Pitch represents the perceived fundamental frequency The fundamental tone, often referred to simply as the fundamental and abbreviated f0 or F0, is the lowest frequency in a harmonic series of a sound.^[1] It is one of the four major auditory The folds of cartilage surrounding the ear canal are called the pinna. Sound waves are reflected and attenuated when they hit the pinna, and these changes provide additional information that will help the brain determine the direction from which the sounds came attributes of sounds Sound is a travelling wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations along with loudness Loudness is the quality of a sound that is the primary psychological correlate of physical strength . 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.", timbre In music, timbre is the quality of a musical note or sound or tone that distinguishes different types of sound production, such as voices or musical instruments. The physical characteristics of sound that mediate the perception of timbre include spectrum and envelope. Timbre is also known in psychoacoustics as tone quality or tone color and sound source location Sound localization is a listener's ability to identify the location or origin of a detected sound in direction and distance or the methods in acoustical engineering to simulate the placement of an auditory cue in a virtual 3D space. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials. Harmonics are partials whose frequencies are whole number multiples of the fundamental These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. Due to a, also known as upper partials, harmonic A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic or otherwise. The human auditory perception system may also have trouble distinguishing frequency differences between notes under certain circumstances. According to ANSI The American National Standards Institute or ANSI [citation needed] is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organization also coordinates U.S. standards with international standards so that American acoustical terminology, it is the auditory attribute of sound according to which sounds can be ordered on a scale from low to high.

Perception of pitch

Pitch is a subjective sensation in which a listener assigns perceived tones to relative positions on a musical scale based primarily on the frequency of vibration. The just-noticeable difference In psychophysics, a just noticeable difference, customarily abbreviated with lowercase letters as jnd, is the smallest detectable difference between a starting and secondary level of a particular sensory stimulus. It is also known as the difference limen or the differential threshold (jnd, the threshold Sensory threshold is a theoretical concept used in psychophysics. A stimulus that is less intense than the sensory threshold will not elicit any sensation. Methods have been developed to measure thresholds in any of the senses at which a change is perceived) depends on the tone's frequency and is about 4.3 cents (1 cent The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes = 1 hundredth of a semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale . This implies that its size is exactly or approximately equal to 100 cents, a) or about 0.36 Hz in frequency within the octave of 1,000–2,000 Hz but within the octave 62–125 Hz the jnd is much coarser with some 40 cents or about 2 Hz between perceived pitch changes. The jnd is typically tested by playing two tones in quick succession with the listener asked if there was a difference in their pitches.^[2] The jnd becomes smaller if the two tones are played simultaneously Simultaneously is the property of two events happening at the same time in at least one frame of reference. The word derives from the Latin simul, at the same time plus the English suffix -taneous (as in instantaneous) as the listener is then able to discern beat frequencies In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two 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 is 120.^[2]

Pitch depends to lesser degree on the sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient atmospheric pressure caused by a sound wave. Sound pressure can be measured using a microphone in air and a hydrophone in water. The SI unit for sound pressure p is the pascal (symbol: Pa) 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 will seem to be one semitone lower in pitch than if it is just barely audible. The pitch of higher tones gets higher as the sound gets louder.^[2] In this way, pitch perception is like other human senses which respond to the intensity of the stimulus as stated in the Weber–Fechner law.

The relative perception of pitch can be fooled, resulting in "aural illusions". There are several of these, such as the tritone paradox, but most notably the Shepard scale A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the base pitch of the tone moving upwards or downwards, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately, 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; percussion instruments are often distinguished by whether they do or do not have a particular pitch. A sound or note of definite pitch is one of which it is possible or relatively easy to discern the pitch. Sounds with definite pitch have harmonic A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic frequency spectra The frequency spectrum of a time-domain signal is a representation of that signal in the frequency domain. The frequency spectrum can be generated via a Fourier transform of the signal, and the resulting values are usually presented as amplitude and phase, both plotted versus frequency or close to harmonic spectra.^[3]

A sound or note of indefinite pitch is one of which it is impossible or relatively difficult to discern a pitch. Sounds with indefinite pitch do not have harmonic spectra or have altered harmonic spectra.

