Final answer:
Periodic complex tones consist of a number of harmonics, which are multiples of the fundamental frequency. These contribute to the unique character or timbre of the tones, determined by their number and relative intensities.
Step-by-step explanation:
An important property of periodic complex tones is that they consist of a number of harmonics, which are also known as overtones. These harmonics are all multiples of a basic unit of music known as the fundamental frequency. The entirety of these frequencies, when combined, help to generate the unique character or timbre of a musical tone. The timbre is affected not just by the presence of these frequencies, but also by their relative intensities.
The idea that a periodic wave repeats the same oscillation for several cycles is associated with simple harmonic motion. Harmonics or overtones in music create the unique sound of instruments; for example, middle C played on a trumpet sounds different from the same note played on a clarinet due to the different combinations of fundamental frequencies and overtones present in the sound waves produced by each instrument.