Just to introduce myself, I'm a founder member of The Warburg Institute's postdoctoral Esoteric Studies Reading Group, at the heart of The University of London's Advanced Studies School, thanks to a study of the roots of the Renaissance, finding common intent in Dufay and van Eyck's work. I also brought the thinking of Sir Geraint Evans to the 14 year old David Roblou, and was one of the London Early Music mob in the 1970s.

The thing to remember is that scientific enlightenment wasn't as clear-cut as now: that was a Victorian movement. Newton, for example, wrote twice as much on alchemy as he did on hard science. Indeed, freemasonic descendants of the Royal Society were behind the recent Cisplatin breakthrough, studying Royal Arch elixir. The very roots of chemistry were alchemical, in van Helmont's 1618 transmutation, which defied a paracelsian theory, you can't get hot dry gold from cold wet mercury. At that point, you can draw a line, so his beginning again, using empirical observation, can be seen as quite distinct from the experiment. And yet, local data from Brussels suggests his unnamed alchemist was a certain Nicholas de Cerclaers, who was behind the Escorial retasking. How did he know mercury becomes gold if you annihilate a proton? The Wet Path upgrade to Dry Path implies plasma energies through conservation of energy. The Brussels claims are not implausible.
Anyway, Scientific Empiricism is derivative from the earlier Quadrivium academic norm, ditching the emotional facets as too wishy-washy. Those facets are music (the right-hemisphere expression of arithmetic) and cosmology (the right-hemisphere expression of geometry), together with the theme (usually theological).
Therefore, Bach's studies of temperament can be seen as an attempt to drag music into the new world of Pythagorean harmonic, emulating Newton's salvation of astronomy, but it didn't work. It that point, the Arts and Science started to diverge, and Handel brought the Italian dynamic from Corelli in, completing the divorce.
And yet, questions of psychological determinism at a universal level are bedevilling quantuum physics now. Essentially, mathematics has proved itself to be bounded, and so all subjects adopting it as a lemma must be likewise constrained. A bound has two sides, enclosed and excluded, proving the unscientific is rational, and cannot be dismissed as erroneous. The fact you can't quantify emotions doesn't make them unfactual: indeed, Edinburgh's Koestler Institute's got precisely nowhere with its scientific studies of the paranormal. It won't behave scientifically. Thus, psychology and third-sector medicine must be considered unscientific, yet deliver consistently. Science, back in the box with you!
This was very pertinent in the early days of MIDI, which proved simplistic mathematical transcription of the dots was inhumanly robotic.
Southern Europe, by comparison, was and is far removed from the Calvinist reductionalism of the Northern Baroque, for all that Welsh developmental input into Fugue is not to be ignored. Venice and Vienna were almost entirely spared it: the closest it got was Prague. Indeed, they were almost privileged by the proximity to Islamic influence in Turkish Janissary music, a refreshment of the original drive from the Crusades, moderated by Alfonso the Wise. It shredded the unhelpful diktat of the Vatican, which could have approached the Communist control of Shostakovich. Will the EU behave similarly? Who knows. There was some evidence of it in dodecacophony, certainly.

You sound like you have some knowledge to dispense but I can't heads or tails of it. You don't type in complete sentences and you jump from thought to another in the blink of an eye. Slower! First things first:

Please explain this von Helmont transmutation and what it actually did.

Dodecacophony - such a delicious term.

Many thanks for your erudite elucidation. One line drew my attention, "It shredded the unhelpful diktat of the Vatican, which could have approached the Communist control of Shostakovich.” My sub-conscious regurgitated a charming composition from a body of work the Vatican referred to as ‘Musica Prohibita’. Only to be performed in the august presense of the clergy and in the dark. In particular Gegory Allegri’s ‘Miserere Mei’ the text of which includes the charming line ‘My mother concieved me in sin’. The Lord doth move in mysterious ways.


https://www.youtube.com/watch?v=IX1zicNRLmY

Ah, but we should give leeway to the polyvalent genius post-doctoral mind habituated to addressing their peers rather than the great unwashed.


https://www.britannica.com/biography...ta-van-Helmont

All there is here are the great unwashed.

Bach is definitely the most mystical figure in music for me, and not only in music. Thank you for such a deep investigation of his creative way and career, I want to research his path more now.