Music summarization allows for higher efficiency in processing, storage, and sharing of datasets. Machine-oriented approaches, being agnostic to human consumption, optimize these aspects even further. Such summaries have already been successfully validated in some MIR tasks. We now generalize previous conclusions by evaluating the impact of generic summarization of music from a probabilistic perspective. We estimate Gaussian distributions for original and summarized songs and compute their relative entropy, in order to measure information loss incurred by summarization. Our results suggest that relative entropy is a good predictor of summarization performance in the context of tasks relying on a bag-of-features model. Based on this observation, we further propose a straightforward yet expressive summarizer, which minimizes relative entropy with respect to the original song, that objectively outperforms previous methods and is better suited to avoid potential copyright issues.