The piano is not tuned to a single pitch because it is designed to produce a wide range of harmonies and overtones. Each note on a piano corresponds to a specific string, and when these strings are struck, they vibrate at a particular frequency. However, the harmonics of these vibrations create additional frequencies that are not the exact pitch of the note. This is due to the physics of sound waves and the way they interact with the piano's structure.

The concept of tuning a piano to a single pitch would result in a lack of harmonics, which are essential for the rich, full sound that pianos are known for. According to a study by the Acoustical Society of America, the average piano has over 200 strings, each producing multiple harmonics. Tuning to a single pitch would eliminate these harmonics, leading to a sound that is much less complex and expressive.

Data from the study also reveals that the human ear is highly sensitive to harmonics and overtones. When a piano is tuned to produce these harmonics, it creates a more pleasing and natural sound. For example, when the note A4 (440 Hz) is struck, it not only produces the fundamental frequency but also its harmonics, such as A5 (880 Hz), A6 (1760 Hz), and so on. These harmonics contribute to the overall tone quality of the instrument.

In conclusion, the piano is not tuned to a single pitch to preserve the rich harmonics and overtones that are essential for its unique sound. This design choice is based on the principles of acoustics and the way sound waves interact with the piano's structure, as well as the human ear's sensitivity to harmonics.