Inharmonicity - so what actually causes it ?

[Newton Hunt]

> 1) WHAT are the specific properties of the piano string and scaling
> components etc. that actually CAUSE it ???
>

Inh is the effect of the tension, speaking length and stiffness of the
wire.  Think of the terminal point of the wire as being not a hinge point
like a grand hammer flange center but a solid piece of metal.  Consider
again that the wire does not flex at the terminal point but at some point
away from the terminal point because of it's stiffness.  Consider also
that the second partial (harmonic) has half the mass of the full string
length to flex the wire with and you get the idea of how Inh begins and
propagates through the higher partials, each with less mass and energy
causing more sharpness in each

> 2) Which of these properties are ranked the MOST significant and the
> least significant contributors ???
>

Wire stiffness which increases with wire diameters and speaking length,
which normally is not controllable.

> 3) How does one justify it in the piano compared with other string
> instruments ???

All stringed instruments have Inh because each string has mass, tension,
stiffness and length.  The piano has the highest of the stringed
instruments.  Bar instruments like marimbas, xylophones, glockenspiels,
etc., have much high inharmonicity than pianos because of their mass and
shape.

> 4) What are the perceptual properties that APPEAL to the listener ???

The flattening of the bass for resonance and perception of sharpening of
the treble, which is what we do when we tune..  This gives the piano
projection and it's ability to be heard over an orchestra.

> 5) Do composers, deliberately or unconsciously, make use of
> inharmonicity ???

I would say yes based upon the above statement.  As a practical matter, it
is only we technicians that conscienceless know about Inh and it's
effects.

> 6) How do we measure it ???

It can be measured with electronic instruments like the Sanderson
Accu-Tuner and it can be calculated with formulae.  It can be graphed to
see it's relationship with other notes.  More importantly it can be
changed, a little in the treble, and a lot in the bass to improve the
sound and tunability of a piano.  Again we are limited by the
manufacturer's bridge layout.  The can be changed also, but at greater
expense and time.

> 7) Should it, or could it, be effectively REDUCED to the betterment of
> the piano sound ???

It can be reduced but more importantly it can be controlled to the
improvement of the piano.  It can also be reduced but experience and
experiment has shown that Inh should fall within certain limits or the
quality of sound diminishes.

I hope you understand all this.  If not, give me a message and I will
answer your questions as best I can.

            Newton
            nhunt@jagat.com