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.
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.
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]
If the original frequencies are closer than about twelve hertz, [4] then the envelope's frequency (f1 − f2/2) is too low below the typical human hearing range to be perceived as an audible tone or pitch and is instead perceived as a periodic variation in the amplitude of the carrier wave.
Because every other burst in the modulation pattern is inverted, each peak is replaced by a trough and vice versa. However, because the human ear is only sensitive to amplitude or intensity but not phase of a sound, only the magnitude of the envelope is heard. Therefore, the envelope is perceived to have twice the frequency of the modulating cosine, which means the audible beat frequency is: [5]
A binaural beat is an auditory illusion perceived when two different pure-tone sine waves, with a less-than 40 Hz or so difference between them, are presented to a listener dichotically (one through each ear).
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. [7]
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.
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.
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 radio communications, single-sideband modulation (SSB) or single-sideband suppressed-carrier modulation (SSB-SC) is a type of modulation used to transmit information, such as an audio signal, by radio waves. A refinement of amplitude modulation, it uses transmitter power and bandwidth more efficiently. Amplitude modulation produces an output signal the bandwidth of which is twice the maximum frequency of the original baseband signal. Single-sideband modulation avoids this bandwidth increase, and the power wasted on a carrier, at the cost of increased device complexity and more difficult tuning at the receiver.
In music, timbre, also known as tone color or tone quality, is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category.
Pitch is a perceptual property that allows sounds to be ordered on a frequency-related scale, or more commonly, pitch is the quality that makes it possible to judge sounds as "higher" and "lower" in the sense associated with musical melodies. Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.
The pitch being perceived with the first harmonic being absent in the waveform is called the missing fundamental phenomenon.
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.
The tritone paradox is an auditory illusion in which a sequentially played pair of Shepard tones separated by an interval of a tritone, or half octave, is heard as ascending by some people and as descending by others. Different populations tend to favor one of a limited set of different spots around the chromatic circle as central to the set of "higher" tones. Roger Shepard in 1963 had argued that such tone pairs would be heard ambiguously as either ascending or descending. However, psychology of music researcher Diana Deutsch in 1986 discovered that when the judgments of individual listeners were considered separately, their judgments depended on the positions of the tones along the chromatic circle. For example, one listener would hear the tone pair C–F♯ as ascending and the tone pair G–C♯ as descending. Yet another listener would hear the tone pair C–F♯ as descending and the tone pair G–C♯ as ascending. Furthermore, the way these tone pairs were perceived varied depending on the listener's language or dialect.
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.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
Acoustic resonance is a phenomenon in which an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration.
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.
Speech science refers to the study of production, transmission and perception of speech. Speech science involves anatomy, in particular the anatomy of the oro-facial region and neuroanatomy, physiology, and acoustics.
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 sound perception and audiology—how the human auditory system perceives various sounds. More specifically, it is the branch of science studying the psychological responses associated with sound. Psychoacoustics is an interdisciplinary field including psychology, acoustics, electronic engineering, physics, biology, physiology, and computer science.
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.
Temporal envelope (ENV) and temporal fine structure (TFS) are changes in the amplitude and frequency of sound perceived by humans over time. These temporal changes are responsible for several aspects of auditory perception, including loudness, pitch and timbre perception and spatial hearing.