How does the fundamental frequency relate to the overtones in a complex tone?

In acoustics, a complex tone is composed of a fundamental—the tone with the lowest frequency—and additional frequencies known as overtones.1

The relationship between these components is defined by their frequency ratios:

• Harmonics: When the frequencies of the overtones are exact whole-number multiples of the fundamental frequency (e.g., 2, 3, 4 times the fundamental), they are referred to as harmonics. These form simple ratios with the fundamental, such as 2:1 or 3:1.12
• Nonharmonic Overtones: Some instruments, such as drums, cymbals, or xylophones, produce overtones that are not exact multiples of the fundamental frequency. These are considered nonharmonic.2

The specific combination, presence, and relative intensities of these overtones determine the timbre (tone colour) of a sound. While the listener typically perceives the fundamental as the primary pitch, the unique emphasis on different overtones is what allows the human ear to distinguish between the sounds of different instruments or voices, even when they are playing the same fundamental note.32