2/1: Difference between revisions

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~~[[Category:Rational intervals]]~~

{{Interwiki

| en = 2/1

| de = Oktave

| es = Octava

| ja = オクターブ

| ro = Octavă

}}

{{Infobox Interval

| Ratio = 2/1

| Name = octave, ditave, diapason

| Name = octave, ditave, duple, diapason

| Color name = w8, wa 8ve

| Sound = jid_2_1_pluck_adu_dr220.mp3

}}{{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.

}}

~~==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''' (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.

~~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~~.

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

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 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.

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

== Octave stretch ==

==~~Alternate~~ names==

'''Ditave''' is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of ~~7-tone~~ scales. The name is ~~derived from~~ the numeral prefix ''δι''- (''di-'', Greek for "two") in analogy to "[[tritave]]" (3/1). ~~A brief but complementary description about it~~ is [[~~:purdal:Ditave~~|~~here~~]].

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 ==

'''Ditave''' is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of [[heptatonic]] scales. The name is a contraction of the numeral prefix ''δι''- (''di-'', Greek for "two") and ''octave'', in analogy to "[[tritave]]" (3/1).

'''Duple''' is a proposed term which relates itself to the ancient Greek concept of [[harmonic|multiples]]. It also fixes the problem of using part of the word ''octave''.

'''Diapason''' is another term also sometimes applied to 2/1. It is also of Greek origin, but not related to the number two; instead it is formed from ''διά'' (''dia'') + ''πασων'' (''pason''), meaning something like "through all the notes".

==See also==

*[[Prime interval]]

== See also ==

*[[Gallery of Just Intervals]]

* [[Prime interval]]

*[[Toctave]]

* [[Gallery of Just Intervals]]

*[[EDO]]

* [[EDO]]

*[[Octave reduction]]

* [[Octave reduction]]

*[[Octave complement]]

* [[Octave complement]]

*[[Octave (interval region)]]

* [[Octave (interval region)]]

==References==

== References ==

@@ Line 1: / Line 1: @@
-[[Category:Rational intervals]]
+{{Interwiki
+| en = 2/1
+| de = Oktave
+| es = Octava
+| ja = オクターブ
+| ro = Octavă
+}}
 {{Infobox Interval
 | Ratio = 2/1
-| Name = octave, ditave, diapason
+| Name = octave, ditave, duple, diapason
 | Color name = w8, wa 8ve
 | Sound = jid_2_1_pluck_adu_dr220.mp3
-}}{{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.
+}}
-==Octave equivalence==
+{{Wikipedia|Octave}}
-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''' (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.
-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.
+It is the first [[prime harmonic]], with the next being [[3/1]].
-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 equivalence ==
+{{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.
-A generalisation where we let a different interval define equivalence is [[equave]], such as the [[tritave]].
+== Octave stretch ==
-==Alternate names==
+{{main|Stretched and compressed tuning}}
-'''Ditave''' is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of 7-tone scales. The name is derived from the numeral prefix ''δι''- (''di-'', Greek for "two") in analogy to "[[tritave]]" (3/1). A brief but complementary description about it is [[:purdal:Ditave|here]].
+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 ==
+'''Ditave''' is an alternative name for the interval 2/1, which was proposed to neutralize the terminology against the predominance of [[heptatonic]] scales. The name is a contraction of the numeral prefix ''δι''- (''di-'', Greek for "two") and ''octave'', in analogy to "[[tritave]]" (3/1).
+'''Duple''' is a proposed term which relates itself to the ancient Greek concept of [[harmonic|multiples]]. It also fixes the problem of using part of the word ''octave''.
 '''Diapason''' is another term also sometimes applied to 2/1. It is also of Greek origin, but not related to the number two; instead it is formed from ''διά'' (''dia'') + ''πασων'' (''pason''), meaning something like "through all the notes".
-==See also==
-*[[Prime interval]]
+== See also ==
-*[[Gallery of Just Intervals]]
+* [[Prime interval]]
-*[[Toctave]]
+* [[Gallery of Just Intervals]]
-*[[EDO]]
+* [[EDO]]
-*[[Octave reduction]]
+* [[Octave reduction]]
-*[[Octave complement]]
+* [[Octave complement]]
-*[[Octave (interval region)]]
+* [[Octave (interval region)]]
-==References==
-<references /><!-- main article -->
+== References ==
+<references/>