The F Operator: A Proposal for a Generative Notation for Frequency Factors in Music
Markus Lepper and Baltasar Trancón Y Widemann | semantics gGmbH Berlin, Technische Hochschule Brandenburg
In music theory and historical musicology, tuning systems can be discussed from a variety of angles, ranging from historically given contingent facts or hypotheses, over physiological and psychological experiments, up to integration into an aesthetic theory. All these different approaches define specific collections of objects and calculation rules and live on a symbolic side. Eventually, these calculations deliver numeric factors to be applied to some reference frequency. These form the factor side. We propose F-operator, a notation system for these values which allows easy identification and labeling of commonly used factors and thus easy comparison of distinct systems from the symbolic side. F-operator is equally well suited for writing, talking, speech recognition, sign language, Braille, and computer representation.
© Markus Lepper
Markus Lepper
Markus Lepper studied composition with Wolfgang Hufschmidt and electronic composition with Dirk Reith at the Folkwanghochschule in Essen. PhD in informatics with Peter Pepper at the Technische Universität Berlin and in musicology with Michael Oehler and Hartmuth Kinzler at the Osnabrück University. Lives and works as computer scientist, composer, and music theorist in Berlin.
© Baltasar Trancón Y Widemann
Baltasar Trancón Y Widemann
Baltasar Trancón Y Widemann studied computer science with Peter Pepper at the Technische Universität Berlin. He holds a PhD and Habilitation degree in computer science. He has worked as a researcher and lecturer at academic institutes in Limerick, Bayreuth, Ilmenau and Elmshorn, and as a software engineer in Karlsruhe. He is a tenured professor at the Technische Hochschule Brandenburg.
A Prosodic Layer for Suprasegmental Features Spanning Rhythm Trees,
Motivated by Carnatic Rhythmical Structures
Daniel Miller | Independent Researcher
Rhythm trees model durational structure as recursive equal subdivision, but musical rhythm often involves suprasegmental patterns that cross-cut the subdivision hierarchy— long-distance dependencies that context-free grammars cannot express. Carnatic rhythmic techniques provide cleartest cases: rhythmic sangati preserves motives across changes in subdivision density and accent placement, while jathi bhedam treats irregular accent spans as compositional units. Drawing on work in prosodic phonology which models intonation as a tree-based hierarchy distinct from segmental structure, we introduce an accent tree that overlays a base rhythm tree. The accent tree acts on a depth projection— a sequence of positions at a chosen metrical level— and partitions those positions into spans that may cross subdivision boundaries. Each span either inherits the underlying rhythm or hosts an attached rhythm tree time-scaled to fill it. Accent trees compile to labeled duration sequences that map back to rhythm trees, so the formalism remains compatible with existing rhythm-tree grammars while capturing long-distance dependencies.
© Sophia Chung
Daniel Miller
Daniel Miller is a multidisciplinary artist and technologist whose creative and research practice explores algorithmic composition, hardware synthesizers, and digitally mediated notation and performance. His work has been supported by organizations including the Fulbright Program, the Watson Foundation, and BMI. Alongside his artistic practice, he has worked as a software engineer, most recently at a startup focused on drone delivery of biomedical supplies. He holds an M.A. in Digital Musics from Dartmouth College and a bachelor’s degree in Music Composition from Lawrence University. He splits his time between Taiwan and Seattle with his wife and daughter.