Play three pure tones together: 220, 330 and 440 hertz. Ask a friend to hum the note they hear and they will often hum something lower: 110 hertz, a pitch that is not in the sound at all. Your ears were given no energy at 110 Hz. Your brain supplied it anyway.
A guitar string, a voice or a clarinet does not vibrate at one frequency. It vibrates at a base frequency, the fundamental, and at whole-number multiples of it called harmonics: two times, three times, four times, and so on. A note at 110 Hz carries energy at 110, 220, 330, 440, 550 Hz and up. How strong each harmonic is gives the instrument its character, its timbre. The fundamental usually decides the pitch you name.
So you would expect that deleting the fundamental should make the note jump up, or vanish. It does neither. The pitch stays put and only the colour of the sound changes, thinner and a little buzzier.
Below is a tone built on 110 Hz. Each button is one harmonic; tap to switch it on or off. The wave shows what the sum of the switched-on harmonics looks like over about 27 milliseconds. Switch off the 1st harmonic and watch the shape: the pattern keeps repeating at exactly the same rate.
Sound is optional and starts quietly. Turn your volume down first, and try it on small phone speakers too: they cannot make 110 Hz anyway.
Try “Only 2, 4, 6”. These are 220, 440 and 660 Hz, and now the repeat rate really does double to 220 Hz: the pitch jumps up an octave. Then try “Only 3, 4, 5” (330, 440, 550 Hz). The three frequencies are all multiples of 110 Hz and share no bigger common factor, so the wave still repeats 110 times a second, and a 110 Hz pitch is what most listeners report.
Look at the wave rather than the list of frequencies. When harmonics 2, 3 and 4 are added, their peaks line up once every 1/110 of a second, about 9.1 milliseconds, and in between they drift in and out of step. The overall shape therefore repeats at 110 Hz even though no single ingredient oscillates that slowly. The repeat rate of a sound of this kind is the largest frequency that divides evenly into every component: the greatest common divisor. For 220, 330 and 440 that is 110.
Your auditory system seems to read this repetition directly. Sound is turned into trains of nerve impulses, and the timing of those impulses carries the period of the wave. Exactly how the brain does the arithmetic is still debated, and no single model explains every case. What is well established is the behaviour: you hear a pitch that matches the repeat rate of the waveform, whether or not that frequency is physically present.
An early idea was that the ear itself distorts loud tones and creates a real 110 Hz component inside the cochlea. In 1954 J. C. R. Licklider tested this by adding masking noise that would have covered any such distortion product, and listeners still heard the missing pitch. The effect is built by the brain, not an artefact of the ear. It also has limits: with only a few harmonics, listeners differ, and some people lean toward hearing the individual overtones instead of the combined pitch.
Ordinary telephones do not carry frequencies below about 300 Hz. A man's speaking voice has a fundamental typically somewhere around 100 to 150 Hz, so that bottom note is never transmitted, yet the voice on the line still sounds like the same low voice at the same pitch. Your brain rebuilds it from the harmonics that did make it through.
Small laptop and phone speakers cannot produce deep bass either, but you can still follow a bass line, because the harmonics are there and the brain fills in the rest. Audio engineers even add harmonics to bass notes on purpose so that a low note feels present on tiny speakers.
Organ builders have used a related trick for centuries. A real 32-foot pipe is enormous and costly, so a builder may sound a 16-foot pipe together with a 10⅔-foot pipe, a perfect fifth higher. Played together, the pair can suggest a note an octave below the lower pipe: the C and G at about 65 and 98 Hz hint at a C near 33 Hz. It works only for the lowest few notes, and organ experts note that what the ear is following is a slow throbbing in the combined sound rather than a real difference tone travelling through the air. Higher up, you just hear two separate pipes.
Pitch is not a measurement of which frequency is loudest or even present. It is your brain's best guess about the rhythm of a repeating wave. Delete the lowest harmonic and the rhythm survives, so the note does too.