Time is without doubt the most important dimension in music. Its representation and manipulation is crucial for the expressiveness of a composition environment, yet has proven to be a formidable problem. Discussions on time can be found in the fields of multimedia authoring, temporal algebra, auditive perception and cognition, musicology, composition, philosophy, and physics. In this section we will limit our discussion mainly to the representation of time found in systems for music and include some issues found in articles on multimedia authoring. We will use the generic term temporal object to denote any object, musical or other, that has a location and duration in time. Structures that group several temporal objects we will call composite (temporal) objects. When we use musical examples, we may use the terms sound or music objects.

The following list gives an idea of some of the issues in the discussion of time representation and organization:

• The description of timing information.

• The contruction of composite temporal objects.

• The use of composite objects as basic elements.

• The definition of temporal relations between objects.

• The manipulation and transformation of composite objects.

• The interactive, dynamic control of a composition.

• The relations between continuous time and event time.

• Time and hierarchy in musical structures.

• The manipulation of continuous time functions.

• The relation between composed time and performance time.

• The representation of temporal information during runtime.

• The relation between ``out-of-time'' structures and ``in-time'' realization [Xen90].

A discussion of some time representation issues in music can be found in [DDH97] and [Hon93]. The last article has the additional merit of trying to link discussions in the field of music cognition to representations used in music composition systems. The above issues are so entangled that we can not discuss them separately. We will therefore organize the following discussion in two main parts. In section 3.1, we discuss the structured organization of music pieces. This part handles the structuring of events and durations. In section 3.2 considers the use of continuous time functions in music pieces.