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The '''octave''' (abbreviation: '''8ve''', symbol: '''oct''', [[frequency ratio]]: '''2/1''') is one of the most basic [[Gallery of just intervals|intervals]] found in musical systems throughout the entire world. It has a frequency ratio of 2/1 and a size of 1200 [[cent]]s. It is used as the standard of [[interval size measure|logarithmic measurement]] for all intervals, regardless if they are justly tuned or not.

It is the first [[prime harmonic]], with the next being [[3/1]].

== Octave equivalence ==

The octave is usually called the '''interval of equivalence''', because tones separated by ~~an octave~~ are perceived ~~to have~~ the same ~~or similar~~ pitch class ~~to the average human listener~~. ~~The reason for this phenomenon~~ is ~~probably due to the~~ strong ~~region of attraction of low [[harmonic entropy]]~~, or the ~~strong amplitude of~~ the ~~second~~ [[~~harmonic~~]] ~~in most harmonic instruments.~~

The octave is usually called the '''interval of equivalence''', because tones separated by this interval are perceived as having the same [[pitch class]] despite their different absolute pitches. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most [[scale]]s repeat at the octave.

~~The Pelog and Slendro scales of~~ the Javanese contain near-octaves even though Gamelan instruments exhibit inharmonic spectra. It is most likely reminiscent of an older musical system, or derived using the human voice instead of inharmonic instruments.

The Wikipedia article includes a short discussion on its ongoing nature–nurture debate and its psychoacoustic bases. For example, it is shown that many animals including monkeys and rats experience octave equivalence to a certain extent<ref>[https://comparative-cognition-and-behavior-reviews.org/wp/wp-content/uploads/2017/04/CCBR_01-Hoeschele-v12-2017.pdf Hoeschele M. ''Animal Pitch Perception: Melodies and Harmonies''. Comp Cogn Behav Rev.]</ref>. Meanwhile, an article in ''Current Biology'' including an 8-minute video shows that octave equivalence might be a cultural phenomenon<ref>[https://www.cell.com/current-biology/fulltext/S0960-9822(19)31036-X?_returnURL=~~https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS096098221931036X%3Fshowall%3Dtrue Nori Jacoby et al. ''Universal~~ and ~~Non-universal Features of Musical Pitch Perception Revealed by Singing''. Current Biology.]</ref>.~~

== Octave stretch ==

~~A generalisation~~ where ~~we let~~ a ~~different interval define equivalence is~~ [[~~equave~~]]~~, such as the~~ [[~~tritave~~]].

Some musical systems exhibit stretched (or compressed) octaves where the octave is tuned slightly different from a pure 2:1 ratio. This occurs in piano tuning (to compensate for inharmonicity in piano strings) and in some traditional music systems, such as the Indonesian [[Pelog]] and [[Slendro]] scales.

== Alternative names ==

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* [[Prime interval]]

* [[Gallery of Just Intervals]]

* [[Toctave]]

* [[EDO]]

* [[Octave reduction]]

@@ Line 14: / Line 14: @@
 {{Wikipedia|Octave}}
 The '''octave''' (abbreviation: '''8ve''', symbol: '''oct''', [[frequency ratio]]: '''2/1''') is one of the most basic [[Gallery of just intervals|intervals]] found in musical systems throughout the entire world. It has a frequency ratio of 2/1 and a size of 1200 [[cent]]s. It is used as the standard of [[interval size measure|logarithmic measurement]] for all intervals, regardless if they are justly tuned or not.
+It is the first [[prime harmonic]], with the next being [[3/1]].
 == Octave equivalence ==
-The octave is usually called the '''interval of equivalence''', because tones separated by an octave are perceived to have the same or similar pitch class to the average human listener. The reason for this phenomenon is probably due to the strong region of attraction of low [[harmonic entropy]], or the strong amplitude of the second [[harmonic]] in most harmonic instruments.
+{{main|Interval of equivalence}}
+The octave is usually called the '''interval of equivalence''', because tones separated by this interval are perceived as having the same [[pitch class]] despite their different absolute pitches. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most [[scale]]s repeat at the octave.
-The Pelog and Slendro scales of the Javanese contain near-octaves even though Gamelan instruments exhibit inharmonic spectra. It is most likely reminiscent of an older musical system, or derived using the human voice instead of inharmonic instruments.
-The Wikipedia article includes a short discussion on its ongoing nature–nurture debate and its psychoacoustic bases. For example, it is shown that many animals including monkeys and rats experience octave equivalence to a certain extent<ref>[https://comparative-cognition-and-behavior-reviews.org/wp/wp-content/uploads/2017/04/CCBR_01-Hoeschele-v12-2017.pdf Hoeschele M. ''Animal Pitch Perception: Melodies and Harmonies''. Comp Cogn Behav Rev.]</ref>. Meanwhile, an article in ''Current Biology'' including an 8-minute video shows that octave equivalence might be a cultural phenomenon<ref>[https://www.cell.com/current-biology/fulltext/S0960-9822(19)31036-X?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS096098221931036X%3Fshowall%3Dtrue Nori Jacoby et al. ''Universal and Non&#45;universal Features of Musical Pitch Perception Revealed by Singing''. Current Biology.]</ref>.
+== Octave stretch ==
+{{main|Stretched and compressed tuning}}
-A generalisation where we let a different interval define equivalence is [[equave]], such as the [[tritave]].
+Some musical systems exhibit stretched (or compressed) octaves where the octave is tuned slightly different from a pure 2:1 ratio. This occurs in piano tuning (to compensate for inharmonicity in piano strings) and in some traditional music systems, such as the Indonesian [[Pelog]] and [[Slendro]] scales.
 == Alternative names ==
@@ Line 34: / Line 36: @@
 * [[Prime interval]]
 * [[Gallery of Just Intervals]]
-* [[Toctave]]
 * [[EDO]]
 * [[Octave reduction]]