frequencies

[Brassard, Denis]

Richard,

One equation used to find the frequency of a note is the following:

(1.a) 2^((N-1)/12) * 27.5 where N is the note number.
      2^((49-1)/12)* 27.5 = 440 hz  ... for A4

I took the next 2 formulas  from Dr. Albert Sanderson:

(1.b)     I=Bn^2 
B is the inharmonicity constant and n is the partial number. B can be
calculated as follows:

(1.c)     B= (330*d)^4/(T*(L^2)) 
 diameter and length are in inches, tension is in pounds.

Let us suppose that this note has an Inharmonicity constant (B) of .9 cents.
I= .9 * (1^2) or .9 cent  for the first partial.
Its frequency is:

(1.d) 2^(((N-1+(I/100))/12)*27.5=    frequency
      2^(((49-1+(.9/100))/12)*27.5 = 440.229 hz

To find the frequency of all the partials on that note use:
(1.e) 2^(((N-1+(I/100))/12)*27.5 * n

For example,the frequency of the 4th partial of note 49 will then be this:
         I= .9 * (4^2) or 14.4 cents
and   2^(((49-1+(14.4/100))/12)*27.5 * 4  or 1774.7 hz

I hope this helps.

Denis

-----Original Message-----
From: Richard West [mailto:rwest1@unl.edu]
Sent: Monday, February 11, 2002 8:52 AM
To: College & University Technicians
Subject: frequencies


Hi, Everyone,

Is there anyone out there who has the formula for calculating the
frequencies of the partials of a string in a piano taking into account
the inharmonicity of the string?  A-440, for example--the actual
frequency of the second partial must be 880.??? or 881.???  At this
point I'm only interested in the plain wire strings.  I know bass string
formulas get to be pretty complex.

Richard West