This week’s theme is…Really Clever Music! All lovers of music respond to its mysterious ability to move them, often describing its effect as soul-deep. Unlike any other art, music most directly communicates emotions and passions extremely convincingly, and that is why it is so loved. But music works on another level as well, an intellectual one. Due to its highly mathematical and systematic nature it can be created to satisfy and delight from an entirely different angle. This angle is often missed in listening because it is usually much easier to see and comprehend this aspect through analysis and score study. Every piece this week is written by a very clever composer who was able to craft a beautiful piece of music while, at the same time, manipulating the musical medium in a surprising way that may be discovered upon analysis, almost like an easter egg.
Really Clever Music, Day 3 – Agnus Dei from Missa l’Homme Armé by Josquin des Prez
I often tell students that the standard system of Western musical notation is one of the glories of the history of human ideas. It is so incredibly logical, anyone can learn how it works, and it can be used to notate literally any musical idea. Granted, it takes considerable practice to read and write it quickly and easily, and some styles of music are better suited to the system than others, but it has achieved a near-universal level of applicability that other styles of notation have not. And it didn’t happen overnight. The process of developing standard Western notation took centuries, and must have involved countless musicians as they collectively arrived at best practices through much trial and error. And it is not really ever finished. Musicians are still tweaking the modern system in the ongoing effort to contain new and unconventional ways of creating musical sounds.
There are countless systems of musical notation throughout geography and history. Notation technically refers to any manner of representing musical sounds with symbols or images, and this can be done in many ways. Just glance through this article to get a sense of the variety that have existed. But, like so much of Western music history, the first point of true significance as far as notation is concerned can be located in the rich tradition of Gregorian Chant.
There are many far-fetched legends about the collection of plainchant in the Western Christian church. Some myths involve Pope Gregory I, who reigned from 590-604, and after whom Gregorian Chant is named, essentially taking by dictation from the Holy Spirit the collection of sacred melodies that came to be included. Some icons of Gregory show this. See the dove floating above his shoulder? That’s a symbol of the Holy Spirit as old as the earliest Christian writings:
But it is generally acknowledged by scholars that the creation of Gregorian Chant was a long codifying process, carried out by collecting and sorting through the myriad of chant traditions active in Christendom and distilling them all into a stylistically-unified system of liturgical practice. This is of course congruent with the Church’s perpetual mission of doctrinal and liturgical unity. It is also thought to have happened during the ninth and tenth centuries, which is considerably later than Pope Gregory’s reign. But his name has become attached to it and the legends which tie him to the process are very much alive. Here is another icon of Gregory which illustrates a highly significant aspect of Gregorian Chant, its notation:
Do you see the music in Gregory’s book? That is what the notation of Gregorian Chant looks like. It was an impressive leap in the direction of the standard system that we know today and features many of the same elements. Others are missing, and some things just work a little differently.
The marks within the 4-line staff are called neumes, and the practice is called neumatic notation. In neumatic notation, the principle of representing different pitches by graphing noteheads on lines and spaces of the staff is identical to modern practice, but the notation of rhythm is a bit different. I have learned to read neumatic notation at a Gregorian Chant workshop, and it was a most enlightening experience. Many present-day choirs in the Catholic tradition still sing from neumatic notation. While I am not completely fluent in realizing it myself, I can attest that it is a complete, working system, ideal for the notation of the musical style for which it was devised. But Gregorian Chant is really the only kind of music you can write with it. So if you want to notate music that sounds like that, this is the tool for you! But if you want the flexibility to compose in other styles, we need to look ahead a couple centuries to further developments that allowed European musicians to notate works of greater complexity.
The next major leap forward is called mensural notation and was used primarily between about 1200 and 1600. Where neumatic notation gave us the best way to notate pitch, mensural notation gave us the same for rhythm, and its essential principle, that all rhythmic values can be represented by various note values related by doubling, with a few dots thrown in when you have to count to 3, still governs our modern notation of rhythm. “Mensural” comes from the Latin word for “measured”, and refers to the strict mathematical relationships that govern its rhythmic values. The notation style looks like this, and you can probably recognize many of the modern rhythmic values:
That’s starting to look a little more like something you could play, doesn’t it? The rhythmic precision afforded to musicians by mensural notation allowed the works of this time to assume a crisp and detailed complexity in their polyphony that was simply not possible before. Brainy composers began to delight in the brilliant games they could play while assembling music for multiple voices. A new polyphonic technique, the mensuration canon, was born.
A mensuration canon exploits the manner in which the new notation allows you to notate the same melody in different rhythmic values. Here’s how it works. Imagine you sing “Row, Row, Row Your Boat”, and at the same time, one friend sings it exactly half as fast, and another friend sings it twice as fast as you. It would sound like mush because Row, Row, Row Your Boat is not written to be performed that way, but some music is. Mensuration canons are also called prolation canons or tempo canons depending on the source, and a number of very calculating and contrapuntally-inclined composers have written them over the centuries, most recently Shostakovich in his 15th Symphony, and before that J.S. Bach in a really interesting appendix to the Goldberg Variations discovered in the 1970s (I had never heard of this and it is astounding! Check it out here and discover a potent catalogue of every canonic technique under the sun compressed into 15 minutes).
But before Bach, mensuration canons were the domain of masterful Flemish polyphonic composers like Johannes Ockeghem, who wrote a haunting mass entirely out of mensuration canons of different stripes in the fifteenth century called the Prolation Mass, and his student (perhaps), one of the most brilliant composers in the history of counterpoint, Josquin de Prez. While not a household name, de Prez was quite famous and renowned during the sixteenth century for the craft and expressive power of his music. Here is a brilliant mensuration canon, the Agnus Dei from his mass based on a French tune called “The Armed Man”. The beginning of the movement is a mensuration canon in 3 voices:
If you look closely you can see that the top line moves three times as fast as the middle line, and one-and-a-half times as fast as the bottom line. Additionally, the middle line starts a fourth below the first line, but all three lines are the same melody. It’s enough to make your head spin!
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