In music, an octave (sometimes abbreviated 8va or P8) is the interval between one musical pitch and another with half or double its frequency. In Music theory, the word inversion has several meanings There are inverted chords, inverted melodies, inverted intervals, and In Music, a unison () is an interval, the ratio of 11 or 0 half steps and zero cents. 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 In Musical set theory, an interval class (usual abbreviation ic) is the shortest distance in Pitch class space between two unordered Pitch classes In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval The cent is a logarithmic unit of measure used for musical intervals. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval Music is an Art form in which the medium is Sound organized in Time. In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical Pitch represents the perceived Fundamental frequency of a sound Frequency is a measure of the number of occurrences of a repeating event per unit Time.

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 hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. 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. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer

Musical relevance

After the unison, the octave is the simplest interval in music. In Music, a unison () is an interval, the ratio of 11 or 0 half steps and zero cents. The human ear tends to hear both notes as being essentially "the same". The ear is the sense organ that detects Sounds The Vertebrate ear shows a common biology from Fish to Humans with variations 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. See also Modern musical symbols Music notation or musical notation is any system which represents aurally perceived Music through the use This is called octave equivalency, and is closely related to harmonics. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer 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. In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or In Music transposition refers to the process of moving a collection of notes ( pitches) up or down in pitch by a constant interval. In Music theory, the word inversion has several meanings There are inverted chords, inverted melodies, inverted intervals, and 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 provides concepts for categorizing musical objects and describing their relationships Thus all C♯s, or all 1s (if C = 0), in any octave are part of the same pitch class. In Music, a pitch class is a set of all pitches that are a whole number of Octaves apart e Octave equivalency is a part of most musics, but is far from universal in "primitive" and early music (e. Early music is commonly defined as European classical music from the Middle Ages, the Renaissance and the Baroque. 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).

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 modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or

Octave (equal temperament)

The file plays middle C, followed by C (a tone 1200 cents sharper than C), followed by both tones together. C or Do is the first Note of the fixed-Do Solfege. In Western Music, the expression " Middle C " refers to the note

Problems listening to the file? See media help.

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 power gain changes by ±6 decibels (a factor of four in power), or more precisely 6. The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity relative to 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). One decade is a factor of 10 difference between two numbers (an Order of magnitude difference measured on a Logarithmic scale.

Example

A magnitude of 400 (52 dB) at 4 kHz decreases as frequency increases at −2 dB/octave. What is the magnitude at 13 kHz?

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 Music theory, a diatonic scale (from the Greek διατονικος, meaning " through tones" also known as the heptatonia prima and A heptatonic scale is a musical scale with seven pitches per octave In mathematics 8 is a Composite number, its Proper divisors being 1, 2, and 4. 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. The chromatic scale is a Musical scale with twelve pitches each a Semitone or Half step apart 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.

In most Western music, the octave is divided into 12 semitones (see musical tuning). Western music is the genres of Music originating in the Western world (Europe and its former colonies including Western classical music, American 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 In Music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice These semitones are usually equally spaced out in a method known as equal temperament. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio.

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. Human voices may be classified according to their vocal range &mdash the highest and lowest pitches that they can produce It is important to remember when hearing this description that a piano has 7+¹⁄₃ octaves total.

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. Sheet music is a hand-written or printed form of Musical notation; like its analogs -- books pamphlets etc " 8va stands for ottava, the Italian word for octave. Italian ( or lingua italiana) is a Romance language spoken by about 63 million people as a First language, primarily in Italy. 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. In Music, a fifteenth (sometimes abbreviated 15ma) is the interval between one musical Note and another with one-quarter or quadruple the " 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

• Solfege
• Pythagorean interval

Sources

• Burns, Edward M. In Music, solfège ('soʊlfɛʒ also called solfeggio, sol-fa, or solfa) is a Pedagogical Solmization technique for the See also Whole-tone scale List of meantone intervals List of intervals in 5-limit just intonation (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.

External links

• Guitar octave map
• Anatomy of an Octave by Kyle Gann
• Octave hardwired in auditory brain