Octave complement: Difference between revisions

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The '''octave complement''' or '''inverse interval''' of an [[interval]] is its ~~interval distance from~~ the [[octave]]. ~~The '''octave complement'''~~ can be seen as a binary symmetric relation over intervals. The concept important in musical practice and most musical theories. Its use is typically restricted to [[octave-reduced]] intervals (including the octave).

The '''octave complement''' or '''inverse interval''' of an [[interval]] is its difference with the [[octave]]. It can be seen as a binary symmetric relation over intervals. The concept is important in musical practice and most musical theories. Its use is typically restricted to [[octave-reduced]] intervals (including the octave).

The octave complement is often simply called '''complement''' in the context of octave-[[equivalent]] scales, but the broader concept of ''complement'' can also apply to other intervals, such as the [[fifth complement]], the [[fourth complement]] and the [[tritave complement]].

== Calculation ==

Depending on the interval representation (name, ratio, monzo, edo steps, ~~cents~~), it's more or less easy to retrieve the complementary interval from a given interval.

Depending on the interval representation (name, [[ratio]], [[monzo]], [[edo]] steps, [[cent]]s), it's more or less easy to retrieve the complementary interval from a given interval.

=== Classical interval names ===

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=== Monzo ===

Intervals represented as ~~[[Monzos]]~~ can be transformed into their octave complement by inverting all arguments and increasing the 2-argument.

Intervals represented as monzos can be transformed into their octave complement by inverting all arguments and increasing the 2-argument.

; Examples

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=== Edo steps ===

Octave-complement intervals represented as ''s\n'' meaning ''s'' steps of ''n''-EDO follow this relation <code>s1 + s2 = n</code>. For given s and n, the unknown x can be calculated by the formula <code>x := n-s</code>.

Octave-complement intervals represented as ''s''\''n'' meaning ''s'' steps of ''n''-EDO follow this relation <code>s1 + s2 = n</code>. For given ''s'' and ''n'', the unknown ''x'' can be calculated by the formula <code>x := n -s</code>.

; Examples

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=== Cents ===

Octave-complement intervals represented as ''s~~¢~~'' follow this relation <code>s1 + s2 = 1200</code>. For given s, the unknown x can be calculated by the formula <code>x := 1200-s</code>.

Octave-complement intervals represented as ''s''¢ follow this relation <code>s1 + s2 = 1200</code>. For given s, the unknown x can be calculated by the formula <code>x := 1200 - s</code>.

; Examples

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== See also ==

* [[Ratio math]]

* [[Octave reduction]]

[[Category:Terms]]

* [[Fifth complement]] -- the analogue for the [[3/2|fifth (3/2)]]

* [[Tritave complement]] -- the analogue for the [[tritave|tritave (3/1)]]

* [https://en.wikipedia.org/wiki/Inversion_(music)#Intervals Inversion (music) - Wikipedia #Intervals]

~~[[Category:Term]]~~

[[Category:~~Theory~~]]

[[Category:Interval]]

[[Category:Octave]]

[[Category:Method]]

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-The '''octave complement''' or '''inverse interval''' of an [[interval]] is its interval distance from the [[octave]]. The '''octave complement''' can be seen as a binary symmetric relation over intervals. The concept important in musical practice and most musical theories. Its use is typically restricted to [[octave-reduced]] intervals (including the octave).
+{{Wikipedia|Complement (music)}}
+{{Wikipedia|Inversion (music) #Intervals}}
+The '''octave complement''' or '''inverse interval''' of an [[interval]] is its difference with the [[octave]]. It can be seen as a binary symmetric relation over intervals. The concept is important in musical practice and most musical theories. Its use is typically restricted to [[octave-reduced]] intervals (including the octave).
+The octave complement is often simply called '''complement''' in the context of octave-[[equivalent]] scales, but the broader concept of ''complement'' can also apply to other intervals, such as the [[fifth complement]], the [[fourth complement]] and the [[tritave complement]].
 == Calculation ==
-Depending on the interval representation (name, ratio, monzo, edo steps, cents), it's more or less easy to retrieve the complementary interval from a given interval.
+Depending on the interval representation (name, [[ratio]], [[monzo]], [[edo]] steps, [[cent]]s), it's more or less easy to retrieve the complementary interval from a given interval.
 === Classical interval names ===
@@ Line 61: / Line 65: @@
 === Monzo ===
-Intervals represented as [[Monzos]] can be transformed into their octave complement by inverting all arguments and increasing the 2-argument.
+Intervals represented as monzos can be transformed into their octave complement by inverting all arguments and increasing the 2-argument.
 ; Examples
@@ Line 69: / Line 73: @@
 === Edo steps ===
-Octave-complement intervals represented as ''s\n'' meaning ''s'' steps of ''n''-EDO follow this relation <code>s1 + s2 = n</code>. For given s and n, the unknown x can be calculated by the formula <code>x := n-s</code>.
+Octave-complement intervals represented as ''s''\''n'' meaning ''s'' steps of ''n''-EDO follow this relation <code>s1 + s2 = n</code>. For given ''s'' and ''n'', the unknown ''x'' can be calculated by the formula <code>x := n  -s</code>.
 ; Examples
@@ Line 76: / Line 80: @@
 === Cents ===
-Octave-complement intervals represented as ''s&cent;'' follow this relation <code>s1 + s2 = 1200</code>. For given s, the unknown x can be calculated by the formula <code>x := 1200-s</code>.
+Octave-complement intervals represented as ''s''¢ follow this relation <code>s1 + s2 = 1200</code>. For given s, the unknown x can be calculated by the formula <code>x := 1200 - s</code>.
 ; Examples
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 == See also ==
+* [[Ratio math]]
-* [[Octave reduction]]
+[[Category:Terms]]
-* [[Fifth complement]] -- the analogue for the [[3/2|fifth (3/2)]]
-* [[Tritave complement]] -- the analogue for the [[tritave|tritave (3/1)]]
-* [https://en.wikipedia.org/wiki/Inversion_(music)#Intervals Inversion (music) &#45; Wikipedia #Intervals]
-[[Category:Term]]
-[[Category:Theory]]
 [[Category:Interval]]
 [[Category:Octave]]
 [[Category:Method]]