Octave
Encyclopedia
In music
, an octave is the interval
between one musical pitch
and another with half or double its frequency
. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". It may be derived from the harmonic series
as the interval between the first and second harmonics.
The octave has occasionally been 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 (or P1), 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.
After the unison
, the octave is the simplest interval in music. The human ear
tends to hear
both notes as being essentially "the same", due to closely related harmonics. Notes in an octave "ring" together, adding a pleasing sound to music
. 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, the assumption that pitches one or more octaves apart are musically equivalent
in many ways, leading to the convention "that scales
are uniquely defined by specifying the intervals within an octave". The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity. Thus all Cs, or all 1s (if C = 0), in any octave are part of the same pitch class
. Octave equivalency is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music
.
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 network
s can form through exposure to pitched notes, without any tutoring, this being derived from the acoustical structure of those notes. Studies have also shown the perception of octave equivalence in rats (Blackwell & Schlosberg, 1943), human infants (Demany & Armand, 1984), and musicians (Allen, 1967) but not starlings (Cynx, 1993), 4-9 year old children (Sergeant, 1983), or nonmusicians (Allen, 1967).
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 to G♯ (13 semitones higher) is an augmented octave (A8), and 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.
, and the other standard heptatonic scales of Western music, there are 7 notes; if one counts both ends (see Fencepost error) there are 8 notes, hence the name "octave", from the Latin octavus, from octo (meaning "eight"). Other scales may have a different number of notes covering the range of an octave, such as the chromatic scale
with 12 notes or Arabic classical scale with 17, 19, or even 24 notes, but the word "octave" is still used in English.
In terms of playing an instrument, "octave" may also mean a special effect involving playing two notes an octave apart at the same time. Some instruments innately provide octaves by having double strings, reeds, etc.—as in the twelve-string guitar or octave harmonica.
Most classical music
systems divide the octave into 12 semitone
s (see musical tuning
). These semitones are usually equally spaced in frequency, in a method called equal temperament
.
The notation 8va is sometimes seen in sheet music
, meaning "play this an octave higher than written." (all' ottava: "at the octave") 8va stands for ottava, the Italian
word for octave (note the 8 and the word 'oct
'). Sometimes 8va also tell the musician to play a passage an octave lower, though 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).
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, an octave is the interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
between one musical pitch
Pitch (music)
Pitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
and another with half or double its frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". It may be derived from the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
as the interval between the first and second harmonics.
The octave has occasionally been referred to as a diapason
Pythagorean interval
In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa...
.
The octave above an indicated note
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....
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
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
, and perfect fifth
Perfect fifth
In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
, are designated PU (or P1), P4, and P5.
Theory
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
, 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.
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, the octave is the simplest interval in music. The human ear
Ear
The ear is the organ that detects sound. It not only receives sound, but also aids in balance and body position. The ear is part of the auditory system....
tends to hear
Hearing (sense)
Hearing is the ability to perceive sound by detecting vibrations through an organ such as the ear. It is one of the traditional five senses...
both notes as being essentially "the same", due to closely related harmonics. Notes in an octave "ring" together, adding a pleasing sound to music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
. 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, the assumption that pitches one or more octaves apart are musically equivalent
Equivalence
Equivalence or equivalent may refer to:*In chemistry:**Equivalent **Equivalence point**Equivalent weight*In computing:**Turing equivalence *In ethics:**Moral equivalence*In history:...
in many ways, leading to the convention "that scales
Musical scale
In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...
are uniquely defined by specifying the intervals within an octave". The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity. Thus all Cs, or all 1s (if C = 0), in any octave are part of the same pitch class
Pitch class
In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
. Octave equivalency is a part of most "advanced musical cultures", but is far from universal in "primitive" and early music
Early music
Early music is generally understood as comprising all music from the earliest times up to the Renaissance. However, today this term has come to include "any music for which a historically appropriate style of performance must be reconstructed on the basis of surviving scores, treatises,...
.
