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== 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.

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 perception of octave equivalence appears to have both biological and cultural components.

Studies have shown that various non-human animals, including rhesus monkeys and rats, experience octave equivalence to a certain extent.<ref>Hoeschele M. [https://doi.org/10.3819/CCBR.2017.120002 ''Animal Pitch Perception: Melodies and Harmonies'']. Comp Cogn Behav Rev. 2017</ref>

However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.17605/OSF.IO/DW39V ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>

~~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>.

When a different interval (such as the [[tritave]]) is used as the interval of equivalence, it is referred to as an [[equave]] or sometimes formal octave.

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

== Octave stretch ==

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 16: / Line 16: @@
 == 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.
-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 perception of octave equivalence appears to have both biological and cultural components.
+Studies have shown that various non-human animals, including rhesus monkeys and rats, experience octave equivalence to a certain extent.<ref>Hoeschele M. [https://doi.org/10.3819/CCBR.2017.120002 ''Animal Pitch Perception: Melodies and Harmonies'']. Comp Cogn Behav Rev. 2017</ref>
+However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.17605/OSF.IO/DW39V ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>
-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>.
+When a different interval (such as the [[tritave]]) is used as the interval of equivalence, it is referred to as an [[equave]] or sometimes formal octave.
-A generalisation where we let a different interval define equivalence is [[equave]], such as the [[tritave]].
+== Octave stretch ==
+{{main|Stretched and compressed tuning}}
+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 ==