Pitch: In musical notation, the different vertical positions of notes indicate different pitches. Play top & Play bottom pitch is a perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as “higher” and “lower” in the sense associated with musical melodies,which require sound whose frequency is clear and stable enough to distinguish from noise.Pit-ch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.

Pitch may be quantified as a frequency, but the Pit-ch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of Pit-ch and Pit-ch 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.

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Pitch | Fundamentals of music | Understanding Western Music Theory

Perception of pitch

Pit-ch and frequency

Pit-ch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on the frequency of vibration.Pit-ch is closely related to frequency, but the two are not equivalent. Frequency is an objective, scientific concept, whereas Pit-ch is subjective. Sound waves themselves do not have a pitch, and their oscillations can be measured to obtain a frequency. It takes a human mind to map the internal quality of pitch. Pitches are usually quantified as frequencies in cycles per second, or hertz, by comparing sounds with pure tones, which have periodic, sinusoidal waveforms. Complex and aperiodic sound waves can often be assigned a Pit-ch by this method.

According to the American National Standards Institute, the Pit-ch is the auditory attribute of sound according to which sounds can be ordered on a scale from low to high. Since the Pit-ch is such a close proxy 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, of the wave. That is, a “high” Pit-ch means very rapid oscillation, and a “low” Pit-ch corresponds to slower oscillation.

Despite that, the idiom relating vertical height to sound Pit-ch 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 Pit-ch 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 decreased.

In most cases, the Pit-ch of complex sounds such as speech and musical notes corresponds very nearly to the repetition rate of periodic or nearly-periodic sounds, or to the reciprocal of the time interval between repeating similar events in the sound waveform.

The Pit-ch 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 can be precisely determined through physical measurement, it may differ from the perceived Pit-ch because of overtones,

also known as upper partials, harmonic, 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 tone 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, which is often the greatest common divisor of the frequencies

present.

Pit-ch depends to a lesser degree on the sound pressure level (loudness, volume) of the tone, especially at frequencies below 1,000 Hz and above 2,000 Hz. The Pit-ch 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 Pit-ch than if it is just barely audible. Above 2,000 Hz, the Pit-ch gets higher as the sound gets louder.

Theories of Pit-ch perception

Theories of Pit-ch 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, Pit-ch perception theories can be divided into place coding and temporal coding. Place theory holds that the perception of Pit-ch is determined by the place of maximum excitation on the basilar membrane.

A place code, taking advantage of the tonotopy 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 potentials.However, a purely place-based theory cannot account for the accuracy of Pit-ch perception in the low and middle-frequency ranges.

Temporal theories offer an alternative that appeals to the temporal structure of action potentials, mostly the phase-locking and mode-locking of action potentials to frequencies in a stimulus. The precise way this temporal structure helps code for Pit-ch at higher levels is still debated, but the processing seems to be based on an autocorrelation 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 Pit-ch perception, appealing to 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 Pit-ch perceptand 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, as via auditory-nerve interspike-interval histograms.Some theories of pitch perception hold that pitch has inherent 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, indicating which octave the pitch may be 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 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 illusions. 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 (a class of percussion instrument) does not produce particular pitches. A sound or note of a definite pitch is one where a listener can possibly (or relatively easily) discern the pitch. Sounds with definite pitch have harmonic 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 other frequencies are overtones.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.

It is still possible for two sounds of indefinite pitch to clearly be higher or lower than one another. For instance, a snare drum sounds higher pitched than a 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. A special type of pitch often occurs in free nature when sound reaches the ear of an observer directly from the source, and also after reflecting off a sound-reflecting surface. This phenomenon is called repetition pitch, because the addition of a true repetition of the original sound to itself is the basic prerequisite.

Pitch standards and Standard pitch

A pit-ch standard (also Concert pi-tch) is the conventional pit-ch reference a group of musical instruments are tuned to for a performance. Concert pitch may vary from ensemble to ensemble and has varied widely over musical history.

Standard pit-ch is a more widely accepted convention. The A above 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 pit-ch, the so-called “Baroque pit-ch”, has been set in the 20th century as A = 415 Hz, exactly an equal-tempered semitone lower than A440, in order to facilitate transposition between them.

Transposing instruments have their origin in a variety of pit-ch standards. In modern times, they conventionally have their parts transposed into different keys from voices and other instruments (and even from each other). As a result, musicians need a way to refer to a particular pit-ch in an unambiguous manner when talking to each other.

