Beat (acoustics)

Last updated
Diagram of beat frequency Beating Frequency.svg
Diagram of beat frequency

In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies.

Contents

With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, [1] the beating starts to sound like a note, and a combination tone is produced.

Mathematics and physics of beat tones

The sum (blue) of two sine waves (red, green) is shown as one of the waves increases in frequency. The two waves are initially identical, then the frequency of the green wave is gradually increased by 25%. Constructive and destructive interference can be seen. WaveInterference.gif
The sum (blue) of two sine waves (red, green) is shown as one of the waves increases in frequency. The two waves are initially identical, then the frequency of the green wave is gradually increased by 25%. Constructive and destructive interference can be seen.

This phenomenon is best known in acoustics or music, though it can be found in any linear system:

"According to the law of superposition, two tones sounding simultaneously are superimposed in a very simple way: one adds their amplitudes". [2]

If a graph is drawn to show the function corresponding to the total sound of two strings, it can be seen that maxima and minima are no longer constant (as when a pure note is played), but change over time: when the two waves are nearly 180 degrees out of phase the maxima of one wave cancel the minima of the other, whereas when they are nearly in phase their maxima sum up, raising the perceived volume.

It can be proven (with the help of a sum-to-product trigonometric identity) that the sum of two unit-amplitude sine waves can be expressed as a carrier wave of frequency f1 + f2/2 whose amplitude is modulated by an envelope wave of frequency f1 - f2/2: [3]

Because every other burst in the modulation pattern is inverted, each peak is replaced by a trough and vice versa. The envelope is perceived to have twice the frequency of the modulating cosine, which means the audible beat frequency (if it is in the audible range) is: [4]

Monaural beats

"Monaural beats are when there is only one tone that pulses on and off in a specific pattern. With only one tone (as opposed to two tones with binaural beats), your brain has a much easier time adjusting and there is no need to balance separate tones.

Monaural beats are combined into one sound before they actually reach the human ear, as opposed to formulated in part by the brain itself, which occurs with a binaural beat.

This means that monaural beats can be used effectively via either headphones or speakers. It also means that those without two ears can listen to and receive the benefits." - Ebonie Allard [5]

A 110 Hz A sine wave (magenta; first 2 seconds), a 104 Hz G# sine wave (cyan; following 2 seconds), their sum (blue; final 2 seconds) and the corresponding envelope (red) Beat.png
A 110 Hz A sine wave (magenta; first 2 seconds), a 104 Hz G sine wave (cyan; following 2 seconds), their sum (blue; final 2 seconds) and the corresponding envelope (red)

Binaural beats

Binaural beats Binaural beats.svg
Binaural beats
To experience the binaural beats perception, it is best to listen to this file with headphones on moderate to weak volume  the sound should be easily heard, but not loud. The sound appears to pulsate only when heard through both earphones. Time duration of 10 seconds
Binaural Beats Base tone 200 Hz, beat frequency from 7 Hz to 12.9 Hz. Time duration of 9 minutes.

"Binaural beats were first discovered by physicist Heinrich Wilhelm Dove in 1839. They are an auditory illusion that is perceived when two different pure-tone sine waves, both with frequencies lower than 1500 Hz and less than a 40 Hz difference between them, are presented to a listener dichotically (one through each ear). This means that they are best listened to through headphones." - Ebonie Allard [5]

For example, if a 530 Hz pure tone is presented to a subject's right ear, while a 520 Hz pure tone is presented to the subject's left ear, the listener will hear beating at a rate of 10 Hz, just as if the two tones were presented monaurally, but the beating will have an element of lateral motion as well.

