Superposed sinusoids with incommensurate frequencies yield nonperiodic motion

Evidence

The idea of combining purely sinusoidal modes to make complex nonsinusoidal and even nonperiodic motion is a crucial one, a key to the vibration of real objects under real circumstances. The resulting combined motion is not usually periodic, even though the component modes are, and is a sum of sinusoids whose frequencies are normally not commensurate (do not bear a simple integer or rational ratio to each other). — Eric J. Heller, Why You Hear What You Hear- An…, 797

Categorization

• DEFINE: Defines commensurate frequencies and why real combined motion is usually nonperiodic.
• XREF: This underlies why plucked strings sound timbrally varied; a real-world link to why an oboe sounds different from a flute playing the same note.