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 is a drum with strands of snares made of curled metal wire, metal cable, plastic cable, or gut cords stretched across the drumhead, typically the bottom. Pipe and tabor and some military snare drums often have a second set of snares on the bottom side of the top (batter) head to make a "brighter" sound, and the Brazilian invariably sounds higher in pitch than a bass drum A bass drum is a relatively large drum that produces a note of low definite or indefinite pitch. The bass drums are of variable sizes and are used in several musical genres (see usage below). Three major types of bass drums can be distinguished: the large orchestral bass drum, the smaller 'kick' drum, and the pitched bass drums. The type usually, 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 any given sound of indefinite pitch does not neatly correspond to a given definite pitch. A special type of pitch often occurs in free nature when the sound of a sound source reaches the ear of an observer directly and also after being reflected against a sound-reflecting surface. This phenomenon is called repetition pitch Repetition pitch is an unexpected sensation of tonality or pitch that often occurs in nature when a sound is reflected against a sound-reflecting surface , and both the original and the reflected sound arrive at the ear of an observer, but with a short time differential between the two arrivals, because the addition of a true repetition of the original sound to itself is the basic prerequisite.

Concert pitch

Concert pitch Pitch represents the perceived fundamental frequency of a sound. It is one of the four major auditory attributes of sounds along with loudness, timbre and sound source location. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, also known as is the pitch reference to which a group of musical instruments A musical instrument is constructed or used for the purpose of making the sounds of music. In principle, anything that produces sound can serve as a musical instrument. The history of musical instruments dates back to the beginnings of human culture. The academic study of musical instruments is called organology are tuned for a performance. Concert pitch may vary from ensemble to ensemble, and has varied widely over musical history.

The A above middle C In classical music, the expression "Middle C" refers to the note "C" located exactly between the two staves of the grand staff and near the top and bottom, respectively, of the bass and soprano voices. When calculated in equal temperament with a reference of A above middle C as 440 Hz, the frequency of the middle C note is is usually set at 440 Hz (often written as "A = 440 Hz A440 or Concert A or Middle A is the 440 Hz tone that serves as the standard for musical pitch. A440 is the musical note A above middle C . The term literally means that the A above Middle C = 440 vibrations per second" or sometimes "A440"), although other frequencies are also often used, such as 442 Hz. Historically, this A has been tuned to a variety of higher and lower pitches (see "History of pitch standards in Western music").

The transposing instruments A transposing instrument is a musical instrument for which written notes are read at a pitch different from concert pitch, which a non-transposing instrument, such as a piano, would play. On a transposing instrument, a concert C is written as a different note; the concert pitch that is played for a written C determines the key that an instrument in an orchestra will conventionally have their parts A part is the music played by an individual instrument or voice within a larger work, such as a melody. It also refers to the printed copy of the music for each instrument, as distinct from the score, which holds the music for all instruments. For example in a string ensemble you would have separate parts for Violin 1, Violin 2, Viola and Cello, transposed into different keys In musical notation, a key signature is a series of sharp or flat symbols placed on the staff, designating notes that are to be consistently played one semitone higher or lower than the equivalent natural notes unless otherwise altered with an accidental. Key signatures are generally written immediately after the clef at the beginning of a line of from the 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 different sections of the orchestra.

For example, the most common type of clarinet The clarinet is a musical instrument that is a part of the woodwind family. The name derives from adding the suffix -et to the Italian word clarino (meaning a type of trumpet), as the first clarinets had a strident tone similar to that of a trumpet. The instrument has an approximately cylindrical bore, and uses a single reed. In jazz contexts, it or trumpet The trumpet is the musical instrument with the highest register in the brass family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BCE. They are constructed of brass tubing bent twice into an oblong shape, and are played by blowing air through closed lips, producing a "buzzing" sound which starts a, when playing a note written in their part A part is the music played by an individual instrument or voice within a larger work, such as a melody. It also refers to the printed copy of the music for each instrument, as distinct from the score, which holds the music for all instruments. For example in a string ensemble you would have separate parts for Violin 1, Violin 2, Viola and Cello, as C, will sound a pitch that would be called B♭ on a non-transposing instrument like a piano. If you wanted to refer to that pitch unambiguously, you would call it "concert B♭", meaning "the pitch that someone playing a non-transposing instrument like a piano would call B♭".

History of pitch standards in Western music

Historically, various standards have been used to fix the pitch of notes at certain frequencies^[4]. Various systems of musical tuning Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. Out of tune refers to a pitch/tone that is either too high or too low (flat) in relation to a given reference pitch. While an instrument have also been used to determine the relative frequency of notes in a scale.