Binaural-beat perception originates in the inferior colliculus of the midbrain and the superior olivary complex of the brainstem, where auditory signals from each ear are integrated and precipitate electrical impulses along neural pathways through the reticular formation up the midbrain to the thalamus, auditory cortex, and other cortical regions. [6]

According to a 2023 systematic review, studies have investigated some of the claimed positive effects in the areas of cognitive processing, affective states (like anxiety), mood, pain perception, meditation and relaxation, mind wandering, creativity, but the techniques were not comparable and results were inconclusive. Out of fourteen studies reviewed, five reported results in line with the brainwave entrainment hypothesis, eight studies reported contradictory, and one had mixed results. The authors recommend standardization in study approaches for future studies so results may be more effectively compared. [7]

Uses

Musicians commonly use interference beats objectively to check tuning at the unison, perfect fifth, or other simple harmonic intervals. [8] Piano and organ tuners use a method involving counting beats, aiming at a particular number for a specific interval.

The composer Alvin Lucier has written many pieces that feature interference beats as their main focus. Italian composer Giacinto Scelsi, whose style is grounded on microtonal oscillations of unisons, extensively explored the textural effects of interference beats, particularly in his late works such as the violin solos Xnoybis (1964) and L'âme ailée / L'âme ouverte (1973), which feature them prominently (Scelsi treated and notated each string of the instrument as a separate part, so that his violin solos are effectively quartets of one-strings, where different strings of the violin may be simultaneously playing the same note with microtonal shifts, so that the interference patterns are generated). Composer Phill Niblock's music is entirely based on beating caused by microtonal differences. [9] Computer engineer Toso Pankovski invented a method based on auditory interference beating to screen participants in online auditory studies for headphones and dichotic context (whether the stereo channels are mixed or completely separated). [10]

Amateur radio enthusiasts use the terms "zero-beating" or "zero-beat" for precisely tuning to a desired carrier wave frequency by manually reducing the number of interference beats, [11] fundamentally the same tuning process used by musicians.

Sample

See also

Related Research Articles

<span class="mw-page-title-main">Frequency modulation</span> Encoding of information in a carrier wave by varying the instantaneous frequency of the wave

Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing.

<span class="mw-page-title-main">Wave interference</span> Phenomenon resulting from the superposition of two waves

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

In music, an octave or perfect octave is a series of eight notes occupying the interval between two notes, one having twice the frequency of vibration of the other. 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". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave have the same name and are of the same pitch class.

<span class="mw-page-title-main">Binaural recording</span> Method of recording sound

Binaural recording is a method of recording sound that uses two microphones, arranged with the intent to create a 3D stereo sound sensation for the listener of actually being in the room with the performers or instruments. This effect is often created using a technique known as dummy head recording, wherein a mannequin head is fitted with a microphone in each ear. Binaural recording is intended for replay using headphones and will not translate properly over stereo speakers. This idea of a three-dimensional or "internal" form of sound has also translated into useful advancement of technology in many things such as stethoscopes creating "in-head" acoustics and IMAX movies being able to create a three-dimensional acoustic experience.

<span class="mw-page-title-main">Head-related transfer function</span> Response that characterizes how an ear receives a sound from a point in space

A head-related transfer function (HRTF) is a response that characterizes how an ear receives a sound from a point in space. As sound strikes the listener, the size and shape of the head, ears, ear canal, density of the head, size and shape of nasal and oral cavities, all transform the sound and affect how it is perceived, boosting some frequencies and attenuating others. Generally speaking, the HRTF boosts frequencies from 2–5 kHz with a primary resonance of +17 dB at 2,700 Hz. But the response curve is more complex than a single bump, affects a broad frequency spectrum, and varies significantly from person to person.

The octave illusion is an auditory illusion discovered by Diana Deutsch in 1973. It is produced when two tones that are an octave apart are repeatedly played in alternation ("high-low-high-low") through stereo headphones. The same sequence is played to both ears simultaneously; however when the right ear receives the high tone, the left ear receives the low tone, and conversely. Instead of hearing two alternating pitches, most subjects instead hear a single tone that alternates between ears while at the same time its pitch alternates between high and low.

<span class="mw-page-title-main">Piano tuning</span> Profession

Piano tuning is the process of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the vibration interaction among notes, which is different for every piano, thus in practice requiring slightly different pitches from any theoretical standard. Pianos are usually tuned to a modified version of the system called equal temperament.

