It is assumed that the solution to a problem is given in the form of a complex multiple Fourier series infinite in each of the original frequencies. In this paper a simple theorem shows that the absolute values of the individual frequency coefficients in the series are independent of the phase relation between the original frequencies. But the coefficient’s division into real and imaginary parts is phase dependent. When the ratios between the frequencies are not irrational numbers there exist in the sum several coefficients giving the same frequency, and hence, the total amplitude for a specific frequency depends on the phase. An example of application shows results from nonlinear acoustics where, e.g., the importance of original phase for parametric arrays can be estimated.