The revival of learning under Charlemagne and his successors brought with it knowledge of the music theory of late antiquity and consequently a desire to relate Gregorian chant to that theory. Section 4.i explains what happened. An important element of the theory was the notion that the whole of creation was ordered according to harmonic principles. At the end of Chapter 3, it was suggested that some of the new chant composed in the eleventh century might have been inspired by a desire to reflect this harmony of the universe in newly composed melody, as it were composition according to theoretical principles. This idea is briefly considered in section 4.ii.

Simultaneously with the assimilation of classical music theory, musical notation was developed, in the form of the signs we call neumes. Musical theory and the notating of chant books were not at first directly linked. Neumes did not indicate precise pitch, and were thus of no use for the description of such matters as musical scales and intervals. But the ninth-century theoretical enterprise included one achievement of crucial importance, the linking of Gregorian chant to the tonal network of classical scale systems. Chant melodies could be imagined as a series of notes placed on the steps of a ladder (Latin scalae means ‘stairs’, hence our ‘scale’), where the pitches at each step and the intervals between them were precisely defined.