Right I've done a little more research and re-watched the beginning of the harmony episode I previously mentioned. Sorry I'm about to go on a bit but I hope it gives some answers to the question of harmony.
Ancient Greeks... Indeed it seems that Pythagoras of Somos (~570 to ~495BC) did demonstrate a mathematical understanding of the laws of music and scale structures.
By ~424 to 347 BC Plato is complaining about people naturally talented musicians ignoring the established laws of music in favour of what sounds good. This has been taken by some to indicate that people were not limiting themselves to the classical modes (scales) in their mathematical structures or ignoring the attributed moods or "ethos" associated with the modes. Other of Plato's works describe the lyre accompanying a singing poet in the "correct" way and yet it is still understood by others that while more than one note would sound at the same time in a complimentary way this is not western harmony.
So I am lead to believe that the Classical Greeks understood scales and were happy for two notes to form a harmony.
Now back to the video, please excuse the direct quoting...
"At its most basic harmony is the intentional coming together of two or more sounds for pleasant effect. All the world's musical cultures share this idea..."
This conforms with what I managed to find in my reading about the Classical Greeks.
"...but harmony in western music is doing something else all together, turning the the collision of notes into a deliberate and complex structure of its own... ...Western harmony began separating off from all other world musics in around the 12th Century."
Howard Goodall then continues to demonstrate how the traditional English round "Summer is icumen in" first put to paper in 1225 is the earliest example of "Western Harmony", as it is understood today, as the combination of cyclic round and moving drone with an overlaid melody result in the formation of a THREE note chord. The rest of the program discusses how the rules of scales enable a pleasing chord progression and how this developed.
Also key was that this style of harmony had apparently not evolved elsewhere but had been blended with nearly all musical cultures once introduced.
So if we can trust the accepted wisdom at all then the Anglo Saxons would have been happy playing their harps in accompaniment to sung lyrics forming basic TWO note harmonies as the Ancient Greeks apparently did and with as much musical proficiency as apparently all the other world cultures.
Daring a little creative thinking, one could suggest that in fact the defining 3 note chord that occurs in Summer is icumen in, was common place throughout folk music of far earlier medieval periods, including the AS period, but that not being church music, had not been recorded until 1225. This doesn't explain though why from this point onwards, and not before, development of western harmony really takes off.
Thanks to anyone who read all that, I hope you found it interesting.
P.s. I'm sorry to do this but I don't particularly like my threads being dismissed out of hand,
But those items seem to deal with techniques developed over the last 300 years, whereas the origins of harmony, which is the bone of contention, goes back to the Greeks .
In what way is 1225 within the last 300 years? My calculations put it closer to 800