A guitar string vibrates in such a way that it not only produces the primary note you hear but also a series of quieter, higher-pitched sounds. These additional sounds are mathematically related to the fundamental frequency, and their presence is key to the rich, full sound we associate with the instrument. This phenomenon accounts for the distinctive tone of different instruments, even when they play the same musical note.

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These additional quieter, higher-pitched sounds created by a vibrating guitar string are called overtones. Understanding the role of overtones in shaping the unique sound of musical instruments is essential for musicians and sound engineers alike. It's fascinating how mathematical relationships govern the complex yet harmonious nature of musical tones.