Pitch perception

When considering perception, the frequency of a sound wave is referred to as pitch. Perceptual psychologists have studied the ability of people to detect a targeted pitch in spite of confusion from sounds consisting of other wavelengths and phases. One fundamental observation is that the auditory perception system performs critical band masking to effectively block out waves that have frequencies outside of a particular range of interest. Another well-studied problem is the perception of differences in pitch (or frequency). For example, for a pure tone at $1000$ Hz, could someone distinguish it from a tone at $1010$ Hz? This is an example of JND. It turns out that for frequencies below $1000$ Hz, humans can detect a change of frequency that is less than $1$ Hz. The discrimination ability decreases as the frequency increases. At 10,000 Hz, the JND is about $100$ Hz. In terms of percentages, this means that pitch perception is better than a $0.1$% difference at low frequencies, but increases to $1.0$% for higher frequencies.

Also regarding pitch perception, a surprising auditory illusion occurs when the fundamental frequency is removed from a complex waveform. Recall from Figure 11.3 that a square wave can be approximately represented by adding sinusoids of smaller and smaller amplitudes, but higher frequencies. It turns out that people perceive the tone of the fundamental frequency, even when it is removed, and only the higher-order harmonics remain; several theories for this are summarized in Chapter 5 of [206].