summer sharpness in low tenor

[David Love]

OK you've convinced me.  Ergo, if the piano is scaled such that all strings
are at the same BP%, pitch changes that accompany swings in humidity should
be much more uniform.

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

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Ron Nossaman
Sent: Tuesday, July 15, 2008 7:51 AM
To: Pianotech List
Subject: Re: summer sharpness in low tenor



> The degree to which a string will change pitch with a given change in 
> length (that's what happens when the case, bridge, board expand or 
> contract) will be a function of tension (or as Ron N has corrected me 
> breakpoint %--though I have some questions about that).  The low tenor 
> is generally the lowest tension (and BP%) and so changes the most.  
> Hockey stick type bridges are where you often see a huge drop off in 
> tension at the bottom of the tenor bridge and it is on those pianos 
> where the pitch changes are the greatest.  Pianos with more uniform 
> tension through the bottom of the tenor bridge will not change in the 
> same way.  

Using the same formulas I use in my scaling spreadsheet 
(Sanderson's, mostly), I find that different wire sizes on a 
given length give the same pitch change with a given change in 
wire movement. Take 0.002" out of the overall wire length, and 
they both react the same.

A wrapped string with the same overall length and same 
speaking length and pitch, will have a bp% around 50%, where 
the plain string is around 25%, will change pitch something 
near half as much as the plain string. The correlation is in 
the core bp%, more than the tension.


>The wound strings tend to be much higher tension (though not 
> necessarily higher BP% and therein lies my question about which it is) 
> and therefore change less.

I don't think I've seen a low tenor scale with both plain and 
wrapped strings on the same bridge where the bp% is similar 
between the two. Is that even possible? You'd have to go to a 
core significantly bigger than the adjacent plain string to 
even get close.



> At any rate, it has little to do with differences in the degree to which 
> the soundboard crown changes in different parts of the piano.  

Yes, very little.


> For example, take two strings of equal length producing equal frequency 
> (the dependent variable) but with different diameters (gauges-they will 
> have different amounts of tension and they will also have different BP%) 
> and then change the length equal amounts and you should see a difference 
> in the change in frequency between the two.  If someone has the formulas 
> handy (too early for me to go looking) maybe they can post it. 

That's not exactly correct. Change the gage size of a plain 
wire unison in your scaling spreadsheet and watch the tension 
and bp%. The tension will change, but the bp% won't. For a 
given pitch the only way to change bp% is by changing speaking 
length.

Ron N