Well it depends on the pace, at the walk they have a four beat rhythm, actually more a 2+2, think John Lennons Imagine. The trot is the classic two-time beat clip clop clip clop. The canter is your three time, with a moment of suspension when all four hooves are off the ground; one foot, diagonal pair, last foot, clip CLOP clip - clip CLOP clip. The gallop is a four time pace, but often sounds more like rolling thunder.
Nothing to do with canals? Boats were normally towed at a walk, short trots are possible. Fast passenger boats apparently went at a canter with one or two horses, one being ridden, and were changed every couple of miles on the fly (without slowing)! I really find it hard to imagine how that was done.