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Criteria for recognizing mensuration

With the evolution of notation in the first decades of the 14th century, four combinations of tempus and prolatio were introduced, attributed to Vitry as the quatre prolacions. The relationships between the note values came to be termed mensurations. A new problem arose: the question of detecting in which mensuration a piece is composed. In order to recognise the mensuration of a piece, the Ars Nova treatises suggested an easily understandable system of signs:

Listing of the four mensuration signs

However, in the most manuscripts from the 14th century these signs are not yet in use. The systematic utilization of mensural signs began only in the 15th century. Often it is only possible to recognise the mensuration by identifying certain groupings of notes, rests or the use of dots.

Here you can find the most important criteria which will help you to recognise in which mensura a composition is meant to be.

1. First you have to look at the relation between the notes. This method helps to make a first estimation, but does not provide a sure result. If between two equal notes three notes of a lower value occur, the mensural relation will probably be perfect:

Notational signs showing the perfect and major relation

If only two consecutive notes occur between two notes of a higher value, this can be a hint for an imperfect relation:

Notational signs showing the imperfect and minor relation

(Watch out because this combination also exists in a perfect tempus or prolatio maior, in which case an alteration of the third note will be necessary).

If you find a series of notes that alternate between a longer and the next shorter value, the mensural relationship can be ternary. But be careful, this combination can be ambiguous:

Notational signs showing the perfect and major relation

2. A second criterion is to look at the dots. Here it is important to find out if we are dealing with a punctum divisionis or a punctum additionis. A punctum divisionis will give us the assurance that it is a ternary tempus or prolatio:

Notational signs showing a punctum divisionis© Madrid, Real Biblioteca del Monasterio, V.III.24, [Escorial A], fol. 38r

A punctum additionis, on the other hand, indicates a binary mensural relation:

Notational signs showing a punctum additionis© Madrid, Real Biblioteca del Monasterio, V.III.24, [Escorial A], fol. 37r

It is always important to look at the context. By doing so, it will be possible to confirm the correct mensuration. The assumption, for example, that the following dot is a punctum additionis can be verified easily:

Square notation and two different transcriptions

As you can see in the first transcription, we can exclude the possibility that it is a punctum divisionis because that would imply a tempus perfectum and a note value (a minima) would not correspond to the total amount of perfect units. On the other hand, there are no missing notes for a punctum additionis; it is, therefore, plausible that the passage is in tempus imperfectum with prolatio maior.

3. Third, you should take a look at the rests. This is the most certain way to determinate the mensuration. Two consecutive rests indicate that the mensuration is maior. Two minim rests, for example, indicate a prolatio maior, a semibrevis rest followed by a single semibrevis indicate a tempus imperfectum:

Notational signs on parchment© London, British Library, Add. 41667 (I), fol. 26r

Finally, we can sum it up as follows:

The tempus perfectum can be indicated by:

  • two consecutive semibrevis rests on the same line
  • groupings of three semibreves
  • the alternation of brevis and semibrevis
  • a brevis and semibrevis followed by a dot (punctum divisionis)

The tempus imperfectum can be indicated by:

  • a single semibrevis rest followed by a semibrevis
  • groupings of two semibreves
  • a dotted brevis followed by a semibrevis (punctum augmentationis)

The prolatio maior can be indicated by:

  • two consecutive minima rests on the same line
  • groupings of three minimae
  • the alternation of semibrevis and minima
  • a semibrevis and minima followed by a dot (punctum divisionis)

The prolatio minor can be indicated by:

  • a single minima rest followed by a minima
  • groupings of two minimae
  • a dotted semibrevis followed by a minima (punctum additionis)

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This article is from the free online course:

From Ink to Sound: Decoding Musical Manuscripts

University of Basel