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Encyclopedia > Octave
Perfect octave
Inverse unison
Name
Other names -
Abbreviation P8
Size
Semitones 12
Interval class 0
Just interval 2:1
Cents
Equal temperament 1200
Just intonation 1200

In music, an octave (sometimes abbreviated 8ve or P8) is the interval between one musical note and another with half or double its frequency. The word octave derives from the Latin word octavus, meaning eight. ... In music theory, the word inversion has several meanings. ... For other uses, see Unison (disambiguation). ... A semitone (also known in the USA as a half step) is a musical interval. ... In music, specifically, musical set theory an interval class, or unordered pitch-class interval, is an interval measured by the distance between its two pitch classes ordered so they are as close as possible. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ... The cent is a logarithmic unit of measure used for musical intervals. ... An equal temperament is a musical temperament â€” that is, a system of tuning intended to approximate some form of just intonation â€” in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ... For other uses, see Music (disambiguation). ... In music theory, the term interval describes the difference in pitch between two notes. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ...

## Examples

An example of an octave, from G4 to G5

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 $frac{1}{2}$ (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. Image File history File links No higher resolution available. ... This article is about the SI unit of frequency. ... This article is about the components of sound. ...

## 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 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 [1] 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). For other uses, see Unison (disambiguation). ... For other uses, see Ear (disambiguation). ... Hearing is one of the traditional five senses, and refers to the ability to detect sound. ... Music notation is a system of writing for music. ... In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i. ... This article is about the components of sound. ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... In music transposition is moving a note or collection of notes (or pitches) up or down in pitch by a constant interval. ... For non-musical meanings of inversion, see inversion. ... In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm, and interdependent in harmony. ... Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... Atonality in a general sense describes music that departs from the system of tonal hierarchies that are said to characterized the sound of classical European music from the sixteenth through the nineteenth centuries. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... Early music is commonly defined as European classical music from the Middle Ages, the Renaissance and the Baroque. ...

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. In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...

 Octave (equal temperament) The file plays middle C, followed by C (a tone 1200 cents sharper than C), followed by both tones together. Problems listening to the file? See media help.

Image File history File links Octave_ET.oggâ€Ž I, the creator of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1. ... In Western music, the expression middle C refers to the note C or Do located exactly between the two staves of the grand staff, quoted as C4 in note-octave notation (also known as scientific pitch notation). ...

## 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 (a factor of two in voltage, 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). The decibel is a dimensionless unit (like percent) that is a measure of ratios on a logarithmic scale. ... A decade on a graphical logarithmic scale represents multiplication by 10 from the previous value. ...

## 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, 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 music theory, a diatonic scale (from the Greek diatonikos, to stretch out; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. ... In music a heptatonic scale is a scale (music) with seven (hepta) degrees. ... Look up eight in Wiktionary, the free dictionary. ... The chromatic scale is a scale with twelve pitches, each a semitone or half step apart. ...

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. The twelve string guitar is an acoustic or electric guitar with twelve strings, which produces a richer, more ringing tone than a standard six string guitar. ...

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. Western music is the genres of music originating in the Western world (Europe and its former colonies) including Western classical music, American Jazz, Country and Western, pop music and rock and roll. ... A semitone (also known in the USA as a half step) is a musical interval. ... In music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice. ... An equal temperament is a musical temperament â€” that is, a system of tuning intended to approximate some form of just intonation â€” in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ...

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 7 1/3 octaves total. This article or section does not cite its references or sources. ...

Many of the dual toned sirens manufactured by the Sentry Siren Company use an octave ratio on their sirens, usually 16/8, which produces a 2/1 octave.

## Notation

An example of the same two notes expressed regularly, in an 8va bracket, and in a 15ma bracket.

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." Col 8 or c. 8va stands for coll'ottava and means to play the notes in the passage together with the notes in the notatated 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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Sheet music is written representation of music. ... In music, an fifteenth (sometimes abbreviated 15ma) is the interval between one musical note and another with one-quarter or quadruple the frequency. ...

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).

In music, solfege (or solmization) is a pedagogical technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfege syllable (or sol-fa syllable). The seven syllables normally used for this practice in the West are: Do, Re... The intervals of Pythagorean tuning are just intervals involving only powers of two and three. ... The cent is a logarithmic unit of measure used for musical intervals. ... It is proposed that this article be deleted, because of the following concern: This article duplicates Scientific pitch notation. ...

## Sources

• 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.
• Fineberg, Joshua (2006). Classical Music, Why Bother?". Routledge. ISBN 041597173X. Cites Bharucha (2003).
• Sachs, C. and Kunst, J. (1962). In The wellsprings of music, ed. Kunst, J. The Hague: Marinus Nijhoff.

Results from FactBites:

 Octave - Wikipedia, the free encyclopedia (773 words) In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. Octave equivalency is a part of most musics, but is far from universal in "primitive" and early music (e.g., Nettl, 1956; Sachs and 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].
 GNU Octave - Wikipedia, the free encyclopedia (758 words) Octave's `andand' and `' logical operators are evaluated in a short-circuit fashion (like the corresponding operators in the C language) and work differently than the element by element operators `and' and `'. Octave has a real mechanism for handling functions that take an unspecified number of arguments, so it is no longer necessary to place an upper bound on the number of optional arguments that a function can accept. The differences between Octave and MATLAB are usually because the authors of Octave decided on a better and subjective implementation than the way MATLAB does it, and so introduced "user preference variables" so as to allow the user to customize Octave's behavior to be either MATLAB-compatible or to use Octave's new features.
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