When an event happens (an onset of a note) one can measure the real time elapsed since the beginning of the piece (called performance time) and also the point in the score where this onset was notated (called score time). The latter can be measured either in seconds (taking the tempo marking in the score serious, or normalising the total score length to the performance), in metrical units like beats or quarter notes (called metrical time), or as an event count (called event time). The last loses so much information that the timing pattern cannot be reconstructed without reference to the score.
Performance time can be shown as a function of score time (called a time map), or vice versa. In these representations it is easy to spot (a)synchronies between voices because they depict points in absolute time.
Calculating differences between subsequent performance times in a time map makes the step from time to duration. Because in such a representation it is difficult to compare notes of different nominal duration, a proportional measure is better. It makes the step from duration to relative duration by dividing two corresponding durations. In case a performance duration is divided by a score duration, this forms a series of duration factors (often misleadingly called tempo). This measure is mostly notated in a graph with the independent axis labelled with metrical or event time. In the case of the inverse calculation, the ratios form the velocity, the local speed of reading the score.
In both cases the measured points are often filled in with line segments - implying the existence of a tempo measurement in between events. This is misleading - the more so because integration does not yield the original time map again.
Gabrielsson (1974) uses note duration expressed in proportion to the length of the bar. This allows for comparison with exact note values in different meters. The method might be generalizable to study timing at different levels of structure.
Tempo is sometimes presented on a logarithmic scale; this is a first step towards the use of subjective magnitudes.
An interesting hypothesis was given by Brown (1979). He argues that a musician makes use of a collection of discrete tempi: a collection of discrete physically possible tempi, where the choice is defined by musical and performing factors.