Objects may persist with varying periodicities. For instance they may appear syncopated against one another. Or they may cross one another, like when you try to beat 3 with one hand and 2 with the other, keeping the same time. It's very satisfying if you can do it. Bill Benzon has a good post about it.
A few years before he went crazy my amazing drummer brother figured out 5 against 4 (it's really not that hard and if you like I shall show you how to do it). I went out for a packet of cigarettes (I smoked in those days). When I came back, he said “Tim! Listen to this! It's 13 over 8!” I believed him...
Consider this passage of Benzon:
In some cultures, including many in Africa, young children are taught 3 against 2 at a very young age. For them it IS easy. That’s not the case, however, in European derived musical traditions. Three against two is not part of basic toddler pedagogy and, as a consequence, learning to do it is a bit more difficult when, and if, the time comes – for some, it never comes. Thus, within the context of the Western classical tradition, three against two is considered moderately difficult rather than being fundamental. Such rhythms are exceptional in classical music, but they are common enough that any moderately skilled keyboard player must know how to execute them.
If you watch the movie Babies you'll see how incredibly adept some very small African kids can be at balancing and dancing. In the almost-desert in which this guy lives, it makes sense to learn how to have rhythms, rhythms that keep you persisting...
Then there's Billy Cobham—just listen to the first few seconds of this:
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