<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <html> <head> <title>RE: partial answers</title> <style>  </style> </head> <body>Right, and very interesting. What was the question again? <img src="cid:cool.gif@39262.9970835995.488" /> Alan Barnard Salem, MO ----- Original message ---------------------------------------- From: "Geoff Sykes" <thetuner@ivories52.com> </thetuner@ivories52.com> To: "Pianotech List" <pianotech@ptg.org> </pianotech@ptg.org> Received: 6/29/2007 10:48:12 PM Subject: RE: partial answers >Assuming no inharmonicity... Given a string of length n, when set into >motion it will create nodes at all the possible even, (meaning without a >remainder), divisions of that length because those are the only ones that >will terminate at a null point equal to the end terminations of the string. >Lots of odd nodes are also generated but they are killed almost instantly >when the reflection of that odd waveform bounces back from one of those end >termination points effectively canceling it out. I'm sure that if you dug >deep enough into the sub harmonics being generated between node null points >you might find some very faint odd harmonics, but certainly nothing we could >ever hear. >The hammer on a piano string hits a specific point on the string selected so >that the string will generate specific and mostly desirable harmonics. It >just so happens that that point is just off from the first null point of >about the 7th harmonic, which also happens to be the point on many >percussion instruments as the point of least harmonic generation. For fun, >to test this, take, say, a metal rod, or a piece of pipe, and hold it >between two fingers exactly 1/7 of the total length from one of the ends, >letting it hang. Now strike that rod with something and it will sing quite >loudly. Viola, tubular bells. Move your fingers only a very little bit from >that point and the sound from the rod will die quite quickly. If the hammer >on a piano struck the string at that 1/7th null point, it would generate >almost no sound. However, since it is striking just off of that 1/7th point, >something closer to the 1/8th point, it is generating a huge number of >harmonics, or partials as we like to call them when inharmonicity is taken >into consideration. >-- Geoff Sykes >-- Los Angeles >-----Original Message----- >From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On Behalf >Of David Boyce >Sent: Friday, June 29, 2007 1:21 PM >To: Pianotech List >Subject: Re: partial answers >Ed, I think what you say is the nub: "that string vibrates, every available >multiple of the lowest frequency is not only a "natural" but also, a logical >consequence." >It may help to think in terms of numbers of nodes, and to consider that no >possible node would be missed out, and that this would mean a harmonic >series - "harmonic" is after all a mathematics concept - it's a type of >numerical series, just as "arithmetic" and "geometric" are types of >numerical series. >I'm even confusing myself now...... >David.    </body> </html>