we play on a piano exists of a fundamental and a few partial sounds.
In short the inharmonicity of a string is the deviation of the
different partial sounds according to each other and according
to the fundamental of the string..
If for instance the fundamental is 440Hz, the first partial is
When that first partial is not exactly 880Hz but for example 880.4Hz
we call this difference the inharmonicity.
The inharmonicity is determined by the stiffness of the string.
The stiffer the string, the higher the inharmonicity.
A short thick string is much stiffer than a long thin one producing
the same sound.
The inharmonicity of the bass strings of a concert grand piano
is much lower, because the strings are much longer and thinner,
sounding much lower than those of a baby grand.
cannot hear the fundamentals of the lowest bass strings. Partially
due to the tones sounding on the limit of the human sense of hearing,
but mainly because the soundboard is not capable to transmit these
to a small transistor radio, that does not give low frequencies
at all, we can tell the difference between a small and a big instrument.
The human ear is used to construct a fundamental from the different
The inharmonicity is perceptible with great ease.
The level of inharmonicity can tell us if we are listening to
a grand piano or a small upright.
do we perceive as a sound being 'beautiful'?
That, of course,
is a matter of taste, but maybe habituation takes a part too.
Very small instruments (high inharmonicity) have a sound we usually
don't like so much.
But do we like the sound of an enormous instrument like the Klavins
This instrument has an extreme low inharmonicity and a enormous
big soundboard too.
Thanks to that colossal soundboard it should be able to radiate
the lower sounds.
Still we have to get used to this sound.
we change the inharmonicity of an instrument?
manufacturers have started to determine the scale by trial-and-error.
(the scale comprises the length and thickness of the strings)
Renowned manufacturers have had more possibilities to experiment
themselves, but the small ones often copied the scale from others.
It was only in the fifties of the last century people have developed
a formula which can be used to calculate the inharmonicity.
In a restoration project it is not possible to change the length
of the strings, but by adapting the thickness of the steel and
the copper of the windings, it is possible to greatly improve
the sound and tuning of the instrument.
For the calculation
of the strings we use a computer program written by mr.Hans Velo
from Maartensdijk in Holland.