Imagine I'm in a room that's silent apart from a clock whose second hand moves with an audible tick.
If I watch the second hand of the clock and clap every time it moves, I'll be clapping at 60 bpm.
I can easily clap at 120 bpm or 180 bpm or 30 bpm by looking at the second hand.
I can clap precisely 90 bpm by clapping three times for each two clock ticks.
I can clap at precisely 150 bpm by clapping five times every two clock ticks.
But if I wanted to construct other tempos, like 50 bpm, 70 bpm or 110 bpm, what would be the best way to do it?
What I'd really like is to have a collection of polyrhythms that I can perform against the second hand to give me a range of tempos, in ~10 bpm increments, starting at 30 bpm, say.
The reason for the question is that if I choose exact 10 bpm increments I might end up with a really awkward polyrhythm, whereas if I'm more relaxed I can get a polyrhythm that's much simpler to perform but still gets close enough to the required tempo.
And I do realise a metronome could give me the tempo. But I want to work for this - I want the challenge of constructing the tempo myself (in my otherwise silent room!)