The Trickiest Music

Composers over the centuries have from time to time indulged themselves in musical tricks and jokes--Mozart even wrote a canon the text for which is too obscene to even mention in this family-oriented blog! But for sheer ingenious complexity it is hard to beat the 15th century, though Bach certainly tried. Perhaps the trickiest of a whole bunch of tricky pieces is the Agnus Dei II from Josquin des Prez's Missa L'Homme Armé super voces musicales.

Composers of the time, like Ockeghem, were famous for feats of contrapuntal virtuosity such as composing canons in which one voice is identical to another voice--just as in "Row, row, row your boat"--but with the second voice being in a different tempo, which in the 15th century was achieved through a different time signature. The other voice could even be a transposition of the first voice! And in a different tempo. Here is the complete score to the Agnus Dei II from Josquin's Missa L'Homme Armé super voces musicales:

This is a canon for three voices, which is much, much harder than one for two. We know it is for three voices because it has three time signatures, what we nowadays would call "cut" time, "common" time and a funny one, "cut" time with a dot. These stand for three different "prolations" or divisions of the long notes. From where they are placed on the staff we can see that the three voices start on three different pitches. The rhythmic values of the lowest voice are divided in half in a second voice and into three in a third voice. Here is a very clever video first showing how the voices perform from the original notation and second, how it looks in modern staff notation.

Josquin des Prez and Yuja Wang?

I get a lot of pleasure out of writing this blog, but some things puzzle me. For example, after we exclude my post on "Guitar Wars" which got an Instalaunch (meaning a link from the Blogfather, Glenn Reynolds), the two most popular posts are the one on pop sensibilities with the photo of Yuja Wang striding onstage in a very brief miniskirt followed by my post on Josquin des Prez. Now the Yuja Wang I can understand, but it is the Josquin des Prez that has me puzzled. That post has been the number one for traffic all this week and today as well.

I would love to know what keeps attracting viewers to this months-old post, but no-one has left a comment. Why not the two posts that I wrote just before on the two "Bills": Guillaume de Machaut or Guillaume Dufay? Is it that people are really more interested in Josquin? That's a real possibility. Well, for whatever the reason, here are a couple of other pieces by Josquin for your listening enjoyment. The first is "Mille Regretz" (A Thousand Regrets), which is a French chanson:

I have performed this piece many times in the setting by Luys de Narvaez (fl. 1526–49), the Spanish vihuelist:

As you can hear, this is a transcription of all the parts with ornaments to fill out the long notes that would die away on the vihuela or guitar. Here is another chanson: Adieu mes amours:

Masterpieces of Music: Josquin des Prez

After Guillaume Dufay the next really important composer is Josquin des Prez, born near Hainaut in territory belonging to the Dukes of Burgundy and passed away in the same region in 1521 after a career that took him to Milan, Rome, France and Ferrara. He is one of the greatest composers of the Renaissance, a period particularly rich in music. He came at a time when the printing of music was just beginning and Josquin's music was a favorite of the early printers. Indeed, music by Josquin was so highly valued that they often printed music attributed to him but actually by another composer. Recent scholarship has been devoted to paring down the list of works to those only by Josquin.

Josquin was a master of complex musical forms but also wrote short, saucy pieces. Here is "Petite Camusette":

He composed many settings of the mass using a variety of techniques such as basing one voice on a pre-existing melody, the cantus firmus, or using variations of a melody in all voices, or creating melodic material by encoding a name or phrase in musical notes (the Missa Hercules Dux Ferrariae uses notes drawn from the musical syllables of the Duke's own name: Re – Ut – Re – Ut – Re – Fa – Mi – Re, in English names for the notes, D C D C D F E D), or by structuring the music in canonic form.


Canon is one of those musical ideas that most of us encounter early on in school when we are taught to sing the round (another name for canon) "Row, row, row your boat" or "Frère Jacques" perhaps. Both are very simple tunes that can be sung by overlapping with themselves. For example, "Row, row, row your boat" is sung at an interval of one measure, four beats. That is, the second voice or singer, comes in when the first voice starts the second measure. This is so easy to demonstrate, but hard to put in words! "Frère Jacques" is sung at an interval of two measures, eight beats:

The idea of using a melody to accompany itself is one of those ideas that fascinates musicians. It is the musical equivalent of one of those M. C. Escher drawings:

There are a lot of ways to write a canon other than having the second voice exactly copy the first. For example, in Josquin's mass Missa L'homme armé super voces musicales, he uses what are called "mensuration" canons extensively. In this type of canon, the voice that follows the leader does so in different rhythmic values. For example, the second section of the Agnus Dei from the mass is in three voices. The middle voice is the slowest. All voices start together and the lower voice is the same as the middle voice, but twice as fast, and the upper voice is the same as the middle, but three times as fast. Here, from Wikipedia, is the opening showing the relationship between the voices:

Click to enlarge

And here is a performance. The passage shown in notation above is heard at the very beginning:

Unearthly music... Here, for contrast is a frottola--a popular song form in Italy at this time--on the Latin text "In te domini speravi", which was supposedly written to remind a cardinal that he owned Josquin money: