Is there a “golden” tempo that is universally appealing, like the Golden Ratio is universally appealing visually? Not to my knowledge… nor search engine Google’s knowledge, for that matter. However, as I was setting a tempo for a piano étude I had composed a few decades ago, it turned out to be about 100 bpm. That was roughly 1 and 2/3 beats per second, or 1.666 approximated, which wasn’t far from 1.618 approximated that I knew to be the rounded value of the Golden Ratio.

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