In music, an octave (
Play (help·info)) or perfect 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".[1] 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.[2]
To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. The octave above or below an indicated note is sometimes abbreviated 8va or 8vb, respectively.
Theory
An example of an octave, from G4 to G5
For example, if one note has a frequency of 440 Hz, the note an octave above it is at 880 Hz, and the note an 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 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, 55 Hz and 440 Hz are one and two octaves away from 110 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".[3] The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.[3] 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 "advanced musical cultures", but is far from universal in "primitive" and early music.[4][5] The languages in which the oldest extant written documents on tuning are written, Sumerian and Akkadian, have no known word for "octave". However, it is believed that a set of cuneiform 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.[6] 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".[7]
Monkeys experience octave equivalency, and its biological basis apparently is an octave mapping of neurons in the auditory thalamus of the mammalian brain[8] 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.[9] Studies have also shown the perception of octave equivalence in rats (Blackwell & Schlosberg, 1943), human infants (Demany & Armand, 1984),[10] and musicians (Allen, 1967) but not starlings (Cynx, 1993), 4-9 year old children (Sergeant, 1983), or nonmusicians (Allen, 1967).[3]
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.
Octaves are identified with various naming systems. Among the most common are the Scientific, Helmholtz, Organ Pipe, Midi, and Midi Note systems.
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, 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 semitones (see musical tuning). These semitones are usually equally spaced in frequency, in a method called equal temperament.
Notation
An example of the same two notes expressed regularly, in an 8va bracket, and in a 15ma bracket.
In writing a specific octave is often indicated through the addition of a number after the note letter name. Thus 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 above is "C5", in a system known as scientific pitch notation.
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 (also meaning "eighth"). 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).
See also
References
- ^ Cooper, Paul (1973). Perspectives in Music Theory: An Historical-Analytical Approach, p.16. ISBN 0-396-06752-2.
- ^ William Smith and Samuel Cheetham (1875). A Dictionary of Christian Antiquities. London: John Murray. http://books.google.com/books?id=1LIPFk6oFVkC&pg=PA550&dq=diatessaron+diapason+diapente+fourth+fifth.
- ^ a b c Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition, , p.252. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0-12-213564-4.
- ^ e.g., Nettl, 1956; Sachs, C. and Kunst, J. (1962). In The wellsprings of music, ed. Kunst, J. The Hague: Marinus Nijhoff.
- ^ e.g., Nettl, 1956; Sachs, C. and Kunst, J. (1962). Cited in Burns, Edward M. (1999), p.217.
- ^ Clint Goss (2012). "Flutes of Gilgamesh and Ancient Mesopotamia". Flutopedia. http://Flutopedia.com/mesopotamian_flutes.htm. Retrieved 2012-01-08.
- ^ Leon Crickmore (2008). "New Light on the Babylonian Tonal System". ICONEA 2008: Proceedings of the International Conference of Near Eastern Archaeomusicology, held at the British Museum, December 4-6, 2008 24: 11-22.
- ^ The mechanism of octave circularity in the auditory brain
- ^ Bharucha 2003, cited in Fineberg, Joshua (2006). Classical Music, Why Bother?". Routledge. ISBN 0-415-97173-X. Cites Bharucha (2003).
- ^ Demany L, Armand F. The perceptual reality of tone chroma in early infancy. J Acoust Soc Am 1984;76:57–66.
External links
|
|
|
Numbers in brackets are the number of semitones in the interval.
Fractional semitones are approximate.
|
|
Twelve-semitone
(Western) |
|
Perfect
|
|
|
|
Major
|
|
|
|
Minor
|
|
|
|
Augmented
|
|
|
|
Diminished
|
|
|
|
Compound
|
|
|
|
| Other systems |
|
Supermajor
|
|
|
|
Neutral
|
|
|
|
Subminor
|
|
|
|
7-limit
|
|
|
|
| Other intervals |
|
Groups
|
|
|
|
|
|
|
|
Measurement
|
|
|
|
Others
|
|
|
|
See crossword solutions for the clue 
