# Octave

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Interval between one musical pitch and another with double its frequency

For other uses, see [Octave (disambiguation)](/source/Octave_(disambiguation)).

Musical interval

Perfect octave Inverse unison Name Other names - Abbreviation P8 Size Semitones 12 Interval class 0 Just interval 2:1[1] Cents 12-Tone equal temperament 1200[1] Just intonation 1200[1]

In [music](/source/Music), an **octave** (Latin: *octavus*: eighth) or **perfect octave** (sometimes called the [**diapason**](/source/Pythagorean_interval))[2] is an [interval](/source/Interval_(music)) between two notes, one having twice the [frequency](/source/Frequency) of vibration of the other. For instance, the interval between C4 and C5 (in [scientific pitch notation](/source/Scientific_pitch_notation)) is an octave.

- Audio playback is not supported in your browser. You can [download the audio file](https://upload.wikimedia.org/score/b/g/bgud6rirs6b1yhq5c3hg0joda5f45lu/bgud6rir.mp3).

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".[3] The interval between the first and second harmonics of the [harmonic series](/source/Harmonic_series_(music)) is an octave. In Western [music notation](/source/Musical_notation), notes separated by an octave (or multiple octaves) have the same [name](/source/Musical_note#Written_notes) and are of the same [pitch class](/source/Pitch_class).

To emphasize that it is one of the [perfect intervals](/source/Interval_(music)#Perfect) (including [unison](/source/Unison), [perfect fourth](/source/Perfect_fourth), and [perfect fifth](/source/Perfect_fifth)), the octave is designated P8. Other [interval qualities](/source/Interval_quality) are also possible, though rare. The octave above or below an indicated [note](/source/Musical_note) is sometimes abbreviated *8a* or *8va* ([Italian](/source/Italian_language): *all'ottava*), *8va bassa* ([Italian](/source/Italian_language): *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

An octave is the [interval](/source/Interval_(music)) between one musical [pitch](/source/Pitch_(music)) and another with double or half its [frequency](/source/Audio_frequency). For example, if one note has a frequency of 440 [Hz](/source/Hertz), 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 {\displaystyle 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 +1⁄2 (or 2 − 1 {\displaystyle 2^{-1}} ) and 4 (or 2 2 {\displaystyle 2^{2}} ) times the frequency, respectively.

The number of octaves between two frequencies is given by the formula: Number of octaves = log 2 ⁡ ( f 2 f 1 ) {\displaystyle {\text{Number of octaves}}=\log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}

		- [Oscillogram](/source/Oscilloscope) of [middle C](/source/C_(musical_note)) (261.62 Hz) (scale: 1 square is equal to 1 [millisecond](/source/Millisecond))

		- C5, an octave above middle C. The frequency is twice that of middle C (523.25 Hz).

		- C3, an octave below middle C. The frequency is half that of middle C (130.81 Hz).

## Music theory

Most [musical scales](/source/Scale_(music)) are written so that they begin and end on notes that are an octave apart. For example, the C major scale is typically written C D E F G A B C (shown below), the initial and final Cs being an octave apart.

Audio playback is not supported in your browser. You can [download the audio file](https://upload.wikimedia.org/score/2/l/2l5rltfdril1owjz0xohro5qu92y4a7/2l5rltfd.mp3).

Because of octave equivalence, notes in a chord that are one or more octaves apart are said to be *[doubled](/source/Voicing_(music)#Doubling)* (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](/source/Contrapuntal_motion#Parallel_motion) one or more octaves apart (see example under Equivalence, below).

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](/source/Augmented_octave) (A8), and G♮ to G♭ (11 semitones higher) is a [diminished octave](/source/Diminished_octave) (d8). The use of such intervals is rare, as there is frequently a preferable [enharmonically](/source/Enharmonic)-equivalent notation available ([minor ninth](/source/Minor_ninth) and [major seventh](/source/Major_seventh) 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](/source/Scientific_pitch_notation), [Helmholtz](/source/Helmholtz_pitch_notation), 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](/source/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.

