Only a pure sinusoid comprises exactly one frequency.

Evidence

The sinusoidal wave stands alone as the only shape that can be said to comprise a single frequency. This is essentially a tautology, yet it was by no means obvious to even very gifted natural philosophers working before Fourier’s theorem became known. Any nonsinusoidal shape necessarily requires more than one term in its Fourier series. — Eric J. Heller, Why You Hear What You Hear- An…, 332

Categorization

• DEFINE: Clarifies the unique status of the sinusoid as the single-frequency shape, tying purity to the geometry of the waveform itself.