Octave
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In
music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...
, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
. 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." The interval between the first and second harmonics of the harmonic series is an octave. In Western
music notation Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...
, notes separated by an octave (or multiple octaves) have the same name and are of the same
pitch class In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
. To emphasize that it is one of the
perfect intervals In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or ha ...
(including
unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or per ...
,
perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...
, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated
note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened version ...
is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff.


Explanation and definition

For example, if one note has a
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of 440  Hz, the note one octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves of a note occur at 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, 55 Hz and 440 Hz are one and two octaves away from 110 Hz because they are (or 2^) and 4 (or 2^) times the frequency, respectively. The number of octaves between two frequencies is given by the formula: : \text = \log_2\left(\frac\right)


Music theory

Most
musical scale In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...
s are written so that they begin and end on notes that are an octave apart. For example, the C major scale is typically written (shown below), the initial and final C's being an octave apart. Because of octave equivalence, notes in a chord that are one or more octaves apart are said to be '' doubled'' (even if there are ''more'' than two notes in different octaves) in the chord. The word is also used to describe melodies played in
parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of ...
in more than multiple octaves. 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 In Western tonal music theory, an augmented octave is the sum of a perfect octave and an augmented unison or chromatic semitone. It is the interval between two notes, with the same note letter on staff positions an octave apart, whose altera ...
(A8), and G to G (11 semitones higher) is a
diminished octave In music from Western culture, a diminished octave () is an interval produced by narrowing a perfect octave by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an d8 not given ...
(d8). The use of such intervals is rare, as there is frequently a preferable enharmonically-equivalent notation available (
minor ninth In music, a ninth is a compound interval consisting of an octave plus a second. Like the second, the interval of a ninth is classified as a dissonance in common practice tonality. Since a ninth is an octave larger than a second, its ...
and
major seventh In music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval number for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as ''major'' because it i ...
respectively), but these categories of octaves must be acknowledged in any full understanding of the role and meaning of octaves more generally in music.


Notation


Octave of a pitch

Octaves are identified with various naming systems. Among the most common are the
scientific Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...
, Helmholtz, organ pipe, and MIDI note systems. In scientific pitch notation, a specific octave is indicated by a numerical subscript number after note name. In this notation, middle C is C4, because of the note's position as the fourth C key on a standard 88-key piano keyboard, while the C an octave higher is C5. :


''Ottava alta'' and ''bassa''

The notation ''8a'' or ''8va'' is sometimes seen in
sheet music Sheet music is a handwritten or printed form of musical notation that uses List of musical symbols, musical symbols to indicate the pitches, rhythms, or chord (music), chords of a song or instrumental Musical composition, musical piece. Like ...
, meaning "play this an octave higher than written" (''all' ottava'': "at the octave" or ''all' 8va''). ''8a'' or ''8va'' stands for ''ottava'', the
Italian Italian(s) may refer to: * Anything of, from, or related to the people of Italy over the centuries ** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance language *** Regional Ita ...
word for octave (or "eighth"); the octave above may be specified as ''ottava alta'' or ''ottava sopra''). Sometimes ''8va'' is used to tell the musician to play a passage an octave ''lower'' (when placed under rather than over the staff), though the similar notation ''8vb'' (''ottava bassa'' or ''ottava sotto'') is also used. Similarly, '' 15ma'' (''quindicesima'') means "play two octaves higher than written" and ''15mb'' (''quindicesima bassa'') means "play two octaves lower than written." The abbreviations ''col 8'', ''coll' 8'', and ''c. 8va'' stand for ''coll'ottava'', meaning "with the octave", i.e. to 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.


Equivalence

After the
unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or per ...
, 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 separated by an octave "ring" together, adding a pleasing sound to music. The interval is so natural to humans that when men and women are asked to sing in unison, they typically sing in octave. For this reason, notes an octave apart are given the same note name in the Western system of
music notation Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...
—the name of a note an octave above A is also A. This is called ''octave equivalence'', the assumption that pitches one or more octaves apart are musically
equivalent Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry * Equivalence class (music) *'' Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *''Equiva ...
in many ways, leading to the convention "that
scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number w ...
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), any number of octaves apart, are part of the same
pitch class In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
. Octave equivalence is a part of most advanced musical cultures, but is far from universal in "primitive" and early music. The languages in which the oldest extant written documents on tuning are written, Sumerian and
Akkadian Akkadian or Accadian may refer to: * Akkadians, inhabitants of the Akkadian Empire * Akkadian language, an extinct Eastern Semitic language * Akkadian literature, literature in this language * Akkadian cuneiform Cuneiform is a logo- syllabi ...
, have no known word for "octave". However, it is believed that a set of
cuneiform Cuneiform is a logo-syllabic script that was used to write several languages of the Ancient Middle East. The script was in active use from the early Bronze Age until the beginning of the Common Era. It is named for the characteristic wedge-sh ...
tablets that collectively describe the tuning of a nine-stringed instrument, believed to be a Babylonian lyre, describe tunings for seven of the strings, with indications to tune the remaining two strings an octave from two of the seven tuned strings. Leon Crickmore recently proposed that "The octave may not have been thought of as a unit in its own right, but rather by analogy like the first day of a new seven-day week". Monkeys experience octave equivalence, and its biological basis apparently is an octave mapping of neurons in the auditory
thalamus The thalamus (from Greek θάλαμος, "chamber") is a large mass of gray matter located in the dorsal part of the diencephalon (a division of the forebrain). Nerve fibers project out of the thalamus to the cerebral cortex in all directions, ...
of the mammalian
brain A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a ve ...
.The mechanism of octave circularity in the auditory brain
", ''Neuroscience of Music''.
Studies have also shown the perception of octave equivalence in rats, human infants, and musicians but not starlings, 4–9 year old children, or nonmusicians.


See also

* * * * * * * * * *


References

Sources * * * * *


External links



by
Kyle Gann Kyle Eugene Gann (born November 21, 1955, in Dallas, Texas) is an American professor of music, critic, analyst, and composer who has worked primarily in the New York City area. As a music critic for ''The Village Voice'' (from 1986 to 2005) an ...
{{Authority control Perfect intervals 0002:0001 Musical notes