Listening to Early Cyclic Masses

We don't often think of listening to music as a skill; after all, those of us who aren't listening for the purpose of writing a paper or preparing for a performance are hoping that the music will serve us. There should be little or no obligation in the other direction...

And it's true, we owe nothing to the music. Nevertheless, I believe we do owe it to ourselves to put in the legwork when we have trouble understanding the appeal of a particular style of musical composition or performance. I can safely say that there have been few things in my life that have been more rewarding than discovering new music, but even putting that aside, understanding the appeal of music from another culture (or subculture, as the case may be) can help us to better understand the people who created it. If all United States politicians went out of their way to develop an appreciation for hip-hop, I guarantee this country would have fewer problems with racism.

There are no real political implications when it comes to developing an appreciation for early music, but the experience can still broaden one's horizons a great deal. For me, the most difficult musical form to develop an appreciation for was the cyclic mass. In addition to being very long (typically 30-90 minutes in length), cyclic masses don't feature a great deal of repetition and seldom put emphasis on melody. It is very easy to become disconnected from the music -- I often caught my mind wandering, even when using headphones.

It may be that part of the problem was my inability to place the music in its proper context. As the name suggests, these pieces were written to accompany religious masses, all together with the solemn adornments, vast halls, and pious followers. As it is, lying in bed with my headphones on scarcely seems an apt replacement. Nevertheless, I believe I am beginning to understand what the Renaissance composers were trying to achieve.

Some modern critics describe early cyclic masses as "ornamental," implying that they served only to decorate an already lavish ceremony. I don't think this description does these pieces justice, however. Late music critic, Wilfrid Mellers, was a bit more generous in reference to John Dunstaple's early cyclic masses:

"He was not concerned with his own emotional response, which could only seek incarnation in time, but was rather, like Machaut, concerned to create, through his music, an 'atmosphere' in which an act of revelation might occur. He did not know when, or even if, it would happen, but he did his best to create the conditions in which it might. Just as an Indian vina player would perform for hours or even, with a few necessary intermissions, all day or all night while his audience of 'participants" came and went, so the ritual music in a medieval cathedral might resound for hours, while the congregation fluctuated."

The reference to an Indian vina player may be a tad obscure, but the point is clear. These masses were not meant to be approached like a movie, for which the director aims to tell a cohesive story that suffers when viewed in pieces. Rather, it is more analogous to a meteor shower. Any momentary display of brilliance may sweep the listener off their feet, but successive bursts do little to build upon one another. A cyclic mass is, quite literally, equal to the sum of its parts.

With this realization, I became less concerned about keeping a constant focus on the music. Often I would play the masses in the background while doing work or surfing the internet and every now and then they would pull me in, providing a fleeting but soothing experience. Whether I will ever achieve a true "revelation" through cyclic masses... only time will tell. In the meantime, I will enjoy them for what they are.

Related Links: Wilfrid Mellers' book

De Cuer Je Soupire and Early Harmony: A Whisper of Things to Come

Album: Music and Chants from the Time of Joan of Arc
Track: "De Cuer Je Soupire" (Track #9)
Composer: Anonymous
Instruments: 2 vocalists
Musical Form: Lai
Year: before 1420

There are many ways in which Medieval and Renaissance music can present a challenge to the modern ear -- not least of which are its use of unfamiliar rhythms, musical modes, and dissonances. Perhaps the most difficult thing of all, however, is learning to listen to compositions that are based on the principles of polyphony. Crudely speaking, polyphony treats the voices of a composition as independent entities, each moving through the musical space in a manner that is conscious of, but not tied to, the motion of the other voices. Unfortunately for the modern fan of early music, the majority of pieces composed since ~1600 have not been polyphonic, but have rather been based on the principles of harmony. Harmony, by contrast, treats the majority of voices in a piece like accompaniment to the melody, all coming together to form chords that change as the piece progresses.

