Foundations of LLCM : Labelled Lambek Calculus for Music Analysis

This paper presents an application of Lambek Calculus, a sequent calculus for categorial grammar, to music analysis. To this end, we propose a Labelled Lambek Calculus for Music (LLCM), where a label represents tonality information. In LLCM, each adjacent category represents a chord interpretation. When combined, they form a cadential category. We have enhanced the system with a rigorous and internally consistent framework that clarifies long-distance dependencies and provides a more explicit representation of relationships across different tonalities, including tonal shifts. A key innovation in LLCM is the introduction of a method for calculating the “depth” of a harmonic analysis. This measure corresponds to the complexity of chord progressions, enabling analysts to objectively compare different harmonic sequences based on their structural intricacy.