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Chantill Codex.

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Newberry Source. G. de Anglia, Collection of Medieval Musical Treatises, ca. 1391.

Calculating Music in the Middle Ages

Ask an early music scholar about the most visually interesting music score he or she can think of, and odds are good you’ll be directed to the love song Belle, bonne, sage (Beautiful, Good, Wise)

Ask an early music scholar about the most visually interesting music score he or she can think of, and odds are good you’ll be directed to the love song Belle, bonne, sage (Beautiful, Good, Wise) or the canon Tout par compas suy composés (With a compass was I composed). Written by the French composer Baude Cordier (ca. 1380–1440) and copied into a manuscript known as the Chantilly Codex, their forms are appealingly self-referential: the love song takes the shape of a heart, and the imitative Tout par compas flaunts its circularity. “You see,” announces your hypothetical musicological interlocutor triumphantly, pointing at George Crumb's Makrokosmos: “ It has all been done before.”

Dubious pronouncements aside, Cordier’s chansons are justifiably famous examples of a medieval musical style sometimes known as the “more refined art” (ars subtilior). The subtlety of this music lies not in the graphic scores (their symbolism is hardly concealed, after all), but rather in the complexity of the notation. [Warning: Do not sight-read this unattended!].

Composers like Cordier reveled in taking characteristic properties of their musical notation to the extreme. This bears some explaining. In the musical "For these medieval musicians, as for their twenty-first century counterparts, such calculated music was delightful—both visually and sonically." notation commonly used today, duration is intrinsic to the note shape (a quarter note is a quarter note is a quarter note). In medieval notation, however, rhythmic durations were contextually determined. Singing pieces in the Chantilly Codex was thus in part an act of computation. A singer encountering the red notes in Tous par compas, for example, would have known to alter the values in comparison to the surrounding black notes, resulting in a brief shift in meter.

As a canon, Tout par compas features an added layer of notational complexity. Well into the seventeenth century, composers displayed their erudition by constructing such musical canons: rather than notating a second voice, a composer or scribe might explain how to derive it from a notated voice following a given rule, or “canon.” (A simple example: “wait four beats, and then enter with the same tune, at the unison”).

My own favorite graphic score is a canon, too—not about love or nicely constructed circles, but about music itself. “The Harp of Melody” (La harpe de Melodie), by Jacob de Senleches (active around the same time as Cordier), survives in two forms. In the Chantilly Codex, it is copied conventionally, unremarkable in the face of Cordier’s flashy hearts and circles. In a collection of music theoretical writings now held in Chicago’s Newberry Library, however, Senleches’s piece stands out: rather than being notated on a conventional musical staff, two voices (a higher voice and a lower voice, or tenor) are written onto the strings of a densely strung harp. Guitar players might note the resemblance of this unique, ad hoc notation to guitar tabs.

The sharp-eyed observer might further note that the piece is for three rather than two voices. Deriving the third voice requires some calculating: an act of computation, following the poem inscribed on the banner that winds around the harp's front post:

"If you would perform me properly,
You should begin with a fifth above the tenor
to be in better accord,
or otherwise you will be in discord.
Let the black and white notes sound by half,
without forgetting, or you will do them wrong."

(Translation: Richard Hoppin)

For these medieval musicians, as for their twenty-first century counterparts, such calculated music was delightful—both visually and sonically. To borrow from the refrain of Senleche's song: "The harp of melody, made without melancholy for pleasure, should greatly delight everyone, to hear, sound, and see its harmony."

Note: The author gratefully notes that these manuscripts are preserved by the librarians and conservators at Chantilly’s Musée Condé and Chicago’s Newberry Library, respectively. These are the Image sources for Chantilly Codex and for the Newberry Source

Erika Honisch
Calculating Music in the Middle Ages
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