Octave (interval region): Difference between revisions

Line 1:

A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[Interval size measure|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, corresponding to a [[just]] [[ratio]] of [[2/1]].

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

The aforementioned function is the interval of equivalence, or [[equave]], 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.

~~'''This~~ page ~~is a work~~-~~in-progress~~.~~'''~~

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

~~An [[octave]] '''(8ve''') 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, corresponding to a just ratio of [[2/1~~]].~~

{{todo|inline=1|review|comment=Mention concordance before harmonic entropy, since harmonic entropy is a single model of concordance}}

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.~~

~~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]].~~

== In just intonation ==

Line 14:

Line 12:

Several notable ones are:

* TBD

== 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.

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

{| class="wikitable"

|+

Line 55:

Line 52:

|}

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).

@@ Line 1: / Line 1: @@
+{{About|the interval region|the octave as a just ratio|2/1}}
+A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[Interval size measure|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, corresponding to a [[just]] [[ratio]] of [[2/1]].
-''This page is about the interval region. For the octave as a just ratio, see [[2/1]].''
+The aforementioned function is the interval of equivalence, or [[equave]], 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.
-'''This page is a work-in-progress.'''
+Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].
-An [[octave]] '''(8ve''') 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, corresponding to a just ratio of [[2/1]].
+{{todo|inline=1|review|comment=Mention concordance before harmonic entropy, since harmonic entropy is a single model of concordance}}
-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.
-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]].
 == In just intonation ==
@@ Line 14: / Line 12: @@
 Several notable ones are:
+{{todo|inline=1|complete list}}
-* TBD
 == 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.
+As the just octave of 2/1 is the interval being equally divided in [[EDO]]s, it is represented perfectly in all of them. The following table lists other octave-sized intervals (> 1140 cents) that exist in various significant EDOs.
 {| class="wikitable"
 |+
@@ Line 55: / Line 52: @@
 |}
 /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).
+{{todo|inline=1|complete table}}
 {{Navbox intervals}}