# What is virtual pitch?

From what I understand, virtual pitch is a concept that is supposed to account for the "missing fundamental" phenomenon. Specifically,

A harmonic sound is said to have a missing fundamental when its overtones suggest a fundamental frequency but the sound lacks a component at the fundamental frequency itself. The brain perceives the pitch of a tone not only by its fundamental frequency, but also by the periodicity implied by the relationship between the higher harmonics. Source: https://en.m.wikipedia.org/wiki/Missing_fundamental

Can someone explain what virtual pitches are and how this explains why the missing fundamental phenomenon occurs?

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.

• "such distortion is not required" -- one way to look at it is that the distortion is occurring in our ears (music.stackexchange.com/questions/26834/…)
– Dave
Sep 10, 2015 at 18:21
• @Dave: I suspect that's the case, but lack the expertise to pass judgment on such claims. Sensory perception is weird in many ways, and many sensory processes "almost" fit certain nice easy physical models but have anomalies that suggest the processes behind them are probably quite different from what the models would suggest. Sep 10, 2015 at 18:30

When presented with a (relatively) complex pitched sound, beyond just frequency extraction, your brain does additional processing to identify harmonic patterns, i.e. sets of frequencies where all of them are integer multiples of some fundamental frequency. This is an important part of our pitch perception. Because of this complex processing there is not always an obvious relationship between the spectral content of a given sound, and the pitch that a listener assigns to it.

There are techniques to combine sounds (combination tones and others) such that listeners will assign a lower pitch to the resulting combination than either of the individual sounds; the fundamental of the pitch of the combined sound is not physically present. This "missing fundamental effect" is somewhat surprising since for most sounds, it is the frequency of the lowest harmonic that determines the perceived pitch.

"Virtual pitch" seems to be a term coined by some music theorists in their attempts to describe some features of (musical) sound perception, e.g. degree of consonance, and is consistent with the well known missing fundamental phenomenon. This theory includes the idea that the brain attempts to assign a "virtual pitch" to sounds, by looking for relationships between the spectral components. To my knowledge this term only applies to ideas that build upon those originally presented by Terhardt in the 1970's, i.e. it reflects a particular school or approach to this kind of analysis.