Sound localization is a listener's ability to identify the location or origin of a detected sound in direction and distance.

Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology, physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music. Examples of areas of study are the function of musical instruments, the human voice, computer analysis of melody, and in the clinical use of music in music therapy.

<span class="mw-page-title-main">Medial geniculate nucleus</span>

The medial geniculate nucleus (MGN) or medial geniculate body (MGB) is part of the auditory thalamus and represents the thalamic relay between the inferior colliculus (IC) and the auditory cortex (AC). It is made up of a number of sub-nuclei that are distinguished by their neuronal morphology and density, by their afferent and efferent connections, and by the coding properties of their neurons. It is thought that the MGN influences the direction and maintenance of attention.

<span class="mw-page-title-main">Acoustic resonance</span> Resonance phenomena in sound and musical devices

Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.

<span class="mw-page-title-main">Interaural time difference</span> Difference in time that it takes a sound to travel between two ears

The interaural time difference when concerning humans or animals, is the difference in arrival time of a sound between two ears. It is important in the localization of sounds, as it provides a cue to the direction or angle of the sound source from the head. If a signal arrives at the head from one side, the signal has further to travel to reach the far ear than the near ear. This pathlength difference results in a time difference between the sound's arrivals at the ears, which is detected and aids the process of identifying the direction of sound source.

Computational auditory scene analysis (CASA) is the study of auditory scene analysis by computational means. In essence, CASA systems are "machine listening" systems that aim to separate mixtures of sound sources in the same way that human listeners do. CASA differs from the field of blind signal separation in that it is based on the mechanisms of the human auditory system, and thus uses no more than two microphone recordings of an acoustic environment. It is related to the cocktail party problem.

Dichotic pitch is a pitch heard due to binaural processing, when the brain combines two noises presented simultaneously to the ears. In other words, it cannot be heard when the sound stimulus is presented monaurally but, when it is presented binaurally a sensation of a pitch can be heard. The binaural stimulus is presented to both ears through headphones simultaneously, and is the same in several respects except for a narrow frequency band that is manipulated. The most common variation is the Huggins Pitch, which presents white-noise that only differ in the interaural phase relation over a narrow range of frequencies. For humans, this phenomenon is restricted to fundamental frequencies lower than 330 Hz and extremely low sound pressure levels. Experts investigate the effects of the dichotic pitch on the brain. For instance, there are studies that suggested it evokes activation at the lateral end of Heschl's gyrus.

<span class="mw-page-title-main">Sound</span> Vibration that travels via pressure waves in matter

In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of 17 meters (56 ft) to 1.7 centimeters (0.67 in). Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges.

Psychoacoustics is the branch of psychophysics involving the scientific study of the perception of sound by the human auditory system. It is the branch of science studying the psychological responses associated with sound including noise, speech, and music. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.

Amblyaudia is a term coined by Dr. Deborah Moncrieff to characterize a specific pattern of performance from dichotic listening tests. Dichotic listening tests are widely used to assess individuals for binaural integration, a type of auditory processing skill. During the tests, individuals are asked to identify different words presented simultaneously to the two ears. Normal listeners can identify the words fairly well and show a small difference between the two ears with one ear slightly dominant over the other. For the majority of listeners, this small difference is referred to as a "right-ear advantage" because their right ear performs slightly better than their left ear. But some normal individuals produce a "left-ear advantage" during dichotic tests and others perform at equal levels in the two ears. Amblyaudia is diagnosed when the scores from the two ears are significantly different with the individual's dominant ear score much higher than the score in the non-dominant ear Researchers interested in understanding the neurophysiological underpinnings of amblyaudia consider it to be a brain based hearing disorder that may be inherited or that may result from auditory deprivation during critical periods of brain development. Individuals with amblyaudia have normal hearing sensitivity but have difficulty hearing in noisy environments like restaurants or classrooms. Even in quiet environments, individuals with amblyaudia may fail to understand what they are hearing, especially if the information is new or complicated. Amblyaudia can be conceptualized as the auditory analog of the better known central visual disorder amblyopia. The term “lazy ear” has been used to describe amblyaudia although it is currently not known whether it stems from deficits in the auditory periphery or from other parts of the auditory system in the brain, or both. A characteristic of amblyaudia is suppression of activity in the non-dominant auditory pathway by activity in the dominant pathway which may be genetically determined and which could also be exacerbated by conditions throughout early development.

