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Pitch is a
perceptual Perception (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the powe ...

perceptual
property of
sound 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 b ...

sound
s that allows their ordering on a
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
-related
scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory)In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set (mathematics), set of point (mathematics), points in some Poli ...
, 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 A melody (from Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight ...

melodies
. Pitch is a major auditory attribute of
musical tone Traditionally in Western music, a musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre In music, timbre ( ), also known as tone color or tone quality (from p ...
s, along with
duration Duration may refer to: * The amount of Time#Terminology, time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a th ...
,
loudness In , loudness is the perception of . More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The relation of physical attributes of sound to percei ...
, and
timbre In music, timbre ( ), also known as tone color or tone quality (from ), is the perceived sound quality of a , sound or . Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables li ...

timbre
. Pitch may be quantified as a
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in psychoacoustics, and has been instrumental in forming and testing theories of sound representation, processing, and perception in the auditory system.


Perception


Pitch and frequency

Pitch is an auditory sensation in which a listener assigns
musical tone Traditionally in Western music, a musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre In music, timbre ( ), also known as tone color or tone quality (from p ...
s to relative positions on a
musical scale In music theory Music theory is the study of the practices and possibilities of music Music is the art of arranging sounds in time through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural aspe ...

musical scale
based primarily on their perception of the
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
of vibration. Pitch is closely related to frequency, but the two are not equivalent. Frequency is an objective, scientific attribute that can be measured. Pitch is each person's ''subjective perception'' of a sound wave, which cannot be directly measured. However, this does not necessarily mean that most people won't agree on which notes are higher and lower. The
oscillations Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. The term ''vibration'' is precisely used to describ ...
of sound waves can often be characterized in terms of ''frequency''. ''Pitches'' are usually associated with, and thus quantified as, ''frequencies'' (in cycles per second, or hertz), by comparing the sounds being assessed against sounds with
pure tone In psychoacoustics Psychoacoustics is the branch of psychophysics involving the scientific study of sound perception and audiology—how humans perceive various sounds. More specifically, it is the branch of science studying the psychological respo ...
s (ones with periodic,
sinusoidal A sine wave or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and ev ...

sinusoidal
waveforms). Complex and aperiodic sound waves can often be assigned a ''pitch'' by this method. According to the
American National Standards Institute The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of Standardization, voluntary consensus standards for products, services, processes, systems, and personnel in the United Sta ...
, pitch is the auditory attribute of sound according to which sounds can be ordered on a scale from low to high. Since pitch is such a close
proxy Proxy may refer to: * Proxy or agent (law), a substitute authorized to act for another entity or a document which authorizes the agent so to act * Proxy (climate), a measured variable used to infer the value of a variable of interest in climate r ...
for frequency, it is almost entirely determined by how quickly the sound wave is making the air vibrate and has almost nothing to do with the intensity, or
amplitude The amplitude of a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Period, a descriptor for ...

amplitude
, of the wave. That is, "high" pitch means very rapid oscillation, and "low" pitch corresponds to slower oscillation. Despite that, the
idiom An idiom is a phrase In syntax and grammar, a phrase is a group of words which act together as a grammatical unit. For instance, the English language, English expression "the very happy squirrel" is a noun phrase which contains the adjective phra ...
relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down. The exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the sound frequency is increased or reduced.Carroll C. Pratt,
The Spatial Character of High and Low Tones
, ''Journal of Experimental Psychology'' 13 (1930): 278–85.
In most cases, the pitch of complex sounds such as
speech Speech is human vocal communication Communication (from Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''c ...
and
musical note In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated concep ...
s corresponds very nearly to the repetition rate of periodic or nearly-periodic sounds, or to the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another poly ...

