source file: mills3.txt Date: Mon, 11 Aug 1997 20:49:19 +0200 Subject: Re: Natural Harmony From: mr88cet@texas.net (Gary Morrison) >The article points out that there's a more common class of seismic >signals called harmonic tremors with a nice overtone series. That strikes me as surprising (although I'm not suggesting that they're lying of course). It seems surprising because of the answer to your second question: >Strikes me a tuning FAQ ought to address the question, are integer overtone >series natural or artificial, where do they come from? Harmonic partials come from vibrating systems with uniform and elastic vibrating media bound by two immobile "nodes". The most obvious example is a vibrating string, the two nodes being the nut (or fret) and bridge. Those systems can set up "standing waves", which resonate strictly at harmonically-related frequencies. I would think that most seismic waves would not fit this model at all, but instead would vibrate along the effectively infinite expanse of the crust of the Earth. But getting back to musical instruments... Systems that produce nonharmonic partials don't follow that scheme at all, an example being a drum head. Systems that produce NEAR-harmonic partials almost always have that essential scheme, but the perfection of one element or another is compromised. High-register piano strings for example, are not entirely harmonic because they are very stiff, and thus compromise the elasticity requirement. Most wind instruments somewhat compromise the absoluteness of the nodal points. The vibrating medium, air itself, is an almost ideal (in this sense of the word) vibrating medium unlike the high-register piano string. The physical basis for this is somewhat more complicated to describe, so bear with me here: In wind instruments, the wave is easiest viewed as an air-pressure wave traveling along the axis of the tube, the nodes being the points where the air-column is exposed to the open atmosphere. At those points the air pressure can't fluctuate very much. Why? Because, unlike within the tube where the air molecules' movement is restricted to the confines of the tube, any attempt to pressurize them in the open atmosphere will be immediately thwarted by their freedom to move so as to disperse that pressure. The compromise to the absoluteness of the nodes occurs right at the opening to the atmosphere. It's called an open-end effect, and it gets even more complicated with woodwind-style toneholes. The air molecules' movement isn't sufficiently unrestricted to form a pure node until they get somewhat outside the tube. How far outside the tube they have to be depends upon a great many factors including the geometry of the tube (e.g., its diameter and whether it's cylindrical or conical), the amplitude of the wave moving them, and yes, the frequency of that wave as well. For a purely cylindrical tube like you'd find on a fife, the effective nodal point is fairly predictable, lying outside the end of the tube about 0.6 times the diameter of the tube. A flared bell like brass instruments have tends to blur the exact placement of that nodal point much more than a simple cut in the tube. The effective vibrating length of the air column therefore varies a bit more between harmonics in brasses than in woodwinds or strings. But, as I've mentioned before on this list, I have quite a bit of direct experience with the tones of orchestral instruments forced to exact harmonic overtone structures, and I think it's important that these are - in the big scheme of things - fairly subtle differences. They are of the magnitude that distinguishes a good simulation of an instrument from a bad one, not ANYWHERE NEAR the sort that distinguishes, say, a flute from trumpet. SMTPOriginator: tuning@eartha.mills.edu From: Denis.Atadan@mvs.udel.edu Subject: Tape Swap is like Soyulent Green PostedDate: 11-08-97 20:50:23 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 11-08-97 20:50:22-11-08-97 20:50:23,11-08-97 20:48:47-11-08-97 20:48:47 DeliveredDate: 11-08-97 20:48:47 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C12564F0.00677A35; Mon, 11 Aug 1997 20:50:14 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA08079; Mon, 11 Aug 1997 20:50:23 +0200 Date: Mon, 11 Aug 1997 20:50:23 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA08075 Received: (qmail 21399 invoked from network); 11 Aug 1997 18:46:28 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 11 Aug 1997 18:46:28 -0000 Message-Id: <199708101900.PAA03640@copland.udel.edu> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu