Why "Hey, tutti taitie" (the tune to "Scots wha hae") Doesn't Sound Medieval

I've actually found a news article from 1913 which, from my limited understanding of French, looks like a fairly thorough debunk of the 'Chateau de Blois' evidence for an early origin of the tune. But as with so many things, it seems the legend is more powerful. Meanwhile Chris offers this commentary based on the tune itself:

As Cait has mentioned there is a curiously widespread notion that "Hey,tutti taitie" (the tune used by Robert Burns for his song "Scots wha hae") is a medieval melody, played at Bannockburn in 1314 and/or by the Scots at the Siege of Orleans in 1429. To most people who see the clear differences (see 'Pre-Early Music') between medieval music (roughly up to 15th C) and Renaissance and later music  this notion is obviously tosh - the melody in no way sounds medieval and seems post-Renaissance (at a guess 18th C). But how can we say that?

I am not a Comparative Musicologist but I have played an awful lot of medieval music. So here is my view of why the tune (at least as found in most editions of Burns' songs, e.g., here) doesn't sound medieval.

1. The rather clear feel of harmony. In each set of two bars the melody concentrates on notes of a triad. It is very rare to see such a rigid structure throughout a medieval melody, though it occasionally happens for short section - but no more than two or three 'bars'.
2. The repeated notes, that occur in many of the two-bar phrases, are rare in medieval melodies, which usually have much more melodic movement.
3. The insistantly dotted rhythm [note from Cait: Emmerson even tries to use this to argue we have here evidence for early origins of the strathspey!]. This is not at all common in medieval music; it is common in the Baroque. It is vaguely possible that the rhythm has been applied later to a melody that originally had a 6/8 sort of rhythm  but it doesn't sound that way.
4. The importance of the sixth in the mid-part of the melody (e.g. bars 5-6 and 9-10). Medieval music rarely has the 6th degree in a structural position.
5. The repeated note of the final before the stress (the 'f' at the end of bars 7 & 15). Medieval music usually resolves on the stress, not before.
6. The awful predictability. It has the four-square blockiness of Renaissance and later music.

For most instances of the word 'Medieval' here you could substitute 'Modal' and use the argument to differentiate western 'Harmonic' music from non-Western 'Modal' music. But that is not a bad guide.