In music, an octave ( Play (help·info)) is the interval between one musical pitch and another with half or double its frequency. Using notes, this would be the same note up or down 12 semitones on the chromatic scale. For example, an A4 note would be one octave lower than an A5 note, and one octave higher than an A3 note. The octave relationship is a natural phenomenon which has been referred to as the "basic miracle of music," the use of which is "common in most musical systems."^{[1]} It may be derived from the harmonic series as the interval between the first and second harmonics.
The octave has occasionally been referred to as a diapason.^{[2]}
The octave above an indicated note is sometimes abbreviated 8va, and the octave below 8vb. To emphasize that it is one of the perfect intervals, the octave is sometimes designated P8; the other perfect intervals, the unison, perfect fourth, and perfect fifth, are designated PU (or P1), P4, and P5.
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Theory
For example, if one note has a frequency of 400 Hz, the note an octave above it is at 800 Hz, and the note an octave below is at 200 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2^{n} times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, etc. and the reciprocal of that series. For example, 50 Hz and 400 Hz are one and two octaves away from 100 Hz because they are ½ (or 2^{ −1}) and 4 (or 2^{2}) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.
After the unison, the octave is the simplest interval in music. The human ear tends to hear both notes as being essentially "the same", due to closely related harmonics. Notes in an octave will "ring" together giving it a very pleasing sound to music. For this reason, notes an octave apart are given the same note name in the Western system of music notation—the name of a note an octave above A is also A. This is called octave equivalency, the assumption that pitches one or more octaves apart are musically equivalent in many ways, leading to the convention "that scales are uniquely defined by specifying the intervals within an octave".^{[3]} This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter of which is generally used only in counterpoint, musical set theory, or atonal theory. The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.^{[3]} Thus all C♯s, or all 1s (if C = 0), in any octave are part of the same pitch class. Octave equivalency is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music.^{[4]}^{[5]}
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