Hi IB, yes I know quite a bit about it. I could rewrite wikipedia here, but I stick to personal observations.
A first eye / ear opener was when I had lessons Gregorian Chant. I learned that choosing a certain pitch was done completely at random by the teacher ((=‘cantor’) without a tuning fork. He observed who was there (quality of voices available), the moment of the day (morning / afternoon / evening) and the accoustics of the venue, repertoire and based on that he chose a pitch. He learned us that Gregorian Chant was usually sung without instruments therefore the pitch does not matter. The pitch start to matter once instruments are involved, and thats the second half of the middleages. Think Ars Antiqua era. Once poliphony kicked in, they started to sing all sorts of colorations around the existing notes so the ‘harmonic progression’ (not known to these fellas!) slowed down. They replaced the slow voices by instruments e.g. the bass was played by an wind instrument or an organ. Example: Leonin: Organum Duplum, "Viderunt Omnes" (comparative transcription) - YouTube
In this piece you see the slow tenor versus the colorations of the superior voice(s).
The point is, pitch and tuning get relevant once instruments start to be involved.
Another eye / ear opener for me was that pitch is also practical in a different way. They higher A is, the smaller the instruments can be. E.g. old organs often have a higher pitch since mid europe was poor around 1600. A higher pitch implied less material needed. Google ‘short octave’ for more information. Old instruments often have reduced options in the bass area.
In the renaissance ‘meantone’ was common, and thats my favourite. Certain chords are perfectly tuned and sound brilliant. Some chords are impossible. One of my favourite pieces of music is this: Sweelinck's Fantasia Chromatica in mean-tone tuning - YouTube A nice performance, which I could play as well.
Meantone is limited though, since not all tonalities are possible. In Bachs’ time a tuning like Werkmeister III was common, but got replaced by ‘well tempered’ tuning - Bach wrote das Wohltemperierte Klavier as an honour to this tuning. Bach visited all 24 options in that work. C (minor / major), C# (minor / major) etc …
From that moment on all sorts of music were possible. Beethoven was possible, Brahms, Bruckner, Beatles and what not.
Music as we know exists based on an imperfect system, an ultimate compromise in tuning.
Personally, I love meantone though. When I visit a church, sit down at the organ and press one key I’m instantly back in 1600 in my personal timecapsule. Its magic really performing old music. These churches existed already 600 years ago, these organs are 500 years old there is nothing what is of recent ages besides myself. There is no way to bring back the past so lively as by performing old music.
This is maybe why hifi is a complete unknown territory to many musicians. It just does not matter.