Out of curiosity: how soon after a small burn that is not treated (i.E. Covered with sterile gauze) can gangrene or tetanus occur?

Burn infections. Tetanus does not occur with burns, it occurs with deep cuts or puncture wounds. Gangrene is an infection caused by one of several bacterial. It starts as a small infection that goes deep into the tissues. It then spreads there and produces a gas. Infections can occur with burns which are not treated, but not always and rarely with the bacteria that causes gangrene.