source file: mills2.txt Date: Sun, 5 Jan 1997 11:30:48 -0800 Subject: strings and things From: William Sethares The problem of figuring out the partials that will sound when a nonuniform string is plucked is dealt with in Kalotas and Lee, ``Transverse modes of a string with variable mass density", Acustica Vol 76 (1992). This paper provides a matrix method that allows you to segment the string into sections, each with its own properties, and to then calculate the partials of the complete system. Thus, for Gary's twist tie string, you could divide the string into three parts, (regular string on left and right, twist tie version in middle) and use Kalotas' method. However, the inverse problem is far more interesting from a musical perspective: define a desired set of partials, and find a string with contour so as to generate the desired partials. Unfortunately, this inverse problem is as yet unsolved. On a slightly different topic, Glen said: I can't imagine the air conducting the sound from one string to the other. I believe that sympathetic strings do indeed work by transferring the energy through the air. As a simple experiment, sing into a string on a guitar, and you can easily set the string to vibrating (sympathetically) with your voice. -Bill Sethares Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 5 Jan 1997 22:07 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02024; Sun, 5 Jan 1997 22:10:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA02022 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA25131; Sun, 5 Jan 1997 13:10:49 -0800 Date: Sun, 5 Jan 1997 13:10:49 -0800 Message-Id: <199701051608_MC1-E34-DC2A@compuserve.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu