Meh. I think that's sort of overstating things. Pythagorean tuning is an iterated, circle of fifths construction of a scale. And as such it... frankly kinda sucks rocks at explaining triad-based harmony. The numbers don't work out. You can get something that kinda sounds like a chord, but not really. And so two millenia of Pythagorean music really didn't get into triadic harmony at all, because the language that it had with which to express those notes didn't permit them.

It wasn't until vocal music in the early enlightenment essentially happened upon major/minor chords and built modalities around them (largely by accident, because they sound good!) that people went back to the drawing board to build a mathematical description of the scale based on integer ratios instead. And from there, it was a quick jump to the equitempered scale we know today, which (unlike the pythagorean scale) actually is a very good approximation to the "real" chords people were singing.

And the first composer to really put all those new tools together into a coherent theory behind how to compose music was... J. S. Bach. He didn't "invent" all that stuff, but his works were the first ones we can look at and recognize what we now call "modern" exploitations of tuning and tonality. Anyone earlier was missing big pieces. Anyone later was only adding something new here or there.

JSB is a genuine discontinuity, and it's worthwhile to celebrate that.

> The answer is resoundingly no.

Not only is it a resounding no, there is ongoing research to find the roots of this cliche.

I can't seem to find the article, but it traces it back to this chemical engineer who did a statistical analysis of the bass lines and cadencial formulae in Bach's chorales.

I've even seen some scans of his analyses, it's wild stuff. Maybe it's on libgen? I can't remember but you can probably do a search for it...

Edit: added a link to the article

Edit2: nope, never mind, that wasn't it. But if I find it I'll add the URL later...

Allen McHose perhaps? :)

And furthered later by Aristoxenus a pupil of Aristotle:

https://soundpostonline.com/music-theory-in-ancient-greece/

Did Pythagoras actually write any music worth listening too?

Not that we have live recordings of.

But there is no doubt that he was a pioneer of music theory.

https://en.wikipedia.org/wiki/Pythagorean_tuning

https://www.jstor.org/stable/24045969 (Pythagoras and the Origin of Music Theory)

https://arxiv.org/pdf/2104.00998.pdf (Dynamical systems, celestial mechanics, and music: Pythagoras revisited)

We don't know. From what I've read, we know a little bit about early theory, but don't know precisely what scales and intervals they were talking about.

We know quite a lot about Greek music theory (Thomas Mathiesen's Apollo's Lyre: Greek Music and Music Theory in Antiquity in the Middle Ages is the go-to source here: https://archive.org/details/mathiesen-1999-apollos-lyre/page...). Of course we don't have recordings, but we do have a solid understanding of the theory, and some very good guesses as to the scales and intervals.