partial answers

[Geoff Sykes]

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.