Music 101: A History of Notation (part 2)
In part 1 of this history of notation, we covered the earliest medieval notation up to the birth of mensural (measured) notation, c. 1300. In part 2, we'll proceed through the developmental stages of mensural notation, up to about 1400. The 14th century has the most challenging repertory in Western history, barring some of the most extreme modernist and avant-garde work of the 20th century. Get comfortable. It's a long read. (1)
As with part 1, the goal of this post is to give lay people a general idea of some of the historical developments in music. The books on this material probably are not very accessible to casual enthusiasts. If you read music and you're looking for more of an introduction to the technical nitty gritty of how to read mensural notation, the Wikipedia article is actually pretty solid. (2) That said, this post is going to get more technical than the last one. Things are about to get geeky. That's just the nature of 14th century music. It doesn't get geekier than the ars subtilior. That works for me, because I am a geek and my intended audience is geeks. But if you're just here for pretty manuscript photos, you'll get those, too.
Franconian notation
We left off in part 1 with Franconian notation, which is the earliest kind of mensural notation, or notation where the note shapes indicate duration. It was used for early sacred polyphony. Today we'll start off with some general technical overview of what mensural notation is. There is no getting around this. Mensural notation was used from c.1300 to c.1600. It is a proportional system, whereas modern notation is a fixed value system. (In the Middle Ages, music was a science, a form of mathematics. The true musician wasn't the performer, but the learned composer. And medieval theorists were aaaaall about numbers and ratios. See Boethius for more information.)
What does it mean that mensural notation isn't a fixed value system? Mensural notation is defined by divisions into 2s or 3s, and conceived by ratios of 2:1 and 3:2. These divisions and ratios aren't totally clear from the notes themselves; they require a time signature or other devices to indicate it. This is what really makes it distinct from modern notation.
For example, this is a semibreve. Just looking at that little old lonely semibreve, you don't know if you subdivide it by two or by three, or hell, even seven (looking at you, Avignon composers). But, modern notation--
This is a whole note. It can ONLY consists of two half notes. Totally without context, I know this. No matter the time signature. This is the difference, and one aspect that makes mensuration proportional rather than fixed. (A time signature in modern notation tells me more about how all of the voices in a work line up. One of the ways historians tend to oversimplify early music is by saying that early music is horizontally conceived, while tonal/common practice music is defined vertically.)
The division of a note value into threes or twos is called perfection or imperfection, respectively. This is how time signatures (mensuration signs) are established: different combinations of perfections and imperfections. I will cover this in more detail when I get to mensuration signs. For now, just remember the pyramid of divisions into twos and threes.
In Franco's system, note values ranged from double-longa (the longest, nach) to semibrevis. Any of these notes could be divided into 2 or 3, but they were still tied to the rhythms of the old modes (see part 1), which each had a triple meter. So, if you divided a note of Franconian notation into two, the two notes are not of equal value; one is longer than the other. It's a 66/33 split, not 50/50.
New developments came quickly at the beginning of the 14th century. Petrus de Cruce--who might have been Franco's student (3)--popularized some major new additions. He is most famous for freely dividing the breve into as many as 7 semibreves, which brought with it the development of the punctum divisionis--literally just a dot on the staff, usually placed next to a note head. Music of this time has no bar lines, so the punctum became a way to show metrical groupings of notes. If 4 semibreves occur between two puncta, then it's understood that these 4 semibreves take the time of 1 breve. This means they are sung faster, relative to semibreves in standard groupings, but it also had the effect of slowing down the pulse. Music that is characterized by willy-nilly subdivision of the breve is called Petronian, after Petrus. In Petronian music, you tend to get a lively upper voice with slower, duller accompanying parts.
This example of two motets (4) from the anthology Music of the Middle Ages (David Fenwick Wilson) beautifully showcases the difference between the Franconian and Petronian styles. The video includes the music in modern notation, so you can follow along if you read music.
In the Franconian example, the eighth note is the semibreve. You can hear how fast they are. In the Petronian example, you'll immediately notice that it's slower, and the top voice has sixteenth notes. Those sixteenth notes are also semibreves. They were not distinguished with a different note value in the original notation. If you don't read music, you can still see, and hear, the different level of activity in the voices. Although the top voice (the triplum) has the tune in the Franconian example, it has some lively exchanges with the duplum. The Petronian one, though, has a noticeably less active duplum.
The Ars Nova
Petronian music is a tiny niche in the history of music, but the "willy-nilly breve subdivision" (stop me if I get too technical) is an important stepping stone to what comes next, so that's why we're taking a little time for it.
Here's a page from the beautiful Montpellier Codex, showing a motet attributed to Petrus (Pierre de la Croix). It has all three voices on it, and you can see clearly from the amount of space given to each that the triplum has more notes than the duplum and tenor combined. You might also notice, Franconian notation doesn't look all that different from square notation. That is about to change.
Circa 1320, witness the birth of a NEW ART! No, really. That's what composer Phillipe de Vitry called it, in his 1322 treatise Ars nova. I mean, he's not lying. The term was first used a couple of years earlier by Johannes de Muris, in his treatise Ars novae musicae, which was also important and influential. But de Muris was a scholar, not a composer, and he served 7 years in prison for helping to murder a guy. Consequently, he is now less famous. Sucks for him.
As I've alluded, the new technology of mensural notation ushered in a huge flourish of innovation in composition. Did the music being made drive the development of the notational technology, or did the new technology drive composition?
The answer is yes. Undoubtedly, the earliest mensural notation arose from an effort to write down what people were already singing, but the new capabilities of writing also drove composition practices, as we'll see. Music was now a written and therefore visual object, and this could affect its conception. I have to imagine that it was hugely novel and exciting at the time. If you're a musician, imagine the first time you encountered a score such as George Crumb's. Fun stuff!
But coming back to de Vitry, the developments of the Ars Nova were huge. They have been likened to the "discovery" of perspective in art. Vitry took Petrus's subdivisions and ran with it. Two major developments associated with Vitry are 1) the division of the semibreve into a smaller note value, called a minim, and 2) the division of a note into two equal subdivisions. 50/50, baby! Shatter that glass ceiling!
The introduction of a minim subdivision brought a new level that Vitry called prolatio. The division of a longa into breves is called the modus. As I said before, this can be perfect or imperfect. The division of a breve into semibreves is the tempus, and likewise, it is perfect or imperfect. For prolation, you usually say major or minor. Put in modern terms, the tempus is how many beats there are in a measure, and the prolation is how many subdivisions the beat gets. This chart will help you visualize the layers of subdivision. It demonstrates the four prolations.
Another fun thing that Vitry did was introduce the idea of colorization, where notes are written in red ink in order to indicate altered tempus or prolation. A division of 2 becomes a division of 3, and vice versa. So if you are in tempus perfectum and you see a series of red semibreves, you will treat them as being in tempus imperfectum. This causes hemiola (a 2 against 3 rhythmic texture). (5) After so much theoretical attention was given to mixed proportions, it's perhaps unsurprising that syncopation becomes a major character trait of 14th century music.
The first place where you can see Vitry's ideas at play is in the magnificent Roman de Fauvel (c.1316), which is both the earliest source of ars nova music and the so-called purest use of Vitry's notation.
The example to the right, from the Roman de Fauvel, showcases both Vitry's notation techniques and some of the many charming illuminations that appear in the manuscript. (It's seriously one of the best illuminated manuscripts of all time, so do yourself a favor and click on the link above to look through it. The link goes to a digitized version of the entire thing. I mean, why would you NOT take the opportunity to look through one of the rarest and most important books in history, in beautiful, high-resolution color, in the comfort of your own home? You don't even have to put on pants! In the old days, not only was flying to France the only way to see this book, you definitely could not look at it in your underwear while drinking a beer.)
I didn't immediately find a recording of the song to the right on YouTube, but you know what I did find? A video story time and manuscript singalong. This is a VHS that someone has digitized, of illuminations from the manuscript with a narrator and music and animated lyrics. And it is amazing. When you have 45 minutes, watch it.
In the very last piece of music to appear in the codex, you find red notes. If I'm not mistaken, they are the first and only place that red notes appear in the Roman de Fauvel, and here, they occur in the tenor. This piece is a motet that is attributed to Vitry himself, "Garrit Gallus/In nova fert/Neuma"
Let's have a look at a few technical aspects of the notation, so you can see this shiny new mensuration tech in action.
