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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.
Most standard musicological references attribute to Bishop Stephen of Liège (†920) the composition of three Offices: for the Holy Trinity, the feast of Saint Lambert (bishop of Liège in the early eighth century to whom the city's cathedral is dedicated) and the Invention of Saint Stephen the protomartyr. From statements by Richarius, Stephen's successor at Liège, and Folcuin of Lobbes (both from the tenth century), and the eleventh-century account of Anselm of Liège, along with the evidence in Brussels, Bibliothèque royale, MS 14650-59 (a tenth-century manuscript produced at Liège during Stephen's episcopate), I conclude that Stephen of Liège did have a hand in the Offices for Saint Lambert and the Holy Trinity. Although he may have composed chants for Saint Lambert, he more likely revised existing ones for the Trinity. No tenth- or eleventh-century testimony attests the attribution of the Office for the Invention of Saint Stephen to Bishop Stephen.
The dualistic relationship of words and music in Machaut's refrain songs (proposed in Part 1 of this article) enables abstraction of the music from the poetic model that inspires it. This situation is at its most extreme in certain rondeaux, representatives of a genre for which a special function in Machaut's output is argued. Studies of specific groups of songs (B9–R4 and B35–R13–R21) illustrate the gradual development and detachment of material in related compositions. Through these accounts, it can be seen that the relationship of words and music proceeds on the same fundamental basis in the seemingly melismatic rondeaux as in the syllabic virelais, despite the apparently closer connection found in these latter. The technical unity at work in Machaut's song composition is constitutive of an aesthetic position. The abstracted musical text is an aspect of the multifaceted voice of Machaut's lyric œuvre and tends to subsume the poetry it sets creating an aesthetic of pure music.