# Octave

For other uses of the word octave, see Octave (disambiguation).

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. Further octaves of a note occur at ${\displaystyle 2^{n}}$ 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, 50 Hz and 400 Hz are one and two octaves away from 100 Hz because they are ${\displaystyle 1/2}$ (${\displaystyle 1/2^{1}}$) and 4 (${\displaystyle 2^{2}}$) times the frequency, respectively, however 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.

The octave is the second simplest interval in music (after the unison). 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 is closely related to the concept of harmonics. This 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. Similarly, 15ma means "play two octaves higher than written." Coll'ottava means to play the passage in octaves. Any of these directions can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected.

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

Octave
# semitones Interval class # cents in equal temperament Most common diatonic name Comparable just interval # cents in just interval Just interval vs. equal-tempered interval
12 0 1200 perfect octave 2:1 1200 0

## 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.