frequencies

[Daniel Gurnee]

on 2/12/02 9:01 AM, Brassard, Denis at Denis_Brassard@BanffCentre.CA wrote:

> 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
> 
Denis,

I expose myself with a lack of understanding of – and come up short by one
octave with formula 1.a.

And thanks for the submission.

Dan Gurnee

> 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
>