An 88-key piano, with the octaves numbered and [Middle C](/source/C_(musical_note)#Middle_C) (turquoise) and [A440](/source/A440_(pitch_standard)) (yellow) highlighted

- Scientific C−1 C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 Helmholtz C,,, C,, C, C c c' c'' c''' c'''' c''''' c'''''' Organ - - 64 foot 32 foot 16 foot 8 foot 4 foot 2 foot 1 foot 1/2 foot 1/4 foot Name Dbl contra Sub contra Contra Great Small 1 line 2 line 3 line 4 line 5 line 6 line MIDI note 0 12 24 36 48 60 72 84 96 108 120

### *Ottava alta* and *bassa*

Similar example with *8vb* and *15mb*

Example of the same three notes expressed in three ways: (1) regularly, (2) in an *8va* bracket, and (3) in a *15ma* bracket

The notation *8a* or *8va* is sometimes seen in [sheet music](/source/Sheet_music), meaning "play this an octave higher than written" (*all' ottava*: "at the octave" or *all' 8va*). *8a* or *8va* stands for *ottava*, the [Italian](/source/Italian_language) 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](/source/Fifteenth_(interval))* (*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.[4]

## Equivalence

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Audio playback is not supported in your browser. You can [download the audio file](https://upload.wikimedia.org/score/r/7/r7y5fsv0ywuy9nsgr8dutz6gr75bmdg/r7y5fsv0.mp3).

Audio playback is not supported in your browser. You can [download the audio file](https://upload.wikimedia.org/score/7/r/7rl8rdjfkjy7rfpor39tcju0b8zpbur/7rl8rdjf.mp3).

Demonstration of octave equivalence. The melody to "[Twinkle, Twinkle, Little Star](/source/Twinkle%2C_Twinkle%2C_Little_Star)" with [parallel harmony](/source/Parallel_harmony). The melody is paralleled in three ways: (1) in octaves ([consonant](/source/Consonance_and_dissonance) and equivalent); (2) in [fifths](/source/Perfect_fifth) (fairly consonant but not equivalent); and (3) in [seconds](/source/Second_(interval)) (neither consonant nor equivalent).

After the [unison](/source/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 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.[5]

For this reason, notes an octave apart are given the same note name in the Western system of [music notation](/source/Music_notation)—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](/source/Equivalence_class_(music)) in many ways, leading to the convention "that [scales](/source/Scale_(music)) are uniquely defined by specifying the intervals within an octave".[6] The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.[6] Thus all C♯s (or all 1s, if C = 0), any number of octaves apart, are part of the same [pitch class](/source/Pitch_class).

Octave equivalence is a part of most musical cultures, but is far from universal in "primitive" and [early music](/source/Early_music).[7] The languages in which the oldest extant written documents on tuning are written, [Sumerian](/source/Sumerian_language) and [Akkadian](/source/Akkadian_language), have no known word for "octave". However, it is believed that a set of [cuneiform](/source/Cuneiform) tablets that collectively describe the tuning of a nine-stringed instrument, believed to be a Babylonian [lyre](/source/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.[8] 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."[9]

Monkeys experience octave equivalence, and its biological basis apparently is an octave mapping of neurons in the auditory [thalamus](/source/Thalamus) of the mammalian [brain](/source/Brain).[10] Studies have also shown the perception of octave equivalence in rats,[11] human infants,[12] and musicians[13] but not starlings,[14] 4–9-year-old children,[15] or non-musicians.[13][6][*[clarification needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify)*]

## See also

- [Blind octave](/source/Blind_octave) – Music composition and performance technique

- [Decade](/source/Decade_(log_scale)) – Unit for measuring ratios on a logarithmic scale

- [Dectave](/source/Dectave), three tenths of a decade (portmanteau of "decimal" and "octave")

- [Eight-foot pitch](/source/Eight-foot_pitch) – Standard pitch designation

- [Octave band](/source/Octave_band) – Frequency band that spans one octave

- [Octave species](/source/Octave_species) – Classification of musical key or scale in ancient Greek music theory

- [One-third octave](/source/One-third_octave)

- [Pitch circularity](/source/Pitch_circularity) – Fixed series of tones that appear to ascend or descend endlessly in pitch

- [Pseudo-octave](/source/Pseudo-octave) – Musical interval which is not a perfect harmonic

- [Pythagorean interval](/source/Pythagorean_interval) – Musical interval

- [Short octave](/source/Short_octave) – Musical keyboard layout

- [Solfège](/source/Solf%C3%A8ge) – Musical pitch reference system

## References

1. ^ [***a***](#cite_ref-Duffin_1-0) [***b***](#cite_ref-Duffin_1-1) [***c***](#cite_ref-Duffin_1-2) Duffin, Ross W. (2008). [*How equal temperament ruined harmony : (and why you should care)*](https://books.google.com/books?id=i5LC7Csnw7UC&q=how+equal+temperament+ruined+harmony) (First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163. [ISBN](/source/ISBN_(identifier)) [978-0-393-33420-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-393-33420-3). [Archived](https://web.archive.org/web/20171205150905/https://books.google.com/books?id=i5LC7Csnw7UC&printsec=frontcover&dq=how+equal+temperament+ruined+harmony&hl=en&sa=X&ved=0ahUKEwiHl-v79eDUAhVOID4KHVp8D4cQ6AEIJjAA) from the original on 5 December 2017. Retrieved 28 June 2017.

