Missing fundamental
Encyclopedia
A sound is said to have a missing fundamental, suppressed fundamental, or phantom fundamental when its overtone
s suggest a fundamental frequency but the sound lacks a component at the fundamental frequency
itself.
However, the brain perceives the pitch of a tone not only by its fundamental frequency, but also by the ratio of the higher harmonic
s. Thus, we may perceive the same pitch (perhaps with a different timbre
) even if the fundamental frequency is missing from a tone.
For example, when a note (that is not a pure tone
) has a pitch
of 100 Hz
, it will consist of frequency components that are integer multiples of that value (e.g. 100, 200, 300, 400, 500.... Hz). However, smaller loudspeakers may not produce low frequencies, and so in our example, the 100 Hz component may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard.
It was once thought that this effect was because the missing fundamental was replaced by distortions introduced by the physics of the ear. 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. It is now widely accepted that the brain processes the information present in the overtones to calculate the fundamental frequency. The precise way in which it does so is still a matter of debate, but the processing seems to be based on an autocorrelation
involving the timing of neural impulses in the auditory nerve.
This very concept of "missing fundamental" being reproduced based on the overtones in the tone has been used to create the illusion of bass in sound systems that are not capable of such bass. In mid-1999, Meir Shashoua of Tel Aviv
, working for Waves Audio
, patented an algorithm to create the sense of the missing fundamental by synthesizing higher harmonics. Waves Audio released the MaxxBass plug-in to allow computer users to apply the synthesized harmonics to their audio files. Later, Waves Audio produced small subwoofer
s that relied on the missing fundamental concept to give the illusion of low bass. Both products processed certain overtones selectively to help small loudspeakers, ones which could not reproduce low-frequency components, to sound as if they were capable of low bass. 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. 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
.
Other software and hardware companies have developed their own versions of missing fundamental-based bass augmentation products. The poor bass reproduction of earbuds has been identified as a possible target for such processing. Many computer sound systems are not capable of low bass, and songs offered to consumers via computer have been identified as ones that may benefit from augmented bass harmonics processing.
Timpani
(kettle drums) are tuned by listening for the missing fundamental. Hit in the usual way (half to three-quarters the distance from the center to the rim), the fundamental note of a timpano is very weak in relation to its second through fifth harmonics. A timpano tuned to 100 Hz will produce sound most strongly at 200, 300, 400 and 500 Hz.
A violin
's lowest air and body resonances generally fall between 250 Hz and 300 Hz. The fundamental frequency of the open G3
string is below 200 Hz in modern tunings as well as most historical tunings, so the lowest notes of a violin have an attenuated fundamental, although listeners seldom notice this.
Most common telephones cannot reproduce sounds lower than 300 Hz, but a male voice has a fundamental frequency approximately 150 Hz. Because of the missing fundamental effect, male voices still sound male over the telephone.
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. 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. Musical signal content above the high-pass part of the crossover filter is sent to the main output which is amplified by the sound system. Low frequency content below the low-pass part of the crossover filter is sent to a circuit where harmonics are synthesized above the low notes. The newly created harmonics are mixed back into the main output to create a perception of the filtered-out low notes. Using a device with this synthetic process can reduce complaints from low frequency noise carrying through walls and it can be employed to reduce low frequency content in loud music that might otherwise vibrate and damage breakable valuables.
A pipe organ sometimes makes use of this phenomenon as a resultant tone.
magazine AUDIO, indicates that the general population can be divided into those who perceive missing fundamentals, and those who primarily hear overtone
s. The magazine article states that the difference between the perceived pitches can be up to 4 octave
s.
Overtone
An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...
s suggest a fundamental frequency but the sound lacks a component at the fundamental frequency
Fundamental frequency
The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids The fundamental frequency, often referred to simply as the fundamental and abbreviated f0, is defined as the...
itself.
However, the brain perceives the pitch of a tone not only by its fundamental frequency, but also by the ratio of the higher harmonic
Harmonic
A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
s. Thus, we may perceive the same pitch (perhaps with a different timbre
Timbre
In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. The physical characteristics of sound that determine the...
) even if the fundamental frequency is missing from a tone.
