source file: mills2.txt Date: Fri, 3 Jan 1997 09:35:32 -0800 Subject: RE: Harmonics at other than integer frequency ratios. From: "Ashcraft AC (Clif)" ------ extPart_000_01BBF96D.205F7960 Content-Type: text/plain; charsets-ascii" Content-Transfer-Encoding: quoted-printable 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 ---------- 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. 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