Missing fundamental

However, experiments subsequently showed that when a noise was added that would have masked these distortions had they been present, listeners still heard a pitch corresponding to the missing fundamental, as reported by J. C. R. Licklider in 1954.

Research conducted at Heidelberg University shows that, under narrow stimulus conditions with a small number of harmonics, the general population can be divided into those who perceive missing fundamentals, and those who primarily hear the overtones instead.

In Parsing the Spectral Envelope: Toward a General Theory of Vocal Tone Color (2016) by Ian Howell, He wrote that although not everyone can hear the missing fundamentals, noticing them can be taught and learned.

Hit in the usual way (half to three-quarters the distance from the center to the rim), the fundamental note of a timpani is very weak in relation to its second through fifth "harmonic" overtones.

The missing fundamental phenomenon is used electronically by some pro audio manufacturers to allow sound systems to seem to produce notes that are lower in pitch than they are capable of reproducing.

[21] In a hardware effects unit or a software plugin, a crossover filter is set at a low frequency above which the sound system is capable of safely reproducing tones.

In mid-1999, Meir Shashoua of Tel Aviv, co-founder of Waves Audio, patented an algorithm to create the sense of the missing fundamental by synthesizing higher harmonics.

Both products included a high-pass filter which greatly attenuated all the low frequency tones that were expected to be beyond the capabilities of the target sound system.

[26] One example of a popular song that was recorded with MaxxBass processing is "Lady Marmalade", the 2001 Grammy award-winning version sung by Christina Aguilera, Lil' Kim, Mýa, and Pink, produced by Missy Elliott.

The bottom waveform is missing the fundamental frequency, 100 hertz , and the second harmonic, 200 hertz. The periodicity is nevertheless clear when compared to the full-spectrum waveform on top.
The GCD of the frequency of all harmonics is the fundamental (dashed).
Timpani bodies modify modes of vibration to match harmonics. [ 18 ] Red: Harmonics of perceived pitch. Dark blue: Prominent modes of vibration. Play C0 harp-timpano-harp