Thalamus
The thalamus is a midline paired symmetrical structure within the brains of vertebrates, including humans. It is situated between the cerebral cortex and midbrain, both in terms of location and neurological connections...
of the mammalian brain
Brain
The brain is the center of the nervous system in all vertebrate and most invertebrate animals—only a few primitive invertebrates such as sponges, jellyfish, sea squirts and starfishes do not have one. It is located in the head, usually close to primary sensory apparatus such as vision, hearing,...
and the perception of octave equivalency in self-organizing neural network
Neural network
The term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...
s can form through exposure to pitched notes, without any tutoring, this being derived from the acoustical structure of those notes. Studies have also shown the perception of octave equivalence in rats (Blackwell & Schlosberg, 1943), human infants (Demany & Armand, 1984), and musicians (Allen, 1967) but not starlings (Cynx, 1993), 4-9 year old children (Sergeant, 1983), or nonmusicians (Allen, 1967).
Diminished octave
In classical music from Western culture, a diminished octave is an interval produced by narrowing a perfect octave by a chromatic semitone. As such, the two notes are denoted by the same letter but have different accidentals...
(d8). The use of such intervals is rare, as there is frequently a more preferable enharmonic
Enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note , interval , or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently...
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.
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 scaleDiatonic scale
In music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...
, and the other standard heptatonic scales of Western music, there are 7 notes; if one counts both ends (see Fencepost error) there are 8 notes, hence the name "octave", from the Latin octavus, from octo (meaning "eight"). Other scales may have a different number of notes covering the range of an octave, such as the chromatic scale
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
with 12 notes or Arabic classical scale with 17, 19, or even 24 notes, but the word "octave" is still used in English.
In terms of playing an instrument, "octave" may also mean a special effect involving playing two notes an octave apart at the same time. Some instruments innately provide octaves by having double strings, reeds, etc.—as in the twelve-string guitar or octave harmonica.
Most classical music
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...
systems divide the octave into 12 semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
s (see musical tuning
Musical tuning
In music, there are two common meanings for tuning:* Tuning practice, the act of tuning an instrument or voice.* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.-Tuning practice:...
). These semitones are usually equally spaced in frequency, in a method called equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
.
Notation
Sheet music
Sheet music is a hand-written or printed form of music notation that uses modern musical symbols; like its analogs—books, pamphlets, etc.—the medium of sheet music typically is paper , although the access to musical notation in recent years includes also presentation on computer screens...
, meaning "play this an octave higher than written." (all' ottava: "at the octave") 8va stands for ottava, the Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
word for octave (note the 8 and the word 'oct
Oct
* An abbreviation of October, the tenth month of the year in the Gregorian calendar*OCT, the professional designation granted to certified teachers in Ontario...
'). Sometimes 8va also tell the musician to play a passage an octave lower, though the similar notation 8vb (ottava bassa) is more common. Similarly, 15ma
Fifteenth
In music, a fifteenth or double octave, abbreviated 15ma, is the interval between one musical note and another with one-quarter the wavelength or quadruple the frequency. The fourth harmonic, it is two octaves. It is referred to as a fifteenth because, in the diatonic scale, there are 15 notes...
(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).
See also
- Blind octaveBlind octaveIn music, a blind octave occurs "in a rapid octave passage when one note of each alternate octave is omitted." The effect is to simulate octave doubling using a solo instrument....
- DecadeDecade (log scale)One decade is a factor of 10 difference between two numbers measured on a logarithmic scale. It is especially useful when referring to frequencies and when describing frequency response of electronic systems, such as audio amplifiers and filters.-Calculations:The factor-of-ten in a decade can be...
- Eight foot pitchEight foot pitchEight-foot pitch is a term common to the organ and the harpsichord. An organ pipe, or a harpsichord string, designated as eight-foot pitch is sounded at standard, ordinary pitch...
- Octave speciesOctave speciesIn early Greek music theory, an octave species is a sequence of incomposite intervals making up a complete octave...
- Pitch circularityPitch circularityPitch is often defined as extending along a one-dimensional continuum from high to low, as can be experienced by sweeping one’s hand up or down a piano keyboard. This continuum is known as pitch height...
- Pseudo-octavePseudo-octaveA pseudo-octave, pseudooctave, or paradoxical octave in music is an interval whose frequency ratio is not 2:1 , that of the octave, but is perceived or treated as equivalent to this ratio, and whose pitches are considered equivalent to each other as with octave equivalency...
- Pythagorean intervalPythagorean intervalIn musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa...
- SolfegeSolfegeIn music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
External links
- Anatomy of an Octave by Kyle GannKyle GannKyle Eugene Gann is an American professor of music, critic and composer born in Dallas, Texas. As a critic for The Village Voice and other publications he has been a supporter of progressive music including such Downtown movements as postminimalism and totalism.- As composer :As a composer his...