The only slight quibble I had was the use of the adjective and would suggest middle ages would be more appropriate for the longer period referred to.

It has always struck me that neither are terribly helpful terms for a period that might be said to have lasted as long as 1500 years. For an interval, that represents a lot of Choc Ices.

That said, I don't understand the disinction between 'mediaeval' and 'middle ages.' They both mean the same don't they?