colonies. In America, despite long pressure to convert to the decimal metric system, introduced as an
“enlightened” by-product of the French Revolution, we still divide feet into twelve inches and pounds
into sixteen ounces. (In Britain itself, the monetary system remained duodecimal until the 1970s, with
twelve pence to the shilling, and 240 pence (12 × 20) to the pound.) Both “inch” and “ounce” are
traceable to the Latin word uncia, which stood for the basic unit of duodecimal measurement, whether of
weight, length, or money. The uncia was the equivalent, in those areas, of the basic unit of musical
measurement, the tempus.
The standard Roman symbol for the uncia—on abacuses used for monetary transactions, for example
—was the circle, and the symbol for one-half of an uncia (called the semuncia), logically enough, was the
semicircle. It is hardly a coincidence, then, that the circle and semicircle were adopted as symbols for the
division of the tempus (breves into semibreves) in Ars Nova notation, thus becoming the first standard
time signatures used in Western music. The circle stood for tempus perfectum—i.e., the “whole” or
“perfect” breve containing three semibreves—and the semicircle stood, correspondingly, for tempus
imperfectum, with two semibreves to a breve.
The signs for major and minor prolation were adapted from the theory of chronaca, in which the
shortest unit of time—sometimes called the atomus, sometimes the momentum, and sometimes, yes, the
minima—was compared with the geometric point (punctum), defined by Euclid as that which cannot be
subdivided. (“A point,” Euclid wrote in his Elements, “is that which has no part.”) The minimal time-unit
was sometimes actually called the punctum, which is undoubtedly why the point, or dot, became the
symbol for the musical minima and its mensuration. The major prolation, in which there were three
minims to a semibreve, was at first indicated by placing three dots inside the circle or semicircle that
represented the breve. The minor prolation was specified by a pair of dots.
Later on scribes figured out that they could save some ink by subtracting two dots from this scheme.
Major prolation could just as well be indicated by a single dot, minor prolation by the absence of a dot.
So by the end of the fourteenth century, the four tempus-cum-prolation combinations or meters listed
above were represented by four standard time signatures: . The last of them, the one that
represented mensuration by two at all levels, still survives (as the sign for “common time”). In the light of
the foregoing discussion, it should be obvious that explaining the “C” for meter as the initial of the
expression “common time” is a folk-etymology. Its actual derivation was from medieval minutiae and
chronaca, and its survival depended on its “imperfection.” The main difference between modern notation
and mensural notation is that although we certainly have our modern ways of indicating triple meter,the
whole ancient idea of triple or “perfect” mensuration has been shed.
The table in Fig. 8-2 sums up the relationships specified by the mensural notation that was first
employed by the Parisian musicians who promulgated the “Ars Nova” in the early fourteenth century, and
these relationships remained the basis for musical notation in Europe almost to the end of the sixteenth
century.