1. **[^](#cite_ref-2)** William Smith & Samuel Cheetham (1875). [*A Dictionary of Christian Antiquities*](https://books.google.com/books?id=1LIPFk6oFVkC&q=diatessaron+diapason+diapente+fourth+fifth&pg=PA550). London: John Murray. [ISBN](/source/ISBN_(identifier)) [9780790582290](https://en.wikipedia.org/wiki/Special:BookSources/9780790582290). [Archived](https://web.archive.org/web/20160430185327/https://books.google.com/books?id=1LIPFk6oFVkC&pg=PA550&dq=diatessaron+diapason+diapente+fourth+fifth) from the original on 2016-04-30. {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: ISBN / Date incompatibility ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date))

1. **[^](#cite_ref-3)** Cooper, Paul (1973). *Perspectives in Music Theory: An Historical-Analytical Approach*, p. 16. [ISBN](/source/ISBN_(identifier)) [0-396-06752-2](https://en.wikipedia.org/wiki/Special:BookSources/0-396-06752-2).

1. **[^](#cite_ref-4)** Prout, Ebenezer & Fallows, David (2001). "All'ottava". In [Sadie, Stanley](/source/Stanley_Sadie) & [Tyrrell, John](/source/John_Tyrrell_(musicologist)) (eds.). *[The New Grove Dictionary of Music and Musicians](/source/The_New_Grove_Dictionary_of_Music_and_Musicians)* (2nd ed.). London: [Macmillan Publishers](/source/Macmillan_Publishers). [ISBN](/source/ISBN_(identifier)) [978-1-56159-239-5](https://en.wikipedia.org/wiki/Special:BookSources/978-1-56159-239-5). ‎

1. **[^](#cite_ref-5)** ["Music"](https://www.netflix.com/watch/80243768?trackId=14277283&tctx=0,0,6408cfd3-9144-40c3-b5e9-38b6e4738eaa-17692375,,). *[Vox](/source/Vox_(website)) Explained*. Event occurs at 12:50. Retrieved 2018-11-01. When you ask men and women to sing in unison, what typically happens is they actually sing an octave apart.

1. ^ [***a***](#cite_ref-Burns_6-0) [***b***](#cite_ref-Burns_6-1) [***c***](#cite_ref-Burns_6-2) Burns, Edward M. (1999). "Intervals, Scales, and Tuning". In [Diana Deutsch](/source/Diana_Deutsch) (ed.). *The Psychology of Music* (2nd ed.). San Diego: Academic Press. p. 252. [ISBN](/source/ISBN_(identifier)) [0-12-213564-4](https://en.wikipedia.org/wiki/Special:BookSources/0-12-213564-4).

1. **[^](#cite_ref-7)** [Nettl 1956](#CITEREFNettl1956), p. 47; [Sachs, Curt](/source/Curt_Sachs); [Kunst, Jaap](/source/Jaap_Kunst) (1962). Jaap Kunst (ed.). *The Wellsprings of Music*. The Hague: Marinus Nijhoff. Cited in [Burns 1999](#CITEREFBurns1999), p. 217.[*[failed verification](https://en.wikipedia.org/wiki/Wikipedia:Verifiability)*]

1. **[^](#cite_ref-Meso_Flutes_8-0)** Clint Goss (2012). ["Flutes of Gilgamesh and Ancient Mesopotamia"](http://Flutopedia.com/mesopotamian_flutes.htm). *Flutopedia*. [Archived](https://web.archive.org/web/20120628142037/http://www.flutopedia.com/mesopotamian_flutes.htm) from the original on 2012-06-28. Retrieved 2012-01-08.

1. **[^](#cite_ref-9)** Leon Crickmore. *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. pp. 11–22. [OCLC](/source/OCLC_(identifier)) [637006343](https://search.worldcat.org/oclc/637006343).

1. **[^](#cite_ref-10)** "[The mechanism of octave circularity in the auditory brain](http://www.neuroscience-of-music.se/eng7.htm) [Archived](https://web.archive.org/web/20100401145359/http://www.neuroscience-of-music.se/eng7.htm) 2010-04-01 at the [Wayback Machine](/source/Wayback_Machine)", *Neuroscience of Music*.

1. **[^](#cite_ref-FOOTNOTEBlackwell_&_Schlosberg1943_11-0)** [Blackwell & Schlosberg 1943](#CITEREFBlackwell_&_Schlosberg1943).

1. **[^](#cite_ref-FOOTNOTEDemany_&_Armand1984_12-0)** [Demany & Armand 1984](#CITEREFDemany_&_Armand1984).

