ChordGeometries 1.1 is a multiplatform application developed by Dmitri Tymoczko (a researched at Princeton University) for a research named “Generalized Chord Spaces”, conducted by Tymoczko himself together with CliftonCallender (Florida State University) and Ian Quinn (Yale University). The hypothesis they are trying to verify is the possibility to generalize some geometrical models describing connections between chords (voice-leading) so as to confer them a general validity. To this end, they’re analyzing some examples of voice-leading to prove that the spaces between a chord and the next one, which are a characteristic of these examples, belong to a wider family of geometrical spaces that share some essential qualities. Thus, if we represent these examples geometrically, we’ll see that a point in these spaces corresponds to a harmonic object (a chord), while a line connecting two points is the connection between them (voice-leading) and the length of this line is the “measure” of the voice-leading it represents. Therefore, the distance between two points is the measure of the minimum voice-leading between two harmonic objects and this implies that the graphs of each example can be treated the same way: they are all factors of the same kind of fundamental space, or spaces that are a result of putting those points in a wider space. To help us understand these complex concepts, the ChordGeometries 1.1 software visualizes chords and voice-leadings in a three-dimensional space. The chords may be inputed using a MIDI interface. For each of them, the application will create a representation where successive voice-leadings are visualized as continue paths in space. The importance of the research of these three American researchers can be understood within the frame of challenging the combinatorial paradigm that dominated the field of music theory in the last decades, and substitute it with a theory based on geometry and topology and – particularly – on the introduction of “space”.

Vito Campanelli