Diminuendo al bottom—Clarifying the semantics of music notation by re-modeling

One of many aspects of musical notation is that of a graphical language which strives to be totally precise, but falls short because it has been defined by historical evolution, cultural construction and de-central ramification. This article applies standard techniques for computer languages to reconstruct a precise model for the syntax and semantics of the historically grown notation systems, taking the conventional way of notating musical dynamics as a simple example. It turns out that no single such model is possible, but a multitude of incompatibles: some have fundamentally different evaluation algorithms, others only slightly different parameter settings. Musical practice is allowed to switch between these models without even noticing their existence, but science may need distinctness. This article constructs and demonstrates an extensible mathematical framework for their precise description and proposes an extensible nomenclature system as a basis for their application and discussion.