1. ^ [***a***](#cite_ref-FOOTNOTEAllen1967_13-0) [***b***](#cite_ref-FOOTNOTEAllen1967_13-1) [Allen 1967](#CITEREFAllen1967).

1. **[^](#cite_ref-FOOTNOTECynx1993_14-0)** [Cynx 1993](#CITEREFCynx1993).

1. **[^](#cite_ref-FOOTNOTESergeant1983_15-0)** [Sergeant 1983](#CITEREFSergeant1983).

**Sources**

- Allen, David. 1967. "Octave Discriminability of Musical and Non-Musical Subjects". *Psychonomic Science* 7:421–22.

- Blackwell, H. R., & H. Schlosberg. 1943. "Octave Generalization, Pitch Discrimination, and Loudness Thresholds in the White Rat". *[Journal of Experimental Psychology](/source/Journal_of_Experimental_Psychology)* 33:407–419.

- Cynx, Jeffrey. 1996. "Neuroethological Studies on How Birds Discriminate Song". In *Neuroethology of Cognitive and Perceptual Processes*, edited by C. F. Moss and S. J. Shuttleworth, 63. Boulder: Westview Press.

- Demany, Laurent, and Françoise Armand. 1984. "The Perceptual Reality of Tone Chroma in Early Infancy". *[Journal of the Acoustical Society of America](/source/Journal_of_the_Acoustical_Society_of_America)* 76:57–66.

- [Nettl, Bruno](/source/Bruno_Nettl) (1956). *Music in Primitive Culture*. Cambridge: Harvard University Press. [ISBN](/source/ISBN_(identifier)) [9780674590007](https://en.wikipedia.org/wiki/Special:BookSources/9780674590007). {{[cite book](https://en.wikipedia.org/wiki/Template:Cite_book)}}: ISBN / Date incompatibility ([help](https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_isbn_date))

- Sergeant, Desmond. 1983. "The Octave: Percept or Concept?" *[Psychology of Music](/source/Psychology_of_Music)* 11, no. 1:3–18.

## External links

Wikimedia Commons has media related to [Octaves](https://commons.wikimedia.org/wiki/Category:Octaves).

- [Anatomy of an Octave](http://www.kylegann.com/Octave.html) by [Kyle Gann](/source/Kyle_Gann)

v t e Intervals Twelve- semitone (post-Bach Western) (Numbers in brackets are the number of semitones in the interval.) Perfect unison (0) fourth (5) fifth (7) octave (12) Major second (2) third (4) sixth (9) seventh (11) Minor second (1) third (3) sixth (8) seventh (10) Augmented unison (1) second (3) third (5) fourth (6) fifth (8) sixth (10) seventh (12) octave (13) Diminished unison (−1) second (0) third (2) fourth (4) fifth (6) sixth (7) seventh (9) octave (11) Compound ninth (13 or 14) tenth (15 or 16) eleventh (17) twelfth (19) thirteenth (20 or 21) fourteenth (22 or 23) fifteenth (24) Other tuning systems 24-tone equal temperament (Numbers in brackets refer to fractional semitones.) Neutral quarter tone (1⁄2) second (1+1⁄2) third (3+1⁄2) major fourth (5+1⁄2) minor fifth (6+1⁄2) sixth (8+1⁄2) seventh (10+1⁄2) Just intonations (Numbers in brackets refer to pitch ratios.) 7-limit septimal quarter tone (36:35) septimal third tone (28:27) septimal chromatic semitone (21:20) septimal diatonic semitone (15:14) supermajor second (8:7) subminor third (7:6) supermajor third (9:7) subminor fifth (7:5) supermajor fourth (10:7) subminor seventh (7:4) Higher-limit minor diatonic semitone (17-limit) Other intervals Groups Microtone 5-limit Comma Pseudo-octave Pythagorean interval Subminor and supermajor Semitones Pythagorean limma Pythagorean apotome Major limma Quarter tones Quarter tone Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma (27.3 cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma (13.8 cents) Kleisma (8.1 cents) Septimal kleisma (7.7 cents) Schisma (1.95 cents) Breedsma (0.72 cents) Ragisma (0.4 cents) Measurement Cent Centitone Millioctave Savart Others Wolf Ditone Semiditone Secor Incomposite interval List of pitch intervals

v t e Voicing in music Blind octave Block chord Close and open harmony Common tone Doubling Root position and Inversion (1st, 2nd, 3rd, and higher inversions) Octave Voice Voice leading

Authority control databases GND

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Adapted from the Wikipedia article [Octave](https://en.wikipedia.org/wiki/Octave) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Octave?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.