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. 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. 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.
However, if one were to use this principle to design a piano, i.e. 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. These differences in string thickness follow from well-understood acoustic properties of strings. 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. The strings of a piano vary in thickness, and therefore in mass per length, with bass strings thicker than treble. Strings vary in length and thickness, so that many octaves can fit on one sounding board
