Inharmonicity - so what?

[Delwin D Fandrich]

Alan, Don, Jim, Jim, Newton, et al.,

Interesting thread.  I'm not sure I'm going to answer any questions here, but I
might pose some additional ones.  At the very least, I might stir up the pot a
bit...

1)    Inharmonicity is basically a function of string length, mass, tension,
etc.  The fact that the string is attached to a less than rigid termination
point at one end may or may not have any effect on this.  I don't know, and from
a piano performance -- as opposed to a piano tuning -- perspective, I don't
care.  In terms of actual piano performance it doesn't really matter all that
much.  Inharmonicity is a greatly over-rated factor in scale design.  String
length relative to string diameter for a given note -- i.e., frequency -- is of
much more importance.

2)    False beats are not a function of inharmonicity or of the strings
vibration patterns.  And they have little to do with how the strings seat on the
bridges or against the bridge pins.  Certain pianos have a propensity toward
false beats and others do not.  Regardless of the condition of their bridges.
If a piano has a propensity toward false beats, no amount of string seating,
etc., is going to make it go away.  At least not for long.  This work will only
change it.  As I have gone into repeatedly and at length in my various classes,
false beats are primarily a function of soundboard design.  It must be solved at
the design stage.

3)    I am not convinced that the string's vibration pattern has any substantive
effect on piano tone.  Either its timbre or its sustain.  The bridge/soundboard
assembly acts as a fairly effective mechanical filter.  The bridge/soundboard is
capable of responding only to the wave energy that is present in the string,
however, there is no law stating that it must respond instantly or uniformly to
all of the wave energy that is in the string.  It is perfectly capable of
rejecting some of it.  And it does.  This is not an area that I have studied
extensively, but at my current level of knowledge I believe that the
bridge/soundboard system simply rejects any string motion that does not move it
in a more-or-less vertical (in a grand piano orientation) direction.  This
rejected wave energy -- whether circular, elliptical, or whatever -- simply
stays in the string until it is oriented in a plane that the bridge/soundboard
can use or until it is dissipated as heat.

As far as I know, the interface between the string and the bridge is still a
poorly understood one.  I have experimented with a number of different types of
string termination devices at the bridge.  So far none of them have stood out as
markedly superior (in terms of audible or measurable acoustic performance) to
the traditional bridge pin arrangement.

So, with my flame suit close at hand, I leave for two "wonderful" days of
sanding and varnishing.

Regards,

Del