Renaissance Polyphony: the Franco-Flemish School

29 April, 2021

Near the beginning of the pandemic I heard a conversation where Brian Eno said that he’d been listening to a radio station on the internet, based somewhere deep in rural Russia, that plays nothing but Eastern Orthodox chants 24 hours a day, with no announcements. He said that this sort of music appealed to him while locked down at home.

Somehow this led to me listening to a lot of early music on YouTube. I started with some Baroque composers I’d never paid attention to before, like Corelli and Albinoni. Previously my interest in classical music started around Beethoven and focused on the 20th century, with Bach and Vivaldi as brilliant pearls surrounded by darkness. As I began listening to more Baroque music I became very happy, like someone who’d been locked in a room for years and suddenly found a key to another room. There was so much to explore.

The Baroque period lasted from about 1580 to 1750: that’s almost two centuries of music! By getting to know it, I’ve been starting to understand the birth of common practice tonality—that is, the language of chord progressions that dominates classical music, and also, to some extent, lots of modern pop music. And I can finally start thinking clearly about what makes Bach great.

Imagine listening to just one rock group, or one jazz band. Practically nobody does that, of course, but imagine it: it would be impossible to distinguish what’s special to the artist you love from what’s common to the style as a whole. So you’d think they were more creative than they really are—but you also wouldn’t know what was truly creative about their work.

I’m still in the midst of this project, which also includes listening to Bach more thoroughly. But I got a bit distracted. I got pulled back further in time—back into Renaissance polyphony. This gave me access to another two centuries of rich, complicated music, roughly 1400 to 1600. And it let me understand the roots of Bach’s music. Bach’s music looks back to polyphony just as much as it looks forward into the future. For this he was considered a bit old-fashioned during his day; only later did people realize his greatness.

The best of Renaissance polyphony is arguably just as complex and interesting as Bach’s counterpoint: it’s just less immediately gripping. The reason is that it doesn’t follow ‘common practice’, with its familiar strategies of building and releasing tension, and its repetitive rhythmic pulse. The vocal lines are often very smooth, flowing like water. So it’s less exciting, but it’s wonderfully entrancing.

I went back even further, into the medieval—but at a certain point I ‘hit bottom’, at least when it comes to the art of harmony and juggling multiple independent melodic lines, which is what I like so much about Baroque counterpoint and Renaissance polyphony. Gregorian chant is great, but it has a single vocal line. The practice of using chords was first documented around 895: in a style called the organum, Gregorian chant was supplemented by either a supporting bass line, two parallel voices singing the melody, or both. But the ‘Big Bang’ of polyphony happened around 1170 when Léonin introduced two independent melody lines. Around 1200 his follower Pérotin went ahead and started using three or four! Imagine the dizzying sense of freedom these guys must have felt, with no precedents to guide them.

Medieval polyphony should be fascinating, and again it’s a huge territory: roughly two centuries, from 1200 to 1400. But right now I seem to be focusing on Renaissance polyphony—and especially the so-called Franco-Flemish school, which is an incredibly rich vein of music.

I’d like to say a lot about the Franco-Flemish school, but for now I just want to list a few of their best-known composers. In fact, I’ll only mention one of each ‘generation’, and give you a sample of their music.

Guillaume Dufay (1397 – 1497)

Dufay is the most famous of the first generation of the Franco-Flemish school. (This first generation is also called the Burgundian School.) He is often considered a transitional figure from the medieval to the Renaissance. His isorhythmic motets illustrate that—their tonality is dissonant and dramatic compared to typical Renaissance polyphony:

Johannes Ockeghem (1410/1425 – 1495)

Ockeghem is the most famous of the second generation of the Franco-Flemish school. His innovations firmly moved this school out of the medieval into the world of Renaissance polyphony. Some of his compositions are almost avant-garde in their structure—a mass that asks you to sing it in any of four modes, a mass where the different vocal lines are sung at different rates and drift out of synch—but they’re carried off so smoothly you might not notice. People tend to call Ockeghem “the Bach of the 1400s”, which is sort of ridiculous because there’s just one J. S. Bach, but it gives a hint of his importance. He was not a prolific composer, but he was also an honored singer, choirmaster, and teacher.

