Previous studies investigating sensitivity to step changes in tempo and prediction of tone onset time have generally utilized isochronous sequences. This study investigates subjects' ability to detect deviations from a gradual change in the tempo of a tone sequence (experiment 1) and their judgment of the perceptually optimal timing of this tone (experiment 2). In experiment 1, inter-onset-intervals within pairs of eight-tone sequences followed a geometric progression to create a gradual tempo change. In one sequence, the final tone was presented either earlier or later than specified by the progression. Subjects performed well at detecting deviations that exaggerated the tempo progression but poorly when it was counteracted. Experiment 2 used similar pairs except that the final tone was always presented earlier in one sequence than the other. Final interval length was adaptively adjusted to subjects' judgments; it was adjudged in best agreement with the progression when its length was roughly half way between the mathematically correct value and the length of the penultimate interval. The data support "multiple-look" and entrainment models of tempo sensitivity and suggest that temporal prediction is based less on the tempo contour of a whole sequence than on the duration of the preceding interval.