Physics of music
Information about Physics of music
Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music — how sounds employed as music work. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody.
When the original sound sources are perfectly periodic, the note consists of several related sine waves (which mathematically add to each other) called the fundamental and the harmonics, partials, or overtones. The sounds have harmonic frequency spectra. The lowest frequency present is the fundamental, and is the frequency at which the entire wave vibrates. The overtones vibrate faster than the fundamental, but must vibrate at integer multiples of the fundamental frequency in order for the total wave to be exactly the same each cycle. Real instruments are close to periodic, but the frequencies of the overtones are slightly imperfect, so the shape of the wave changes slightly over time.
Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
The fundamental frequency is considered the first harmonic and the first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear above the fundamental. So strictly speaking, the first overtone is the second partial (and usually the second harmonic). As this can result in confusion, only harmonics are usually referred to by their numbers, and overtones and partials are described by their relationships to those harmonics.
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.
The opposite is also true. A system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, at least one even harmonic will be produced (and probably also odd).
Additionally, the two notes will have many of the same partials. For instance, a note with a fundamental frequency of 200 Hz will have harmonics at:
A note with fundamental frequency of 300 Hz will have harmonics at:
The two notes have the harmonics 600 and 1200 in common, and more will coincide further up the series.
The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of harmony.
When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone. This is called beating, and is considered to be unpleasant, or dissonant.
The frequency of beating is calculated as the difference between the frequencies of the two notes. For the example above, |200 Hz - 300 Hz| = 100 Hz. As another example, a combination of 3425 Hz and 3426 Hz would beat once per second (|3425 Hz - 3426 Hz| = 1 Hz). This follows from modulation theory.
The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval to be dissonant. Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz. [1]
The following table shows the ratios between the frequencies of all the notes of the just major scale and the fixed frequency of the first note of the scale.
There are other scales available through just intonation, like for instance the minor scale. Scales which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as temperaments, of which equal temperament is the most used. Temperaments, though they obscure the acoustical purity of just intervals often have other desirable properties, such as a closed circle of fifths.
An overtone is a natural resonance or vibration frequency of a system.
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Methods and fields of study
- Frequency analysis
- Computer analysis of musical structure
- Synthesis of musical sounds
- Music cognition, based on physics (also known as psychoacoustics)
Physical aspects
Whenever two different pitches are played at the same time, their sound waves interact with each other — the highs and lows in the air pressure reinforce each other to produce a different sound wave. As a result, any given sound wave which is more complicated than a sine wave can be modelled by many different sine waves of the appropriate frequencies and amplitudes (a frequency spectrum). In humans the hearing apparatus (composed of the ears and brain) can usually isolate these tones and hear them distinctly. When two or more tones are played at once, a variation of air pressure at the ear "contains" the pitches of each, and the ear and/or brain isolate and decode them into distinct tones.When the original sound sources are perfectly periodic, the note consists of several related sine waves (which mathematically add to each other) called the fundamental and the harmonics, partials, or overtones. The sounds have harmonic frequency spectra. The lowest frequency present is the fundamental, and is the frequency at which the entire wave vibrates. The overtones vibrate faster than the fundamental, but must vibrate at integer multiples of the fundamental frequency in order for the total wave to be exactly the same each cycle. Real instruments are close to periodic, but the frequencies of the overtones are slightly imperfect, so the shape of the wave changes slightly over time.
Subjective aspects
Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called "sound". Most sound that people recognize as "musical" is dominated by periodic or regular vibrations rather than non-periodic ones (called a definite pitch), and we refer to the transmission mechanism as a "sound wave". In a very simple case, the sound of a sine wave, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very "pure" tone. Pure tones can be produced by tuning forks or whistling. The rate at which the air pressure varies governs is the frequency of the tone, which is measured in oscillations per second, called hertz. Frequency is a primary determinate of the perceived pitch.)
A spectrogram of violin playing. The bright lines along the bottom are the fundamentals of each note, and the other bright lines are (nearly) harmonic overtones; collectively, they are spectra.
Harmonics, partials, and overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials.Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
The fundamental frequency is considered the first harmonic and the first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear above the fundamental. So strictly speaking, the first overtone is the second partial (and usually the second harmonic). As this can result in confusion, only harmonics are usually referred to by their numbers, and overtones and partials are described by their relationships to those harmonics.
Harmonics and non-linearities
)
A half-wave symmetric and asymmetric waveform. The red contains only the fundamental and odd harmonics, the green contains the fundamental, odd, and even harmonics.
)
200 and 300 Hz waves and their sum, showing the periods of each.
)
A spectrogram of a violin playing a note and then a perfect fifth above it. The shared partials are highlighted by the white dashes.
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.
The opposite is also true. A system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, at least one even harmonic will be produced (and probably also odd).
Harmony
Additionally, the two notes will have many of the same partials. For instance, a note with a fundamental frequency of 200 Hz will have harmonics at:
- (200,) 400, 600, 800, 1000, 1200, …
A note with fundamental frequency of 300 Hz will have harmonics at:
- (300,) 600, 900, 1200, 1500, …
The two notes have the harmonics 600 and 1200 in common, and more will coincide further up the series.
The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of harmony.
When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone. This is called beating, and is considered to be unpleasant, or dissonant.
