A.k.a. “rim.” A circular piece of wood or metal that lays on top of the drumhead and presses it against the drum shell. The hoop is pulled against the head by tension rods secured by lugs. Adjusting the tension rods/lugs allows the head to be tuned to the desired tightness/pitch.
There are three primary types of hoops: flanged metal, which are made by bending or stamping a strip of metal, then welding it into a circular shape; die-cast metal, which are made by pouring molten metal into a mold; and wood, which are made by laminating and bending multiple plies of wood, usually maple. The type and rigidity of the hoop, as well as the material used to make it, will affect how easily and evenly the drum can be tuned and the tone of the drum. For example, a wooden hoop can act as an extension of the drum shell, providing additional resonance to the tone.
While it might seem as if a heavier, more rigid hoop would be ideal for best tuning, this isn’t always the case. If the drum is slightly out of round or if the edge of the drumshell that the head/rim rest against isn’t well made, the result can be a dry, muffled sound from the drum.