Piano acoustics is the set of physical properties of the piano that affect its sound. It is an area of study within musical acoustics. String length, mass and tension 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 (0.85 mm, string size 13) 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 will vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano, i.e. if one began with the highest notes and then doubled the length of the strings again and again for each lower octave, it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, when strings vibrate, the width of the vibrations is related to the string length; in such a hypothetical ultra-long piano, the lowest strings would strike one another when played. 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 shorter than the "double with each octave" rule would predict, and are much thicker than the others. The other factor that can affect pitch, other than length, density and mass, is tension. Strings in an upright piano usually have a tension of 750 to 900 N (75-90 kg weight) each. Inharmonicity and piano size 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