Micrologus; The Isorhythm Man Cometh

84-04 THE ISORHYTHM MAN COMETH

Some time ago on Micrologus, we explored the roots of the motet—the first hundred.years or so after its origins, around the year 1200. That exploration ended in the early 14th century with the works of Philippe de Vitry and the compositional technique which he applied to the motet form: isorhythm.

I mentioned in that earlier program that there was a great deal of number symbolism which could be detected in isorhythmic motets. The reason numbers are so apparent within isorhythmic works is that there is such structural organization, particularly in the tenor voice—that part which was normally based on a fragment of a Gregorian chant and which moved much more slowly than the other parts.

Isorhythm—which translates as "same rhythm"—involves the application of a rhythmic pattern to the music of the tenor voice. The pattern is repeated a certain number of times throughout the piece, and since the rhythmic values of the pattern are of long duration, there usually are not too many repetitions. Meanwhile. the melody of the tenor voice is also a repeated pattern; and wouldn't you know, the rhythmic pattern and the melodic pattern rarely correspond in length.

The motet by de Vitry that we heard before was "Garrit Gallus/In Nova fert." Its tenor voice has six statements of a rhythmic pattern applied to two statements of a melodic pattern—not the kind of thing that is easy to perceive in performance.

But composers of the generation after de Vitry, led by Guillaume de Machaut, began to make the isorhythmic structure even more complex. In the motet we are about to hear, there appears to be a rhythmic pattern of only three measures in length applied to a melodic pattern of 12 measures in the tenor. But Machaut was extremely clever: he applied isorhythmic principles to the upper parts as well, so that they appear to move in 9-measure phrases. The upper parts thus impose a rhythmic grouping of three 3-measure patterns in the tenor, and the resulting piece is 36 measures long: with four statements of the 9-measure rhythmic pattern applied to three statements of the 12-measure melodic pattern. Again, it is hard to hear all that organization, but there is a distinctive syncopated section within each of the four rhythmic phrases, so you will be able to hear those go by, at least.

[MUSIC: "Qui es promesses/Ha! Fortune." by Guillaume de Machaut, performed by the Early Music Consort of London]

Machaut's greatest claim to fame is his Mass, the earliest setting of the so-called Ordinary movements of the Mass to be composed by a single composer. Machaut used a number of different compositional techniques throughout this Mass but in the Kyrie, Sanctus, and Agnus Dei movements, he used isorhythm. The melodic patterns of the tenor he took from Gregorian chant melodies for those movements. The rhythmic patterns, he simply made up for each movement. In the Agnus Dei of Machaut's Mass, there are two statements of the rhythmic pattern in each of the three sections of the movement. In fact, the first and the third Agnus sections are identical in all voices, but the second Agnus uses a different rhythmic pattern from the other two. In addition, Machaut inserts little non-isorhythmic passages at the beginning of each of the three sections. So we have three sections in the Agnus Dei, each of which begins with a freely composed passage followed by one statement of the melodic pattern in the tenor, using two statements of the rhythmic pattern. Here is the Agnus Dei from Machaut's Messe de Notre Dame, sung by the Hilliard Ensemble.

[MUSIC]

Toward the end of Machaut's life, most of his production of isorhythmic works consisted of motets with Latin texts in the upper voices, and this is something which is continued by composers after his death. Johannes Ciconia is perhaps the most important composer of the late 14th and early 15th centuries. His motet "Albane misse celitus/Albane doctor maxime,” shows the trend toward isorhythmic motets functioning as occasional pieces: in this case, commemorating the appointment of Albane Micheli as Bishop of Padua, in 1406.

Isorhythmically, Ciconia makes use of a similar technique to the one Machaut used in the Agnus we just heard, beginning with a non-isorhythmic section, followed by a statement of the rhythmic pattern, another non-isorhythmic section, and a second statement of the rhythmic pattern.

[MUSIC: "Albane missa celitus/Albane doctor maxime,” performed by the Early Music Quartet, directed by Thomas Binkley]

In England, the surprising aspect of isorhythm during this period is the number of times it was applied to Mass movements, perhaps after the example of Machaut. Most of these Mass movements are individual pieces or pairs of movements, like Gloria-Credo or Sanctus-Agnus. The first complete Mass to be composed as a unit, using a single isorhythmic tenor throughout all movements was Leonel Power's Missa “Alma redemptoris mater." In the Sanctus movement Leonel begins, as seemed to be the fashion, with a non-isorhythmic section followed by an isorhythmic section in triple time, and then an isorhythmic section in duple time.

[MUSIC: The Sanctus from Leonel Power's isorhythmic Mass cycle on the melody "Alma redemptoris mater,” sung here by the Hilliard Ensemble]

The last piece on today's program is by the last great composer of isorhythmic works, Guillaume Dufay. It is characteristic of great composers that they experiment with the prevailing forms of music. And with the isorhythmic motet, Dufay experimented in one case by having two isorhythmic tenors going simultaneously, and in the motet we are about to hear, by having the tenor melody in canon with itself at a different pitch level and with a different rhythmic pattern. In addition, each time the rhythmic pattern is repeated, the notes get only a portion of their original value, so that the four sections of the piece are in a ratio of duration of 6:4:2:3. This quickening or diminution of the rhythmic pattern had been used to some extent by composers in the 14th century to increase momentum towards the end of a piece. But, in this case, 6:4:2:3 also happens to correspond exactly to the proportions of length of the nave, the width of the transept, the length of the apse, and the height of the dome of the Cathedral of Santa Maria del Fiore in Florence. This motet, "Nuper rosarum flores." was composed by Dufay for the consecration of that very church, on March 25th, 1436. The performance is by the Capella Antiqua of Munich, under Konrad Ruhland.

[MUSJC]

All these isorhythmic pieces are mathematically oriented, mostly in ways that cannot be easily perceived by a listener. So why did they do it? In order to relate their works to conceptions of harmony and proportion in the universe, and to symbols of religious significance. It is no accident that Dufay's motet, for example, is found to have numbers like 7, 4, and 28 in its overall scheme. Each of Dufay's 4 sections has 28 measures, there are 14 notes in his tenor melody, 7 lines of text in each section, 7 syllabies in each line.

7 represents the pillars of the Church, the days of creation, the nucleus of the universe, the planets, and the Virgin Mary

4 was called the basic number of the cosmos: it represented the elements, the gospels and the extremities of the cross

28 was called the 2nd perfect number: it is 4 x 7, and it is the 7th triangular number (that is: 1 + 2 + 3 and so on up to 7), it represented the lunar month.

All of these things as manifestations in works of art had significance for the medieval mind. And even if such things could not be perceived by the general public, it may have been enough for medieval artists and composers that the full significance of their designs was understood only by themselves and God.

I wonder if there is any significance to the fact that every Micrologus program has exactly 28 minutes.