Temporal pattern is a series of time intervals, without any interpretation or structure.
Rhythm is a temporal pattern with durational and accentual relationships and possibly structural interpretations (Dowling & Harwood, 1986).
Beat refers to a perceived pulse marking off equal durational units (Dowling & Harwood, 1986, p. 185). They set the most basic level of metrical organisation. The interval between beats is sometimes called a "time-span" (Lerdahl & Jackendoff, 1983), or, less abstract, beat duration, beat period or metrical unit (Longuet-Higgins & Lisle, 1989).
Metre involves a ratio relationship between at least two time levels (Yeston, 1976). One is a referent time level, the beat period, and the other is a higher order period based on a fixed number of beat periods, the measure. It imposes an accent structure on beats, because beats initiating higher level boundaries are considered more important.
Tempo refers to the rate at which beats occur (often expressed as beats per minute), and is therefore closely linked to the metrical structure.
Density is used to refer to the average presentation rate taken across events of different duration (i.e. events per second) when a piece has events of different durations and the beat is hard to determine unambiguously, if at all (Dowling & Harwood, 1986).
It is important to note that rhythm, tempo, metre and density can be conceived independently: it is possible to maintain the same tempo while changing density; for example, a musical fragment can have a lot of embellishments (i.e. have a high density) and still be perceived as having a slow tempo. Furthermore, rhythm can exist without a regular metre and any type of rhythmical grouping can occur in any type of metrical structure (Cooper & Meyer, 1960).
Tactus is the tempo expressed at the level at which the units (beats) pass at a moderate rate (Lerdahl & Jackendoff, 1983). This rate is around the "preferred" or "spontaneous" tempo of about 100 beats per minute (Fraisse, 1982).