For example, when a note (that is not a pure tone
Pure tone
A pure tone is a tone with a sinusoidal waveshape.A sine wave is characterized by its frequency, the number of cycles per second—or its wavelength, the distance the waveform travels through its medium within a period—and the amplitude, the size of each cycle...
) has a pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
of 100 Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
, it will consist of frequency components that are integer multiples of that value (e.g. 100, 200, 300, 400, 500.... Hz). However, smaller loudspeakers may not produce low frequencies, and so in our example, the 100 Hz component may be missing. Nevertheless, a pitch corresponding to the fundamental may still be heard.
Explanation
A low pitch (also known as the pitch of the missing fundamental or virtual pitch) can sometimes be heard when there is no apparent source or component of that frequency. This perception is due to the brain interpreting repetition patterns that are present.It was once thought that this effect was because the missing fundamental was replaced by distortions introduced by the physics of the ear. 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
J. C. R. Licklider
Joseph Carl Robnett Licklider , known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history...
in 1954. It is now widely accepted that the brain processes the information present in the overtones to calculate the fundamental frequency. The precise way in which it does so is still a matter of debate, but the processing seems to be based on an autocorrelation
Autocorrelation
Autocorrelation is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them...
involving the timing of neural impulses in the auditory nerve.
This very concept of "missing fundamental" being reproduced based on the overtones in the tone has been used to create the illusion of bass in sound systems that are not capable of such bass. In mid-1999, Meir Shashoua of Tel Aviv
Tel Aviv
Tel Aviv , officially Tel Aviv-Yafo , is the second most populous city in Israel, with a population of 404,400 on a land area of . The city is located on the Israeli Mediterranean coastline in west-central Israel. It is the largest and most populous city in the metropolitan area of Gush Dan, with...
, working for Waves Audio
Waves Audio
Waves Audio Ltd. is a developer and supplier of professional audio signal processing technologies and audio effects, used in recording, mixing, mastering, post production, surround, live, and broadcast sound...
, patented an algorithm to create the sense of the missing fundamental by synthesizing higher harmonics. Waves Audio released the MaxxBass plug-in to allow computer users to apply the synthesized harmonics to their audio files. Later, Waves Audio produced small subwoofer
Subwoofer
A subwoofer is a woofer, or a complete loudspeaker, which is dedicated to the reproduction of low-pitched audio frequencies known as the "bass". The typical frequency range for a subwoofer is about 20–200 Hz for consumer products, below 100 Hz for professional live sound, and below...
s that relied on the missing fundamental concept to give the illusion of low bass. Both products processed certain overtones selectively to help small loudspeakers, ones which could not reproduce low-frequency components, to sound as if they were capable of low bass. Both products included a high-pass filter
High-pass filter
A high-pass filter is a device that passes high frequencies and attenuates frequencies lower than its cutoff frequency. A high-pass filter is usually modeled as a linear time-invariant system...
which greatly attenuated all the low frequency tones that were expected to be beyond the capabilities of the target sound system. One example of a popular song that was recorded with MaxxBass processing is "Lady Marmalade
Lady Marmalade
"Lady Marmalade" was also covered by Italian pop star Sabrina. It was released in 1987 as the album's second single by Baby Records. In some countries, including France and the Netherlands, the song was known as "Voulez-vous coucher avec moi? " and was released in 1988.-Track listings:7" maxi#...
", the 2001 Grammy award-winning version sung by Christina Aguilera
Christina Aguilera
Christina María Aguilera is an American recording artist and actress. Aguilera first appeared on national television in 1990 as a contestant on the Star Search program, and went on to star in Disney Channel's television series The Mickey Mouse Club from 1993–1994...
, Lil' Kim
Lil' Kim
Kimberly Denise Jones , better known by her stage name Lil' Kim, is an American rapper and actress who was a member of the group Junior M.A.F.I.A.....
, Mýa
Mya
-A person:* Bo Mya , Chief Commander of the Karen National Union* Mýa , American R&B singer-songwriter and actress** Mýa , a 1998 album by Mýa-A code:* Burmese language, ISO 639-3 code is mya* Moruya Airport's IATA code...
, and Pink
Pink (singer)
Alecia Beth Moore , better known by her stage name Pink , is an American singer-songwriter, musician and actress....
