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 >
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