reciprocal
of the time interval between repeating similar events in the sound waveform. The pitch of complex tones can be ambiguous, meaning that two or more different pitches can be perceived, depending upon the observer. When the actual
fundamental frequency The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is th ...
can be precisely determined through physical measurement, it may differ from the perceived pitch because of
overtones partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency). An overtone is any frequency greater than the fundamental frequency of a sound. In other words, overtones are higher pitches resulting from the lowest note or fundamental. Whil ...
, also known as upper partials,
harmonic A harmonic is any member of the harmonic series Harmonic series may refer to either of two related concepts: *Harmonic series (mathematics) *Harmonic series (music) {{Disambig .... The term is employed in various disciplines, including music ...
or otherwise. A complex tone composed of two sine waves of 1000 and 1200 Hz may sometimes be heard as up to three pitches: two spectral pitches at 1000 and 1200 Hz, derived from the physical frequencies of the pure tones, and the
combination toneImage:Sum and difference tones A220.png, 300px, Combination tones: Unison, just perfect fifth, and octave are played in top row while A220 is sustained in second row, producing third row sum tones and fourth row difference tones. Frequencies are mark ...
at 200 Hz, corresponding to the repetition rate of the waveform. In a situation like this, the percept at 200 Hz is commonly referred to as the
missing fundamental A harmonic of a vibrating string are harmonics. A harmonic is any member of the harmonic series (music), harmonic series. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio tech ...

missing fundamental
, which is often the
greatest common divisor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gene ...

greatest common divisor
of the frequencies present. Pitch depends to a lesser degree on the
sound pressure Sound pressure or acoustic pressure is the local pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from '' ...
level (loudness, volume) of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The pitch of lower tones gets lower as sound pressure increases. For instance, a tone of 200 Hz that is very loud seems one semitone lower in pitch than if it is just barely audible. Above 2,000 Hz, the pitch gets higher as the sound gets louder. These results were obtained in the pioneering works by S. Stevens Stevens S. S. The relation of pitch to intensity//J. Acoust. Soc. Amer. 1935. Vol. 6. P. 150-154. and W. Snow.Snow W. B. (1936) Change of Pitch with Loudness at Low Frequencies. J. Acoust. Soc. Am/ 8:14–19. Later investigations, i.e. by A. Cohen, had shown that in most cases the apparent pitch shifts were not significantly different from pitch‐matching errors. When averaged, the remaining shifts followed the directions of Stevens' curves but were small (2% or less by frequency, i.e. not more than a semitone).Cohen, A. (1961). Further investigation of the effects of intensity upon the pitch of pure tones. Journal of the Acoustical Society of America, 33, 1363–1376. https://dx.doi.org/10.1121/1.1908441


Theories of pitch perception

Theories A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or researc ...
of pitch perception try to explain how the physical sound and specific physiology of the auditory system work together to yield the experience of pitch. In general, pitch perception theories can be divided into place coding and temporal coding. Place theory holds that the perception of pitch is determined by the place of maximum excitation on the
basilar membrane The basilar membrane is a stiff structural element within the cochlea The cochlea is the part of the inner ear involved in hearing. It is a spiral-shaped cavity in the bony labyrinth, in humans making 2.75 turns around its axis, the modiolus (coch ...
. A place code, taking advantage of the
tonotopy In physiology Physiology (; ) is the scientific study of functions and mechanisms in a living system. As a sub-discipline of biology Biology is the natural science that studies life and living organisms, including their anatomy, physic ...
in the auditory system, must be in effect for the perception of high frequencies, since neurons have an upper limit on how fast they can phase-lock their
action potential In physiology Physiology (; ) is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence ...

action potential
s. However, a purely place-based theory cannot account for the accuracy of pitch perception in the low and middle frequency ranges. Moreover, there is some evidence that some non-human primates lack auditory cortex responses to pitch despite having clear tonotopic maps in auditory cortex, showing that tonotopic place codes are not sufficient for pitch responses. Temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the and
mode-locking Mode-locking is a technique in optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studie ...
of action potentials to frequencies in a stimulus. The precise way this temporal structure helps code for pitch at higher levels is still debated, but the processing seems to be based on an
autocorrelation File:Comparison convolution correlation.svg, 400px, Visual comparison of convolution, cross-correlation, and autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different point ...
of action potentials in the auditory nerve. However, it has long been noted that a neural mechanism that may accomplish a delay—a necessary operation of a true autocorrelation—has not been found. At least one model shows that a temporal delay is unnecessary to produce an autocorrelation model of pitch perception, appealing to
phase shifts In physics and mathematics, the phase of a periodic function F of some real number, real variable t (such as time) is an angle-like quantity representing the number of Period (physics), periods spanned by that variable. It is denoted \phi(t) and ex ...

