Mensural Proportions and the Tactus

Proportion signs and the tactus put tempo on the page, turning the beat into a written grid.

Related

RenaissanceMedievalTime SignatureTempo

Once note shapes showed relative length, a piece still needed a base speed. Medieval theorists made that speed calculable with proportion signs and the tactus, and the beat acquired a basis on the page.

Time and place

From the thirteenth to the sixteenth century, in Paris, the Low Countries and Italy. Franco of Cologne organised mensural notation in the late thirteenth century, Philippe de Vitry's Ars nova added new note values in the 1320s, and manuscripts and printed books of the fifteenth and sixteenth centuries carry a variety of proportion signs. The dates are scattered and cannot be reduced to one year.

What happened

Mensural notation used note shapes for relative length, but relative length still needed a reference. Theorists called the beat the tactus, usually compared to a human pulse. Time was graded in two levels, perfect or imperfect and major or minor, marked by combinations of O and C with dots. Proportion signs, written as 3, 2 or as fractions, told singers that a new section moved twice or one and a half times as fast as the last; triple proportion often carried a Trinitarian meaning. A singer had to read note shapes, proportions and time signs at once to work out each note's real duration, so tempo was calculated rather than negotiated.

What changed

Tempo became a parameter that could be written down instead of a habit of performance. A composer could make sections of one Mass speed up or slow down in exact ratios, which strengthened large-scale shape. The price was complicated notation, and modern editors must translate the ratios into 4/4, 6/8 and metronome numbers, a choice that directly fixes the speed you hear. The idea of the bar line grew from the same ground: the beat moved from the hand to a grid on paper.

Listen for the turn

Begin with Machaut's Mass of Our Lady, where sections use different proportions and the pace of similar melodic writing shifts with them. Then Ockeghem's Fors seulement, three voices aligned by the tactus, each note sinking in the slow passages. Finally Josquin's Missa L'homme arme, whose sections switch between two and three, the sudden widening or narrowing that proportion signs produce. A modern tempo is the choice of an editor and a conductor, not the single answer the manuscript gives.

Related

This turn belongs to Renaissance and follows Medieval; see Time Signature and Tempo.

Sources

• Grove Music Online, entry Mensuration — signs and proportions checked, not quoted
• Anna Maria Busse Berger, Medieval Music and the Art of Memory (University of California Press) — transmission context checked, not quoted

Used for fact-checking only; all prose is original.