In the table of the 4 prolations above, the top line shows mensuration signs. Theses are the time signatures. They aren't yet in use, though, so you figure out the prolation by looking at the music. It's usually not terribly difficult to figure out, you just have to read through a little and see how things are grouped. I've marked the beats with a yellow line. As you can hear in the recording, this motet has a clear duple meter, so it's tempus imperfectum. In this instance, the breve gets the beat, and they are divided into two semibreves--something else you can hear well throughout--so that makes it minor prolation. (6)
So at a glance, you can see how randomly distributed the beats are, visually. This notation doesn't space things to scale. When there's a group of 4 semibreves (for example) in the space of 1 breve, these are functionally minims. They are not yet written differently, but in the decades immediately after, a stem was added to semibreves, to differentiate minims. You can see the stems in this Machaut song that was copied in the 1350s:
In the Vitry example, you can see puncta throughout both of the upper voices, where there are runs of semibreves, even when they're recta (unaltered, occurring normally according to the prolation). The puncta are not only for alteration, they generally keep groupings clear when context doesn't otherwise serve. In the example above, I bracketed in green a few areas where puncta indicate normal subdivision. Areas that are underlined with orange highlight some of the altered groupings.
So as you might gather, sight reading from this music requires a degree of foresight. You frequently have to look ahead to see how to sing the note you're on. It's a little clunky (this is still an early technology), but it's not really an obstacle. It's not as if there was no rehearsal in the 14th century, and the average singer probably learned his part by ear, anyway.
The Ars Subtilior
Last but not least, we come to the last few decades of the 14th century, where the century's notational developments culminate in a highly intricate, technical school of composition called the ars subtilior. The name ars subtilior comes from modern historians, but it is based on a comment made in a treatise of the time, that composers were moving away from the ars nova (typified by composers such as Machaut) and into a "more subtle" art. The courts of Avignon, during the Great Schism, were the main center of this school. The repertory consists almost exclusively of secular songs.
The music of this style employs a huge number of notational pyrotechnics. It is both difficult to read and difficult to perform. Some of the works can be written in a more straight-forward, simple fashion (and later copies in simpler notation exist, as some popular works spread), but where was the fun in that? This is music by connoisseurs, for connoisseurs. Composers clearly enjoyed the games that could be played on parchment. Some of these puzzles are undetectable in performance; you would only know about them if you had seen the manuscript. Other "tricks" are just cute visual gimmicks that don't affect the actual performance of the music. Two famous examples of this "eye music" are from Cordier. The page below is "Tout par compas," which is a canon. The song begins, "With a compass I was composed," and this is mimicked in circular writing. Between the manuscript, the lyrics, and the process of singing in canon, there is a whole web of references to circles, with this rondel.
You all know what canons are. Grab the person next to you to help you sing 'Row Your Boat" and there you have it. You have one short tune that you sing over and over, at staggered entrances, until all voices have sung it through. Hence, the circular motive in "Tout par compas." When you finish the line of music, you immediately go back to the beginning. This particular canon has a tenor, who sings his part over and over, and two upper voices who sing the top part in canon.
You can see at the beginning of the staff that we now have mensuration signs. Multiple signs are given on the top part, indicating the different mensuration in which each singer proceeds. There's nothing impressive about having the top voices sing exactly the same thing at different times, so Cordier has them move in two different proportional speeds. They eventually end, with the tenor, at the same time. That's impressive.
Such works are called, appropriately, mensuration canons. This will become important in the 15th century. But this all is still not enough dazzling mastery of mensuration for Cordier! If you follow around the outer circle, you'll see numerous changes of mensuration sign, in addition to the colorized notes, which alter the prolation in their own way. This creates an added layer of difficulty and variety in the way that the voices of the canon line up. As you can hear, there is a great deal of syncopation. The pulse is rarely regular and predictable. This is typical of ars subtilior music.
With this experimental age came additional developments in notation, but they were all building upon the work of Vitry and Muris. Mostly, what you get is greater diversity of subdivisions, which now have their own graphical note styles. Stems were added to semibreves to distinguish minims, and subdivisions of minims got little flags. Here's how our note values have progressed:
The notes are looking downright modern, aren't they? The only major change to come after this, in terms of actual note shape, was the development of barring groups of notes. This comes in the Baroque, along with the obsolescence of puncta and adoption of bar lines.
The Chantilly Codex is one of the most important sources for ars subtilior music. The Cordier example above is from it. Here is another example from Chantilly--one that you don't have to tilt your head to look at. (On the left, "Joieux de cuer en seumellant estoye." On the right, Fumeux fume par fumée.") You can see at a glance how much more complicated this work is, compared to what we've seen before. Listen to "Fumeux fume" here!
But wait...
Surprise Twist Ending
Note about the manuscript images: most of them will open as high resolution if you open them in a new tab. I've just realized that the built in Blogger viewer opens them to an arbitrary size that you can't zoom in.
