The Missing Fundamental Phenomenon: The Brain’s Remarkable Musical Perception

What is the Missing Fundamental Effect?

Missing Fundamental Effect

Ever manipulated an EQ, applied a high-pass filter, and noticed you can still discern the pitch even when the fundamental frequency is cut off? This is the “missing fundamental effect.” It’s a phenomenon where, even when a specific sound’s fundamental frequency is absent, our brain perceives it as if it’s genuinely present. This occurrence showcases our brain’s ability to compare past experiences with the current situation, inferring missing information, and converting it into a complete picture.

The Relationship Between Fundamental and Harmonics

Fundamental and Harmonics

Sounds or music are composed of a fundamental frequency and its corresponding harmonics. The fundamental represents the basic frequency of the sound, while harmonics are the frequency components that occur as integer multiples of this fundamental. For example, if the fundamental is 100Hz, the harmonics would appear at 200Hz, 300Hz, 400Hz, and so on.

Link to Timbre and Harmonics document

Experience and the Brain’s Sound Recognition


The Missing Fundamental Phenomenon
In the lower waveform, the fundamental at 100Hz and the second harmonic at 200Hz are missing. Yet, when compared with the full spectrum waveform on top, the periodicity is evident.

Throughout our lives, we encounter a plethora of sounds and music. These experiences store information about musical patterns, structures, and the characteristics of sounds in our brain. Therefore, when a part of a specific sound is missing, the brain compares this stored information with the currently heard sound and “infers” the missing components.

Examples of the Missing Fundamental Effect

As previously mentioned, when a piano sound composed of a 100Hz fundamental and harmonics at 200Hz, 300Hz, and 400Hz is played without the 100Hz fundamental, most listeners still recognize the pitch of the sound. This is because the brain “predicts” the existence of the fundamental, making it feel as if it’s truly present to our ears.

maxxbass

Furthermore, in the mid-1990s, Meir Shashoua, co-founder of Waves Audio, patented an algorithm to recreate the missing fundamental effect by synthesizing higher harmonics. Waves Audio later introduced the MaxxBass plugin, allowing users to apply these synthesized harmonics to their audio files. Following this, Waves Audio also developed small subwoofers designed to give an auditory perception of deep bass, based on the principle of “missing fundamental”. Both products selectively process certain harmonics, making even small speakers, which may have limitations in producing low frequencies, sound as if they are delivering deep bass. These products also include a filter that significantly attenuates the low frequencies expected to exceed the playback capabilities of the target sound system. A notable application of this technology can be found in the Grammy-awarded 2001 version of “Lady Marmalade”, sung by Christina Aguilera, Lil’ Kim, Mýa, and Pink and produced by Missy Elliott, which was processed using MaxxBass.

Given these characteristics, it’s common to see devices that cannot reproduce low frequencies utilize the missing fundamental effect to provide a more powerful bass sensation.