I think it would be more helpful to bring some latin in than lots of music theory. The mathematically more complex pythagorean theory of Boethius was widely taught, but more as a philosophical subject (math, physics, ontology, theology, astronomy ...). The idea was: first think math (math is ideal reason and like god), then world follows. The real music didn't make it into the academics and reverse. There were the preparative schools for the pueri where they actually sang, but that might have been all.The music theory which dealt with real things out of mouths and into ears of real humans started with the intellectual benefit of the crusades in the 13th century, and this kind of theory was arabic-aristotelian: first what there is to be experienced (what you see and hear people doing) and secondly the maths. So you will be surprised how little of the modern theory you'll need. There is nearly no harmony theory, because there were no chords because the music was widely monophonic. Mostly the movement is I-Area V-Area I-Area, that's it. In the little polyphonic music we have left the rudimentary harmony progressions (call it chord successions if you like) are not purely random, but very secondary to the overlay effects of melodic figures in the different voices. Now you understand why the scales (and sometimes the scale changes) provide expression and meaning, as well as the melodic figures do and their pattern-like repetitions and modifications. Imagine them monks having to sing-pray these melodies for hours each day and night each day of the year - and no one knows totally if they read or remembered or mentally constructed (in the moment of singing!) this huge amount of melodies. If you got this the rest follows: they didn't sing monophonic because of being too stupid for harmony or counterpoint. Maybe this is just the only kind of music which can be beard in these large amounts. (By the way here is no deprived music in history. In each age the music people made was the perfect fulfillment for their needs and expanded their imagination. They simply recognized other details than we do nowadays. The student's encounter with medieval music resembles much the study of far-eastern classical music.) There had been all kinds of chants throughout Europe until they were standardized by the court of emperor charlemagne around 800. This was imperial power politics. Pope Gregor has depicted as having them received from an even higher power. Some scientists say that the music notation from which our present one stems was invented for exactly this purpose: teach the unified melodies throughout Europe in the same manner. (This notation does not "show" the pitch to the eyes. It tells: go up. go down, rest, do this or that little figure. In order to find out the pitch of one certain syllable you have to follow the whole melodic line from the beginning on, which is sophisticated and needs knowledge and experience.) Nevertheless in some places some old chants survived, but the vast majority is lost forever. Well and don't forget the mavericks who might have sung in more than one voices from quite early on. This could be related to rural poiyphonic singing e.g. by mediterranean shepards from antiquity on. Be aware: we only have left what was written down by monks as working musician's sheet material. And even of these sheets we only have left some luckily preserved ones. And we don't know at all what humans did outside of the monasteries. They just hadn't to write anything down. Here is much room for your fantastic speculation.
Be prepared for terminological twists: what we call Modes or scales might be called Tonus/toni and what they call modi might belong to rhythms. Definite rhythms are needed not for monophonic singning but to organize more-than-one-voices, which elaborately happened in the school of Notre Dame, Paris. After Boethius there are mainly two books: musica enchiriadis around 900 by no one knows exactly and the masterpiece Micrologus of Guido of Arezzo around 10xx. For the first one understand what a tetrachord is. The second one is a revolutionary explosion of techniques, even of polyphonic ones. In their down-to-eath clarity and intellectual precision both appear to be future alien artefacts in a way but on the other hand both also show what is already being done at their time. (There are descriptive and more speculative/theoretical parts, but no nonsense at all.) In Paris around 1200 it went up to 4 independent intermingling voices. It sounds totally mind blowing and futuresque. One thing I forgot to say: the idea of the dominance of the line can be driven further. Our chord progressions (I IV V7 I and others) can be derived from ruled characteristic melodic line endings in the renaissance, which are in turn based on the characteristic melodic outlines in the pure-melody-music of the middle ages. Yes, chordie's grandpa was monk.