Octave 37726 225151876 2008-07-12T04:13:43Z Thijs!bot 1392310 robot Adding: [[sk:Oktáva]] {{Otheruses}} {{Infobox Interval| main_interval_name = Perfect octave| inverse = [[unison]]| complement = octave| other_names = - | abbreviation = P8 | semitones = 12 | interval_class = 0 | just_interval = 2:1| cents_equal_temperament = 1200| cents_just_intonation = 1200 }} In [[music]], an '''octave''' (sometimes abbreviated '''8va''' or '''P8''') is the [[interval (music)|interval]] between one musical [[Pitch (music)|pitch]] and another with half or double its [[frequency]]. == Examples == [[Image:Octave example.png|frame|left|An example of an octave, from G4 to G5]] For example, if one note has a frequency of 400 [[Hertz|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 2<sup>''n''</sup> 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<sup>&nbsp;&minus;1</sup>) and 4 (or 2<sup>2</sup>) times the frequency, respectively. However, 300 Hz is not a whole number octave above 100 Hz, despite being a [[harmonic]] of '''100''' Hz. == Musical relevance == After the [[unison]], the octave is the simplest interval in music. The human [[ear]] tends to [[Hearing (sense)|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]]&mdash;the name of a note an octave above A is also A. This is called '''octave [[equivalence|equivalency]]''', and is closely related to [[harmonic]]s. 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&nbsp;=&nbsp;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 [http://web.telia.com/~u57011259/eng7.htm] 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{{Unicode|♮}} to G♯ (13 semitones higher) is an '''augmented octave (A8)''', and G{{Unicode|♮}} 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. {{Listen|filename=Octave_ET.ogg|title=Octave (equal temperament)|description=The file plays [[middle C]], followed by C (a tone 1200 cents sharper than C), followed by both tones together.}} ==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 6.0206 decibels when the frequency changes by a factor of 2. This response is equivalent to ±20dB per [[decade (log scale)|decade]] (a change in frequency by a factor of 10). '''Example''' A magnitude of 400 (52 dB) at 4 kHz decreases as frequency increases at &minus;2 dB/octave. What is the magnitude at 13 kHz? : <math>\text{number of octaves} = \log_2\left(\frac{13}{4}\right) = 1.7</math> : <math>\text{Mag}_{13\text{ kHz}} = 52\text{ dB} + (1.7\text{ octaves} \times -2\text{ dB/octave}) = 48.6\text{ dB} = 269.\,</math> == 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 "[[8 (number)|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 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 [[semitone]]s (see [[musical tuning]]). These semitones are usually equally spaced out in a method known as [[equal temperament]]. 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 {{frac|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 {{frac|16|8}}, which produces a {{frac|2|1}} octave. == Notation ==<!-- This section is linked from [[Coll'ottava]] --> [[Image:Ottava Ex.png|thumb|right|300px|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 language|Italian]] word for octave (note the 8 and the word '[[oct]]'). 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, '''[[fifteenth|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== * [[Solfege]] * [[Pythagorean interval]] ==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. == External links == * [http://wikiguitar.net/index.php?title=Octave Guitar octave map] * [http://www.kylegann.com/Octave.html Anatomy of an Octave] by [[Kyle Gann]] * [http://web.telia.com/~u57011259/eng7.htm Octave hardwired in auditory brain] * [http://www.guitarbinge.com/2008/03/easy-way-to-know-where-all-notes-are-on.html Shortcut method for guitar octaves] {{Musical notation}} {{Diatonic intervals}} [[Category:Intervals]] [[ar:مسافات موسيقية]] [[bg:Октава]] [[ca:Octava]] [[cs:Oktáva (hudba)]] [[da:Oktav]] [[de:Oktave]] [[et:Oktaav]] [[es:Octava]] [[eo:Okto]] [[fa:اوکتاو]] [[fr:Octave (musique)]] [[fy:Oktaaf]] [[gl:Oitava]] [[ko:옥타브]] [[hr:Oktava]] [[id:Oktaf]] [[is:Áttund]] [[it:Ottava (musica)]] [[he:אוקטבה]] [[lv:Oktāva]] [[lt:Oktava]] [[hu:Oktáv]] [[nl:Octaaf (muziek)]] [[ja:オクターヴ]] [[no:Oktav]] [[nn:Oktav]] [[pl:Oktawa (interwał)]] [[pt:Oitava]] [[ru:Октава]] [[simple:Octave]] [[sk:Oktáva]] [[sr:Октава (музика)]] [[fi:Oktaavi]] [[sv:Oktav]] [[th:อ็อกเทฟ]] [[tr:Oktav]] [[uk:Октава]] [[zh:八度]]