Pitch_(music)

context: Pitch is an auditory sensation in which a listener assigns musical tones to relative positions on a musical scale based primarily on their perception of the 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, which cannot be directly measured. However, this does not necessarily mean that most people won't agree on which notes are higher and lower.

context: This creates a linear pitch space 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.

context: The relative pitches 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 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, for example), different methods of musical tuning were used. Almost all of these systems have one interval 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 is 880 Hz (info).

context: According to the American National Standards Institute, 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 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, "high" pitch means very rapid oscillation, and "low" pitch corresponds to slower oscillation. Despite that, the idiom 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 decreased.

context: 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.

context: 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 can be precisely determined through physical measurement, it may differ from the perceived pitch 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.

context: 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.

context: 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.

context: 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 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 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 standard to map fundamental frequency, f, to a real number, p, as follows

context: 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 pitch 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 pitch 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 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, 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, that indicates the octave the pitch is in.