, thank you, perhaps yours needs a
bit more work.

 

That's the best I can do with the explanation for now-I gotta go to woik.  

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

-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Richard Brekne
Sent: Monday, June 11, 2007 11:15 AM
To: caut at ptg.org
Subject: [CAUT] pre-stretching new string?

 

David

I'n not being antagonistic at all. I am just trying to help you understand
something you seem clearly confused about. The two unknown formula link you
offered for example.... there is no way you can use that in the context you
have suggested.  Its a completely different problem type.

The Tension formula is T = f^2*L^2*d^2* K  where K = the string density * PI
/ 981

You cant fit that into solving for an  aX+bY=c problem.  

There is no way around it. You can calculate the change in length and
measure the pitch change to get tension... or you can calculate change in
length and change in tension to get pitch.... but you have to get two of
these in order to get the third.

As far as the diameter is concerned.  Use the spreadsheet I supplied with
accompanying justifying formulas.  You can easily enough juggle the input
tension for different wire diameters for same wire lengths to get the same
starting frequencies. Then change the deflection input for both strings.  As
long as they are the same length... any same deflection will cause the same
frequency change.

Cheers
RicB


See my other post but of course diameter plays a role.  It is a factor in
determining break point percentage.  A thicker string will have a higher
break point percentage and a thicker string will need to be at a higher
tension to achieve a certain frequency at a given length than will a thinner
string.  Simple stuff.  The claim about BPP as a factor in determining which
string will go out of tune more goes way back.  You don't need to use BPP in
the formula, you can simply calculate it for the two strings in question and
observe the relationship-see my other (corrected post).  Please don't be so
antagonistic.  I'm really trying to help you here.    

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