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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


  1. 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.