tempointervalit

Tempointervalit is a concept used in music analysis to describe the relationship between tempo variations over time and the resulting rhythmic intervals in a performance. The term combines tempo and interval and is employed to examine how changes in speed affect the durations between successive onsets.

Formally, tempointervalit refers to a sequence of time intervals between consecutive note onsets, observed under a tempo trajectory T(t). The tempo trajectory may be piecewise constant or smoothly varying. Each onset time t_n yields I_n = t_{n+1} - t_n, with the local tempo corresponding to T(t_n) in beats per minute. The tempointervalit can be characterized by the mapping from the tempo profile to the interval distribution, and by statistics such as mean I, variance, skewness, and the sensitivity of I_n to changes in T.

Measurement of tempointervalit typically relies on performance data, using onset detection on audio or MIDI to derive onset times and a tempo curve T(t). Analysts may compare the observed I_n with idealized intervals under a reference tempo to assess rubato, tempo accelerations or decelerations, and rhythmic consistency.

Applications of the concept appear in music information retrieval, performance analysis, pedagogy, and algorithmic composition. Tempointervalit provides a framework for quantifying how tempo dynamics shape rhythm and timing in a piece. The term remains informal and is used primarily in niche studies; not all researchers formalize it identically. Critics note that tempo and interval are interdependent and are influenced by expressive timing, instrument, and acoustics, which can complicate strict definitions.