We present work-in-progress on RTG, a domain specific language embedded in Haskell designed to explore the affordances of geometry as a means to generate and manipulate rhythmic patterns in live coded music. Examples of how simple geometry is capable of producing interesting rhythms are shown to support our use of binary lists as a pattern representation. We introduce Erlangen’s Program notion of geometry as encoded in groups, using such structure as the focus of a combinator interface based on an archetypal RhythmicPattern type implemented using a type class. Future works targets the definition of Group instances for different rhythmic pattern types such that the group laws are fulfilled and its operations lifts to the interface in a musically coherent and engaging way.

Xavier Góngora was introduced to jazz improvisation by composer and engineer Alberto Palomo in Mérida, Yucatán. While pursuing his degree in mathematics at UNAM, he delved into complex and quantum geometry under the mentorship of mathematical physicist Micho Durdevich, who ignited his passion for the transdisciplinary exploration of mathematics and music. He went on to earn a Master’s degree in Music Technology from UNAM, with a thesis on remixing and sampling as forms of composition and re-appropriation, guided by sound artist and composer Jorge David García. Currently, he works on his doctoral thesis exploring the intersections of programming languages, music, and geometry. His personal musical project, Niño Artillero, embodies his interdisciplinary approach, blending elements of art, mathematics, and technology.