As with part 1, the goal of this post is to give lay people a general idea of some of the historical developments in music. The books on this material probably are not very accessible to casual enthusiasts. If you read music and you're looking for more of an introduction to the technical nitty gritty of how to read mensural notation, the Wikipedia article is actually pretty solid. (2) That said, this post is going to get more technical than the last one. Things are about to get geeky. That's just the nature of 14th century music. It doesn't get geekier than the ars subtilior. That works for me, because I am a geek and my intended audience is geeks. But if you're just here for pretty manuscript photos, you'll get those, too.
Franconian notation
We left off in part 1 with Franconian notation, which is the earliest kind of mensural notation, or notation where the note shapes indicate duration. It was used for early sacred polyphony. Today we'll start off with some general technical overview of what mensural notation is. There is no getting around this. Mensural notation was used from c.1300 to c.1600. It is a proportional system, whereas modern notation is a fixed value system. (In the Middle Ages, music was a science, a form of mathematics. The true musician wasn't the performer, but the learned composer. And medieval theorists were aaaaall about numbers and ratios. See Boethius for more information.)
What does it mean that mensural notation isn't a fixed value system? Mensural notation is defined by divisions into 2s or 3s, and conceived by ratios of 2:1 and 3:2. These divisions and ratios aren't totally clear from the notes themselves; they require a time signature or other devices to indicate it. This is what really makes it distinct from modern notation.
The division of a note value into threes or twos is called perfection or imperfection, respectively. This is how time signatures (mensuration signs) are established: different combinations of perfections and imperfections. I will cover this in more detail when I get to mensuration signs. For now, just remember the pyramid of divisions into twos and threes.
In Franco's system, note values ranged from double-longa (the longest, nach) to semibrevis. Any of these notes could be divided into 2 or 3, but they were still tied to the rhythms of the old modes (see part 1), which each had a triple meter. So, if you divided a note of Franconian notation into two, the two notes are not of equal value; one is longer than the other. It's a 66/33 split, not 50/50.
New developments came quickly at the beginning of the 14th century. Petrus de Cruce--who might have been Franco's student (3)--popularized some major new additions. He is most famous for freely dividing the breve into as many as 7 semibreves, which brought with it the development of the punctum divisionis--literally just a dot on the staff, usually placed next to a note head. Music of this time has no bar lines, so the punctum became a way to show metrical groupings of notes. If 4 semibreves occur between two puncta, then it's understood that these 4 semibreves take the time of 1 breve. This means they are sung faster, relative to semibreves in standard groupings, but it also had the effect of slowing down the pulse. Music that is characterized by willy-nilly subdivision of the breve is called Petronian, after Petrus. In Petronian music, you tend to get a lively upper voice with slower, duller accompanying parts.
This example of two motets (4) from the anthology Music of the Middle Ages (David Fenwick Wilson) beautifully showcases the difference between the Franconian and Petronian styles. The video includes the music in modern notation, so you can follow along if you read music.
In the Franconian example, the eighth note is the semibreve. You can hear how fast they are. In the Petronian example, you'll immediately notice that it's slower, and the top voice has sixteenth notes. Those sixteenth notes are also semibreves. They were not distinguished with a different note value in the original notation. If you don't read music, you can still see, and hear, the different level of activity in the voices. Although the top voice (the triplum) has the tune in the Franconian example, it has some lively exchanges with the duplum. The Petronian one, though, has a noticeably less active duplum.
The Ars Nova
Petronian music is a tiny niche in the history of music, but the "willy-nilly breve subdivision" (stop me if I get too technical) is an important stepping stone to what comes next, so that's why we're taking a little time for it.
Circa 1320, witness the birth of a NEW ART! No, really. That's what composer Phillipe de Vitry called it, in his 1322 treatise Ars nova. I mean, he's not lying. The term was first used a couple of years earlier by Johannes de Muris, in his treatise Ars novae musicae, which was also important and influential. But de Muris was a scholar, not a composer, and he served 7 years in prison for helping to murder a guy. Consequently, he is now less famous. Sucks for him.
As I've alluded, the new technology of mensural notation ushered in a huge flourish of innovation in composition. Did the music being made drive the development of the notational technology, or did the new technology drive composition?
The answer is yes. Undoubtedly, the earliest mensural notation arose from an effort to write down what people were already singing, but the new capabilities of writing also drove composition practices, as we'll see. Music was now a written and therefore visual object, and this could affect its conception. I have to imagine that it was hugely novel and exciting at the time. If you're a musician, imagine the first time you encountered a score such as George Crumb's. Fun stuff!
