I am looking for data that either confirm or refute the following statement:
During the Renaissance (let's say, 14th to 16th centuries), Western European languages changed very rapidly. The pace of language change was much greater than before or after that period.
Background: I have observed that in both English and Portuguese, the language used in literary texts changed significantly during that period. Chaucer's Middle English is very different from Shakespeare's Early Modern English, which, by contrast, can be reasonably well understood by today's English speakers. Similarly, Gil Vicente's Old Portuguese clearly contrasts with Luís de Camões's Modern Portuguese. 21st century Portuguese speakers can understand Camões's language with almost no difficulty. This is just anecdotal evidence, so feel free to challenge these assumptions, as well.
Update: As Cerberus pointed out, it may not be a good idea to try to understand this phenomenon from a modern speaker's perspective. But I hope that historical linguists have an objective way of measuring and evaluating the process of change in a certain period, as well as making comparisons between different historical periods. The anecdotal evidence above was intended merely to show the motivation for the question, so please don't get much distracted by it.