tempoen

Tempoen is a theoretical metric used in music theory and computational musicology to describe tempo trajectories and expressive timing in performances. It extends the concept of beats per minute by incorporating tempo fluctuations and inertia, enabling a single numeric value to summarize both the general speed and the consistency of a passage.

A Tempoen value, denoted Tp, is derived from the performance’s tempo curve estimated from note onsets. Instantaneous tempo is computed at short intervals and then smoothed with a brief window. The Tempoen value for a segment is the average of these smoothed tempo estimates, expressed in Tempoen units per minute. By convention, a Tp of 60 corresponds roughly to a steady tempo of 60 BPM. Some analyses also include a tempo inertia factor to reflect resistance to rapid tempo changes, which modulates Tp to emphasize gradual trends rather than sudden shifts.

Applications of Tempoen include comparative analysis of tempo trajectories across performances, examination of rubato and expressive timing in genres such as classical and jazz, and as an objective target in computational models of timing. It provides a compact summary of both speed and stability, complementing traditional BPM and rubato descriptions.

History and reception: The concept emerged in academic discussions about timing representation in the 2010s and remains a niche metric. It is not standardized and depends on onset-detection methods, window length, and model assumptions, which can limit cross-study comparability.

Related topics include tempo, BPM, tempo rubato, and tempo maps.