Interval: Difference between revisions

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

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.

An interval is ~~rational if its~~ ratio is a rational number~~, and its~~ logarithmic measure is then necessarily irrational. Conversely, an interval is ~~irrational if its~~ frequency ratio is an 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.

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.

Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance|consonance and dissonance]].

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* [[Gallery of just intervals]]

* [[Interval size measure]]

== References ==

[[Category:Interval| ]]

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 {{Wikipedia|Interval (music)}}
 {{Wikipedia|Dyad (music)}}
-An '''interval''' or '''dyad''' (less commonly, '''diad''') is a [[chord]] of two different notes.
+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.
-An interval is rational if its ratio is a rational number, and its logarithmic measure is then necessarily irrational. Conversely, an interval is irrational if its frequency ratio is an 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.
+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.
 Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance|consonance and dissonance]].
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 * [[Gallery of just intervals]]
 * [[Interval size measure]]
+== References ==
+<references/>
 [[Category:Interval| ]] <!-- main article -->