Mensuration

What it means

Mensuration designates the ratio in which the note values of mensural notation stand to one another. Unlike today, where every value always divides into two smaller ones, a note in this system can comprise two or three smaller ones. Which of the two applies is specifically indicated — separately for several levels of the value hierarchy. The twofold division is called imperfect, the threefold perfect; the latter counted as the more perfect one.

In the notation

Mensuration is indicated by a sign at the beginning of a piece or section: a full circle for the threefold, a half circle for the twofold division of the higher level, with or without a dot in the middle, which indicates the division of the next-lower level. From the half circle the modern sign for common time developed, from the crossed half circle the sign for cut time. Numbers beside the sign refer to proportions, that is, to a changed speed ratio to what preceded.

Musical use

The system allows a flexibility that modern bar organization does not know: different voices can stand simultaneously under different mensurations, and a change in the middle of a piece alters the rhythmic structure without a barline being necessary. Barlines do not exist in these sources at all — the organization arises from the values and from the text. With the establishment of the consistently twofold division and the barline in the seventeenth century, mensuration lost its function.

The term is to be distinguished from today's time signature, which fixes only a counting order, and — in a quite different context — from the mensuration in instrument-making, where the word designates an instrument's scale dimensions.

Performance practice

Before reading a source, clarify which mensuration sign applies and what it means for the individual value levels; without this the note values are ambiguous. For study, use a modern transcription, but let the critical report tell you which decisions the editor made — at mensuration changes, readings diverge.