# Transversal

In the language of mathematics, a **transversal** is a selection of one representative element from each set of a collection of sets. Transversals may be used to define scales tempered by a regular temperament in a way which is precise, useful for several purposes, and independent of the exact tuning used by the temperament. For each note of a scale which is defined in *p*-limit temperament, there is a set of *p*-limit rational intervals which is tempered by the temperament to that note. This gives us a collection of sets, and selecting a representative element from each set gives us a transversal. Transversals may also be used to denote all of the intervals of a regular temperament, usually by confining the intervals of the transversal to a subgroup of the group tempered by the temperament. For instance, Pythagorean tuning provides a transversal for meantone.