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Hi all,

I have a terminology problem. Or actually not a problem, but taking my baby steps into the world of ETD's, I'm getting confused.

I am familiar with an "inharmonicity coefficient", used in various formulas I've encountered. For a midrange string, 0.0004 would be a normal value.

How does the coefficient relate to an "inharmonicity constant", often referred to in ETD discussions? Is there an easy way to convert these two values to get the other one, or are they measuring different things?

The inharmonicity constant is the number, B, so that the offset of the n-th partial, in cents, is

B x n x n.

The number 0.0004 seems awfully small to be the B described above. Do you have a precise definition of the "inharmonicity coefficient"?

Robert, here is an excerpt for the formula:



... and here is a link to the whole paper from which the quote is excerpted:

http://www.speech.kth.se/prod/publications/files/qpsr/1994/1994_35_1_135-144.pdf

and yet another one, with a definition of B itself:



original source:

http://www.acoustics.hut.fi/~mak/PUB/ICMC99may22.pdf

The two constants are different. One works directly with the frequencies, one is a cents offset. The one Robert describes is more useful for tuning, the one in the paper better for the science. I think you can convert between them as follows:

If we take F(n) = n f(0) as being the harmonic partial (0 inharmonicity), then the offset is:

F(n) - f(n) = n f(0) - n f(0)(1+Bn^2)^1/2

Divide this by F(n), take the log base 2, and multiply by 1200, and you have the offset in cents. Divide by n squared and you should have the 'B' value that Robert describes.

Hope this helps!

Thx Phil, it sure does!