, produced by Missy Elliott
Missy Elliott
Melissa Arnette "Missy" Elliott , is an American rapper, singer-songwriter, record producer, and actressA five-time Grammy Award winner, Elliott, with record sales of over seven million in the United States, is the only female rapper to have five albums certified platinum by the RIAA, including one...
.
Other software and hardware companies have developed their own versions of missing fundamental-based bass augmentation products. The poor bass reproduction of earbuds has been identified as a possible target for such processing. Many computer sound systems are not capable of low bass, and songs offered to consumers via computer have been identified as ones that may benefit from augmented bass harmonics processing.
Examples
On-line sound examples comparing pure and complex tones and complexes with missing fundamentals can be found here.Timpani
Timpani
Timpani, or kettledrums, are musical instruments in the percussion family. A type of drum, they consist of a skin called a head stretched over a large bowl traditionally made of copper. They are played by striking the head with a specialized drum stick called a timpani stick or timpani mallet...
(kettle drums) are tuned by listening for the missing fundamental. Hit in the usual way (half to three-quarters the distance from the center to the rim), the fundamental note of a timpano is very weak in relation to its second through fifth harmonics. A timpano tuned to 100 Hz will produce sound most strongly at 200, 300, 400 and 500 Hz.
A violin
Violin
The violin is a string instrument, usually with four strings tuned in perfect fifths. It is the smallest, highest-pitched member of the violin family of string instruments, which includes the viola and cello....
's lowest air and body resonances generally fall between 250 Hz and 300 Hz. The fundamental frequency of the open G3
Scientific pitch notation
Scientific pitch notation is one of several methods that name the notes of the standard Western chromatic scale by combining a letter-name, accidentals, and a number identifying the pitch's octave...
string is below 200 Hz in modern tunings as well as most historical tunings, so the lowest notes of a violin have an attenuated fundamental, although listeners seldom notice this.
Most common telephones cannot reproduce sounds lower than 300 Hz, but a male voice has a fundamental frequency approximately 150 Hz. Because of the missing fundamental effect, male voices still sound male over the telephone.
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. In a hardware effects unit
Effects unit
Effects units are electronic devices that alter how a musical instrument or other audio source sounds. Some effects subtly "color" a sound, while others transform it dramatically. Effects are used during live performances or in the studio, typically with electric guitar, keyboard and bass...
or a software plugin, a crossover filter
Audio crossover
Audio crossovers are a class of electronic filter used in audio applications. Most individual loudspeaker drivers are incapable of covering the entire audio spectrum from low frequencies to high frequencies with acceptable relative volume and lack of distortion so most hi-fi speaker systems use a...
is set at a low frequency above which the sound system is capable of safely reproducing tones. Musical signal content above the high-pass part of the crossover filter is sent to the main output which is amplified by the sound system. Low frequency content below the low-pass part of the crossover filter is sent to a circuit where harmonics are synthesized above the low notes. The newly created harmonics are mixed back into the main output to create a perception of the filtered-out low notes. Using a device with this synthetic process can reduce complaints from low frequency noise carrying through walls and it can be employed to reduce low frequency content in loud music that might otherwise vibrate and damage breakable valuables.
A pipe organ sometimes makes use of this phenomenon as a resultant tone.
Differences in perception
Research conducted at Heidelberg University, as described in the January 2006 issue of the German audiophileAudiophile
An audiophile is a person who enjoys listening to recorded music, usually in a home. Some audiophiles are more interested in collecting and listening to music, while others are more interested in collecting and listening to audio components, whose "sound quality" they consider as important as the...
magazine AUDIO, indicates that the general population can be divided into those who perceive missing fundamentals, and those who primarily hear overtone
Overtone
An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the...
s. The magazine article states that the difference between the perceived pitches can be up to 4 octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
s.
External links
- Pitch Paradoxical
- Structural and functional asymmetry of lateral Heschl's gyrus reflects pitch perception preference - abstract of the Heidelberg research, as published in Nature Neuroscience 8, 1241–1247 (2005); downloading the full article requires payment
- How do you hear tones? - discussion forum thread about the Heidelberg research, with a link to a sound file used in the research so that readers can determine whether they are fundamental or overtone hearers