Visualising and interacting with music-theoretic structures

Abstract

Music theory and mathematics originate from completely di erent points of view. We will show, however, how music theory correlates with mathematics. There are certain music-theoretic structures that are meaningful in science and mathematics. This is one of the main reasons why there is an ongoing scienti c study in music theory. Apart from various musical terms, in this dissertation we shall focus on what musical scales are, and explore their geometric properties. It was found [Dou91] that some scales have maximal properties known as maximally even sets and maximal area sets. Up till now, these properties were all demonstrated and computed manually on paper. This dissertation presents a software application tool that can help apprehend whoever is interested about this subject. The user of this application can input the desired parameters to visualise the said properties and results. Moreover, this software application allows the user to choose between two di erent instruments: clock diagram and piano keyboard (see chapter 2). The two instruments show the same results in a di erent visualisation. In addition to this, another intriguing detail for the end user is the visualisation of microtonal music. The software application was implemented for Android using mostly Java language. Finally, the application was evaluated from both algorithmic and qualitative perspectives. The evaluation contributed to come up with ideas for future related work and improvements.