partial answers

[Alan Barnard]

Right, and very interesting. What was the question again? 



Alan Barnard

Salem, MO



----- Original message ----------------------------------------

From: "Geoff Sykes" 

To: "Pianotech List" 

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 at ptg.org [mailto:pianotech-bounces at 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. 



  
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