Musical meter typically functions as a structural constant in music, providing a framework of
regular pulses upon which rhythms unfold. In Western music, meter generally remains
consistent over extended musical sections, or even throughout entire pieces. However, this
regularity is occasionally disrupted by metric shifts or polymetric structures, which challenge
conventional conceptions of meter.
Here, we understand meter as composed of smaller units—simple meters—that serve as its
basic building blocks. This view allows for the decomposition of both regular and irregular
metric structures into their fundamental components. In doing so, it provides a means to
analyze and quantify the structural complexity of individual meters as well as of sequences of
meters in both monophonic and polyphonic music.
Based on this perspective, we propose a measure for the complexity of meters and sequences
of meters that depends on the cardinality (i.e., the number of pulses) and the number and type
of its component simple meters. In this context, we also outline the concept of metric stability,
a holistic feature of a piece of music. It serves as a new parameter for describing the degree to
which a meter remains consistent over time. We demonstrate our music-theoretical framework
through computational analyses of Hugo Distler’s motets, which are characterized by
pronounced metric irregularities.
Key findings show that Distler’s motet collection Der Jahrkreis employs a total of 16 distinct time
signatures, resulting in an overall high degree of metric complexity. Individual motets feature up
to six different meters, with an average of 2.57 distinct meters per piece. The metric complexity
values exhibit substantial variability across the motets and are, on average, approximately five
times higher than those found in Bach’s chorales, which themselves show very low variability.
Similarly, Distler’s motets exhibit fluctuating metric stability, whereas Bach’s chorales
demonstrate high stability.