Mensuration signs in Portuguese cancioneiros and their implications on tempo

There has been extensive discussion about issues of rhythm, metre, and tempo in the early Renaissance Iberian polyphonic song. Particularly, the usage of mensuration signs and the meaning of diminution have been the subject of distinct readings.
Authors such as Charles Jacobs and Manuel Morais have considered that the
notation of the songs in the Cancionero de Palacio show unsystematic use of the
tempus imperfectum and tempus imperfectum diminutum signs to indicate duple metre, a supposed indication of a gradual simplification of the proportional notation system occurring during the 16th century. However, music treatises by Spanish theorists of the first half of that century, such as Francisco Tovar (1510) and Juan Bermudo (1550), suggest that the choice of a diminutum sign had practical implications on the tempo at which a piece was performed, which would mean that the use of these signs was not interchangeable. In fact, the notation found in Portuguese cancioneiros shows a remarkable degree of consistency in the use of mensuration signs that conform to the latter interpretation. This is especially true of the Cancioneiro de Paris, and also something that Gil Miranda had briefly argued in the preface to his edition of the Cancioneiro de Elvas.
Thus, in this paper, I will analyse the use and meaning of mensuration signs in the Portuguese cancioneiros and show evidence of their conscious application,
consistent with the testimonies of music theorists. This will also reveal how Iberian scribes and composers of secular music would work around the proportional system to indicate different ranges of tempo.