There are two natural sources of harmonics which are small integral multiples of a single fixed underlying frequency:

- The vibrating string has integral overtones because the eigenvalues of the second spatial derivative over an interval on the real line or a square in the plane, are indeed the integers.
- Non linear oscillators.

Another independent common source of integral overtones results from from non-linear vibrations which are periodic. Fourier showed that periodic functions can be expressed as a sum of sinusoidal functions whose frequencies were integral multiples of the fundamental. The human voice is a non-linear oscillator.

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