Describe how overtones relate to fundamental frequency.

Overtones are frequencies that occur above the fundamental frequency, contributing to the richness and complexity of a sound.

In more detail, the fundamental frequency is the lowest frequency of a periodic waveform. In music, it is the lowest pitch that is perceived, and it is produced by the vibration of the entire object. Overtones, on the other hand, are higher frequencies than the fundamental frequency. They are produced by the vibration of parts of the object.

For example, when a guitar string is plucked, it vibrates as a whole, producing the fundamental frequency. But parts of the string also vibrate at higher frequencies, producing overtones. These overtones are integral multiples of the fundamental frequency, meaning they occur at frequencies 2, 3, 4, etc. times the fundamental frequency. These are also known as harmonic overtones, and they contribute to the timbre or tone colour of the sound, making it richer and more complex.

The relationship between the fundamental frequency and the overtones is such that if the fundamental frequency changes, the frequencies of the overtones change proportionally. This is because the overtones are multiples of the fundamental frequency. So, if the fundamental frequency doubles, the frequencies of the overtones also double. This is why the pitch of a note changes when the tension in a guitar string is adjusted: the fundamental frequency and the frequencies of the overtones all change.

In summary, overtones are higher frequencies that occur above the fundamental frequency. They are produced by the vibration of parts of the object, and they contribute to the richness and complexity of the sound. The relationship between the fundamental frequency and the overtones is such that if the fundamental frequency changes, the frequencies of the overtones change proportionally.