Given a time series, the change point detection task consists in finding the instants where the statistical distribution of the series abruptly changes. The classic approach based on optimization techniques are too rigid and entangled, for which recent approaches advocate building a complete solution path, ranking all the possible change points of the series. This article extends this paradigm by providing a chain of subsets, corresponding to a hierarchy of changes, where different levels imply a finer detection granularity. Our proposal is to compute all levels from a single score vector through a recursive thresholding mechanism, where the threshold maps to the desired detection granularity. We contrast our proposal against state-of-the-art approaches on public benchmarks with human expert labeling, showing: (i) best-in class performance (overall F1-score of 0.87), (ii) a statistically significant and remarkable improvement over the state of the art in the practical case where a single cost function and threshold setting is selected over multiple levels (F1-score of 0.76) and (iii) a qualitative alignment with different human experts for different levels, suggesting that each expert may find a different suitable level in practice.