But coming back to de Vitry, the developments of the Ars Nova were huge. They have been likened to the "discovery" of perspective in art. Vitry took Petrus's subdivisions and ran with it. Two major developments associated with Vitry are 1) the division of the semibreve into a smaller note value, called a minim, and 2) the division of a note into two equal subdivisions. 50/50, baby! Shatter that glass ceiling!
The introduction of a minim subdivision brought a new level that Vitry called prolatio. The division of a longa into breves is called the modus. As I said before, this can be perfect or imperfect. The division of a breve into semibreves is the tempus, and likewise, it is perfect or imperfect. For prolation, you usually say major or minor. Put in modern terms, the tempus is how many beats there are in a measure, and the prolation is how many subdivisions the beat gets. This chart will help you visualize the layers of subdivision. It demonstrates the four prolations.
 |
| Chart made by a user on Quora |
Another fun thing that Vitry did was introduce the idea of colorization, where notes are written in red ink in order to indicate altered tempus or prolation. A division of 2 becomes a division of 3, and vice versa. So if you are in tempus perfectum and you see a series of red semibreves, you will treat them as being in tempus imperfectum. This causes hemiola (a 2 against 3 rhythmic texture). (5) After so much theoretical attention was given to mixed proportions, it's perhaps unsurprising that syncopation becomes a major character trait of 14th century music.
The first place where you can see Vitry's ideas at play is in the magnificent Roman de Fauvel (c.1316), which is both the earliest source of ars nova music and the so-called purest use of Vitry's notation.
The example to the right, from the Roman de Fauvel, showcases both Vitry's notation techniques and some of the many charming illuminations that appear in the manuscript. (It's seriously one of the best illuminated manuscripts of all time, so do yourself a favor and click on the link above to look through it. The link goes to a digitized version of the entire thing. I mean, why would you NOT take the opportunity to look through one of the rarest and most important books in history, in beautiful, high-resolution color, in the comfort of your own home? You don't even have to put on pants! In the old days, not only was flying to France the only way to see this book, you definitely could not look at it in your underwear while drinking a beer.)I didn't immediately find a recording of the song to the right on YouTube, but you know what I did find? A video story time and manuscript singalong. This is a VHS that someone has digitized, of illuminations from the manuscript with a narrator and music and animated lyrics. And it is amazing. When you have 45 minutes, watch it.
In the very last piece of music to appear in the codex, you find red notes. If I'm not mistaken, they are the first and only place that red notes appear in the Roman de Fauvel, and here, they occur in the tenor. This piece is a motet that is attributed to Vitry himself, "Garrit Gallus/In nova fert/Neuma"
Let's have a look at a few technical aspects of the notation, so you can see this shiny new mensuration tech in action.
So at a glance, you can see how randomly distributed the beats are, visually. This notation doesn't space things to scale. When there's a group of 4 semibreves (for example) in the space of 1 breve, these are functionally minims. They are not yet written differently, but in the decades immediately after, a stem was added to semibreves, to differentiate minims. You can see the stems in this Machaut song that was copied in the 1350s:
In the Vitry example, you can see puncta throughout both of the upper voices, where there are runs of semibreves, even when they're recta (unaltered, occurring normally according to the prolation). The puncta are not only for alteration, they generally keep groupings clear when context doesn't otherwise serve. In the example above, I bracketed in green a few areas where puncta indicate normal subdivision. Areas that are underlined with orange highlight some of the altered groupings.So as you might gather, sight reading from this music requires a degree of foresight. You frequently have to look ahead to see how to sing the note you're on. It's a little clunky (this is still an early technology), but it's not really an obstacle. It's not as if there was no rehearsal in the 14th century, and the average singer probably learned his part by ear, anyway.
The Ars Subtilior
Last but not least, we come to the last few decades of the 14th century, where the century's notational developments culminate in a highly intricate, technical school of composition called the ars subtilior. The name ars subtilior comes from modern historians, but it is based on a comment made in a treatise of the time, that composers were moving away from the ars nova (typified by composers such as Machaut) and into a "more subtle" art. The courts of Avignon, during the Great Schism, were the main center of this school. The repertory consists almost exclusively of secular songs.
