summer sharpness in low tenor

[David Love]

Yes, Ron Nossaman pointed that out already.  I stand corrected (again).  

 

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 Joe DeFazio
Sent: Tuesday, July 15, 2008 9:39 AM
To: pianotech at ptg.org
Subject: RE: summer sharpness in low tenor

 

on July 15, 2008, David Love wrote:






An examination of the formula for frequency of a string as a function of
tension (or BP%), diameter, length (BP%) and looking at the differences in
the rate of change depending on tension levels should yield more clarity.   

 

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.  

 

Although I am far from an expert in rescaling or the physics of piano
strings, I don't believe that the part of this about BP% is accurate.  My
understanding is that two strings of equal length producing equal frequency
will both be at exactly the same percentage of their respective breaking
points.  For instance:

 

Note 40 (C4), speaking length, 715mm , diameter of 0.040",  tension
199.957lbs, %breakpoint 49.436%

Note 40 (C4), speaking length, 715mm , diameter of 0.038",  tension
180.461lbs, %breakpoint 49.436%

 

(figures from Pscale)

 

In other words, though the second string is smaller in diameter, and will be
at a lower tension when producing the note "middle C," since its diameter is
in fact smaller, its breaking point will be lower, and it will be at exactly
the same percentage of its breaking point.  As I understand it, this is
because, as its diameter changes, its breaking point changes proportionally.
See pages 33-35 in John Travis' "A Guide to Restringing" (in the section by
James Hayes) for a simple experiment you can do to demonstrate this
empirically.

 

The aspect of the string's behavior that does change in the example above is
inharmonicity:

 

Example above with 0.040 diameter, inharmonicity = 0.192

Example above with 0.037 diameter, inharmonicity = 0.173

 

If I am wrong in my conceptual understanding, someone please correct me.  I
want to be sure that I understand this correctly.

 

I will also point out that, from my archive reading and past posts, there
are at least two formulae out there for calculating breakpoint and
breakpoint percentage, so some of you might plug my numbers into your
formula and get a different value for %breakpoint. However, that value
should be identical for the two wire diameters given above.

 

Joe DeFazio

Pittsburgh

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