During the Middle Ages, the Parisian cathedral of Notre Dame was a hotbed of musical innovation. Two of the brightest musical lights of the late twelfth and early thirteenth centuries worked there: Masters Leonin and Perotin.

Leonin’s fame came from his collection of two-voiced organa to be used for both church Masses and Offices. This tome is known as Magnus Liber Organi, or The Great Book of Organum, and was completed by about 1180. Perotin’s fame came a generation later, from developing organum with three voices, and even four voices.

But Leonin and particularly Perotin needed to pin down rhythms in order to make music from potential chaos. The School of Notre Dame’s fame comes from meeting this problem head-on. Taking a cue from the Church’s melodic modes, musicians at the School of Notre Dame came up with rhythmic modes.

There were six rhythmic modes, all based on groups of three beats. Three was seen as a “perfect” basis for rhythm, since three was the number for the Father, Son, and Holy Spirit of the Christian Trinity. Using “short” for one beat, “long” for two beats, and “very long” for three beats, the modes were as follows:

• Mode 1 (Trochaic): long, short = three beats altogether
• Mode 2 (Iambic): short, long = three beats altogether
• Mode 3 (Dactylic): very long, short, long = six beats altogether
• Mode 4 (Anapaestic): short, long, very long = six beats altogether
• Mode 5 (Spondaic): very long, very long = six beats altogether
• Mode 6 (Tribrachic): short, short, short = three beats altogether

Just as musicians mixed voice motions within a single work, they also mixed rhythmic values. Musicians realized that an entire work in only one mode would be hypnotically boring. But with no bar lines and only neumes to work with, how could a person know when one group of modal threes was turning into another? The full answer is much too complicated for inclusion here, but it involved ligatures which are “sticks” tacked onto the rectangular notes, making them look somewhat like notes of today. Depending on where the ligatures were placed, and how many unmarked notes followed, musicians knew which rhythmic mode to use.

For modern ears, this music acquires a rather skipping or “sing-song” quality because of the short and long beats that always add up to groups of three. But for listeners in the Middle Ages, this music must have been as exciting (and possibly as disturbing) as atonal works were at the start of the twentieth century.

Three-part organum with rhythmic modes became the rage of thirteenth-century Church music. With the addition of a third voice, the names of the parts changed once again. Everything was still based on an original Gregorian chant, and that voice, placed on the bottom, was still known as the cantus firmus. But now the vox organalis became the duplum (second voice) and was directly above the original chant. The triplum (third voice) sat on top of the others. Again, all the voices were of equal value.

It is important to remember that every line, no matter how many, related only to the cantus firmus. It didn’t matter whether the top two lines clashed, as long as neither line clashed with the cantus firmus. (Remember, listeners heard the lines horizontally and not vertically.) These voices fitted together, largely because all the notes fell into groups of three beats, and yet they each had their own independent rhythms. The cantus firmus began to slow down and acquired the longest beats.

Soon it became impossible to use the entire chant at this snail’s pace. So a portion of chant was used, known as a clausula (just as a clause is only part of a complete sentence). Eventually this line’s note values became so long that historians believe it might have been played on an instrument. This idea is bolstered when the cantus firmus line has no text printed on its part. But that is only one theory.

The top two voices acquired more independence. They could mirror one another’s rhythms, or one (usually the top voice) could become still faster. But with three voices, a rhythmic style called copula evolved. In this style, one voice would relate to the cantus firmus in the neume-to-neume descant style, while the other voice would simultaneously relate to the cantus firmus in the florid or purum style. Thus, two styles were being sung simultaneously. A modern mnemonic device to remember this style is that the musicians were using a “couple of” (copula) styles at the same time.

While most Church music clung to some form of Gregorian chant as the cantus firmus—its “home base”—one type of Church music became unusually independent. The conductus, music performed during church services but not part of the Mass, was sung while priests went from one place to another during the service.

These melodies were freely composed and had nothing to do with any precomposed music. There was no cantus firmus. This was entirely newly composed material. By the thirteenth century, the conductus was being treated polyphonically—that is, two or three voices of freely composed music made into a musical work. Although the conductus certainly did not undermine or destroy the idea of having a cantus firmus, it offered an outlet for creative freedom that was unusual in its time.