Aperiodic sounds emerge when continuous in-between frequencies cancel periodic repeats

Evidence

However, some instruments, especially percussion, do not have pitch and hence are nonperiodic, or aperiodic. How can we analyze these instruments in terms of a basic waveform, such as a sine wave, which is inherently periodic? The answer is shown in Figure 1.53. Here the square wave example discussed earlier has had four more sine waves added to it. However, these sine waves are between the harmonics of the square wave and so are unrelated to the period, but they do start off in phase with the harmonics. The effect of these other components is to start canceling out the repeat periods of the square waves, because they are not related in frequency to them. By adding more components, which sit in between the harmonics, this cancellation of the repeats becomes more effective so that when in the limit, the whole space between the harmonics is filled with sine wave components of the appropriate amplitude and phase. These extra components will add constructively only at the beginning of the waveform and will interfere with successive cycles due to their different frequencies. Therefore, in this case, only one square wave will exist. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 459

Categorization

• DEFINE: Explains the mechanism by which aperiodic waveforms are built from periodic sine components, connecting Fourier analysis to unpitched percussion sounds.
• XREF: connects to: Noise-like sounds have non-repeating waveforms and continuous, inharmonic spectra — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822