Perceptual-based 3D sound localization is the application of knowledge of the human auditory system to develop 3D sound localization technology.

Virtual hammock describes the effect of using structured sound from two isolated, stationary speakers playing into opposite ears to induce the perception of being in the presence of a single sound source which is moving back-and-forth. Rather than relying solely on a variation in sound amplitude of one speaker compared to the other, the Virtual Hammock effect utilizes a shift in phase of the sound wave of one side compared with the other. This stimulates the same physiological response in the Medial Superior Olive (MSO) portion of the brain stem—the first processing stop for auditory nerves—as is induced by an actual moving sound source. Any waveform within certain frequency bounds can be used to achieve this effect. The specific case of playing sinusoidal waves of different frequencies, which creates a continuously varying sensation of the sound source moving from side-to-side, is referred to as a binaural beat. Similarly, playing square waves of two different frequencies will create a sensation of swaying back and forth.

Binaural unmasking is phenomenon of auditory perception discovered by Ira Hirsh. In binaural unmasking, the brain combines information from the two ears in order to improve signal detection and identification in noise. The phenomenon is most commonly observed when there is a difference between the interaural phase of the signal and the interaural phase of the noise. When such a difference is present there is an improvement in masking threshold compared to a reference situation in which the interaural phases are the same, or when the stimulus has been presented monaurally. Those two cases usually give very similar thresholds. The size of the improvement is known as the "binaural masking level difference" (BMLD), or simply as the "masking level difference".

References

  1. Levitin, Daniel J. (2006). This is Your Brain on Music: The Science of a Human Obsession. Dutton. p. 22. ISBN   978-0525949695.
  2. Winckel, Fritz (1967). Music, Sound and Sensation: A Modern Exposition, p. 134. Courier. ISBN   978-0486165820.
  3. "Interference beats and Tartini tones", Physclips, UNSW.edu.au.
  4. Roberts, Gareth E. (2016). From Music to Mathematics: Exploring the Connections, p. 112. JHU. ISBN   978-1421419190.
  5. 1 2 Allard, Ebonie (Jan 15, 2024). "Binaural beats, where science meets spirituality?".
  6. Oster, G (October 1973). "Auditory beats in the brain". Scientific American. 229 (4): 94–102. Bibcode:1973SciAm.229d..94O. doi:10.1038/scientificamerican1073-94. PMID   4727697.
  7. Ingendoh, R. M.; Posny, E. S.; Heine, A. (2023). "Binaural beats to entrain the brain? A systematic review of the effects of binaural beat stimulation on brain oscillatory activity, and the implications for psychological research and intervention". PLOS ONE. 18 (5): e0286023. Bibcode:2023PLoSO..1886023I. doi: 10.1371/journal.pone.0286023 . PMC   10198548 . PMID   37205669.
  8. Campbell, Murray; Greated, Clive A.; and Myers, Arnold (2004). Musical Instruments: History, Technology, and Performance of Instruments of Western Music, p. 26. Oxford. ISBN   978-0198165040. "Listening for beats can be a useful method of tuning a unison, for example between two strings on a lute,..."
  9. "Identity through instability" (PDF). 2012-12-13.
  10. "Screening For Dichotic Acoustic Context And Headphones In Online Crowdsourced Hearing Studies". Canadian Acoustics. 49 (2). 2021-07-07. Retrieved 2021-07-07.
  11. WØSTU, Stu (2022-01-15). "Zero Beat (G2C06)". hamradioschool. Retrieved 2024-04-28.

Further reading