in 'a concise history of western music' (updated version) it says:
'treatises in the age of charlemagne and in the later middle ages reflected actual practice to a greater extent than the more speculative earlier writings. they always spoke of boethius with reverence and passed along the mathematical fundamentals of scale building, intervals, and consonances that he transmitted from the greeks. but reading boethius did not help solve the immediate problems of how to sing intervals, memorize chants, and later, read notes at sight. theorists addressed these goals in establishing the system of eight modes, or toni (tones) as medival writers called them.
the medieval modal system developed gradually, achieving its complete form by the eleventh century. it encompassed eight modes, each defined by the sequence of whole tones and semitones in a diatonic octave built on a finalis, or final. in practice, this note was usually the last note in the melody. the modes were identified by numbers and grouped in pairs; the odd numbered modes were called authentic, and the even-numbered modes plagal (collateral).'
**note from pg. 34 'in the tenth century, a few authors, misreading boethius, applied the names of the greek tonoi to the church modes, even thought the two systems were not at all parallel. although neither medieval treatises nor modern liturgical books refer to the modes by the greek names (preferring numerals), their original ethnic designations appear in modern textbooks on counterpoint and analysis.'