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> "Ashcraft AC (Clif)" wrote:

> Thanks for the reference. I believe that piano tuners "stretch their > octaves" a bit to minimize beating caused by anharmony. This has the > effect of making the higher strings sound in tune with the upper > partials of the lower strings. Tuners don't tend to discuss stretching > in these terms, but I think it is a large part of the basis for it.
> Clif Ashcraft
>
> [deletia...]
>
> ------ extPart_000_01BBF96D.205F7960
> Content-Type: application/ms-tnef
> Content-Transfer-Encoding: base64
>
> eJ8+IhERAQaQCAAEAAAAAAABAAEAAQeQBgAIAAAA5AQAAAAAAADoAAENgAQAAgAAAAIAAgABBJAG
> ADABAAABAAAADAAAAAMAADADAAAACwAPDgAAAAACAf8PAQAAAE0AAAAAAAAAgSsfpL6jEBmdbgDd
> AQ9UAgAAAAB0dW5pbmdAZWFydGhhLm1pbGxzLmVkdQBTTVRQAHR1bmluZ0BlYXJ0aGEubWlsbHMu
> [...]

What's this last part, application/ms-tnef, and how do I read it?

Matt Nathan



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> I got similar results from a harpsichord, but didn't have time to try
> recording a low piano note

In the case of the low piano tones, from what I've seen anyway, I doubt
if you'll find much of anything particularly nonharmonic other than some
very low-frequency stuff resulting from the chorus effect between the two
or three strings in each course.

High piano tones however will almost certainly show a moderately
significant amount of aharmonicity.

You'll probablly see a very small, but definitely significant, amount of
aharmonicity in typical brass tones.

Just as a general matter though, you would probably get somewhat more
resolute results (if that's of interest) using the Phase Vocoding
algorithm's method of tracking near-harmonic partials' frequency
deviations. It does that by taking the time derivative of each partials'
phase values. You have to have to look at a very short sliver of time to
do that though.

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