Labeling pitches

Pitches can be labeled using letters, as in Helmholtz pitch notation Helmholtz pitch notation is a musical system for naming notes of the Western chromatic scale. Developed by the German scientist Hermann von Helmholtz, it uses a combination of upper and lower case letters , and the sub- and super-prime symbols ( ˌ ′ ) to describe each individual note of the scale. It is one of two formal systems for, using a combination of letters and numbers, as in scientific pitch notation Scientific pitch notation is one of several methods that name the notes of the standard Western chromatic scale by combining a letter-name, accidentals, and a number identifying the pitch's octave. The definition of scientific pitch notation in this article is that proposed to the Acoustical Society of America in 1939, where C0 is in the region of, or by a number representing frequency. For example, one might refer to the A above middle C as a', A4 or A440. In standard Western equal temperament Equal temperament is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps . For classical music, the most common tuning system is twelve-tone equal temperament, inconsistently, the notion of pitch is insensitive to spelling: the description "G4 double sharp" refers to the same pitch as "A4".

Human pitch perception is approximately logarithmic with respect to fundamental frequency The fundamental tone, often referred to simply as the fundamental and abbreviated f0 or F0, is the lowest frequency in a harmonic series: the perceived distance between the pitches "A220" and "A440" is the same as the perceived distance 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 , pronounced /ˈmɪdi/, is an industry-standard protocol defined in 1982 that enables electronic musical instruments, such as keyboard controllers, computers and other electronic equipment, to communicate and also to control and synchronize with each other. MIDI allows computers, synthesizers, MIDI controllers, sound cards, samplers and drum standard to map fundamental frequency f to a real number p as follows

This creates a linear pitch space In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches placed farther apart. Depending on the complexity of the relationships under consideration, the models may be 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. Distance in this space corresponds to musical distance as measured in psychological experiments and understood by musicians. (An equal-tempered semitone is subdivided into 100 cents The cent is a logarithmic unit of measure used for musical intervals. Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes .) 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.

Scales

The relative pitches of individual notes in a scale In music, a scale is a group of musical notes collected in ascending and descending order, that provides material for or is used to conveniently represent part or all of a musical work including melody and/or harmony. Scales are ordered in pitch or pitch class, with their ordering providing a measure of musical distance may be determined by one of a number of tuning Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. Out of tune refers to a pitch/tone that is either too high or too low (flat) in relation to a given reference pitch. While an instrument systems. In the west, the twelve-note chromatic scale The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones is the most common method of organization, with equal temperament Equal temperament is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps . For classical music, the most common tuning system is twelve-tone equal temperament, inconsistently 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 Well temperament is a type of tempered tuning described in twentieth-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, Well-Tempered Clavier. The phrase wohl temperiert also occurs in the works of Bach's predecessor, the organ tuner and music theorist Andreas systems (as used in the time of Johann Sebastian Bach Johann Sebastian Bach (31 March 1685 [O.S. 21 March] – 28 July 1750) (often referred to simply as Bach) was a German composer, organist, harpsichordist, violist, and violinist whose ecclesiastical and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity, for example), different methods of musical tuning Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as A = 440 Hz. Out of tune refers to a pitch/tone that is either too high or too low (flat) in relation to a given reference pitch. While an instrument were used. Almost all of these systems have one interval In music theory, the term interval describes the relationship between the pitches of two notes in common, the octave, where the pitch of one note is double the frequency of another. For example, if the A above middle C is 440 Hz, the A an octave above that will be 880 Hz (info).

Other musical meanings of pitch

In atonal, twelve tone, or musical set theory a "pitch" is a specific frequency while a pitch class is all the octaves of a frequency. Pitches are named with integers because of octave and enharmonic equivalency (for example, C♯ and D♭ are 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" (Sachs & Kunst, 1962) and "indeterminate-pitch chants" (Malm, 1967). Gliding pitches are used in most cultures, but are related to the discrete pitches they reference or embellish (Burns, 1999).

Changing the pitch of a vibrating string

There are three ways to change the pitch of a vibrating string. String instruments are tuned by varying the strings' tension because adjusting length or mass per unit length is impractical. Instruments with a fingerboard are then played by adjusting the length of the vibrating portion of the strings.

Length

Pitch can be adjusted by varying the length of the string. A longer string will result in a lower pitch, while a shorter string will result in a higher pitch. The frequency is inversely proportional to the length:

A string twice as long will produce a tone of half the frequency (one octave lower).

Tension

Pitch can be adjusted by varying the tension of the string. A string with less tension (looser) will result in a lower pitch, while a string with greater tension (tighter) will result in a higher pitch. The frequency is proportional to the square root of the tension:

Density

The pitch of a string can also be varied by changing the density of the string. The frequency is inversely proportional to the square root of the density:

A string that is denser will produce a lower pitch.

See also

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