French composer Baude Cordier was born around 1380 in the city of Reims and died before 1440. Two of his manuscripts that are part of the Chantilly Codex are often cited as examples of ars subtilior.
This manuscript has a high aesthetic quality. The unusual way the music is written is related to the meaning of the text and methods of translating rhythmic complexity and compositional techniques into musical notation.
On the left page Belle, bonne, sage - Beautiful, Good, Wise - a love song in the shape of a heart.
On the right page Tout par compas suy composé, an infinite, perpetual or circular canon in the shape of a circle.
The main voice of Belle, bonne, sage is written in the top part of the heart:
The two other voices appear at the bottom of the page:
The two voices that form the canon Tout par compas suy compose - With a compass was I composed - are written in the outer circle. A third voice is written in the inner circle:
We must rotate the score to read it...
We do not pretend to explain in this article how to transcribe these manuscripts. We will only try to shed some light on how contemporary notation relates to mensural notation using Belle, bonne et sage as an example.
According to Wikipedia mensural notation "is the musical notation system used for European vocal polyphonic music from the later part of the 13th century until about 1600".
Around 1280, Franco de Cologne describes note values in his book Ars Cantus Mensurabilis (Richard Rastall, The Notation of Western Music, 1982, p. 47):
By the time of Cordier, smaller notes values were already in use:
Willi Apel in his book The Notation of Polyphonic Music (p. 96) points to the difficulty in determining the relationship between different note values:
"In modern notation this relation is always duple i.e., a given note, unless dotted, is always equal to two of the next smaller species. In mensural notation, however, an undotted note may be either duple or triple i.e., equal to two or three smaller notes, depending upon the mensuration of the piece and the value of the neighbouring notes. A ternary note is called perfect; a binary, imperfect."
This means that:
|An imperfect breve equals 2 semibreves:
|A perfect breve equals 3 semibreves:
|An imperfect semibreve equals 2 minimas:
|A perfect semibreve equals 3 minimas:
As Apel points out, a note is perfect or imperfect "depending upon the mensuration of the piece and the value of the neighbouring notes".
In 1319 the mathematician, astronomer, astrologer and music theorist Johannes de Muris in his book Ars Novae Musica describes three levels of mensuration (Rastall, p. 69):
Phillipe de Vitry proposed symbols (quatre prolacions) to indicate the mensuration of the breve (tempus) and the semibreve (prolatio) (Rastall, p. 70):
A circle - symbol of perfection - means ternary breve with binary semibreve:
Tempus perfectum, prolatio imperfecta
Add a dot inside the circle for ternary semibreve:
Tempus perfectum, prolatio perfecta
An incomplete or imperfect circle means binary breve and semibreve:
Tempus imperfectum, prolatio imperfecta
Add a dot for ternary semibreve:
Tempus imperfectum, prolatio perfecta
Apel suggest in his book (p. 98) the following modern time signatures for each of the mensurations:
Unfortunately, these symbols were not adopted immediately.
Mensural notation uses symbols called ligatures, a heritage from the old pneumatic notation. Each of these symbols represent two or more notes. It is not until the sixteenth century that they begin to fall into disuse. Some examples of ligatures are shown using blue rectangles:
Finally, bar lines and ties are not yet used.
We must begin by identifying the clef. Cordier uses the C clef over the second line (indicated by the blue rectangle) to write the main voice:
The C clef is followed by two vertical lines occupying two spaces on the staff. These lines are two maxima rests. Each maxima equals 2 longas (if the lines were 3 spaces long, each maxima would equal 3 longas). In this transcription, the longa is one measure long, so the 2 maxima rests are 4 measures long.
No mensuration sign is specified.
Maxima rests are followed by 2 semibreve rests (the two small vertical lines). A D semibreve completes the measure:
We find our first ligature (see Apel, p. 87 - 94 for more information about ligatures). The line begins on D and extends to C. Therefore, we have a D followed by a C. A semibreve (B) completes the measure:
A breve followed by 2 minimas and a second ligature (G - D) and 2 minimas complete the next two measures:
Cordier now uses red notes. Apel explains the use of color:
"The term coloration (color) first occurs in the fourteenth century to designate the use of red notes for certain variations from the normal values which, at that time, were written as black notes...." A red note "loses one-third of its value" (p. 126).
The passage can be transcribed using eighth notes triplets. There is a minima rest (small slash) before the last two notes:
We finally find a mensuration sign. Apel relates this sign to the modern 6/8 time signature (binary measure of ternary subdivision).
According to Apel (p. 425) "the introduction of prolatio perfecta adds three-fold augmentation, with the minima equalling the semibreve..."
For ease of reading, we can continue using the 3/4 time signature (both time signatures have 6 eighth notes):
A ligature followed by minima, semibreve and minima are written using white notes. According to Apel (p. 425) the "white notes ... indicate diminutio dupla within the augmentation of the prolatio perfecta."
In other words, in the transcription each bar now has only 2 quarter notes instead of 3. The solution of our notation system is somewhat clumsy (quarter notes duplets in a 3/4 time signature):
"The figure 3 produces here the same effect that it has in the modern writing of triplets: three notes of the triplet-group equal two ordinary notes of the same kind" (Apel p. 159). White notes bring us back to binary subdivision:
"The sign ⦵ ... indicates (or confirms) the return to normal tempus perfectum" (Apel p. 425). The semibreve is now our time unit.
The red notes now indicate the use of hemiola (quarter notes of the two measures are grouped 2 - 2 - 2 instead of 3 - 3:
The figure 3 reappears, this time followed by a 8 over an 9.
"The sign 8/9 indicates that the subsequent eight notes are equal to the nine notes of the preceding passage" (Apel p. 426).
In other words, we must now play 8 eighth notes in the same time as the preceding 9 eighth notes. Modern notation offers no easy solution:
After this short tour of the complex world of mensural notation, let's listen to Cordier's music...
Belle, bonne, sage recording by Ensemble Fortuna