Isorhythm
A method of structuring a piece of
music by using recurring rhythmic patterns.
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Fig
1: Guillaume de Machaut, greeted by Dame Fortune |
[Example 1: Machaut: Messe de Nostre Dame, Kyrie I: CD 292]
Isorhythm is a method of structuring a piece of music by using recurring rhythmic patterns. It was a common compositional technique from about 1300 to about 1430, and was used primarily to structure motets and sections of the Mass.
Some early examples of isorhythmic composition appear in the works of Philippe de Vitry (1291-1361) and Guillaume de Machaut (1300-1377), both of whom were considered to be part of the school of the "New Art," or Ars Nova. Later composers who used isorhythm include John Dunstable (ca. 1385-1453) and Guillaume Dufay (1400-1474).
Isorhythm can be a challenging concept because it is sometimes difficult for us to identify it as we listen to isorhythmic music. During the late Middle Ages and early Renaissance, composers were not afraid of using musical devices that were all but inaudible. For them, such hidden structures had a beauty and meaning in themselves, rather like the intricate design of a Gothic cathedral, invisible without a bird's-eye view, or an architectural plan.
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Fig
2: Aerial view, from "Notre-Dame, Cathedral of Amiens: The
Power of Change in Gothic" |
Isorhythmic patterns are difficult to hear because they often occur in the tenor part of a polyphonic piece. In medieval and Renaissance music, the tenor is usually the lowest or next-to-lowest part in a polyphonic texture (see Polyphony). This means that an isorhythmic pattern found in the tenor alone often seems to be "buried" by the other voices. In music we are more familiar with, significant rhythmic patterns usually appear in the part that carries the melody as well as the other parts, so that you can easily follow the pattern with your ear alone.
The tenor was seen by medieval and early Renaissance composers as the basis for the rest of their compositions. One early 14th-century musician and theorist said: "the tenor of the composition is the voice on which all the others are based, just as the parts of a house or a building are erected on the foundations" [Johannes Grocheo] You might think again of the Gothic cathedrals, many of which were built at the same time as isorhythm was beginning to be used. In these intricate buildings, the structure supporting the soaring arches is partially hidden from view. The isorhythmic tenor is similar: though it's hidden, the whole piece depends on it, and the other voices are structured rhythmically -- and sometimes melodically -- in relation to it.
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Fig
3: Cathedral, with labyrinth design (source as Fig. 2) |
You can see the difficulty when you try to identify the isorhythm in the music we've been hearing, a Kyrie from Guillaume de Machaut's Mass for Our Lady. Try to listen to the second-lowest voice alone.
[Example 3: Machaut: Kyrie I (opening)]
The tenor alone, without isorhythm patterning, sounds like this:
[Example 4: Kyrie plainchant melody]
In fact, this tenor comes from a pre-existing monophonic source (see Monophony), in this case a Kyrie ("Lord have mercy") from traditional Gregorian chant that would have been easily recognizable to Machaut's listeners if sung alone. For composers like Machaut, borrowing material for tenors from older sources was very appealing, and very common, since the earlier source often had a text which contributed to the "hidden meaning" of the tenor. Here, the polyphonic Kyrie is based on a monophonic Kyrie, in a sense reinforcing the meaning of the polyphonic piece.
The tenor, with the isorhythmic pattern Machaut has chosen for this mass movement, sounds like this:
[Example 5: Machaut: Kyrie I, tenor (opening)]
You can hear how the tenor has been divided up into sections, and that each section has an identical rhythmic pattern. In general, isorhythmic tenors are divided in this way -- that's why we use the term "isorhythm": isos is Greek for "same" or "identical." Each of these identical sections is called a talea. Sometimes melodic patterns occur too, either synchronized with the rhythmic pattern or overlapping with it -- that is, the melodic pattern's beginning and ending may or may not coincide with the rhythmic pattern's beginning and ending. If there is a melodic pattern as well, each instance of that pattern is called a color.
Now, try to identify the tenor again as it appears with the other three voices:
[Example 6: Machaut: Kyrie I (opening)]
Now that your ear is trained, you may be able to hear the isorhythm, but it probably is still somewhat obscured by all the activity in the other voices. In fact, these voices are composed in relation to the isorhythm, but again, not in a way that is obvious to the ear. The fact that you cannot easily recognize any similarity or relationship between the various polyphonic voices may help you to identify this music as a form of non-imitative polyphony.
Often, an entire isorhythmic composition will be based on a proportion: for example, in the second half of the piece, the isorhythmic pattern from the first half might be repeated, but twice as fast. That's what happens in this motet by Machaut. Here the tenor is played on an instrument rather than sung, and it appears as the lowest of three voices, so it may be easier to hear:
[Example 7, Machaut: Quant en moi/Amor et biaute/Amara valde (opening)]
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Fig
4: isorhythm proportion |
Again, even when such a pattern is difficult to hear, the composer is interested in the intricate relations between the tenor and the other parts, and in the mathematical challenge involved in laying out the isorhythms and proportions. Remember, for composers of this period, music was one of the subjects in the Quadrivium, or number arts -- the subjects dedicated to topics of number and proportion, like arithmetic, geometry, and astronomy. Once again we can think of the Gothic cathedral and all its intricacies, barely discernible to us but certainly meaningful in a culture that believed hidden detail was always visible to God.
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Fig
5: Pythagoras measuring interval proportions.
Gafurius, Theorica musie (Milan, 1496) |
Summary:
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Visual & Sound Materials from the Gabe M. Wiener Music & Arts Library of Columbia University | |
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Isorhythm written by:
Annalisa Poirel Recording & Mixing: Terry Pender & Bradford Garton Sung Examples: Eric Rice |
Narration:
Annalisa Poirel Technology & Design: Maurice Matiz Architectural Images: Media Center for Art History, Columbia Univ, c.Trustees of Columbia University |