Octave 

For the numerical computation software, see GNU Octave.

In music, an octave (sometimes abbreviated to 8ve) is the interval between one musical note and another whose pitch is twice its frequency. For example, if one note is pitched at 400Hz, the note an octave above it is at 800Hz, and the note an octave below is at 200Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1.

The octave is the most fundamental interval in music. The human ear tends to hear both notes as being essentially "the same". 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.

As well as being used to describe the relationship between two notes, the word is also used when speaking of a range of notes that fall between a pair an octave apart. In the diatonic scale, this is 8 notes if one counts both ends, hence the name "octave", from Italian for 8. In the chromatic scale, this is 13 notes counting both ends, although traditionally, one speaks of 12 notes of the chromatic scale, not counting both ends. Other scales may have a different number of notes covering the range of an octave, but the word "octave" is still used.

In most Western music, the octave is divided into 12 semitones (see musical tuning). These semitones are usually equally spaced out in a method known as equal temperament.

The notation 8va is sometimes seen in sheet music, meaning "play this an octave higher than written." 8va stands for ottava, the Italian word for octave. Sometimes 8va will also be used to indicate a passage is to be played an octave lower, although the similar notation 8vb (ottava basso) is more common.

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