Tempograms

Tempograms are a time–tempo representation used in music information retrieval to track how the tempo of a piece changes over time. In contrast to a single global tempo estimate, a tempogram expresses tempo as a function of time, typically in beats per minute (BPM). It is usually presented as a two dimensional map T(t, BPM) or T(t, τ) where t is time and BPM or period τ is the tempo candidate.

To compute, an audio signal is first transformed into an onset detection function (ODF) that highlights moments with likely note onsets. A short-time windowed analysis is then applied to extract the tempo information. Two common constructions are the autocorrelation tempogram, which applies an autocorrelation to the ODF in each short window and maps lag to tempo via BPM = 60/τ; and the Fourier tempogram, which applies a short-time Fourier transform to the ODF and interprets frequency components as tempo candidates.

Tempograms enable tracking tempo changes, such as accelerando or ritardando, and reveal periodicities or tempo modulations; they support beat tracking, alignment, and musicological study.

Limitations include sensitivity to onset detection quality and polyphonic ambiguity; the choice of window length affects time and tempo resolution; tempo estimates can be uncertain when multiple periodicities coexist. Despite these limits, tempograms provide a compact, interpretable view of tempo dynamics and are widely used in research and music analysis.