Oy... medieval music theory is such a huge subject that I couldn't begin to do it justice in a HN comment. The short version is that some time in the 9th century monks developed neumes, an early form of musical notation, to write down the chants they chanted at different times of the day. Medieval music theorists classified those chants according to the last note (what we now call the "tonic") and the most common note (what we now call the "dominant"). There were 262144 theoretically possible melodies (8 notes long, 6 possible notes, but some were rejected for music-theoretic reasons so the actual space was rather smaller) which could be indexed by their sequence in a collated list of melodies ("on the Sunday after Pentacost sing the 7th chant in the Lydian mode" or whatever).
If I had to pick a "best-of" reading list, I'd say the 9th-century "Musica Enchiriadis", Berno's "Prologus in Tonarum", and Boethius's "De Institutione Musica". These all assume a familiarity with Platonic music theory, so at least skim through Plato's "Timaeus" first. There will also be more references to astronomy than will make sense to somebody in the modern age, because music and astronomy were believed to be essentially the same thing. Also more recent research has found that actual musicians of the time seem to have completely ignored the theorists. Some things never change.
In the 18th Century Presbyterian Church, they only sang Biblical psalms set to simple (but distinct) tunes and without any musical accompaniment. This was known as exclusive psalmody.
The psalms weren't the prose-style you'll find in any print Bible though, they were their own translation called the Metrical Psalms. Its 1650 edition proved very long lasting.
Many of these psalms were set to common metre, meaning that if you found such a psalter and tried singing it to some well-known tune it will very likely 'fit' the lyrics. You could try Psalm 23 set to the tune of The British Grenadiers, or Amazing Grace, or even The Star-Spangled Banner: https://thewestminsterstandard.org/psalm-23/
This was actually how the psalms were practised by congregations in my home country. The psalm lyrics were considered too sacred for practice, so they set the same tunes to other (sometimes comical) lyrics and practised those during the week. Then on Sunday the minister would say something like 'we will now sing Psalm xx to the tune of lilies', and the congregation would know the tune even if they hadn't memorised the psalm lyrics.
Still happening in the Free Church of Scotland. They have psalters with pages split horizontally, so you have the words at the top and the tune at the bottom.
