Mensuration and the Old Ways of Composing.

A few days ago I got a couple of very challenging comments on my blog. One was on the post "A Cathedral and a Motet" and asked the following:

Do you know of a book that explains how Dufay, Ockeghem, etc. wrote their more intricate compositions? Not just a simple explanation of isorhythm or a rudimentary explanation of 15th->16th century counterpoint, but: if I am Dufay and I am going to write the music above in your post, how exactly do I go about accomplishing that?

Now I spend most of my time trying to write, you know, 21st century music, not 15th century music, but this is such an interesting question that I wondered how it could be answered. First I went to my shelf to see what books might contain some answers. Composition is, for a very large part, notation. In other words, what we can write down and how we write it down IS the piece, or at least the definitive instructions for performing the piece. So I took down one of the oldest books in my library The Notation of Polyphonic Music 900 - 1600 by Willi Apel, originally published in 1942 and, I believe, still in print. It is the most thorough textbook on the old systems of notation. It contains facsimiles of a lot of older notation. Here, for example, is a three-part chanson in white mensural notation by Guillaume DuFay.

If you look very closely at the top, there is a little line of text above the staff that says "Guillermus du" and then a little bit of staff with the note "fa". This is often how he signed his name on a music score. But wait, this is not a music score in the modern sense. I will explain below.

There are two pieces on the page. At the top is Quel fronte signorille and the bottom is the chanson "Dona i ardenti". Transcribing this kind of notation into modern notation is the work of a graduate doctoral seminar in musicology. As you can see, reading the original manuscripts is not easy! For comparison, here is the beginning of that chanson in modern notation:

Click to enlarge

The transcription into a modern score does several things: it takes all the original pitches and puts them on modern clefs and also changes all those weird boxy hollow notes (hence, "white" mensural notation -- there is also black and even red) into modern rhythmic values. But one other very important thing happens. The original is three separate parts just stacked up. They are not aligned rhythmically at all. A big part of the problem of transcription is figuring out exactly how the parts align. At this point in music history the score, where the various parts are precisely aligned rhythmically and corralled within barlines, had not yet been invented.

This gives us an important clue about DuFay's compositional methods: he did not compose in score! Like most composers before the 17th century, DuFay was a singer. The others, like Francesco da Milano, were largely lutenists. As a singer, how he likely composed was each line separately. In other words, what he probably did was write down the tenor and then compose the cantus and then the countertenor. This is not how modern composers work, by the way.

In the text, the DuFay chanson is chosen as an example of [2, 2], meaning, in the orthography of the text, that the tempus and prolatio are both imperfect. Huh? Ah yes, nothing like a bit of Latin to brighten one's day. In answer to a question in the comments about mensuration, in modern notation there is, within the notation, only one kind of subdivision to any note: duple.* In other words, every whole note contains only two half notes, every half only two quarter notes and so on. But in white mensural notation they had two possibilities: duple and triple or imperfect and perfect. In this kind of notation the brevis and semibrevis (usually rendered in modern transcription as a whole note and a half note or a half note and a quarter note) are the ones where we see the division into three. The mensuration or subdivision of the brevis is called the tempus and the two possibilities are perfectum and imperfectum and this was indicated in the time signature. The mensuration or subdivision of the semibrevis is called prolatio and, again, there are the two possibilities of perfect and imperfect, i.e. triple or duple subdivision. There are, therefore, four possibilities as indicated in this handy chart from the text:

The old time signatures are interesting. For one thing, this is where our "C" time signature comes from, often called, by ill-educated music teachers, "common" time. As you can see it is the old white mensuration time signature for "tempus imperfectum cum prolatione imperfecta". The so called "cut" time, which is the same half-circle with a slash through it indicates in modern music that the half note takes the beat.

Now that doesn't tell you exactly how to write a mensuration canon à la Guillaume DuFay, but it will give you an idea of the notation at least. For practical exercises in modal counterpoint I can do no better than recommend another excellent text, this one by another McGill professor, Peter Schubert, titled Modal Counterpoint, Renaissance Style, which was published in 2008.

*In modern notation we can indicate any subdivision whatsoever, but we do it with a workaround, essentially going outside the notation itself. To indicate a triple subdivision we write a little 3 with a bracket. But we can also write a 5 or a 7 or anything. The most extreme I have seen is something like 13 in the time of 12. This is how we think of it: we stuff extra notes into a fixed beat. Works quite well.

Luckily we can find the DuFay chanson on YouTube. Here is Dona i ardenti with unknown performers: