Question

Passage:

The transition from the Ars Antiqua to the Ars Nova in medieval European music represents one of the most profound shifts in music theory and notation, primarily concerning the conceptualization and measurement of musical time. During the thirteenth century, the rhythmic modes governed musical composition. The theorist Johannes de Garlandia formalized this system, categorizing rhythm into six standard patterns based on the poetic meters of classical antiquity, which relied heavily on contextual interpretation rather than absolute durational values. Under Garlandia’s framework, the exact duration of a note was not fixed by its shape alone but was dictated by its position within a sequence of ligatures (connected notes). This required performers to possess an extensive working memory of standard rhythmic patterns.

As polyphonic complexity grew, the limitations of the modal system became increasingly apparent. In the late thirteenth century, Franco of Cologne introduced a revolutionary paradigm shift in his treatise *Ars cantus mensurabilis*. Franco asserted that the shape of a note should independently signify its exact mathematical duration, divorcing rhythmic value from melodic context. This Franconian notation established distinct shapes for the longa, brevis, and semibrevis, providing composers with unprecedented precision and paving the way for more intricate rhythmic syncopation. Franco's system, while groundbreaking, still heavily prioritized ternary (triple) divisions.

However, the most radical transformation occurred in the early fourteenth century with the emergence of the Ars Nova, championed by Philippe de Vitry. De Vitry’s innovations fundamentally restructured the mensural system by elevating duple (imperfect) meter to the same theoretical status as triple (perfect) meter, which had previously been favored due to its theological association with the Holy Trinity. Furthermore, de Vitry introduced the minim as a functional rhythmic unit and codified mensuration signs—the precursors to modern time signatures—allowing for complex proportional relationships at multiple structural levels of a composition.

These advancements did not go unchallenged. Conservative theorists vehemently criticized the new methods for what they perceived as a degradation of musical purity. Jacobus of Liège, in his voluminous *Speculum musicae*, launched a fervent defense of the Ars Antiqua. He argued that the Ars Nova’s reliance on duple meter and smaller subdivisions fractured the natural perfection of ternary rhythm. Jacobus contended that the older, more restrained system better reflected the harmonious proportions of the cosmos, dismissing the Ars Nova's intricate rhythmic divisions as excessive and spiritually discordant.

Question:
Based on the passage, match each medieval music theorist to the specific contribution or philosophical stance explicitly attributed to them in the text.