What is the phantom fundamental?


Illustration: Filip Fröhlich

Also known as the ‘missing fundamental’ or ‘virtual pitch,’ the phantom fundamental is a spooky audio illusion that has us hearing pitches that may not actually exist!

That’s right—it’s possible for us to perceive a certain musical pitch, even if that fundamental frequency isn’t actually being played through a speaker or instrument. The secret lies in making sure that we’re hearing the harmonics (the higher multiples of that frequency) all at the same time. Today, let’s dive deeper into the phantom fundamental and explore some common examples of the phenomenon that you may have unknowingly experienced yourself.

Spooky sounds that aren’t there

So how is it possible that we can hear something without it actually being there? Sound physics and psychoacoustics help us understand how complex sounds are constructed, how they travel, and how our bodies interpret them. For example, a musical instrument like a piano can play a note with a fundamental frequency or pitch of 100 Hz, but you actually get much more than that in the form of harmonic frequencies or overtones at regular multiples of that frequency (like 200 Hz, 300 Hz, and so on). Since our ears and brain receive all of these frequencies at the same time and make those harmonic connections, we hear it all as one single pitch instead of a bunch of different parts. Where things start to get spooky is that if we heard those same harmonic frequencies, but without the fundamental base note at 100 Hz, our brains will still perceive it as that note!

It seems hard to believe, right? Below is an example of a single sine wave, with different harmonic frequencies subsequently added or taken away. The first few seconds contain the fundamental frequency at 100 Hz, but it’s missing after that. Despite that, did your perception of the note or pitch actually change? While the timbre or texture of the sound itself shifts around, the pitch we perceive doesn’t change, even when the fundamental (100 Hz) is completely removed.

It’s all around us

Though it may remain unclear exactly how our ears and brain are being fooled here, the phantom fundamental suggests that the upper harmonics are just as important (if not more important) than the fundamental itself when it comes to our perception of pitch. It’s really the relationship between these related harmonics that gives our ears and brain the information they need to reproduce the underlying note. What’s more, it also enhances our experience of quite a few things in the sonic space—below are just a few examples:

  • Smaller speakers aren’t able to directly reproduce low frequencies beyond a certain threshold, but you still get a sense of those low bass pitches because of the harmonics that are being played.
  • Many telephone speakers can’t go below 300 Hz, but this phenomenon helps retain the character and pitch of even deeper male voices, which commonly have fundamentals that fall between 80 and 250 Hz.
  • While some percussion instruments like timpani don’t create perfect harmonic overtones, they’re often tuned in order to suggest a lower fundamental note than the frequencies they’re mostly generating.
  • The small wooden bodies of violas and violins aren’t able to resonate at the fundamental frequency for notes on their lowest strings, but the phantom fundamental helps make up the difference.

In other words, while this perplexing phenomenon is happening all over the place, it’s really nothing to be worried about. Have you cracked the secret of the phantom fundamental? Let us know in the comments!

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October 31, 2021

Matteo Malinverno Matteo Malinverno is a New York-based music producer currently working on the Content team at Splice.