Interval

In the Western music-theoretical tradition, intervals are basic and foundational. They are also transhistorical, occupying theorists continually from classical origins to the present. Considering their foundational position, one might assume that intervals have a primitive, elementary character with little ideational content, and that the relevant literature is weakly innovative. Intervals appear within systems that reflect certain styles of thinking about musical objects and musical spaces. There are various modes of movement in those spaces, expressed as various counting rules, complicated by a tension between theoretical conventions that regard intervals as magnitudes and theoretical conventions that regard intervals as directed magnitudes. Reflecting on the relevant intuitions and exploring the systems associated with these conventions teaches us important lessons about foundational music-theoretical constructs in Western music theory.