Something simple that I've found curious:
When people 'count in' a tune, to get all the players ready to start at the same time, I often hear them do it first at half-speed, then at full speed. e.g. if the tune is in 4/4, and there are 4 characters to a bar below, they'll say:
1_2_1234 ^everyone starts playing here i.e. 1_2_ (either 2 beats (counts) at half the expected tempo;or a whole bar of the 'right' tempo, but saying 'two' on the 3rd beat) 1234 (a 4-beat bar at the 'right' tempo for the upcoming tune)
I realise not everyone does this; some just go: 1234 or 12341234 at 'full-speed', but it's quite common, and I wondered why. I guess it's a just a getting-you-ready introduction.
When I hear someone start with their initial 'one two', is there a way to tell immediately whether that 'one two' is the first two beats at the real tempo, or just the half-speed into, with a doubling of the speed about to follow?