I'm refreshing this in the hopes that someone will take an interest in my question.

In the meantime I've learned that Wind That Shakes the Barley and Mairi's Wedding are in major keys, not Mixolydian. Wind That Shakes the Barley has two sharps in its signature but seems to centre around the note A, so I thought it was A Mixolydian, but I guess maybe it's just one of the "circular" tunes that have been mentioned.

And in the hopes of luring M.Ted back into the water... I wonder if you've already answered my question with:

"Other things that major/minor scales do that modes don't, is allow for the possibility of key changes, and allow the melody to be changed from major to minor..." (M.Ted, above).

So does that mean if you start with a G major tune you can switch casually to an E minor tune, and make a leap to some other major key and have it not sound too disjointed... whereas if you start with a tune in E Dorian it should only be followed by other tunes in E Dorian?

I'm also trying to understand this statement:

"Through the use of changing harmonies, they make it possible to change the tone center of the melody to any of the other scale notes, without changing the underlying tonality of the melody--" (M.Ted again).

So if you have a song where you play G chord on the first two bars, then C on the next two bars, then D on the next two bars... does that mean that in bars 3 and 4 the tone centre is C, and in bars 5 and 6 the tone centre is D, and the underlying tonality is G? Is that what you mean by changing the tone centre? Or can you say that bars 3 and 4 are actually in the key of C major and that there has been a short-lived modulation?

Thanks, Marion