Proportional notation

What it means

One speaks of proportional notation when, within mensural notation, numerical indications fix a changed ratio of the note values to the preceding section. Such an indication does not say how fast to play but in what ratio the values from now on stand to the previous ones: at a ratio of two to one, the same signs run twice as fast, at three to two one and a half times as fast.

In the notation

Proportions are indicated by numbers or pairs of numbers after the mensuration sign, occasionally also by a stroke through the mensuration sign. The designations of the ratios are formed in Latin and name the numerical relation. The basic measure to which everything relates is the tactus — the constant beat unit by which the performers orient themselves. Precisely herein lies the idea of the system: the tactus stays, the values change their ratio to it.

Musical use

This procedure was widespread in the polyphony of the fourteenth to sixteenth centuries, especially in movements built on a given cantus firmus. One voice could present the given melody in a changed proportion — diminished or augmented — while the other voices continued at the accustomed measure. This made it possible to construct artful relations between the voices that were both audible and recognizable in the notation as a riddle; some sources even deliberately encode the instruction.

From this system comes today's sign for cut time, the crossed-out half circle, and with it the idea that a stroke doubles the tempo.

The proportions of mensural notation were indicated with numbers such as 3 or 3/2.

Performance practice

When making music from modern transcriptions, rely on the editor's decisions and read up on how they resolved the proportions — here readings diverge, and the choice changes the character of a whole section. In ensemble, fix the tactus together before changing a proportion; the transition succeeds only if everyone has the same reference unit in mind.