Josquin de Prez (~1450 – 1521)

Josquin, of the third generation, is the real superstar of the Franco-Flemish school. Luther wrote that “He is the master of the notes. They must do as he wills; as for the other composers, they have to do as the notes will.” He was influenced by Ockeghem, and composed a motet in commemoration of Ockeghem’s death. But he polished Ockeghem’s ideas and in some ways simplified them, making music that was easier to understand and more popular. Despite being prolific and very influential, nothing is known of his personality, and the only known writing that may be in his own hand is a piece of graffiti on the wall of the Sistine Chapel.

Nicholas Gombert (1495 – 1460)

Gombert is probably the most famous of the fourth generation of the Franco-Flemish school. He wrote polyphonic masses and motets with as many as 6 separate melody lines, and sometimes with one voice imitating another after a very short time interval. His work marks the height of complexity of the Franco-Flemish school.

Orlande de Lassus (1530 – 1594)

Lassus, of the fifth generation of the Franco-Flemish school, is one of the composers of a style known as musica reservata—roughly, sophisticated and highly chromatic music. But he also wrote drinking songs in German, and one of his motets satirizes poor singers. He wrote over 2,000 pieces of music, all vocal—none purely instrumental! In the “The Adventure of the Bruce-Partington Plans,” Sherlock Holmes said he was working on a monograph about the polyphonic motets of Lassus.

So there you are: a microscopic overview of a musical tradition lasting over 200 years.

Maybe listing one just composer of each generation was a bad idea: I feel I’m doing an injustice to Gilles Binchois of the first generation, often considered the finest melodist of the 1400s, and Jacob Obrecht of the third generation, who was the most famous composer of masses in the late 1400s before Josquin came along. Obrecht was very adventurous: he often played melodies backwards (in retrograde), and once he even took the notes from a melody and played them in order of duration, long to short, to get a new melody.

There is also a lot going on in Renaissance polyphony outside the Franco-Flemish school! There’s the British tradition, including great composers such as William Byrd and Thomas Tallis. And I haven’t even mentioned the most famous of all polyphonists: Giovanni Pierluigi da Palestrina! Or the most dissonant and in some ways the most intriguing of the lot: Carlo Gesualdo.

But it’s easy to get lost in unfamiliar territory, so I just wanted to give a quick outline of the Franco-Flemish school. At the very least, listening to their music should be fun.

Dufay’s Isorhythmic Motets

23 April, 2021

I’ve been reading about Renaissance music. People sometimes say that it began in the early 1400s when musicians rebelled against the dry, complicated mathematical structures of late medieval music and switched to a more emotionally expressive style. For example, the New Oxford History of Music writes:

The isorhythmic motet, the highest achievement of medieval rationalism, reached its climax during Dufay’s prentice years (c. 1410-20), with works in which the quasi-mathematical construction arouses more admiration than pleasure.

But since I’m a mathematician, this actually got me interested in isorhythmic motets!

I found them hard to understand from written descriptions. Isorhythm involves a rhythmic pattern called a talea which is applied to different melodies. Often the talea lasts for a different amount of time than the melody, which leads to some interesting effects. For example, here is a melody that lasts for 28 measures divided into 7 talea that each last for 4 measures:

This is from a composition written sometime around 1360. Isorhythm gets a lot more complicated than this! The music typically has several parts, in which talea get sped up or slowed down independently. But reading about these things didn’t give me much of a feel for what isorhythmic motets actually sound like.

When I listened to some by Guillaume Dufay, they didn’t sound dry at all! For example:

It’s quite thrilling and romantic, actually! Listen to how he uses the leading-tone, the note one half a step below the tonic, to build tension. This is a big medieval thing. If you don’t know what the heck I’m talking about, wait to the very end of the piece! Here Dufay clobbers us with a loooong leading-tone, the medieval equivalent of the wail of electric guitar at the end of a classic rock song. He’s really hamming it up.

Now, Dufay is famous for being the first really major Renaissance composer and breaking from the medieval traditions, so maybe his isorhythmic motets are more exciting than average. But still, I hear they are intensely mathematical.

