Meta-Models Matter --- The tscore R&D Project and “Die Kunst der Fuge”

Authors: Lepper, Markus / Trancón y Widemann, Baltasar

Date: Thursday, 7 September 2023, 4:15pm to 5:45pm

Location: Main Campus, L 1 <campus:stage>


The fundamental analysis by Lepper (2021) shows that for precisely defining any music notation or encoding system (a) a clean separation of the syntactic sphere from the semantic sphere is necessary, based on which (b) mathematical quadrupels must be defined which cover the structures of both spheres plus the mappings between them, in both directions. But each practical notation/encoding system has turned out (c) as a pipeline or even as a branching network between multiple such spheres.

When choosing the data for digital encoding, often we cut somewhere into the middle of some larger evaluation pipeline. For instance, explicitly storing spelled pitches (“SPCs” according to Hentschel (2021), like “e flat” and “e natural”) skips non-trivial steps of traditional reading, namely computing the combined effect of key signature, sequences of “white key” note heads (“GPCs”), local accidentals, and rules for scoping and priority.

In computer science, encoded objects are often called models. Their type definition is called a meta-model. The interpretation of any model is only sensible based on its meta-model, which gives the rules for its syntactic and semantic interpretation. Therefore modeling music requires the construction of an appropriate meta-model.

At first glance, this seems a tedious obligation, which in practice often is replaced by “common sense” or “obvious obviousness”. But it also is a chance: Making the meta-model explicit for a family of models allows

(a) to check syntax and semantics right from the beginning of the construction,

(b) to reduce all input, edit, and control efforts to the really necessary,

(c) to disambiguate the interpretation of the applied notation,

(d) to re-use the encoded data with a different focus of modeling, by switching the meta-model,

(e) to extend any notation as needed into a new meta-model without conflicts with other authors and styles, and, last not least,

(f) to combine and compare models from unrelated sources without the need of an a priori agreement about the encoding format.

All this requires “only” that meta-models can be compared and combined, and that models can be converted between meta-models by applying their forward and backward mappings. To automate this as far as possible, computer engineering for one particular realm always aims at one particular meta-meta-model to define the meta-models.

Contrarily, Raimond-Adbdallah (2007) and Fields (2011) define the formats for particular music performance and structure data: thus they define a meta-model for these models. The meta-meta-model employed by both is a general purpose one, namely Web Ontology Language (OWL).

Lepper (2021) has shown that in the realm of mere conventional usage of Common Western Notation (CWN) more than eight hundred meta-model parameters are relevant. The strategy to find one single meta-model covering all these variants (up to 6.6E240 !) appears unfeasible, esp. if not only the syntax but also the semantics shall be meta-modelled precisely.

The authors’ “tscore” project thus takes the different approach of constructing a dedicated meta-meta-model into which particular meta-models can be plugged in as needed (Lepper 2013). It realizes a generic input format similar to the conventional orchestra score, with freely definable time model (currently restricted to one global) and arbitrarily mixed parameter tracks, independent for each voice.

The approach is co-algebraic: The self-identity of each “notation event” (according to Lepper (2021)) is axiomatic, all parameters are just accidental. This allows to encode any phase of the above-mentioned pipelines, from concrete front-end syntax to pure semantic data (late states in traditional notation evaluation).

The meta-model ingredients are currently combined using the Java programming language plus Embedded Domain Specific Languages (EDSLs = library API calls or library classes, which to combine means to do programming).

The implementation is open source and in the public domain. It currently provides meta-models for experimental graphic composition (tscore 2020), and a family of meta-models for conventional Common Western Notation, with several translation algorithms into (subsets of) musicXML, lilyPond, MEI, etc. (Lepper-Trancón 2019). The EDSLs are carefully designed to support the usage by domain experts (non-computer-language experts), employing sophisticated algorithms for error diagnosis (Lepper-Trancón 2018).

Thanks to property (b) from above, the complete “Die Kunst der Fuge” has been entered in only three days. The co-algebraic Java model is now in the public domain and can be used for further transformation, analysis, and interpretation.


Fields, Ben, Kevin Page, David De Roure, and Tim Crawford (2011) The Segment Ontology: Bridging Music-Generic and Domain-Specific. ICME 2011.

Hentschel, Johannes, Fabian C. Moss, Andrew McLeod, Markus Neuwirth, and Martin Rohrmeier (2021) Towards a Unified Model of Chords in Western Harmony, in: Proceedings of the Music Encoding Conference MEC 2021,

Lepper, Markus (2021) de Linguis Musicam Notare. epOs, Osnabrück.

Lepper, Markus and Baltasar Trancón y Widemann (2013) tscore: Makes Computers and Humans Talk About Time, in: Proceedings of KEOD 2013, 5th Int. Conference on Knowledge Engineering and Ontology Development, Instincc, Portugal, 2013, p. 176-183, doi:10.5220/0004540701760183.

Lepper, Markus and Baltasar Trancón y Widemann (2019) metricSplit: An Automated Notation of Rhythm Aligned with Metric Structure, in: Journal of Mathematics and Music, Taylor Francis, London.

Lepper, Markus and Baltasar Trancón y Widemann (2018) Translets —– Parsing Diagnosis in Small DSLs, with Permutation Combinator and Epsilon Productions, in: Tagungsband des 35ten Jahrestreffens der GI-Fachgruppe “Programmiersprachen und Rechenkonzepte”, IFI Reports, Vol. 482, University of Oslo, Oslo, 2018, p. 114-129.

Raimond, Yves and Samer Abdallah (2007) The Timeline Ontology

tscore (2020) Example Instances of the TScore Project Infrastructure

About the authors

Markus Lepper, composer, music theorist, and computer scientist. He holds a PhD each in computer science and musicology. Works and lives in Berlin and is co-founder of semantics gGmbH Berlin.

Baltasar Trancón Widemann holds a PhD in computer science from TU Berlin and a Habilitation degree from the University of Bayreuth. He has worked as a researcher in academia and as an industrial software engineer. He is currently professor of programming at Nordakademie Elmshorn, and co-founder of semantics gGmbH Berlin.

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