Interval: Difference between revisions
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 | An '''interval''' is the difference in [[pitch]] between two notes. | ||
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. | 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 | A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number|rational number]]. Its size in cents 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>, unless the interval happens to be an octave or some multiple of an octave. 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 cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. But some intervals have both irrational ratios and irrational cents. | ||
Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance|consonance and dissonance]]. | Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance|consonance and dissonance]]. | ||
Revision as of 08:43, 20 October 2024
An interval is the difference in pitch between two notes.
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 size in cents is then necessarily irrational[1], unless the interval happens to be an octave or some multiple of an octave. 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 cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. But some intervals have both irrational ratios and irrational cents.
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.