Interval: Difference between revisions
Distinguish interval and dyad |
Terms used interchangeably, link to Wikipedia for logarithmic pitch perception |
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{{Wikipedia|Interval (music)}} | {{Wikipedia|Interval (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''' is the difference in [[pitch]] between two notes. Since two notes form a [[dyad]], the terms ''interval'' and ''dyad'' are sometimes used interchangeably. | ||
Human pitch perception is [[Wikipedia:Logarithm#Music|logarithmic]], therefore an interval can be described with a [[ratio|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. | |||
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. | 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 == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Interval size measure]] | * [[Interval size measure]] | ||