Editing Octave (section)

== Equivalence ==
{{anchor|Equivalency|Equivalent}}<!--[[Octave equivalence]] redirects directly to this section.-->
{{Image frame|content=<score sound="1"> {
\relative c' {
   \clef treble 
   \time 4/4
   \key c \major
   <c c'>4^\markup { "(1) Parallel octaves (doubled)" } <c c'> <g' g'> <g g'> <a a'> <a a'> <g g'>2 
   <f f'>4 <f f'> <e e'> <e e'> <d d'> <d d'> <c c'>2
} }
</score>

<score sound="1"> {
\relative c' {
   \clef treble 
   \time 4/4
   \key c \major
   <c g'>4^\markup { "(2) Parallel fifths" } <c g'> <g' d'> <g d'> <a e'> <a e'> <g d'>2 
   <f c'>4 <f c'> <e b'> <e b'> <d a'> <d a'> <c g'>2
} }
</score>

<score sound="1"> {
\relative c' {
   \clef treble 
   \time 4/4
   \key c \major
   <c d>4^\markup { "(3) Parallel seconds" } <c d> <g' a> <g a> <a b> <a b> <g a>2 
   <f g>4 <f g> <e f> <e f> <d e> <d e> <c d>2
} }
</score>|width=420|caption=Demonstration of octave equivalence. The melody to "[[Twinkle, Twinkle, Little Star]]" with [[parallel harmony]]. The melody is paralleled in three ways: (1) in octaves ([[Consonance and dissonance|consonant]] and equivalent); (2) in [[Perfect fifth|fifths]] (fairly consonant but not equivalent); and (3) in [[second (interval)|seconds]] (neither consonant nor equivalent).}}

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 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.<ref>{{Cite episode|title=Music|url=https://www.netflix.com/watch/80243768?trackId=14277283&tctx=0,0,6408cfd3-9144-40c3-b5e9-38b6e4738eaa-17692375,,|access-date=2018-11-01|series=[[Vox (website)|Vox]] Explained|time=12:50|quote=When you ask men and women to sing in unison, what typically happens is they actually sing an octave apart.}}</ref>

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 equivalence'', the assumption that pitches one or more octaves apart are musically [[Equivalence class (music)|equivalent]] in many ways, leading to the convention "that [[scale (music)|scales]] are uniquely defined by specifying the intervals within an octave".<ref name="Burns">{{cite book|last=Burns|first=Edward M.|year=1999|chapter=Intervals, Scales, and Tuning|title=The Psychology of Music|editor=[[Diana Deutsch]]|edition=2nd|page=252|location=San Diego|publisher=Academic Press|isbn=0-12-213564-4}}</ref> The conceptualization of pitch as having two dimensions, pitch height (absolute frequency) and pitch class (relative position within the octave), inherently include octave circularity.<ref name="Burns" /> Thus all C{{music|#}}s (or all 1s, if C&nbsp;=&nbsp;0), any number of octaves apart, are part of the same [[pitch class]].

Octave equivalence is a part of most musical cultures, but is far from universal in "primitive" and [[early music]].<ref>{{harvnb|Nettl|1956|p=47}}; {{cite book|last1=Sachs|first1=Curt|author1-link=Curt Sachs|last2=Kunst|first2=Jaap|author2-link=Jaap Kunst|year=1962|title=The Wellsprings of Music|editor=Jaap Kunst|location=The Hague|publisher=Marinus Nijhoff}} Cited in {{harvnb|Burns|1999|p=217}}.{{Failed verification|date=June 2020|reason=Burns says that, but this is not exactly what Nettl or Sachs write.}}</ref> The languages in which the oldest extant written documents on tuning are written, [[Sumerian language|Sumerian]] and [[Akkadian language|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.<ref name="Meso_Flutes">{{cite web |url=http://Flutopedia.com/mesopotamian_flutes.htm |title=Flutes of Gilgamesh and Ancient Mesopotamia |author=Clint Goss |year=2012 |work=Flutopedia |access-date=2012-01-08 |url-status=live |archive-url=https://web.archive.org/web/20120628142037/http://www.flutopedia.com/mesopotamian_flutes.htm |archive-date=2012-06-28 }}</ref> 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."<ref>{{cite conference|author=Leon Crickmore|title=New Light on the Babylonian Tonal System|conference=ICONEA 2008: Proceedings of the International Conference of Near Eastern Archaeomusicology, held at the British Museum, December 4–6, 2008|pages=11–22|oclc=637006343}}</ref>

Monkeys experience octave equivalence, and its biological basis apparently is an octave mapping of neurons in the auditory [[thalamus]] of the mammalian [[brain]].<ref>"[http://www.neuroscience-of-music.se/eng7.htm The mechanism of octave circularity in the auditory brain] {{webarchive|url=https://web.archive.org/web/20100401145359/http://www.neuroscience-of-music.se/eng7.htm |date=2010-04-01 }}", ''Neuroscience of Music''.</ref> Studies have also shown the perception of octave equivalence in rats,{{sfn|Blackwell & Schlosberg|1943}} human infants,{{sfn|Demany & Armand|1984}} and musicians{{sfn|Allen|1967}} but not starlings,{{sfn|Cynx|1993}} 4–9-year-old children,{{sfn|Sergeant|1983}} or non-musicians.{{sfn|Allen|1967}}<ref name="Burns" />{{clarify|reason=Human infants are not musicians.|date=May 2022}}