When a person hears a combination of sounds which are at many precise or nearly-precise multiples of a common frequency, and are not common multiples of a higher frequency, the person will often perceive a at that common frequency, whose timbre will be influenced by the combination of frequencies above it. This effect can be experienced even if the amplitude of sound at the common frequency itself is zero.
Note that it is possible to perceive multiple simultaneous distinct tones which
are multiples of a common frequency if the individual tones themselves have a
distinct harmonic signature. For example, if one hears the following
combination of frequencies (amplitudes expressed linearly)
Freq 1000 2000 3000 4000 5000 6000 7000 8000 9000 10k
1.0 1.5 0.33 0.75 0.20 0.50 0.14 0.38 0.11 0.30
one would likely perceive a combination of harmonically-rich sounds at 1000Hz and 2000Hz. Although all the frequencies are multiples of 1,000Hz, those which
are also multiples of 2,000Hz would be much louder. If instead one had heard
the following combination of frequencies:
Freq 1000 2000 3000 4000 5000 6000 7000 8000 9000 10k
0.0 0.5 0.33 0.25 0.20 0.17 0.14 0.12 0.11 0.10
one would perceive a single harmonically rich sound at 1,000Hz even though there is no frequency content there, because there is no other higher frequency whose multiples are more dominant than the other multiples of 1,000Hz.
In cases where sounds are subjected to harmonic distortion, the process will add spectral content at frequencies which are sums and differences of multiples of the original frequencies. If the 1000Hz example above were distorted, for example, because all multiples of the original frequencies are also multiples of 1,000Hz, the process would generate spectral content at 1,000Hz. Power chords on a guitar use this principle, since the three strings have pitches in a 2:3:4 ratio, thus generating a fundamental an octave below the lowest string. Although virtual pitch is enhanced by electronic distortion, such distortion is not required. Some pipe organs have 2 2/3' and 1 3/5' stops whose pipes are one third and one fifth the length of the principle 8' stop; some add a 1 1/7' stop which is one seventh the length. If one starts playing a melody line using those stops in combination with the 8' stop, and then turns off the 8' stop, the melody may be perceived as continuing at its original pitch even without any frequency content there. On some organs, especially those with the 1 1/7' stop, it's possible to hear the appropriate pitch without having to be led to it, but with just the 2 2/3' and 1 3/5' stops the effect doesn't work as well.
