How do nonharmonic overtones differ from harmonic overtones?

In the context of musical sound, the primary difference between harmonic and nonharmonic overtones lies in their frequency relationship to the fundamental tone.

• Harmonic overtones (or harmonics) occur when the frequencies of the overtones are exact integer multiples of the fundamental frequency (e.g., 2:1, 3:1, 4:1). These are produced by ideal vibrating systems, such as stretched strings or air columns, where the medium divides into equal parts to create a harmonic series.12
• Nonharmonic overtones occur when the frequencies of the overtones are not multiples of the fundamental frequency. These are typically produced by instruments where the vibrating medium is not a simple string or air column, such as metal, wood, or stone bars (e.g., marimbas, xylophones), plates (e.g., cymbals), or membranes (e.g., drums).1

While the ear often perceives the fundamental pitch as the primary sound, the specific combination and intensity of these overtones—whether harmonic or nonharmonic—are what define an instrument's timbre, or tone color.13