source file: mills2.txt Date: Tue, 7 Jan 1997 14:12:07 -0800 From: Heikki Jamsa >From: William Sethares >To: tuning >Subject: stretching of strings >A couple of days ago, someone asked >how close to harmonic real strings are. >One early article that addressed this is >Young shows that the partials of piano wire are >``stretched" by a factor of about 1.0013, which is >about 2 cents per octave. >-Bill Sethares Mathematical formula is in small amplitudes f a ( n + k n^2 ) / ( 1 + k ) where f is frequenz of n:th partial, a is frequenz of grundtone, i.e 1:st partial, n is integer, number of partial, k is small constant, it depends from stiffness, tension and mass of the string. Heikki Jamsa Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 8 Jan 1997 02:39 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19476; Wed, 8 Jan 1997 02:42:04 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA19474 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA23110; Tue, 7 Jan 1997 17:42:00 -0800 Date: Tue, 7 Jan 1997 17:42:00 -0800 Message-Id: <199701072039_MC1-E45-7C84@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu