How did the renaissance influence medieval music?

I have had a blog post with this title in mind for a while, intending to discuss how modern musicians (especially if classically trained 'early music' specialists) tend to come at medieval music from renaissance music, or even from baroque. Although some are very adept (or very conscientious) at swapping styles, others seem unaware of the baggage of theory and technique they are, anachronistically,  transferring backwards.

As it turns out, the title is also very appropriate to describe the argument in Berger's first chapter (see yesterday's post) about the musicology of Friedrich Ludwig. Ludwig was in many ways an ideal scholar, compiling, cataloguing and accurately transcribing vast amounts of medieval music, arguably the first to decipher modal rhythmic notation in early polyphony (at least  the first to provide a clear written account of it, although unfortunately guilty of then insisting all early monophonic song should comply). However, as Berger explains:

"Ludwig saw medieval polyphony as the first step on an evolutionary ladder leading up to the great master Palestrina. We read in [his] 1929 text: “In the Middle Ages the lead was taken nevertheless by representatives of the polyphonic ideal, which found its highest and purest embodiment in the pure vocal music of Palestrina.”

And this has direct consequences because it means the 'importance' of medieval pieces is judged relative to their detectable conformance to the Palestrina ideal, which includes:

"sacred text, the same in all parts, purely vocal texture, consonant counterpoint producing fully triadic vertical harmonies, slowly moving parts, imitation and canons, or at least independent voice leading in all parts. When any of these are present, the pieces become more important and better for Ludwig." 

Whether as a direct influence of Ludwig, or independently motivated, I think this "seeking for the Renaissance" in the medieval is still common.