How do horses move their heads differently at the walk, trot, and gallop?

In horsemanship, a horse’s head movement varies significantly depending on its gait:

• Walk: The horse’s head moves in a rhythmic motion, shifting down and forward, then up and back. During a free walk, the horse is granted freedom of its head and neck, whereas a collected walk requires the head and neck to be balanced and controlled by the rider.123
• Trot: Unlike the other gaits, the horse’s head remains relatively still during the trot. While an extended trot may allow for some forward extension of the head and neck, the gait is generally characterized by the horse springing from one diagonal pair of legs to the other.24
• Gallop: Similar to the walk, the horse’s head moves down and forward, then up and back. However, at the gallop—the horse's fastest gait—the animal typically carries its head relatively high, and the reins are held more loosely than at a canter.25