Ktismatics

30 January 2007

Musica Universalis (Crosby continued)

Filed under: Culture, Ktismata, Language — ktismatics @ 9:22 am

The classical Greeks thought of music as a kind of mathematics. A medieval scholar who had mastered the trivium – grammar, logic, and rhetoric – moved on to the quadrivium – arithmetic, geometry, music, and astronomy. Arithmetic is pure number, geometry is number in space, music is number in time, astronomy is number in space and time. But music, says Crosby, was the only one of the four members of the quadrivium in which measurement had immediate practical application.

Medieval European music was not quantified sound. Gregorian chant had no “beat”: its rhythms conformed to the flow of the Latin text and the spirit of the liturgy. The pitch generally went up and down at agreed-upon places, but there was no uniformity of practice as to precise intervals. Music was performed from memory, which became quite challenging as the number of chants began to increase. No one wrote the music down, because no one had yet invented an adequate system of musical notation.

The musical staff, developed in the 11th century, was Europe’s first graph: The x-axis measures time from left to right; the y-axis measures pitch. The intervals of the scale were standardized around an old and familiar hymn of the time:

Ut queant laxis Resonare fibris
Mira gestorum Famuli tuorum
Sove polluti Labii reatum
Sancte Iohannes

If you knew the melody, then you knew the standard pitch intervals and their names: ut, re, mi, fa, so, la, si.

Chants were sung solo or in unison: there were no harmony parts. The mid-9th century witnessed the introduction of a high harmony on top of the traditional melody. Eventually the traditional chant part was reduced to a low drone, freeing the soprano to embellish. By the end of the 12th century Leonin and Perotin, the first masters of this new polyphonic music, were actually composing new tunes in addition to adapting the traditional songs.

The works of Leonin and Perotin were equivalent in innovation to the Gothic cathedrals. It is probable that they were first performed in one of the most magnificent of these cathedrals, Notre Dame de Paris. As Western music moved from Gregorian simplicity to polyphonic complexity, it also moved from the cloister and countryside to the cathedral and the city, that is to say, into the realm of the university and marketplace. From the 12th to the 14th century Paris was the center for the development of Western polyphony, as for so much else.

Popular music began finding its way into the sacred chant harmonies. Virtuosos became famous. And the Schoolmen at the University applied themselves to music: its structure and logic, the proportionalities of pitch and meter, its genres and subgenres, its logic and grammar. The annotation for a “rest” as the absence of sound was introduced around the same time as the number zero began circulating in the West. Standardized proportional time units (whole notes, half notes, quarters, eighths, etc.) were added to the musical staff, making it possible for performers to play more metrically complex harmonies. Musical time became an abstract measuring stick into which the composer could insert notes like variables in an equation. Rather than restricting musical expression, annotation set it free. Ensembles could play innovative and complex pieces without sounding like noise. Musical innovation became the norm rather than the exception. 12th century Paris experienced the kind of artistic explosion we usually associate with the Italian Renaissance.

Musical annotation — the visual representation of sound — converged on its modern standardized form at least fifty years before the invention of the mechanical clock. Did the invention of modern music and what Crosby calls its faith in absolute time influence the modern Western worldview? Galileo, Descartes, Kepler and Huyghens were trained musicians; all of them wrote about music.

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