source file: mills2.txt Date: Tue, 11 Feb 1997 05:55:15 -0800 Subject: Ghosttones 2 From: Gary Morrison Charles Lucy posed a whole big slew of questions about viewing a vibrating string from various angles and in various lights. Unfortunately if he was trying to come to some sort of point with those questions, I'm afraid I totally missed it, despite having read them twice. Best I can tell his last questions were something of a summary: > Could the integer frequency ratios be approximations? > Can you "prove" that the integer frequencies ratios is the > only possible mathematical model to describe what you > observe? The idea that strings, and most air columns as well, used in common musical practice have precisely harmonic partials is indeed only an approximation. It is also very good approximation. You can see that readily by decomposing and then recreating such a tone with absolutely perfectly harmonic partials, which I personally have done. Without a doubt it's certainly noticeably different, but its effect upon harmony is far less than, for example, chorus effect. The relative amplitudes of the partials are almost certainly more significant to the perceived character of harmonies than such minuscule pitch deviations. That however is not even close to true for characteristically nonharmonic instruments like xylophones, bells, timpani, and is only marginally true for the piano. One of these days I'll have my internet/web act together and post some strictly harmonic tones with their "original" versions. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 11 Feb 1997 15:54 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02459; Tue, 11 Feb 1997 15:54:21 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA02457 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id GAA22422; Tue, 11 Feb 1997 06:52:18 -0800 Date: Tue, 11 Feb 1997 06:52:18 -0800 Message-Id: <009AFBBBE70AE82D.2562@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu