This paper examines the judgment of segmented temporal intervals, using short tone sequences as a convenient test case. In four experiments, we investigate how the relative lengths, arrangement, and pitches of the tones in a sequence affect judgments of sequence duration, and ask whether the data can be described by a simple weighted sum of segments model. The model incorporates three basic assumptions: (i) the judgment of each segment is a negatively accelerated function of its duration, (ii) the judgment of the overall interval is produced by summing the judgments of each segment, and (iii) more recent segments are weighted more heavily. We also assume that higher-pitched tones are judged to last longer. Empirically, sequences with equal-sized segments were consistently judged longer than those with accelerating or decelerating structures. Furthermore, temporal structure interacted with duration, such that accelerating sequences were judged longer than decelerating ones at short durations but the effect reversed at longer durations. These effects were modulated by the number of tones in the sequence, the rate of acceleration/deceleration, and whether the sequence had ascending or descending pitch, and were well-described by the weighted sum model. The data provide strong constraints on theories of temporal judgment, and the weighted sum of segments model offers a useful basis for future theoretical and empirical investigation.