How do the number and strength of overtones affect timbre?

In the context of musical sound, timbre—often described as tone color—is primarily determined by the specific combination of overtones (or harmonics) present in a sound and their relative intensities.12

While a fundamental tone establishes the perceived pitch, the number and strength of the accompanying overtones define the unique quality of that sound. The relationship works as follows:13

• Presence and Number: A sound’s richness is largely dictated by which overtones are present. For instance, instruments like the violin are rich in overtones, whereas a flute or a tuning fork may produce a sound approaching a pure tone with very few overtones.12
• Relative Intensity: The "color" of a sound changes based on which overtones are emphasized. For example, the "woody" quality of a clarinet results from an emphasis on low-frequency odd harmonics, while the nasal quality of an oboe is created by the presence of all harmonics with a stronger emphasis on higher frequencies.3
• Wave Form: These factors combine to create a complex wave form. By varying the number and amplitude of these overtones, the resulting timbre can be drastically altered, allowing the ear to distinguish between different instruments even when they play the same pitch.12