Musical information can be classified as either continuous or discrete. Continuous information changes over time (or perhaps as a function of other variables) and is typically represented by digital sampling, by splines (including piecewise linear functions), or by arbitrary mathematical functions. In contrast to continuous data that fill time intervals, discrete information usually represents events at a point in time. A MIDI Note On event is an exarnple. It is sometimes advantageous to represent discrete events using time intervals rather than points (Honing 1992). There is a natural correspondence to musical notes, which have duration as well as starting time. Also, intervals and sequences of intervals can be appended.
Continuous information is found in the signals of Music V and also in the Groove system (Mathews and Moore 1970) Groove was a real-time, multichannel, continuous information recorder and manipulator; it is highly recommended for further study.
Music representation systems have generally had a difficult time integrating continuous and discrete data. For example, many modem sequencers support smooth changes in controls such as volume, but functions of time are not first-class entities that can be combined with mathematical operations. Another issue is the use of continuous data as parameters to discrete events. If a continuous function is to be used as a pitch contour, should each note sample the function to obtain a constant pitch, or should pitch vary over the course of the note? Finding general representations that incorporate continuous and discrete data is still an active area of research.
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