A rational interval is an interval whose frequency ratio is a rational number. Its logarithmic measure is then necessarily irrational. 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.