phase shifts
between cochlear filters; however, earlier work has shown that certain sounds with a prominent peak in their autocorrelation function do not elicit a corresponding pitch percept, and that certain sounds without a peak in their autocorrelation function nevertheless elicit a pitch. To be a more complete model, autocorrelation must therefore apply to signals that represent the output of the
cochlea The cochlea is the part of the inner ear involved in hearing. It is a spiral-shaped cavity in the bony labyrinth, in humans making 2.75 turns around its axis, the modiolus (cochlea), modiolus. A core component of the cochlea is the Organ of Cort ...

cochlea
, as via auditory-nerve interspike-interval histograms. Some theories of pitch perception hold that pitch has inherent
octave In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated co ...

octave
ambiguities, and therefore is best decomposed into a pitch ''chroma'', a periodic value around the octave, like the note names in western music—and a pitch ''height'', which may be ambiguous, that indicates the octave the pitch is in.


Just-noticeable difference

The '' just-noticeable difference (jnd)'' (the threshold at which a change is perceived) depends on the tone's frequency content. Below 500 Hz, the jnd is about 3 Hz for sine waves, and 1 Hz for complex tones; above 1000 Hz, the jnd for sine waves is about 0.6% (about 10 cents). The jnd is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches. The jnd becomes smaller if the two tones are played
simultaneously Simultaneity is the relation between two Spacetime#Basic concepts, events assumed to be happening at the same time in a given frame of reference. According to Einstein's theory of relativity, simultaneity is not an absolute relation between event ...
as the listener is then able to discern beat frequencies. The total number of perceptible pitch steps in the range of human hearing is about 1,400; the total number of notes in the equal-tempered scale, from 16 to 16,000 Hz, is 120.


Aural illusions

The relative perception of pitch can be fooled, resulting in ''
aural illusionAuditory illusions are false perceptions of a real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the Stimulus (physiology), stimulus, or sounds ...
s''. There are several of these, such as the tritone paradox, but most notably the Shepard scale, where a continuous or discrete sequence of specially formed tones can be made to sound as if the sequence continues ascending or descending forever.


Definite and indefinite pitch

Not all musical instruments make notes with a clear pitch. The
unpitched percussion instrument An unpitched percussion instrument is a percussion instrument A percussion instrument is a musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound ca ...
(a class of
percussion instrument A percussion instrument is a musical instrument that is sounded by being struck or scraped by a beater (percussion), beater including attached or enclosed beaters or Rattle (percussion beater), rattles struck, scraped or rubbed by hand or ...
) does not produce particular pitches. A sound or note of definite pitch is one where a listener can possibly (or relatively easily) discern the pitch. Sounds with definite pitch have
harmonic A harmonic is any member of the harmonic series Harmonic series may refer to either of two related concepts: *Harmonic series (mathematics) *Harmonic series (music) {{Disambig .... The term is employed in various disciplines, including music ...
frequency spectra or close to harmonic spectra. A sound generated on any instrument produces many modes of vibration that occur simultaneously. A listener hears numerous frequencies at once. The vibration with the lowest frequency is called the ''
fundamental frequency The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is th ...
''; the other frequencies are ''
overtones partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency). An overtone is any frequency greater than the fundamental frequency of a sound. In other words, overtones are higher pitches resulting from the lowest note or fundamental. Whil ...
''. ''
Harmonics A harmonic is any member of the harmonic series Harmonic series may refer to either of two related concepts: *Harmonic series (mathematics) *Harmonic series (music) {{Disambig .... The term is employed in various disciplines, including music ...

Harmonics
'' are an important class of overtones with frequencies that are integer multiples of the fundamental. Whether or not the higher frequencies are integer multiples, they are collectively called the partials, referring to the different parts that make up the total spectrum. A sound or note of indefinite pitch is one that a listener finds impossible or relatively difficult to identify as to pitch. Sounds with indefinite pitch do not have harmonic spectra or have altered harmonic spectra—a characteristic known as
inharmonicity In music, inharmonicity is the degree to which the frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency an ...
. It is still possible for two sounds of indefinite pitch to clearly be higher or lower than one another. For instance, a
snare drum The snare drum or side drum is a percussion instrument that produces a sharp staccato sound when the head is struck with a drum stick, due to the use of a series of stiff wires held under tension against the lower skin. Snare drums are often us ...
sounds higher pitched than a
bass drum The bass drum, or kick drum, is a large drum , at the Battle of Gettysburg The Battle of Gettysburg () was fought July 1–3, 1863, in and around the town of Gettysburg, Pennsylvania Pennsylvania ( ) ( pdc, Pennsilfaani), ...

bass drum
though both have indefinite pitch, because its sound contains higher frequencies. In other words, it is possible and often easy to roughly discern the relative pitches of two sounds of indefinite pitch, but sounds of indefinite pitch do not neatly correspond to any specific pitch.


