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]] | ||
Revision as of 14:31, 21 July 2023
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 logarithmic, therefore an interval can be described with a frequency ratio or a logarithmic measure of that ratio, such as cents.
A rational interval is an interval whose frequency ratio is a rational number. Its logarithmic measure is then necessarily irrational[1]. 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 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 consonance and dissonance.
See also
References
- ↑ See example on Wikipedia: Irrational number#Logarithms. A full proof would rely on the fundamental theorem of arithmetic to generalize the results to all pairs of coprime natural numbers.