Dodecaphony and Interval Vectors

The exploration of the profound and intrinsic cohesion between mathematics and music is certainly nothing new – it actually dates all the way back to Pythagoras (c. 570 BCE – c. 495 BCE). However, the introduction of the dodecaphonic (twelve-tone) system developed by Arnold Schoenberg (1874 – 1951) has taken this study to entirely new levels, and has instituted such concepts as set theory, ordered sets, vectors, and various types of spaces as useful tools in music theory. In this paper we will look into one of these tools, namely the notion of interval vectors.