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MUSICAL NOTATION
http://en.wikipedia.org/wiki/Octaves

All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

# Octave

(Redirected from Octaves)

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

## Examples

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 2n 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 1 / 2 (1 / 21) and 4 (22) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.

## Musical relevance

After the unison, the octave is the 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 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). 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].

While octaves commonly refer to the perfect octave (P8), the interval of an octave in music theory encompasses chromatic alterations within the pitch class, meaning that G natural to G# (13 semitones higher) is an augmented octave (A8), and G natural to G-flat (11 semitones higher) is a diminished octave (d8). The use of such intervals is rare, as there is frequently a more preferable enharmonic notation available, but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more generally in music.

## Electrical Relevance

In electronics design, an amplifier or filter may be stated to have a frequency response of +/-6dB per octave over a particular frequency range, which signifies that the voltage gain changes by +/-6 decibels when the frequency changes by a factor of 2. A frequency response of +/-6dB per octave is equivalent to +/-20dB per decade (a change in frequency by a factor of 10).

## Other uses of term

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, since there are 12 intervals. Other scales may have a different number of notes covering the range of an octave, such as the Arabic classical scale with 17, 19, or even 24 notes, but the word "octave" is still used.

In terms of playing an instrument, "octave" may also mean a special effect involving playing two notes that are an octave apart at the same time. This effect may have to be created by the musician. However, some instruments are purposely tuned or designed to produce this effect, for example, the twelve-string guitar and the octave harmonica.

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.

In the Electrical Sense +/- 6 db per octave is actually equal to 19.93157, which is almost 20.

## Notation

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 (quindicesima) means "play two octaves higher than written" and 15mb (quindicesima bassa) means "play two octaves lower 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.

• Solfege
• diapason
• cent (music)
• Octave scale

## Source

• Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0-12-213564-4.
• Sachs, C. and Kunst, J. (1962). In The wellsprings of music, ed. Kunst, J. The Hague: Marinus Nijhoff.

• Guitar octave map
• Anatomy of an Octave by Kyle Gann
• Tonalsoft Encyclopedia of Tuning
• Octave hardwired in auditory brain