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'''Frequency''' is the inverse of time. In music, specifically it refers to the number of oscillations per unit of time of a vibrating object. Frequency is typically measured in [[Wikipedia:Hertz|hertz]] (Hz), defined as one oscillation per second.
Sound is created through air pressure waves—concentric spherical regions emanating from the sound-creating object of high pressure and low pressure, which travel at the speed of sound while the object generates more pressure waves. In music, the '''frequency''' of a sound is equal to the frequency of the sine wave that represents the same pitch, where the frequency of the sine wave is measured in the number of times per second high pressure is sensed. Notes with high frequency sound high, and notes with low frequency sound low. Middle C, roughly in the center of the piano, has a frequency of about 255 [[Hertz]] (abbreviated Hz), or oscillations per second, while human hearing range is from about 20 to 20,000 Hz.


A sound's [[pitch]] is associated with the fundamental frequency of its frequency spectrum.
If an instrument generates a single note, when pressure at a given point near the instrument is graphed, the resulting graph<ref>By taking the [[wikipedia:Fourier_transform|Fourier transform]].</ref> is a sum of sine waves of various levels of frequency and amplitude. The frequency of the lowest sine wave is generally perceived as the frequency of a sound, even if this sine wave does not have the largest amplitude. The entire list of frequencies together with their amplitudes is called the '''frequency spectrum''', and differences in frequency spectra cause different instruments to sound different even if they are playing the same pitch.


== Definition ==
Frequency is different from [[pitch]], because multiplications in frequency translate to additions in pitch; successive octaves are equally spaced in pitch, but exponentially increasing in frequency.
By convention, frequency refers to the '''linear''' measure of how "high" or "low" a sound is. That is, a sound that is twice the frequency has twice as many oscillations per second.
[[Category:Tuning]]
[[Category:Tuning]]
[[Category:Terms]]
[[Category:Terms]]
Usually, absolute frequency in Hz is not of interest to musicians (even in xenharmony), because human hearing perceives ratios of frequency instead of absolute frequencies. Because of this, a standard frequency is usually set (by convention, at 440 Hz), and the frequencies of other notes in the scale are defined by multiplying that base frequency by ratios.  
== Intervals and concordance ==
When two notes have frequencies a:b where b/a is rational, the interval between the two notes is within [[Just intonation]] and denoted b/a.


Frequency is different from [[pitch]], which is the '''logarithmic''' measure of how "high" or "low" a sound is. Multiplications in frequency translate to additions in pitch; the notes in an equal tuning are equally spaced in pitch.
When two notes are played at once where their frequency spectra share a high-amplitude frequency, these two notes sound concordant when played together. If the two notes have frequency spectra where all non-negligible frequencies are multiples of the lowest frequency (as is the case with most methods of sound production, including the human voice, most instruments, and square/saw/triangle waves) they will sound concordant when the interval between them is within just intonation (especially if the just-intonation ratio is low complexity). If these two notes are related by the [[just intonation]] interval b/a, then the frequency they share lies at [[Lcm|LCM]](a, b).


== Overtones ==
== References ==
Frequency ratios that take the form of simple fractions are concordant. This is because of the way notes sound when played on most instruments: the frequency of the note being heard is called the '''fundamental''' frequency (let's say, 440 Hz), but the sound wave also contains other frequencies at integer multiples of the fundamental, called harmonics or overtones: the [[2/1|perfect octave]] at twice the frequency (880 Hz), the [[3/1|third harmonic]] at 3 times the frequency (1320 Hz), and so on. The relative volume of these harmonics determines what sound the instrument has. When the harmonics of two sound waves coincide, the two frequencies are considered concordant. This obviously happens with two sound waves that have the same frequency (i.e. a ratio of [[1/1]]), but also happens with other simple ratios, which include harmonics, but also include ratios like [[3/2]] and [[5/4]]. Because of this, concordance can be considered how much two notes sound like "the same note". {{Stub}}
<references />

Latest revision as of 18:42, 14 March 2025

English Wikipedia has an article on:

Sound is created through air pressure waves—concentric spherical regions emanating from the sound-creating object of high pressure and low pressure, which travel at the speed of sound while the object generates more pressure waves. In music, the frequency of a sound is equal to the frequency of the sine wave that represents the same pitch, where the frequency of the sine wave is measured in the number of times per second high pressure is sensed. Notes with high frequency sound high, and notes with low frequency sound low. Middle C, roughly in the center of the piano, has a frequency of about 255 Hertz (abbreviated Hz), or oscillations per second, while human hearing range is from about 20 to 20,000 Hz.

If an instrument generates a single note, when pressure at a given point near the instrument is graphed, the resulting graph[1] is a sum of sine waves of various levels of frequency and amplitude. The frequency of the lowest sine wave is generally perceived as the frequency of a sound, even if this sine wave does not have the largest amplitude. The entire list of frequencies together with their amplitudes is called the frequency spectrum, and differences in frequency spectra cause different instruments to sound different even if they are playing the same pitch.

Frequency is different from pitch, because multiplications in frequency translate to additions in pitch; successive octaves are equally spaced in pitch, but exponentially increasing in frequency.

Intervals and concordance

When two notes have frequencies a:b where b/a is rational, the interval between the two notes is within Just intonation and denoted b/a.

When two notes are played at once where their frequency spectra share a high-amplitude frequency, these two notes sound concordant when played together. If the two notes have frequency spectra where all non-negligible frequencies are multiples of the lowest frequency (as is the case with most methods of sound production, including the human voice, most instruments, and square/saw/triangle waves) they will sound concordant when the interval between them is within just intonation (especially if the just-intonation ratio is low complexity). If these two notes are related by the just intonation interval b/a, then the frequency they share lies at LCM(a, b).

References

  1. ↑ By taking the Fourier transform.
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