Railsback curve

Piano acoustics are the physical properties of the piano that affect its sound.

The strings of a piano vary in thickness, and therefore in mass per length, with bass strings thicker than treble. A typical range is from 1/30 inch (.85 mm) for the highest treble strings to 1/3 inch (8.5 mm) for the lowest bass. These differences in string thickness follow from well-understood acoustic properties of strings.

Given two strings, equally taut and heavy, one twice as long as the other, the longer would vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, in such a hypothetical, gigantic piano, the lowest strings would travel so far in vibrating that they would strike one another. Instead, piano makers take advantage of the fact that a heavy string vibrates more slowly than a light string of identical length and tension; thus, the bass strings on the piano are much thicker than the others.

Any vibrating thing produces vibrations at a number of frequencies above the fundamental pitch. These are called overtones. When the overtones are integer multiples (e.g., 2×, 3× ... 6× ... ) of the fundamental frequency (called harmonics), then - neglecting damping - the oscillation is periodic—i.e., it vibrates exactly the same way over and over. Humans seem to enjoy the sound of periodic oscillations. For this reason, many musical instruments, including pianos, are designed to produce nearly periodic oscillations, that is, to have overtones as close as possible to the harmonics of the fundamental tone.

In an ideal vibrating string, when the wavelength of a wave on a stretched string is much greater than the thickness of the string, the wave velocity on the string is constant and the overtones are at the harmonics. That is why so many instruments are constructed of skinny strings or thin columns of air.

However, for high overtones with short wavelengths that approach the diameter of the string, the string behaves more like a thick metal bar: its mechanical resistance to bending becomes an additional force to the tension, which 'raises the pitch' of the overtones. Only when the bending force is much smaller than the tension of the string, are its wave-speed (and the overtones pitched as harmonics) unchanged. The frequency-raised overtones (above the harmonics), called 'partials' can produce an unpleasant effect called inharmonicity. Basic strategies to reduce inharmonicity include decreasing the thickness of the string or increasing its length, choosing a flexible material with a low bending force, and increasing the tension force so that it stays much bigger than the bending force.

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