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Encyclopedia > Octaves
For the numerical computation software, see GNU Octave.

In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. For example, if one note is pitched at 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.

The octave is the second simplest 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. This is called octave equivalency and in some ways is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter two of which are generally used only in musical set theory or atonal theory. 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 musics, but is far from universal in "primitive" and early music (e.g., Nettl, 1956; Sachs & Kunst, 1962).

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 bassa) is more common. Both directions can be cancelled with the word loco.

For music-theoretical purposes (not on sheet music), octave can be abbreviated as P8.

## Source

• Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.
• Sachs, C. and Kunst, J. (1962). In The wellsprings of music, ed. Kunst, J. The Hague: Marinus Nijhoff.

Results from FactBites:

 Octave - Wikipedia, the free encyclopedia (773 words) In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. Octave equivalency is a part of most musics, but is far from universal in "primitive" and early music (e.g., Nettl, 1956; Sachs and Kunst, 1962). Also monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain [1].
 GNU Octave - Wikipedia, the free encyclopedia (758 words) Octave's `andand' and `' logical operators are evaluated in a short-circuit fashion (like the corresponding operators in the C language) and work differently than the element by element operators `and' and `'. Octave has a real mechanism for handling functions that take an unspecified number of arguments, so it is no longer necessary to place an upper bound on the number of optional arguments that a function can accept. The differences between Octave and MATLAB are usually because the authors of Octave decided on a better and subjective implementation than the way MATLAB does it, and so introduced "user preference variables" so as to allow the user to customize Octave's behavior to be either MATLAB-compatible or to use Octave's new features.
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