In this paper, we consider the problem of continuous dissemination of time series data, such as sensor measurements, to a large number of subscribers. These subscribers fall into multiple subscription levels, where each subscription level is specified by the bandwidth constraint of a subscriber, which is an abstract indicator for both the physical limits and the amount of data that the subscriber would like to handle. To handle this problem, we propose a system framework for multi-scale time series data dissemination that employs a typical tree-based dissemination network and existing time-series compression models. Due to the bandwidth limits regarding to potentially sheer speed of data, it is inevitable to compress and re-compress data along the dissemination paths according to the subscription level of each node. Compression would caused the accuracy loss of data, thus we devise several algorithms to optimize the average accuracies of the data received by all subscribers within the dissemination network. Finally, we have conducted extensive experiments to study the performance of the algorithms.