Octave (interval region): Difference between revisions

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#REDIRECT [[2/1]]{{interwiki
| de = Oktave
| en = Octave
| es = Octava
| ja = オクターブ
| ro = Octavă
}}
{{Infobox Interval
| Ratio = 2/1
| Name = octave, ditave, 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.
''This page is about the interval region. For the octave as a just ratio, see [[2/1]].''


== Octave equivalence ==
'''This page is a work-in-progress.'''  
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 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.
An [[octave]] is an interval that is approximately 1200 [[Cent|cents]] in size. While a rough tuning range for octaves is sharper than 1140 cents, the term "octave" tends to imply a function within music that only works with intervals that are exactly (or almost exactly) 1200 cents.


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>.  
The aforementioned function is as 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. As such, it is common practice to "[[Octave reduction|octave-reduce]]" intervals so that they lie within the octave.


A generalisation where we let a different interval define equivalence is [[equave]], such as the [[tritave]].
Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[Comma and diesis|commas and dieses]].


== Alternate names ==
== In just intonation ==
The only "perfect" octave is the interval [[2/1]], which can be stacked to produce all other 2-limit intervals. It is 1200 cents in size, by definition. However, various "out-of-tune" octaves exist, usually flat or sharp of an octave by a small interval such as a comma.


'''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]].
Several notable ones are:


'''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".
* TBD


== See also ==
== In tempered scales ==
 
As the just octave of 2/1 is the interval being equally divided in [[EDO|EDOs,]] it is represented perfectly in all of them. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs.
* [[Prime interval]]
{| class="wikitable"
* [[Gallery of Just Intervals]]
|+
* [[Toctave]]
!EDO
* [[EDO]]
!Suboctaves
* [[Octave reduction]]
|-
* [[Octave complement]]
|22
 
|TBD
== References ==
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<references/>
|24
 
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[[Category:Tritave-reduced harmonics]]
|25
[[Category:Interval size measures]]
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[[Category:Terms]]
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|26
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|27
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|29
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|31
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|34
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|41
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|53
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2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).

Revision as of 00:35, 26 February 2025

This page is about the interval region. For the octave as a just ratio, see 2/1.

This page is a work-in-progress.

An octave is an interval that is approximately 1200 cents in size. While a rough tuning range for octaves is sharper than 1140 cents, the term "octave" tends to imply a function within music that only works with intervals that are exactly (or almost exactly) 1200 cents.

The aforementioned function is as 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. As such, it is common practice to "octave-reduce" intervals so that they lie within the octave.

Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to commas and dieses.

In just intonation

The only "perfect" octave is the interval 2/1, which can be stacked to produce all other 2-limit intervals. It is 1200 cents in size, by definition. However, various "out-of-tune" octaves exist, usually flat or sharp of an octave by a small interval such as a comma.

Several notable ones are:

  • TBD

In tempered scales

As the just octave of 2/1 is the interval being equally divided in EDOs, it is represented perfectly in all of them. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs.

EDO Suboctaves
22 TBD
24
25
26
27
29
31
34
41
53

2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).

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