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In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the 'basic miracle of music', the use of which is 'common in most musical systems'. The interval between the first and second harmonics of the harmonic series is an octave. In music, an octave (Latin: octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the 'basic miracle of music', the use of which is 'common in most musical systems'. The interval between the first and second harmonics of the harmonic series is an octave. In music notation, notes separated by an octave (or multiple octaves) have the same letter name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated 8a or 8va (Italian: all'ottava), 8va bassa (Italian: all'ottava bassa, sometimes also 8vb), or simply 8 for the octave in the direction indicated by placing this mark above or below the staff. For example, if one note has a frequency of 440 Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 2 n {displaystyle 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, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are 1⁄2 (or 2 − 1 {displaystyle 2^{-1}} ) and 4 (or 2 2 {displaystyle 2^{2}} ) times the frequency, respectively.

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