Why do shorter and thinner piano strings produce higher pitches?

The fundamental frequency of a vibrating string is determined by its physical properties, a relationship described by Mersenne’s laws. According to these principles, the pitch produced by a string is governed by the following factors:

• Length: The fundamental frequency is inversely proportional to the length of the string. Shorter strings vibrate more rapidly, resulting in a higher pitch.12
• Mass and Thickness: The fundamental frequency is inversely proportional to the square root of the mass per unit length (thickness/density). Thinner, lighter strings have less mass, allowing them to vibrate at higher frequencies than thicker, heavier strings.12

In a piano, these physical laws are utilized to achieve a wide range of notes while maintaining relatively uniform tension across the instrument's frame. By making the higher-pitched strings shorter and smaller in diameter, manufacturers ensure that the strings can produce the desired high frequencies without requiring excessive tension that could warp the piano's structure. Conversely, lower-pitched strings are made longer and heavier—often by winding them with additional wire—to produce lower frequencies at a comparable tension.1