10E: Auditory Illusions

One important auditory phenomena that cannot easily be explained by either theory of hearing is the missing fundamental or virtual pitch. Some sources refer to the effect as residue pitch. As we saw in the chapter on Fourier analysis, musical instruments have overtones which are harmonic, meaning they are multiples of the fundamental frequency. When you hear a guitar play a note with a frequency of 100 Hz there are harmonic frequencies of 200 Hz, 300 Hz, 400 Hz, etc. present in the sound. Your ear-brain system perceives this as a single note of 100 Hz instead of a collection of individual frequencies. An interesting auditory phenomena is that if you are listening to a series of frequencies of 200 Hz, 300 Hz, 400 Hz, etc. your ear-brain system will ALSO perceive a single note of 100 Hz even if the 100 Hz fundamental is missing.

Simulation Exercise: Go back to the Fourier simulation and reset it so that the fundamental frequency, f1, is 200 Hz. Push all of the sliders to the far right (amplitude of 1.00) for all of the harmonics. Listen to the sound (you may need to use external speakers or good headphones since the built-in speakers in your computer are usually not very good). Now slide the first slider, A1, to zero. You will notice a change in the timbre of the sound but the perceived pitch (the note being played) will be the same. Try sliding both the A1 and A2 amplitudes to zero, leaving the other amplitudes at 1.00. This also will be perceived as a 200 Hz note.

The missing fundamental is what makes it possible to hear music over small speakers that cannot reproduce the full range of frequencies. Small speakers often do not produce the lower base note frequencies but you still hear them because the higher harmonics are present and your ear-brain system fills in the missing fundamental. As we will see, for many musical instruments, percussion instruments in particular, the missing fundamental is the note we hear when the instrument is playing.

Experiments done with pure tones through headphones show that in fact you only need two frequencies, for example 200 Hz and 300 Hz, to perceive a missing fundamental of 100 Hz if the notes are in phase. Even stranger is the fact that you will perceive the missing fundamental when the individual harmonics are played to different ears. Somehow the brain combines signals from both ears to hear one note at a frequency that isn’t present. Any theory of how the ear works must be able explain this and other curious auditory phenomena.

The idea that certain regions of the basilar membrane respond to certain frequencies as an explanation for sound perception seems to be basically correct. The place theory, however, cannot explain the missing fundamental phenomena. If a fundamental frequency is missing it cannot cause that region of the basilar membrane to vibrate yet we perceive the frequency as being present. Somehow the harmonics add up to give us that experience. In fact, we would expect that if the harmonics were exciting different regions we might perceive separate harmonic tones instead of one single note but we don’t; nearly all listeners hear a single missing fundamental.

In support of the temporal theory, the missing fundamental shifts in a peculiar way if the harmonics shift. For example a missing fundamental of 200 Hz is heard when harmonics of 1800 Hz, 2000 Hz and 2200 Hz are played. It would be tempting to say that the difference of 200 Hz between the harmonics causes the perception of a 200 Hz signal. But if these frequencies are shifted to 1860 Hz, 2060 Hz and 2260 Hz, also a difference of 200 Hz, the ear-brain system perceives a missing fundamental of about 207 Hz. The temporal theory can explain this because the peak to peak period of the second combination of frequencies is around 4.83 ms which would be the same as a pure tone of 207 Hz. On the other hand, the temporal theory predicts a greater sensitivity to the phase of a wave than we experience (under most circumstances we are unaware of the phase of a given frequency). The place theory does not have this problem. Most likely the mechanisms for both theories combine somehow to give us our perception of musical sound.

It is possible (and there is some evidence to support the idea) that both place and temporal mechanisms work but operate in different frequency regimes. The place theory seems to be the more likely mechanism for frequencies above 5000 Hz while the temporal theory seems to be a better explanation for frequencies under 5000 Hz. Someone with perfect hearing can hear frequencies up to 20,000 Hz but our sense of pitch and ability to distinguish differences in frequency gets much weaker for frequencies above 5000 Hz as noted in Section 8c on just noticeable differences in frequency. This feature of our ear-brain system fits with a dual system of frequency detection.

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