The ninth century witnessed a fundamental change in the way Western musicians thought about music. Before the Carolingians assimilated ancient music theory, they had no functional concept of how the intervals between pitches of the scale differed from one another and how those differences affected melodic structure. The transition to interval-based thinking may be traced in writings about music. The first half of Aurelian of Réôme's mid-century Musica disciplina quotes from Boethius, Cassiodorus and other ancient authors, but fails to make sense of what they say about intervals. The second half describes the rise and fall of chant melodies without reference to intervals. Treatises of the later ninth century (the Enchiriadis treatises, Hucbald's Musica) are the first to treat music in terms of individual pitches and explain how patterns of whole tones and semitones define modes and scales. However, an early draft of Musica enchiriadis, the Inchiriadon, still displays no awareness of the role that semitones played. A parallel evolution occurred in notation. Neumes, which outline melodic direction but not precise intervals, can be documented from the second quarter of the ninth century and are likely older. They lack pitch content because musicians who invented them lacked a conceptual framework for understanding pitch. Pitched notations do not appear until late in the century and their use is confined to examples in theory treatises.