To better understand the differences between the two approaches, think of a piece of music as a building. The parts of a polyphonic composition (the girders, bricks, etc.) are carefully interwoven so that the composite whole can remain stable and please the senses. However, this building lacks a foundation, so there are a limited number of ways in which pieces can be combined to achieve stability and still remain aesthetically pleasing. The use of harmony, however, provides the building with a foundation. Although the composer may use up many of the available parts to build this foundation, the stability it provides allows them more freedom in the design of the building. Whether or not the use of harmony over polyphony is better is a question of personal taste, but it is certainly easier, both on the composer and the listener.

Early Renaissance music was still being composed on the principles of polyphony, but there were hints of movement towards a more harmony-oriented style of composition. I already discussed the development of triads in 15th-century England. In "De Cuer Je Soupire," an anonymous composition included in a French manuscript written around ~1420, we hear two voices interacting in a manner that almost sounds like a chord progression. The higher voice clearly sings the melody and the lower voice acts as accompaniment. They undergo oblique motion for most of the piece, as the lower voice changes its pitch only for cadences and line changes. The effect is stunning, and perhaps somewhat familiar, at least in comparison to other compositions from the same time period.

Related Links: YouTube

Veni Sancte Spiritus and Missa Caput: Two Giant Leaps

Album: Dunstable: Sweet Harmony Masses and Motets
Track: "Veni Sancte Spiritus - Veni Creator" (Track #11)
Composer: John Dunstaple
Instruments: four vocalists
Musical Form: isorhythmic motet
Year: ~1431

Although early Renaissance composers were in many respects less experimental than their late medieval predecessors, there were still a great many musical forms and techniques that were being developed in the early 15th century. In an earlier post, I discussed John Dunstaple's pioneering the use of triadic harmony in his compositions; this technique can be heard again in "Veni Sancte Spiritus," a popular motet composed around ~1430. The piece is progressive in many respects, including its use of a musical mode that corresponds to the modern major scale and also its relatively wide range of pitches (called the "tessitura").

The wide pitch range of "Veni Sancte Spiritus" is most noticable in the tenor, which at times functions like a bass line. The tenor fails to truly carry the rest of the piece as a modern bass line would, but each time it strikes a low note, the piece is given new life. It does not move towards a dynamical climax as we might expect from a symphony, but is rather almost cyclic, as the isorhythmic tenor paces the higher voices. With each repetition, we are given a new opportunity for spiritual transcendence, but it is not just handed to us... we must find it for ourselves.

Although we hear hints of it here, a true bass part would not appear in a Renaissance composition until "Missa Caput," a cyclic mass composed by an anonymous English composer sometime around 1440. I haven't been able to locate any easily accessible recordings of this mass, but many other mid-15th century masses were modeled after it and I will review some of these in later entries. English composers were particularly influential on their continental counterparts during this period, in part because of the English occupation of France during the Hundred Years War.

Related Links: Allmusic

On Math and Music: Pythagorean Tuning

How was the first instrument tuned? On first glance, this question may seem similar to the chicken and egg quandary we learned as children -- simple but circular. When most of us tune an instrument, we generally resort to a mechanical device or another instrument. However, it turns out that the precise mathematical relationships that define musical intervals allow the unaided ear a limited ability to determine relative pitches without any mechanical assistance. As such, the first instrument could have, you might say, been tuned to "itself."

In fact, tuning by ear was quite common in the medieval and Renaissance periods, using a system called Pythagorean tuning. To understand how this works, consider first the octave. Given an arbitrary note, most people could quickly learn to find a pitch that was an octave above or below. The 2:1 ratio between the frequencies of the notes of an octave makes it easy for the ear to pinpoint these pitches, particularly if the two notes are played simultaneously. Therefore, from a starting pitch, the unaided ear could tune the pitches that were at intervals of 2:1, 4:1, 8:1, 16:1, etc. by finding the note an octave above the starting note, followed by the note an octave above that, and so forth. Using the inverse process, one could also identify notes at intervals of 1:2, 1:4, 1:8, 1:16, etc. Unfortunately, that only leaves us with a musical scale that sounds like this: listen.

Fortunately, the human ear can, without too much training, learn to identify another interval, the fifth. At a ratio of 3:2, this interval blends almost as smoothly as the octave, and again becomes easier to identify when the notes are played simultaneously. At first glance, the ability to tune a fifth may seem like a minor improvement, but this development actually gives us a great deal more freedom in frequency space. This fact is easier to see from the mathematical point of view.

Suppose I were to tackle the standard problem of constructing a scale of twelve tones between a pitch of arbitrary frequency and a pitch one octave up (frequency ratio of 2:1). Since I can tune a fifth, I automatically have one additional note at a ratio of 3:2, which gives me the following scale: 1:1, 3:2, 2:1 (listen). However, I can add to this by considering the pitch that is a fifth below the starting pitch: 2:3. Although this particular pitch is not between 1:1 and 2:1 and therefore does not belong in my scale, remember that I can tune intervals of both an octave and a fifth. Therefore, the following set of tunings is allowed:

1:1 -> down a fifth (x 3:2) = 2:3 -> up an octave (x 2:1) = 4:3

I now have a way to tune the following pitches: 1:1, 4:3, 3:2, and 2:1 (listen). Another pitch can be added with the following set of operations:

1:1 -> up a fifth (x 3:2) = 3:2 -> up a fifth (x 3:2) = 9:4 -> down an octave (x 1:2) = 9:8

If I continue performing tunings of this kind, I can construct a full twelve-tone scale with the following intervals from the root pitch: 1:1, 256:243, 9:8, 32:27, 81:64, 4:3, 1024:729, 3:2, 128:81, 27:16, 16:9, and 243:128. This technique of tuning is also known as the "circle of fifths," for obvious reasons. Note, however, that the scale doesn't include some of the small-number ratios I discussed in my intervals post, most notably 5:4 and 5:3. Although it includes intervals that are close to these frequency ratios (81:64 and 27:16, respectively), the major third and the major sixth still tend to sound more dissonant in the Pythagorean tuning system than in systems that give them small-number ratios. In fact, it was in part due to the widespread use of this tuning system that medieval composers favored intervals of a fourth and fifth over intervals of a third or a sixth. In the 15th century, as triadic harmony saw more widespread use in compositions, musicians began to favor other tuning methods.

Related Links: Extended discussion (medieval.org); Meantone temperament (wikipedia)

Guillaume Dufay's Chansons: A More Precise Melancholy

Album: Guillaume Dufay: Tempio dell'Onore e delle Vertù
Track: "Ma belle dame souverainne" (Track #4)
Composer: Guillaume Dufay
Instruments: 4 vocalists
Musical Form: Rondeau
Year: ~1420-1430

A simple-minded approach to the music of the Burgundian School might involve a survey of Guillaume Dufay's masses and motets, leaving Binchois as the sole purveyor of early-15th-century secular music. Although you wouldn't be far off the mark with that approach, Dufay's body of secular compositions is nothing to sneeze at. Fortunately, Cantica Symphonia recorded 18 of Dufay's chansons in Guillaume Dufay: Tempio dell'Onore e delle Vertù, showcasing this great composer's gift for melody as well as contrapuntal precision.

The result is a mixed bag. Dufay's style of epic, unrestrained polyphony is particularly well suited to songs that indulge in melancholy, such as "Ma belle dame souverainne." However, his more upbeat chansons, like "Navré je sui d'un art penetratif," have a tendency to sound bouncy and a tad frivolous. Perhaps it is actually the simplicity demanded by the genre that Dufay so struggles with -- one who makes a living adorning cathedral halls might struggle painting a portrait...

I think there is no question that Binchois is more graceful in his ability to relate to the optimism of the masses, but when Dufay strikes a sad chord, I find I am often slow to recover.

Related Links: Allmusic; YouTube

On Math and Music: Intervals

Some believe that the most fundamental aspects of reality -- everything that we are and everything that we perceive -- ultimately come down to mathematics. It is the language of science and perhaps the only surviving bastion of irrefutable truths in the aftermath of the Age of Enlightenment. It is this irrefutable quality, this perfection of sorts, that also lends mathematics a certain beauty; in fact, the origin of all beauty may come down to simple mathematical relationships.

Our brains perceive mathematical relationships in countless ways, but perhaps none are so direct as the way in which we process sound. Suppose I were given two tuning forks, one designed for a frequency of 440 Hz and the other for 880 Hz. When I strike the first, the metal begins to vibrate, moving back and forth at a rate of 440 times per second. This vibration, in turn, causes the surrounding air molecules to oscillate at the same frequency, an oscillation that travels outwards from the tuning fork and reaches my ear. Assuming that the tuning fork continues to vibrate at this frequency, my brain will interpret the oscillation of air molecules as a steady and constant "pitch."

Now suppose I strike the second tuning fork, which vibrates 880 times per second. This new pitch corresponds to a frequency twice that of the first, and if I strike the second tuning fork while the first is sounding, they together produce a sound something like this. Notice how smoothly the pitches blend together. The interval heard here is called an "octave," a musical term reserved for any pair of pitches with a frequency ratio of 2:1. Our ear easily identifies the relationship between these two pitches because their frequencies are in a small, natural-number ratio to one another. By contrast, listen to the major seventh, an interval that corresponds to a frequency ratio of about 15:8. The blend is not nearly so pleasing to the ear.

When two pitches blend together well, like the octave, they are referred to as "stable," or a "consonance." Those that don't blend so well, such as the major seventh, are referred to as a "dissonance." In medieval music, the consonances were the octave (2:1), the perfect fifth (3:2, listen), and the perfect fourth (4:3, listen). In the early 15th century, starting with the Burgundian School, intervals of a major third (5:4, listen) and a major sixth (5:3, listen) began to be treated as consonances, allowing for developments such as triadic harmony.

Nuper Rosarum Flores: The Power of Dynamics

Album: Guillaume Dufay: Quadrivium (motets)
Track: "Nuper Rosarum Flores" (Track #15)
Composer: Guillaume Dufay
Instruments: 4+ vocals, trumpet, organ, fiddle, harp
Musical Form: Isorhythmic motet
Composition for Comparison: "Lithium" by Nirvana (1991)
Year: 1436

As a teenager of the early '90s, still in the throes of adolescence, it was difficult to not get swept up in the pounding rhythms and catchy melodies of the grunge movement. In high school, I remember waking up every morning to "Smells Like Teen Spirit" -- the raucous transition between the opening guitar riff and distortion-heavy entrance of the bass and drums gave me something to be excited about at the start of a day that likely would, in all other respects, only erode my increasingly paltry teenage ego. There was something about the anticipation created by those guitar chords... a sort of musical foreplay by a song that knew to understate what it was soon to deliver.

This "soft-and-loud" dynamical technique was quite common in Nirvana's music and is perhaps most vividly demonstrated in "Lithium," a track off of their groundbreaking album, Nevermind. Note how the verse keeps a relatively low profile, emphasizing the lyrics and melody over the rhythm, while the chorus is an explosion of sound and a perfect expression of the "angst" that grunge music was known for exploiting. Kurt Cobain credited the Pixies with influencing his dynamical style, but this general technique had been around for many centuries before. Compare the verse-chorus transition of "Lithium" to the dynamical structure of Guillaume Dufay's "Nuper Rosarum Flores." To my ear, the effect is very similar. The melismatic, almost madrigaleque lines in the Triplum and Motetus (top two voices) are placed in contrast to the steady, booming rhythm provided by the bassus and tenor (bottom two voices) that enter 1:00 into the piece. I can imagine the dynamical changes would have sounded even more dramatic within the confines of a church sanctuary.

"Nuper Rosarum Flores" is famous for a variety of other reasons, perhaps most of all for being the last great isorhythmic motet. To some scholars, this represented a symbolic ending point for the medieval period of music, as the Renaissance style was noted for having a more free rhythmic form. Some have even claimed that the mathematical structure of the motet was formulated in order to mimic the proportions of the Santa Maria del Fiore cathedral, the building for which the piece was composed. My research has left me skeptical of this claim, however.

Related Links: YouTube (Dufay), YouTube (Nirvana), YouTube (Dufay, alternate version)