In fact there’s an album of Dufay’s isorhythmic motets with the great title Quadrivium which features a booklet by a mathematical physicist named Guido Magnano, an expert on general relativity at the University of Turin. On a Russian website I read:

This album by the Italian vocal-instrumental group Cantica Symphonia takes off from the proportional aspect of large Dufay works like the motet Nuper rosarum flores, long thought to have been based on the proportions of the great cathedral of Florence but recently discovered to have probably been modeled on another building. The album was actually sponsored by the mathematics department of the University of Turin, and an essay by professor Guido Magnano explores the mathematical bases of the musical system Dufay knew. For the average listener the musical manifestations of these principles are going to be hard to hear sitting in front of your stereo; the chief interpretive decision made by Cantica Symphonia is to strive for a transparent texture, judiciously using a small instrumental ensemble to bring out structural details. Save for the fact that the voice parts are sung solo, it’s a Renaissance performance in the classic “pure” mold. For the numerologically inclined or for the serious student of the Renaissance era, the disc is an interdisciplinary goldmine. Recorded in an Italian church, the disc matches its engineering to its aims, and the packaging by the Spanish label Glossa is uncommonly attractive.

I decided I needed to get my hands on that booklet. The album is on YouTube:

Unfortunately the actual CD costs $47.53 on Amazon. Luckily I was able to get it for much less online from Barnes and Noble… thereby procuring the booklet, which is what I really want. This should arrive in a week or so, so with luck I’ll tell you more later. I’m also quite fascinated by Dufay and the whole Franco-Flemish school of Renaissance music that he helped start, and—as usual when I’m just starting to learn about something—I have dreams of blogging about it.

In the meantime, I found out a bit from an interview with Guido Magnano, where he says this:

Your first disc for Glossa, Quadrivium, placed special emphasis on the question of mathematical proportions in Dufay’s motets. If these considerations apply also to the works recorded here, can you provide some examples of how this came through in practice?

Guido Magnano: Mathematical proportions do not occur in medieval and Renaissance music as occasional, accessory stylistic elements: the Pythagorean-Platonic paradigm states that music itself is nothing but “auditory perception of numbers”. The hypothetical relationship between the mensural proportions of the motet Nuper rosarum flores and the proportions of Brunelleschi’s Duomo, although fascinating and quite plausible, should not obscure that in other motets, particularly in the later isorythmic motets (Fulgens iubar and Moribus et genere), Dufay attains an even higher degree of formal complexity.

The motet Magnam me gentes, (12:4:2:3) also included in this CD, has a mensural structure very close to Nuper (6:4:2:3). Worth noting is that the 15th century humanist Marsilio Ficino introduced a “Platonic-Hermetic” movement, attributing occult significance to numerical relations. Did Dufay himself share these ideas? Do the numerical ratios in his motets hide a symbolic content? Some modern scholars have claimed so, even though the pieces for which numerological interpretations have been proposed were written some thirty years before Ficino’s works, and it is impossible to obtain a conclusive proof that such interpretations reflect Dufay’s intentions.

More concretely, one could ask to what extent mathematical proportions can be perceived by the listener. The “mensural proportions” (which are but one example of numerical ratios in this music) are merely changes of meter: in an isorhythmic motet, for instance, the basic sequence of note values (talea) is repeated with all durations multiplied by a fixed ratio (e.g. 2:1, 1:2 or 2:3). Whenever the change occurs simultaneously in all voices, it can be clearly heard; in other cases, it remains hidden in the polyphonic texture. The mensural proportions also determine the ratio of the lengths of the various sections of the piece, and the choice of appropriate proportions was considered to be essential to the overall structure of the piece, much as in the Pythagorean scale where such ratios (1:2, 2:3, …) determine the consonance of a chord. As Leibniz states three centuries later: “Music is the pleasure the human mind experiences from counting without being aware that it is counting.”

Here is Nuper rosarum flores as played by Cantica Symphonia:

This is the isorhythmic motet that Dufay wrote for the consecration of the cathedral in Florence in 1436, the one with Brunelleschi’s famous dome. He was 35 then, living in Florence and working for the Pope. Later he would return to Cambrai, in what is now Northern France.

I’ve visited this cathedral and taken the terrifying tour that lets you climb up to the dome, go above it into the rafters between the dome and roof, and then out onto the roof. It’s an amazing structure:

For sheer joy, so far my favorite performance of Dufay’s isorhythmic motets is the album O gemma lux by the Huelgas Ensemble:

Here’s the man himself—Guillaume Dufay:

To be honest, nobody is completely sure whether this is Guillaume Dufay or another famous composer of the early 1400s, Gilles Binchois.