Representing musical and audio (sample) time in ways that maximises reversible conversion between the two of them. Musical time is typically spoken of (in western culture) in terms of "bars" (or "measures") and "beats". The relationship to audio (sample) time is defined by a "tempo map" which defines the number of beats per minute and the number of beats per bar.

The mapping between the two is monotonic, non-linear, and can be stationary. If the tempo map is allowed to contain ramps (accelerando and ritardando in music speak), there are implicitly exponential sections in the function that maps between them.

Using floating point arithmetic leads to errors that have immediate effects. A musical time that should be considered to be at sample N is instead considered to be at sample N-1 or N+1.

It's surprisingly hard to do it correctly.