See his Œuvres complètes (1883).
The octave is occasionally referred to as a diapason.
The octave above an indicated note is sometimes abbreviated 8va, and the octave below 8vb. To emphasize that it is one of the perfect intervals, the octave is sometimes designated P8; the other perfect intervals, the unison, [[perfect fourth, and perfect fifth, are designated PU, P4, and P5.
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 ½ (or 2 −1) and 4 (or 22) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a harmonic of 100 Hz.
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 harmonics. This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter of which is generally used only in counterpoint, 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). However, monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain and the perception of octave equivalency in self-organizing neural networks can form through exposure to pitched notes, without any tutoring, this being derived from the acoustical structure of those notes (Bharucha 2003, cited in Fineberg 2006).
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♮ to G♯ (13 semitones higher) is an augmented octave (A8), and G♮ to G♭ (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.
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 power gain changes by ±6 decibels (a factor of four in power), or more precisely 6.0206 decibels when the frequency changes by a factor of 2. This response is equivalent to ±20dB per decade (a change in frequency by a factor of 10).
A magnitude of 400 (52 dB) at 4 kHz decreases as frequency increases at −2 dB/octave. What is the magnitude at 13 kHz?
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, and the other standard heptatonic scales of Western music, this is 8 notes if one counts both ends, hence the name "octave", from the Latin octavus, from octo (meaning "eight"). 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.
Many times singers will be described as having a four-octave range or a five-octave range. This is technically a misnomer, and is described here: five-octave vocal range. It is important to remember when hearing this description that a piano has octaves total.
Many of the dual toned sirens manufactured by the Sentry Siren Company use an octave ratio on their sirens, usually , which produces a octave.
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 (note the 8 and the word 'oct'). 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." Col 8 or c. 8va stands for coll'ottava and means "play the notes in the passage together with the notes in the notated 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 (which is an abbreviation for Perfect Eighth, the interval between 12 semitones or an octave).