Ars Nova and Common Time

We think of music theorists as being rather remote from actual musical practice, living in their own world of abstractions, but in the early 14th century music theory, at least as it concerned mensuration and notation, was being revolutionized by actual mathematicians--and ones who wrote in Latin no less!

The older Franconian notation used rhythmic modes but this system was not flexible enough for the needs of the newer music, the ars nova. Mathematicians such as Nicole d'Oresme and Levi ben Gershom, author of the treatise De numeris harmonicis, wrote about integral and fractional exponents and, as the title indicates, this was regarded as revealing the truths of how God ordered the cosmos.

On the more prosaic level of musical mensuration, the goal was to tweak the old notation so that it could handle both the perfect, i.e. triple, division of the long notes (ironically named "breves") and the imperfect division, i.e. duple. 14th century theory saw two levels of division: the breve into semibreves and the semibreves into minims. The first was referred to as the tempus and the second, the prolation. With both the triple and duple subdivisions, that allowed for four different metric systems, what we would call "time signatures." Here is a chart from Taruskin's History (p. 254):

Sorry for the blurry image--the original was quite tiny. But I think you can see the modern equivalents, from the top down: 9/8, 3/4, 6/8 and 2/4. The interesting thing is the symbols used as key signatures: the circle with the dot indicating triple tempus and triple prolation: tempus imperfectus, prolation major, the circle without the dot indicating duple on both levels and so on.

All of these symbols are long gone, of course, given that they are six centuries out of date. But wait a minute, what about that bottom one, the half-circle indicating tempus imperfectum, prolatio minor? Could that possibly be the same as the one still in use to indicate 4/4? Yes, you bet! Music teachers (except the ones trained in musicology) tell their students that this is a "C" standing for "common time" but of course it is not, just the last remaining holdover from the ars nova notational system.

To go with this, here is a little motet in the new style by Philippe de Vitry, Tribum / Quoniam secta / Merito hec patimur. One of the new elements is that all the texts are in Latin.

https://www.youtube.com/watch?v=aVxbibHvu0Q

This is from the Roman de Fauvel, one of the most viciously satirical pieces of musical narrative ever composed.

UPDATE: Looking over that chart and my comment, I think there are two errors. First, in the chart, the second item should read tempus perfectum, prolatio minor because the breve is divided into three semibreves, not two. And then I followed the error in my comment: on this one I should have said "the circle without the dot indicating triple tempus and duple prolation." Mea culpa! But the chart is also wrong.