Many approaches have been proposed for the visualization of time series. The reduced line charts (small multiples for time series) and the more recent horizon graphs are two of these visualization techniques with benefits for visualizing multiple time series that we propose to unify, using a variant of the pan and zoom interaction on the y axis. We compare in a user study reduced line charts, horizon graphs, and our own contribution---progressive horizon graphs---for different tasks and numbers of concurrent time series using datasets with small variations. While recent work has compared horizon graphs with others visualization techniques and has made some recommendations on their usability, the real advantages of this technique are not clear. The results of our controlled user study show that progressive horizon graphs overcome these two visualization techniques when the number of charts increases.