Here we play with beats of 2, 3 and 4 divisions. I start with 3, which I am playing with a swing feel on the recording. At “hip” I take a way a division (e.g. 3 divisions becomes 2), at “hop” I add one (e.g. 3 divisions becomes 4). I am playing in a measure of 2 or a duple meter. “Return” signals a change back to 3. It could be notated in 6/8 with a dotted quarter beat for “3”; 2/4 with a quarter note beat for “2”, and 2/2 with a half note beat (and eight note subdivision) for “4”. The eighth note is kept at a constant tempo–or at least that is my intention! This is known as a “reaction” game or activity in Dalcroze parlance. In this case the signal is verbal (they can also be visual, musical or tactile).
Try bouncing and catching a ball on the beat. Bounce from one hand and catch to the other, alternating hands each time. It becomes a short study in the relationship between time, space and energy.
It is common practice in jazz to move between 2’s, 3’s, 4’s, however most often the beat stays constant (rather than the division or subdivision). I do remember Wynton Marsalis experimenting with this device on a couple early albums from the 1980’s, however. I’ll see if I can find it and update this post if I do.
Or… maybe you have an example in any genre of music you’d like to share?