Pitch standards and standard pitch

A pitch standard (also
concert pitch Concert pitch is the pitch Pitch may refer to: Acoustic frequency * Pitch (music), the perceived frequency of sound including "definite pitch" and "indefinite pitch" ** Absolute pitch or "perfect pitch" ** Pitch class, a set of all pitches that a ...
) is the conventional pitch reference a group of
musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who play ...
s are tuned to for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over musical history. Standard pitch is a more widely accepted convention. The A above
middle C C or Do is the first note Note, notes, or NOTE may refer to: Music and entertainment * Musical note In music, a note is a symbol denoting a musical sound. In English usage a note is also the sound itself. Notes can represent the Pitch (music) ...

middle C
is usually set at 440 Hz (often written as "A = 440 Hz" or sometimes "A440"), although other frequencies, such as 442 Hz, are also often used as variants. Another standard pitch, the so-called ''Baroque pitch'', has been set in the 20th century as A = 415 Hz—approximately an equal-tempered semitone lower than A440 to facilitate transposition. The ''Classical pitch'' can be set to either 427 Hz (about halfway between A415 and A440) or 430 Hz (also between A415 and A440 but slightly sharper than the quarter tone). And ensembles specializing in
authentic performance Historically informed performance (also referred to as period performance, authentic performance, or HIP) is an approach to the performance of Western classical music, classical music, which aims to be faithful to the approach, manner and style of ...
set the A above middle C to 432 Hz or 435 Hz when performing repertoire from the
Romantic Romantic may refer to: Genres and eras * The Romantic era, an artistic, literary, musical and intellectual movement of the 18th and 19th centuries ** Romantic music, of that era ** Romantic poetry, of that era ** Romanticism in science, of that er ...
era.
Transposing instruments A transposing instrument is a musical instrument A musical instrument is a device created or adapted to make Music, musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that ...
have their origin in the variety of pitch standards. In modern times, they conventionally have their parts transposed into different
keys KEYS (1440 AM broadcasting, AM) is a radio station serving the Corpus Christi, Texas, Corpus Christi, Texas area with a talk radio, talk format. It broadcasts on AM broadcasting, AM frequency 1440 kHz and is licensed to Malkan AM Associates, L. ...
from voices and other instruments (and even from each other). As a result, musicians need a way to refer to a particular pitch in an unambiguous manner when talking to each other. For example, the most common type of
clarinet The clarinet is a family of woodwind instrument Woodwind instruments are a family of musical instruments A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be cons ...

clarinet
or
trumpet The trumpet is a brass instrument A brass instrument is a that produces sound by of air in a tubular in sympathy with the vibration of the player's lips. Brass instruments are also called labrosones or labrophones, from Latin and Greek ...

trumpet
, when playing a note written in their
part Part, parts or PART may refer to: People *Armi Pärt Armi Pärt (born 18 June 1991) is an Estonian handballer, playing in French D2 for Massy Essonne Handball. He is also a member of Estonian national team. Club career HC Kehra Armi Pärt ...
as C, sounds a pitch that is called B on a non-transposing instrument like a violin (which indicates that at one time these wind instruments played at a standard pitch a tone lower than violin pitch). To refer to that pitch unambiguously, a musician calls it ''concert B'', meaning, "...the pitch that someone playing a non-transposing instrument like a violin calls B."


Labeling pitches

Pitches are labeled using: * Letters, as in
Helmholtz pitch notation Helmholtz pitch notation is a system for naming musical note In music, a note is a symbol denoting a musical sound. In English usage, a note is also the sound itself. Notes can represent the Pitch (music), pitch and Duration (music), duration o ...

