partial answers

[David Andersen]

Great job, Geoff. Lucid yet unwonky. You win.
DA


On Jun 29, 2007, at 8:48 PM, Geoff Sykes wrote:

> 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.
>
>