From fux to ragas-morphing contrapuntal worlds

Julien Junod, Guerino Mazzola

Research output: Contribution to conferencePaperpeer-review

2 Scopus citations


The mathematical modeling of classical counterpoint in [Maz02] complements the classical Fux system [Fux42] by five other "exotic" systems of rules for composition. They all derive from the same algebraic model, but only the traditional Fuxian system has been used by musicians, leaving five unexplored counterpoint worlds for the composition of new music. In this paper, we present and discuss concepts, algorithms, and the implementation in software modules of the Rubato composer system [MM06] for the possible morphing transitions between these systems. This enables the creation of exotic contrapuntal compositions by structural transport. To do so, we represent authorisations and interdictions within different counterpoint systems by directed graphs. Morphing contrapuntal compositions from one world into contrapuntal compositions compliant with the rules of another world then reduces to the construction of a set of distinguished digraph morphisms. This shows that the worlds do not only coexist independently: a procedure is given to morph music from one world into an other, thus connecting them to a network of contrapuntal travels. Using our Rubato implementation, composers can play with counterpoints by exploring a complete catalogue of possible transformations.

Original languageEnglish (US)
Number of pages8
StatePublished - 2007
EventInternational Computer Music Conference, ICMC 2007 - Copenhagen, Denmark
Duration: Aug 27 2007Aug 31 2007


OtherInternational Computer Music Conference, ICMC 2007


Dive into the research topics of 'From fux to ragas-morphing contrapuntal worlds'. Together they form a unique fingerprint.

Cite this