Call for scaling spreadsheets

[Richard Moody]

This is from "The Piano-Its Acoustics" by W.V. McFerrin.  It should be
available from one of the supply houses. 

 

The formula for inharmonicity is given as I=B*n^2    Which reads, I equals B
times n squared, where I is inharmonicity,  B is the coefficient of
inharmonicity and n squared is the mode of vibration or partial number where
the fundamental is partial number one and the  division of the string into
two vibration units is the second partial etc.    So if you want to know the
inharmonicity of the second partial then multiply B by 4, for the third
partial  B  times 9.     

 

To calculate B if the string is in inches figure out how to enter into a
spread sheet; five times ten to the twelfth power times the diameter of the
string squared.   It might be 5*(10^12)*d.   Then divide this by the square
of the frequency times the length of the string to the fourth power.. Or
F^2*L^4. 

For clarity and to be sure the processor takes the operations in order I
would use (F^2)*(L^4) .  So hopefully by pasting in this formula...
5*(10^12)*d/(F^2)*(L^4)  where d  F and L are cell references that contain
the corresponding values  you get  B  which you have to multiply by the
square of the partial you want to know the inharmonicity of. 

 

For metric in centimeters try   3.4*(10^13)*d^2/F^2*L^4  

And remember to multiply this by the square of the partial.   

The value for inharmonicity will be in cents so your numbers should be
between .2 and 4.  This is for plain wire.  Forget about bass string
calculations, unless you have a string winding machine and try the results
on the spot imho.    

 

The references given by McFerrin are:

 

"Observations on the Vibrations of Piano Strings", by O.H. Schuck and R. W.
Young in the Piano Technician's Journal, January, 1964.   

 

Also: Railsback, O.L. Journal of Acoustical Society of America, Vol. p 274,
1938.

 

And: Young, Robert W., "Inharmonicity of Plain Wire Piano Strings." JASA
Vol.24, May 1952.  

 

 

-----Original Message-----
From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of William Benjamin
Sent: Thursday, September 28, 2006 3:13 PM
To: 'Pianotech List'
Subject: RE: Call for scaling spreadsheets

 

 

From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf
Of Jason Kanter
Sent: Thursday, September 28, 2006 3:12 PM
To: Pianotech List; Richard Moody
Subject: Re: Call for scaling spreadsheets

 

Thanks!

I can handle MSWorks. 

 

The most pressing formula at the moment is inharmonicity. There seems to be
a wide range of methods for looking at this. Some of them use "special
sauce." (arcane lookup tables, mysterious constants). Whaddyagot?

 

----- Original Message ----- 

From: Richard <mailto:remoody at midstatesd.net>  Moody 

To: 'Pianotech List' <mailto:pianotech at ptg.org>  

Sent: Thursday, September 28, 2006 10:53 AM

Subject: RE: Call for scaling spreadsheets

 

If any of you have and are willing to share your scaling spreadsheets -
please send to me

 

 

Glad to see your post Jason.   It turns out all my scaling spreadsheets are
in MSWorks or Quattro Pro and getting them over to xcel is easier done by re
doing them by hand in excel rather than trying to import or copy.   

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