Waveforms become non-periodic because higher normal-mode frequencies are not equally spaced

Evidence

If you create waveforms using only the lower frequency amplitudes, leaving the higher frequency modes undisturbed, the wave will be approximately periodic. This is a direct result of the excited frequencies being nearly equally spaced. If, however, you use higher frequencies in making your waveforms, the resulting shape is not nearly periodic. The reason for this is the unequal spacing of the higher frequencies, which have been excited if you choose them among the amplitudes, or if you pluck only a single bead, which does the same thing. — Eric J. Heller, Why You Hear What You Hear- An…, 851

Categorization

• DEFINE: Explains why equal frequency spacing produces periodic waveforms while unequal spacing destroys periodicity.
• XREF: Connects to why plucking a single point on a string excites a rich non-harmonic spectrum — relevant to timbre and inharmonicity in piano/bell physics.