Interval: Difference between revisions

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~~{{Wikipedia|Dyad (music)}}~~

An '''interval''' is the difference in [[pitch]] between two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

An '''interval''' ~~(or '''dyad'''; less commonly, '''diad''') is a [[chord]] of two different notes.~~

~~The main property of an interval~~ is ~~its size, defined as~~ the difference in [[pitch]] between ~~its~~ two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s~~. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself~~.

A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.

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== See also ==

* [[Dyad]]

* [[Gallery of just intervals]]

* [[Interval size measure]]

* [[:Category:Interval naming]]

== References ==

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 {{Wikipedia|Interval (music)}}
-{{Wikipedia|Dyad (music)}}
+An '''interval''' is the difference in [[pitch]] between two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.
-An '''interval''' (or '''dyad'''; less commonly, '''diad''') is a [[chord]] of two different notes.
-The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.
 A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.
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 == See also ==
+* [[Dyad]]
 * [[Gallery of just intervals]]
 * [[Interval size measure]]
+* [[:Category:Interval naming]]
 == References ==