The music of this style employs a huge number of notational pyrotechnics. It is both difficult to read and difficult to perform. Some of the works can be written in a more straight-forward, simple fashion (and later copies in simpler notation exist, as some popular works spread), but where was the fun in that? This is music by connoisseurs, for connoisseurs. Composers clearly enjoyed the games that could be played on parchment. Some of these puzzles are undetectable in performance; you would only know about them if you had seen the manuscript. Other "tricks" are just cute visual gimmicks that don't affect the actual performance of the music. Two famous examples of this "eye music" are from Cordier. The page below is "Tout par compas," which is a canon. The song begins, "With a compass I was composed," and this is mimicked in circular writing. Between the manuscript, the lyrics, and the process of singing in canon, there is a whole web of references to circles, with this rondel.
You can see at the beginning of the staff that we now have mensuration signs. Multiple signs are given on the top part, indicating the different mensuration in which each singer proceeds. There's nothing impressive about having the top voices sing exactly the same thing at different times, so Cordier has them move in two different proportional speeds. They eventually end, with the tenor, at the same time. That's impressive.
Such works are called, appropriately, mensuration canons. This will become important in the 15th century. But this all is still not enough dazzling mastery of mensuration for Cordier! If you follow around the outer circle, you'll see numerous changes of mensuration sign, in addition to the colorized notes, which alter the prolation in their own way. This creates an added layer of difficulty and variety in the way that the voices of the canon line up. As you can hear, there is a great deal of syncopation. The pulse is rarely regular and predictable. This is typical of ars subtilior music.
With this experimental age came additional developments in notation, but they were all building upon the work of Vitry and Muris. Mostly, what you get is greater diversity of subdivisions, which now have their own graphical note styles. Stems were added to semibreves to distinguish minims, and subdivisions of minims got little flags. Here's how our note values have progressed:
The notes are looking downright modern, aren't they? The only major change to come after this, in terms of actual note shape, was the development of barring groups of notes. This comes in the Baroque, along with the obsolescence of puncta and adoption of bar lines.
The Chantilly Codex is one of the most important sources for ars subtilior music. The Cordier example above is from it. Here is another example from Chantilly--one that you don't have to tilt your head to look at. (On the left, "Joieux de cuer en seumellant estoye." On the right, Fumeux fume par fumée.") You can see at a glance how much more complicated this work is, compared to what we've seen before. Listen to "Fumeux fume" here!
But wait...
Surprise Twist Ending
Did it occur to you throughout this discussion that we were only talking about French people? Well, we were. You know why? Because the Italians developed their own, separate mensuration system that has completely different terminology. YAY
All manuscript photos from BnF's Gallica, except Codex Chantilly, which is at Musée Condé.
A couple of years before Vitry, Marchetto da Padova wrote his Pomerium in arte musice mensurate. Marchetto is actually in agreement with Vitry and Muris on most points. When I say the Italian system is separate, it isn't a wholly unique system. Clearly, the ideas were in contact. But there are some important differences. I'm only going to go into one, just as a bit of trivia.
A big conceptual difference is that in Italian mensuration, a perfection can never equal an imperfection in time. Because how can a perfect thing and an imperfect thing be the same? Duh-doy! (The French heretic pigs, with their Antipope, clearly thought differently.)
This might sound like a tiny difference, but it can make a huge impact in performing. Under the French system, if you have perfect tempus against imperfect, the breves are equivalent. Beats will be the same length. That's what allows hemiola. But if you're dealing with Italian music from the mid-14th century, this won't be true. Theoretically, the imperfect breve should be 1/3 shorter.
This is more of a theoretical point than a practical one, but occasionally you get multiple simultaneous mensurations that can raise some sticky issues in performance. How do you work out the correct proportions? There is rarely a consensus.
By the end of the century, French notation had infiltrated Italy, and the two systems more or less merged into one. So going forward, the system followed French rules, with a few things absorbed from the Italians.
- As long as this post is, you should know that I have grossly oversimplified almost everything in it.
- For an introduction to a different type of musical nitty gritty, check this out.
- He was certainly Franco's student in that he followed Franco's ideas, but he might have literally studied under Franco at the University of Paris.
- A motet is a sacred work outside of the standard liturgy. They're typically based on Latin cantus firmi (existing chants that are used as the harmonic basis of a new work, in the tenor voice). One of their defining features is the use of multiple texts--each voice gets its own text, which is a unique trait. In extreme cases, you might hear 3-4 languages sung at once.
- Listen to this kid clap, for a demonstration of what hemiola is.
- I don't know how much of this diagram is of interest, since many of my readers probably don't have grounds for comparison, but hey. It seemed like a thing to do.
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