It’s worth noting that 5 and 10 are only “natural” to us because we have 5 fingers on each hand (10 in total).
I’d argue the counts 4,8,16 are common for basically the same reason those numbers are common in computing: splitting things into two is the simplest way to split things up. Makes it very easy to have units that each contain some sort of contrast within themselves. You can have a question/answer, a busy/quiet section, a “happy”/“sad” dichotomy. And even more complicated mixtures of some or all of those.
But other counts are also very common. 3,6,9,12. Even 5 and 7. They all serve different purposes for how you’re creating contrast in your music.
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