My friend's chord progression.

I didn't say G was the pivot - I said D was. That's the chord used in both keys, as the temporary tonic in D and the primary subdominant in A. That would make it a direct modulation from A to D, with a return to A by pivot. And yes, there's an authentic V-I cadence, when the progression repeats, moving from E to A - there's no requirement that a cadence immediately follow a modulation; it's simply usual practice to reaffirm the new key.

But it's speculation on both our parts - whether it's considered a modulation or a non-harmonic chord depends on something we don't know - how the music sounds. If the G chord lasts only a beat or two, your view wins; if the segement with the G harmony lasts several bars, followed by a few more of D, it's a modulation - the new key is established.

While it's obvious this is a highly involved and spirited conversation, it's also obvious that the original thread is being highjacked.

So I'm locking it up. Nivoil (cute name, by the way) and Tom - you can PM each other about all the niceties if you'd like.

Peace