Frequency

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Frequency

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 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).