RE: Harmonics at other than integer frequency ratios.

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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

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From: Manuel Op de Coul[SMTP:Manuel.Op.de.Coul@ezh.nl]
Sent: Friday, January 03, 1997 9:24 AM
To: aaaabb1@peabody.sct.ucarb.com
Subject: Harmonics at other than integer frequency ratios.

There is also an article that provides a quantitative analysis of the
inharmonicity of piano strings:

AUTHOR: RASCH, Rudolf A.; HEETVELT, Vincent
TITLE: String inharmonicity and piano tuning.
SOURCE: Music perception, USA Vol. III/2 (winter 1985) 171-89.
LANGUAGE: English.
DOC TYPE: ap -- Article in a periodical
CLASS: MUSIC AND RELATED DISCIPLINES - Physics, mathematics,
acoustics, architecture
ABSTRACT: Inharmonicity is a well-known property of stiff strings such
as those used in the modern piano. The inharmonicities
measured in a medium-sized grand piano are in excellent
correspondence with the predictions by formula from the
physical properties of the strings. Strings with higher
frequencies usually have higher inharmonicity than strings
with lower frequencies; this cancels out part of the effect
of inharmonicity on beat frequency. (Authors, abridged)



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