Helmholtz pitch notation
* A combination of letters and numbers—as in
scientific pitch notation Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN), is a method of specifying musical pitch Pitch may refer to: Acoustic frequency * Pitch (music), the perceived frequenc ...

scientific pitch notation
, where notes are labelled upwards from C0, the 16 Hz C * Numbers that represent the frequency in
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...

hertz
(Hz), the number of cycles per second For example, one might refer to the A above middle C as ''a′'', ''A4'', or ''440 Hz''. In standard Western
equal temperament An equal temperament is a or , which approximates by dividing an (or other interval) into equal steps. This means the ratio of the of any adjacent pair of notes is the same, which gives an equal perceived step size as is perceived roughly a ...
, the notion of pitch is insensitive to "spelling": the description "G4 double sharp" refers to the same pitch as ''A4''; in other temperaments, these may be distinct pitches. Human perception of musical intervals is approximately logarithmic with respect to
fundamental frequency The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is th ...
: the perceived interval between the pitches "A220" and "A440" is the same as the perceived interval between the pitches ''A440'' and ''A880''. Motivated by this logarithmic perception, music theorists sometimes represent pitches using a numerical scale based on the logarithm of fundamental frequency. For example, one can adopt the widely used
MIDI MIDI (; an acronym for Musical Instrument Digital Interface) is a technical standard A technical standard is an established norm (social), norm or requirement for a repeatable technical task which is applied to a common and repeated use o ...

MIDI
standard to map fundamental frequency, ''f'', to a real number, ''p'', as follows : p = 69 + 12\times\log_2 This creates a linear
pitch space space is an example of a pitch space. Image:Heinichen musicalischer circul.png, The circle of fifths is another example of pitch space. In music theory Music theory is the study of the practices and possibilities of music. ''The Oxford Compani ...
in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and A440 is assigned the number 69. (See Frequencies of notes.) Distance in this space corresponds to musical intervals as understood by musicians. An equal-tempered semitone is subdivided into 100 cents. The system is flexible enough to include "microtones" not found on standard piano keyboards. For example, the pitch halfway between C (60) and C (61) can be labeled 60.5. The following table shows frequencies in Hertz for notes in various octaves, named according to the "German method" of octave nomenclature:


Scales

The relative pitches of individual notes in a
scale Scale or scales may refer to: Mathematics * Scale (descriptive set theory)In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set (mathematics), set of point (mathematics), points in some Poli ...
may be determined by one of a number of
tuning systems In music, there are two common meanings for tuning: * #Tuning practice, Tuning practice, the act of tuning an instrument or voice. * #Tuning systems, Tuning systems, the various systems of Pitch (music), pitches used to tune an instrument, and th ...
. In the west, the twelve-note
chromatic scale The chromatic scale is a set of twelve pitches (more completely, pitch class In , a pitch class (p.c. or pc) is a of all that are a whole number of s apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C sta ...

chromatic scale
is the most common method of organization, with
equal temperament An equal temperament is a or , which approximates by dividing an (or other interval) into equal steps. This means the ratio of the of any adjacent pair of notes is the same, which gives an equal perceived step size as is perceived roughly a ...
now the most widely used method of tuning that scale. In it, the pitch ratio between any two successive notes of the scale is exactly the twelfth root of two (or about 1.05946). In well-tempered systems (as used in the time of
Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque music, Baroque period. He is known for instrumental compositions such as the Cello Suites (Bach), Cello Suites and ''Brandenburg Concertos''; keyboard ...

Johann Sebastian Bach
, for example), different methods of
musical tuning In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated co ...
were used. In almost all of these systems of the
octave In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General include common elements such as (which governs and ), (and its associated co ...

octave
doubles the frequency of a note; for example, an octave above
A440 A440 or A-440 may refer to: * A440 (pitch standard) A440 (also known as Stuttgart pitch) is the musical pitch Pitch is a perceptual property of sound In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (ep ...
is 880 Hz. If however the first
overtone An overtone is any frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosoph ...

overtone
is sharp due to
inharmonicity In music, inharmonicity is the degree to which the frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency an ...
, as in the extremes of the piano, resort to octave stretching.


