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This term is usually reserved for the 5th and 6th centuries. Re-enactors who re-create the next period of history - 7th to 11th centuries - often refer to this as Early medieval. The 12th to 14th are High medieval.
The principal aim of this sort of reenactment is to re-create historical battles or methods of combat. The variations range from the training of historical dueling practices (usually with an appropriate period sword.