source file: mills2.txt Date: Sun, 16 Feb 1997 07:08:37 -0800 Subject: can anyone explain these "ghosttones"? From: Gary Morrison > No, harmonics from physical sources such as flutes and oboes and > bells are not integrally separated. Generally one solves families > of solutions to Bessel or Legendre type equations, and these are not > simple integer multiples. "Sources such as flutes and oboes and bells", eh? That's kind of like saying "numbers like 2, 3, and 3738239.7564108". Bells are a totally different matter entirely from flutes, oboes, or other woodwinds and strings. True, none of them have mathematically exact integer multiple partials, but bells are many many times further from harmonic than woodwinds and strings. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 16 Feb 1997 19:35 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07837; Sun, 16 Feb 1997 19:35:52 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA07840 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id KAA08084; Sun, 16 Feb 1997 10:34:08 -0800 Date: Sun, 16 Feb 1997 10:34:08 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu