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)

Fauxbourdon: A Treat for the Masses

Album: Dufay: Music for St. James the Greater
Track: "Missa Sancti Jacobi: IX. Communio" (Track #9)
Composer: Guillaume Dufay
Instruments: 3 vocals
Musical Form: Mass setting
Year: ~1430

One of the chief challenges of composing polyphonic music in the 15th century, as well in all previous centuries, was satisfying your own artistic needs, while simultaneously satisfying the needs of the church/court for which you were composing. This problem was particularly severe with sacred music, where the church often demanded that the scripture be clearly understandable to churchgoers in hymns and masses. This would limit composers to using parallel and oblique motion for much of the duration of the piece, greatly decreasing its complexity. In modern music, this is somewhat analogous to a songwriter being forced to write simple pop tunes in order to garner attention and raise money for their work.

Perhaps as a response to this limitation, Guillaume Dufay invented a technique called "fauxbourdon," a form of three-part parallel vocal harmony in which the two bottom voices sing at intervals of a perfect fourth and a sixth below the top voice. To imagine how such a harmony would be constructed, think of the notes in a triadic harmony (the example given in the link is from "Twist and Shout"), but adjust the root note up an octave. Here is an example of what it sounds like when used in a piece of religious music (skip to 0:45). The net effect is to give the music a more full (or "tonal") sound than simple homophony, while leaving the lyrics easily understandable.

The first known example of this technique is in the last section (the Communion) of Dufay's "Missa Sancti Jacobi," composed around 1430. The sound is not quite as pleasing as Dunstaple's moving triads, but it serves its purpose. After Dufay's introduction of it in this mass, fauxbourdon would see widespread use in continental polyphony through the end of the 15th century, particularly by Burgundian composers.

Related Links: Allmusic, Youtube

Ga-ga for Google Books

One of the most important events of the Information Age will be taking shape in the coming months. In October 2004, Google premiered its latest search engine at a book fair in Frankfurt, Germany. Then called Google print, the service allowed users to browse books that had been scanned into an electronic library using optical character recognition. The service is now called Google Books and has scanned over 7 million books into their library; certainly an impressive feat considering that only ~32 million books have been published in human history. Furthermore, after reaching a settlement with the Author's Guild and the publishing industry over copyright issues, Google is poised to greatly expand the fraction of their library that is available for preview and purchase.

Although some folks are still concerned about the terms of the settlement (privacy and antitrust issues, see the ASJA link below), it looks likely that the online availability of published material is going to increase in the coming months and years. In addition to being a major milestone for humanity, this service has been a tremendous help in researching my Hopeless Journey. When I search their database on a particular composer or composition, the volume of useful information that I can obtain from Google Books far exceeds that I can get from an ordinary Google search. Even for those books with limited previews, I need only browse a couple of paragraphs of the section that matched my search terms in order to obtain the information I'm looking for.

There is no doubt that Google Books will contribute a great deal to this blog. I'm old enough to remember what life was like before the internet... I have to say, this is a truly exciting time to be alive.

Related Links: Google Books, NYTimes article, Opposition from ASJA

The Development of the Cyclic Mass: A Great Service

Album: Dunstaple: Musician to the Plantagenets
Track: "Missa Rex Seculorum" (Tracks #12-15)
Composer: John Dunstaple
Instruments: 3 vocals
Musical Form: Cyclic Mass
Year: ~1410 - 1440

When we consider the composers of early music, it is important to judge them not just on the music they themselves wrote, but also the future music they contributed to. Unlike a scholarly paper, a mass or a symphony does not include citations -- it is the task of music historians to trace the origins of the forms and styles that the composer used. In this respect, the early composers perhaps deserve more credit than our ears are inclined to give, as they helped to develop the conventions we now take for granted.

As the 15th century opened, composers were restricted to short musical forms; that is, secular chansons and sacred motets (both typically ~5-10 minutes in length). The first long-duration musical form to see mainstream popularity would be the cyclic mass, developed by the composers of the Burgundian school in the mid-15th century. You may recall that I first discussed the concept of a cyclic mass in a post on La Messe de Nostre Dame. That mass setting, which was composed by Guillaume de Machaut, may well have been the first of its kind, but was either unknown to his contemporaries or failed to inspire further development of the form, because it wasn't until the early 15th century that the cyclic mass was acknowledged as a genuine mode of composition. The first cyclic masses (after Machaut's) were written in England and were unified by a musical theme at the beginning of each section.

The example given, "Missa Rex Seculorum," was written by John Dunstaple and includes a Gloria, Credo, Sanctus, and Agnus Dei. Notice the uniformity in scoring and rhythm between the Gloria and Credo -- each starts with a duo, not adding the third voice until about a minute and half in, at which point the rhythm changes as well. The Sanctus benefits the most from Dunstaple's pre-Renaissance style, the thirds blending to create an elegant and immediately-appealing texture that wasn't possible in Machaut's sonic framework. Overall, however, the piece is lacking the energy and invention of Machaut's mass, suffering somewhat from the limited vocal arrangment (2- or 3-part polyphony). Even Dunstaple himself has composed individual mass settings with more flair.

Just as with triadic harmony, the early development of the cyclic mass has been lost to history due to the purging of the monasteries in 16th-century England. Fortunately, however, the form would quickly catch on in continental Europe and composers such as Dufay and Busnois would continue to develop it. In fact, many of their inventions would survive for over a century, as the cyclic mass wouldn't truly fall out of favor until the Baroque period, starting around 1600.

Just YouTube It

Up till now, I hadn't been bothering with YouTube as a resource for medieval and Renaissance music, assuming that most of it was too obscure to be posted on that service. However, when I actually went and checked today, I was pleasantly surprised to discover that not only are many of the Hopeless Journey songs available, but also many of the specific recordings I've been listening to.

Since a link to YouTube allows casual web browsers to hear the songs I'm describing at the click of a mouse, I've decided to incorporate these links into the post headers. Whenever there is a link over a song title in one of my post headers, it goes to a YouTube recording of that composition. It won't always be the recording that I'm recommending in the header, but it will be to one that I think is similar enough to get my point across. If you want the specific recording referenced in the post header, it will usually be available on iTunes.

If a YouTube link goes dead, let me know and I'll try to find a replacement for it. I don't know what the typical lifetime of a YouTube link is, so I may abandon the practice if I find that they go dead too quickly.

John Dunstaple and Triadic Harmony: The Burgundian Three, Part III

Album: Dunstable: Sweet Harmony Masses and Motets
Track: "Quam pulchra es" (Track #1)
Composer: John Dunstaple
Instruments: 3 vocals
Musical Form: Motet
Year: ~1410-1453
Composition for Comparison: "Twist and Shout" by the Beatles and "Surfer Girl" by the Beach Boys

The elegant melodies of Binchois inspired a generation of musicians and Dufay's epic compositions elicit awe and respect even from modern listeners, but the real revolution of Renaissance music began with John Dunstaple. This great English composer is credited with introducing a technique that is often taken for granted by the 21st-century ear: triadic harmony.

In short, a musical triad consists of the root, third, and fifth of a major scale and contains intervals of a third between successive notes. For you music-theory beginners out there, I've selected some modern, well-known songs to demonstrate what this sounds like. The first is "Twist and Shout" as performed by the Beatles, a rendition that should be familiar to anyone who has seen Ferris Bueller's Day Off. The majority of the song uses a single lead vocal with a pair of backing harmonies, but if you play to 1:25 into the recording, you'll hear the Beatles build into a triadic harmony, one note at a time. It begins with John Lennon singing the root note ("Ahhh...") over the twanging of George Harrison's lead guitar. Next George chimes in with the third, followed soon after by Paul with the fifth. At 1:28, they're in a full triadic harmony. It only holds a complete triad for the few seconds after 1:28 -- the sequence continues after that to the seventh, breaking the triad. The notes of a triad can also be struck simultaneously: C Triad.

It's not uncommon to hear full triadic harmony in modern music, particularly in pop music of the '50s and '60s. In "Surfer Girl," a song by the Beach Boys from 1963, they utilize it throughout much of the song, crafting the melody over top of the moving triads. In fact, the arrangement is in many ways similar to that of "Quam Pulchra Es," one of John Dunstaple's motets from the mid-15th century. This motet is one of the more blatant examples of how the interval of a third was being gradually promoted to the status of a consonance (that is, a stable musical interval) in the early Renaissance period. For those that have been following my Journey, this sudden addition of musical triads should be a very noticeable (and very welcome) change to early polyphony. Compare it to this early mass movement by Guillaume de Machaut, where fourths, fifths, and octaves dominate the harmonic structure. Although such intervals achieve a more "pure" sound, they are almost too easy for the human brain to process and we may be left feeling like something is missing.

Triadic harmonies were commonplace through most of the 15th century in England, but it won't be until the late 15th and early 16th centuries that the musical changes initiated by John Dunstaple and his English contemporaries begin to permeate the music coming from continental Europe. Unfortunately, because of Henry the VIII's dissolution of the monasteries in the 1530's, very little music survives from England in the preceding century and the process by which triadic harmony was introduced into polyphony may forever remain a mystery. Dunstaple was famous enough that some of his music has come down to us from continental sources, but the catalog of surviving music doesn't even approach that of contemporaries like Dufay and Binchois. This is indeed a shame, as many argue that John Dunstaple was the most influential English composer of all time.

Related Links: Allmusic, YouTube, Triads in Medieval Music, Intervals