Other musical meanings of pitch

In
atonal Atonality in its broadest sense is music that lacks a tonal center In music Music is the art of arranging sounds in time through the elements of melody, harmony, rhythm, and timbre. It is one of the universal cultural aspects of all hu ...

atonal
,
twelve tone The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law of ...
, or musical set theory a "pitch" is a specific frequency while a
pitch class In , a pitch class (p.c. or pc) is a of all that are a whole number of s apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to , a pitch cla ...
is all the octaves of a frequency. In many analytic discussions of atonal and post-tonal music, pitches are named with
integer An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to ...
s because of octave and enharmonic equivalency (for example, in a serial system, C and D are considered the same pitch, while C4 and C5 are functionally the same, one octave apart). Discrete pitches, rather than continuously variable pitches, are virtually universal, with exceptions including " tumbling strains" and "indeterminate-pitch chants". Gliding pitches are used in most cultures, but are related to the discrete pitches they reference or embellish.Burns, Edward M. (1999). "Intervals, Scales, and Tuning", ''The Psychology of Music'', second edition. Deutsch, Diana, ed. San Diego: Academic Press. .


See also

*
3rd bridge The 3rd bridge is an extended playing technique used on the electric guitar An electric guitar is a guitar The guitar is a fret (in the background, coloured white) and first four frets A fret is a space between two fretbars on th ...
(harmonic resonance based on equal string divisions) *
Absolute pitch Absolute pitch (AP), often called perfect pitch, is a rare ability of a person to identify or re-create a given musical note In music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of t ...
* Diplacusis *
Eight foot pitchAn organ pipe, or a harpsichord A harpsichord ( it, clavicembalo, french: clavecin, german: Cembalo, es, clavecín, pt, cravo, nl, klavecimbel) is a musical instrument A musical instrument is a device created or adapted to make Music, musical ...
* Harmonic pitch class profiles *
Just intonation In music, just intonation or pure intonation is the attempt to tune all musical intervals as whole number ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six ...
*
Meantone temperament Meantone temperament is a musical temperament, that is a Musical tuning#Tuning systems, tuning system, obtained by slightly compromising the fifths in order to improve the thirds. Meantone temperaments are constructed the same way as Pythagorean tun ...
*
Music and mathematics of a violin waveform, with linear frequency on the vertical axis and time on the horizontal axis. The bright lines show how the spectral components change over time. The intensity colouring is logarithmic (black is −120 dBFS). Music theory M ...
*
Piano key frequencies This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in Equal temperament#Twelve-tone equal temperament, twelve-tone equal temperament, with the 49th key, the ...

Piano key frequencies
* Pitch circularity *
Pitch class In , a pitch class (p.c. or pc) is a of all that are a whole number of s apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to , a pitch cla ...
*
Pitch detection algorithm A pitch detection algorithm (PDA) is an algorithm of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers ''a'' and ''b'' in locations named A and B. The algorithm proceeds by successive subtract ...
* Pitch of brass instruments * Pitch shifter *
Pitch pipe A pitch pipe is a small device used to provide a pitch reference for musicians. Although it may be described as a musical instrument A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produce ...
*
Relative pitch Relative pitch is the ability of a person to identify or re-create a given musical note by comparing it to a reference note and identifying the interval between those two notes. Relative pitch implies some or all of the following abilities: * Deter ...
*
Scale of vowels A scale of vowels is an arrangement of vowel A vowel is a Syllable, syllabic speech sound pronounced without any stricture in the vocal tract. Vowels are one of the two principal classes of speech sounds, the other being the consonant. Vowels va ...
*Template:Vocal and instrumental pitch ranges, Vocal and instrumental pitch ranges


References


Further reading

* Moore, B.C. & Glasberg, B.R. (1986) "Thresholds for Hearing Mistuned Partials as Separate Tones in Harmonic Complexes". ''Journal of the Acoustical Society of America'', 80, 479–83. * Parncutt, R. (1989). ''Harmony: A Psychoacoustical Approach''. Berlin: Springer-Verlag, 1989. * Schneider, P.; Sluming, V.; Roberts, N.; Scherg, M.; Goebel, R.; Specht, H.-J.; Dosch, H.G.; Bleeck, S.; Stippich, C.; Rupp, A. (2005). "Structural and Functional Asymmetry of Lateral Heschl's Gyrus Reflects Pitch Perception Preference". ''Nat. Neurosci.'' 8, 1241–47. * Terhardt, E., Stoll, G. and Seewann, M. (1982). "Algorithm for Extraction of Pitch and Pitch Salience from Complex Tonal Signals". ''Journal of the Acoustical Society of America'', 71, 679–88.


External links

{{DEFAULTSORT:Pitch (Music) Pitch (music), Perception Auditory perception Psychoacoustics Cognitive musicology Sound Acoustics