# Interval

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.