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Beats (i.e. pulses that describe the pace of the music, or foot taping) are time markers, which in the XML response come with a confidence level (between 0 and 1). They're aligned with the music, so they'll move along, accelerating and slowing down when necessary... Tempo, on the other hand is an overall estimation, therefore more or less relevant, depending on whether the beat duration is constant or not. It also comes with a confidence value.
We don't have loudness distribution examples at hand, but that would be fairly easy to compute. What do you mean by rhythm distribution though? Rhythm is hardly described by a single number so it is a bit hard to display as a distribution.
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