For example, the most common type of clarinet or trumpet, when playing a note written in their part as C, sounds a pit-ch 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 pit-ch a tone lower than violin pit-ch). In order to refer to that pit-ch unambiguously, one may call it concert B♭, meaning, “…the pit-ch that someone playing a non-transposing instrument like a violin calls B♭.”

Labeling pit-ches

For a comprehensive list of frequencies of musical notes, see Scientific pitch notation and Frequencies of notes. Pitches are labeled using:

Letters, as in Helmholtz pitc-h notation
A combination of letters and numbers—as in scientific pit-ch notation, where notes are labelled upwards from C0, the 16 Hz C

Note frequencies, four-octave C major diatonic scale, starting with C1.

The number that represents the frequency in 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, the notion of pit-ch is insensitive to “spelling”: the description “G4 double sharp” refers to the same pit-ch as A4; in other temperaments, these may be distinct pit-ches. Human perception of musical intervals is approximately logarithmic with respect to fundamental frequency: the perceived interval between the pit-ches “A220” and “A440” is the same as the perceived interval between the pit-ches A440 and A880.

Motivated by this logarithmic perception, music theorists sometimes represent pit-ches using a numerical scale based on the logarithm of the fundamental frequency. For example, one can adopt the widely used MIDI standard to map fundamental frequency, f, to a real number, p, as follows

This creates a linear pit-ch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have a size of 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 pit-ch halfway between C (60) and C♯ (61) can be labeled 60.5.

Scales

The relative pit-ches of individual notes in a scale may be determined by one of a number of tuning systems. In the west, the twelve-note chromatic scale is the most common method of organization, with equal temperament now the most widely used method of tuning that scale. In it, the pit-ch 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, for example), different methods of musical tuning were used.

Almost all of these systems have one interval in common, the octave, where the pi-tch 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 is 880 Hz .

Other musical meanings of pit-ch

In atonal, twelve tone, or musical set theory a “pit-ch” is a specific frequency while a pit-ch class is all the octaves of a frequency. In many analytic discussions of atonal and post-tonal music, pit-ches are named with integers because of octave and enharmonic equivalency (for example, in a serial system, C♯ and D♭ are considered the same pit-ch, while C4 and C5 are functionally the same, one octave apart).

Discrete pi-tches, rather than continuously variable pit-ches, are virtually universal, with exceptions including “tumbling strains” and “indeterminate-pit-ch chants”.Gliding pit-ches are used in most cultures, but are related to the discrete pit-ches they reference or embellish.

Pitch circularity

Pitch circularity is a fixed series of tones that appear to ascend or descend endlessly in pitch.

Pitch is often defined as extending along a one-dimensional continuum from high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height. However pitch also varies in a circular fashion, known as pitch class: as one plays up a keyboard in semitone steps, C, C♯, D, D♯, E, F, F♯, G, G♯, A, A♯ , and B sound in succession, followed by C again, but one octave higher. Due to the fact that the octave is the most consonant interval after the unison,

tones that stand in octave relation, and are so of the same pitch class, have a certain perceptual equivalence—all Cs sound more alike to other Cs than to any other pitch class, as do all D♯s, and so on; this creates the auditory equivalent of a Barber’s pole.

Researchers have demonstrated that by creating banks of tones whose note names are clearly defined perceptually but whose perceived heights are ambiguous, one can create scales that appear to ascend or descend endlessly in pitch. Roger Shepard achieved this ambiguity of height by creating banks of complex tones, with each tone composed only of components that stood in octave relationship. In other words, the components of the complex tone C consisted only of Cs,

but in different octaves, and the components of the complex tone F♯ consisted only of F♯s, but in different octaves. When such complex tones are played in semitone steps the listener perceives a scale that appears to ascend endlessly in pitch. Jean-Claude Risset achieved the same effect using gliding tones instead so that a single tone appeared to glide up or down endlessly in pitch.Circularity effects based on this principle have been produced in orchestral music and electronic music, by having multiple instruments playing simultaneously in different octaves.

Normann et al.showed that pitch circularity can be created using a bank of single tones; here the relative amplitudes of the odd and even harmonics of each tone are manipulated so as to create ambiguities of height. A different algorithm that creates ambiguities of pitch height by manipulating the relative amplitudes of the odd and even harmonics,

was developed by Diana Deutsch and colleagues. Using this algorithm, gliding tones that appear to ascend or descend endlessly are also produced. This development has led to the intriguing possibility that using this new algorithm, one might transform banks of natural instrument samples so as to produce tones that sound like those of natural instruments but still have the property of circularity. This development opens up new avenues for music composition and performance.

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Pitch in music theory | Fundamentals of music | Understanding Western Music Theory