The frequency of beating is calculated as the difference between the frequencies of the two notes. For the example above, |200 Hz - 300 Hz| = 100 Hz. As another example, a combination of 3425 Hz and 3426 Hz would beat once per second (|3425 Hz - 3426 Hz| = 1 Hz). This follows from modulation theory.
The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval to be dissonant. Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz. [1]
Scales
The following table shows the ratios between the frequencies of all the notes of the just major scale and the fixed frequency of the first note of the scale.
| C | D | E | F | G | A | B | C |
|---|---|---|---|---|---|---|---|
| 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 15/8 | 2 |
There are other scales available through just intonation, like for instance the minor scale. Scales which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as temperaments, of which equal temperament is the most used. Temperaments, though they obscure the acoustical purity of just intervals often have other desirable properties, such as a closed circle of fifths.
See also
- Sound
- Acoustics
- Harmony
- Mathematics of musical scales
- Vibrating string
- Open tube
- Closed tube
- String resonance (music)
External links
- Physics of music course - links and illustrations - University of Maryland
- Music acoustics - sound files, animations and illustrations - University of New South Wales
- Acoustics collection - descriptions, photos, and video clips of the apparatus for research in musical acoustics by Prof. Dayton Miller
- The Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA)
- The Musical Acoustics Research Library (MARL)
- Acoustics and Music Technology courses - University of Edinburgh
- Speech, Music and Hearing - About the music acoustics group
- The physics of harpsichord sound
- Equal beating tuning
- Music & Acoustics
- Sound & Hearing
- Visual music
- Acoustics, audio and video group - University of Salford
- The research repository of stringed musical instrument technology - An open access of research articles
Acoustics is the branch of physics concerned with the study of sound (mechanical waves in gases, liquids, and solids). A scientist who works in the field of acoustics is an acoustician. The application of acoustics in technology is called acoustical engineering.
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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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A musical instrument is a device constructed or modified with the purpose of making music. In principle anything that, produces sound, and can somehow be controlled by a person playing it, can serve as a musical instrument.
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human voice consists of sound made by a human using the vocal folds for talking, singing, laughing, crying, screaming etc. The vocal folds, in combination with the lips, the tongue, the lower jaw, and the palate, are capable of producing highly intricate arrays of sound.
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Interpersonal communication is the process of sending and receiving information between two or more people.
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Types of Interpersonal Communication
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Singing is the act of producing musical sounds with the voice, which is often contrasted with speech. Contrary to common thought, air is not expelled with the diaphragm, but is inhaled using the diaphragm and exhaled or expelled, using the abdominal and lower pelvic muscles, as
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melody, also tune, voice, or line, is a series of linear events or a succession, not a simultaneity as in a chord (see harmony). However, this succession must contain change of some kind and be perceived as a single entity (possibly Gestalt) to be called a
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frequency analysis is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and
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Frequency analysis is based on the fact that, in any given stretch of written language, certain letters and
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Musical analysis can be defined as an attempt to answer the question how does this music work?. The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis.
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Psychoacoustics is the study of subjective human perception of sounds. Alternatively it can be described as the study of the psychological correlates of the physical parameters of acoustics.
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frequency spectrum of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a flat line. Therefore, flat-line spectrums in general are often referred to as white
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Hearing (or audition) is one of the traditional five senses, and refers to the ability to detect sound. In humans and other vertebrates, hearing is performed primarily by the auditory system: sound is detected by the ear and transduced into nerve impulses that are perceived
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outer ear is the most external portion of the ear. The outer ear includes the pinnae (also called auricle), the ear canal, and the very most superficial layer of the ear drum (also called the tympanic membrane).
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In animals, the brain or encephalon (Greek for "in the skull"), is the control center of the central nervous system, responsible for behavior. The brain is located in the head, protected by the skull and close to the primary sensory apparatus of vision, hearing,
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note has two primary meanings: 1) a sign used in music to represent the relative duration and pitch of a sound; and 2) a pitched sound itself. Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis
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Fundamental may refer to:
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- Fundamental frequency, a concept in music or phonetics, often referred to as simply a "fundamental".
- Fundamentalism, the belief in, and usually the strict adherence to, the simplistic or "fundamental" ideas based on faith of a system of thought.
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harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.
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Partial may refer to:
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- bias
- overtone
- partial function
- partial algorithm
- Partial derivative
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- "Overtones" redirects here. For the album by Just Jack, see Overtones (album).
An overtone is a natural resonance or vibration frequency of a system.
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harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc.
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frequency spectrum of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a flat line. Therefore, flat-line spectrums in general are often referred to as white
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Air or Earth's atmosphere is a layer of gases surrounding the planet Earth.
Air may also refer to:
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Air may also refer to:
- Air (1977 video game), an air combat based mainframe computer game
- Air (band), a French electronic music duo
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.
Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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outer ear is the most external portion of the ear. The outer ear includes the pinnae (also called auricle), the ear canal, and the very most superficial layer of the ear drum (also called the tympanic membrane).
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Sound is a disturbance of mechanical energy that propagates through matter as a wave (through fluids as a compression wave, and through solids as both compression and shear waves).
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Periodicity is the quality of occurring at regular intervals or periods (in time or space) and can occur in different contexts:
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- A clock marks time at periodic intervals.
- A metronome ticks at periodic intervals of time.
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