Meaning of basic mensuration signs

[craigsapp]

This thread presents the core mensuration signs that deal only with the number of divisions that each rhythmic level is divided into in order to create the next shorter rhythmic level (another thread should present proportions that can modify these basic mensuration signs). The following chart list these basic mensuration signs along with their meanings (how many shorter notes are need to create a note of the next longer level):

This table is from the second edition (1771) of Thomas Morley's Plain and Easy Introduction to Practical Music (p. 17)

Click to view links to online scans of cited work.

https://s9.imslp.org/files/imglnks/usimg/6/6f/IMSLP03933-Morley.pdf
https://imslp.org/wiki/A_Plain_and_Easy_Introduction_to_Practical_Music_(Morley%2C_Thomas)

Color scan (more readable) from the University of North Texas:
https://digital.library.unt.edu/ark:/67531/metadc86/m1/40

First edition from 1597:
https://s9.imslp.org/files/imglnks/usimg/b/bc/IMSLP160042-PMLP09691-morley_1597.pdf
(see IMSLP for other higher-resolutions of the first edition).

The mensuration signs are listed at the bottom of the table (highlighted in yellow). The numbers above each mensuration sign are the number of divisions that each level is subdivided into in order to get to the next shorter rhythmic level. Here is a diagram showing how the long is divided into smaller note values in circle mensuration:

(ibid., p. 16)

Reading upwards in the table, the number of divisions for each level in Circle mensuration are 2, 2, 3, 2. This means that the maxima is divided into two longs (Latin: longa), the long is divided into two breves, the breve is divided into 3 semibreves, and the semibreve is divided into 2 minims. These four levels, indicated on the right side of the table, are called (in Latin) @modusmaior, @modusminor, @tempus and @prolatio. According to Morley, the English name for modus major is maximodus, modus minor is just modus, tempus is tempo (but not good to use since this is not the modern concept of tempo), and prolatio is prolation.

The left side of the table gives the note@dur value that describes each rhythmic level. It is important to understand that the mensural use of note@dur is not exactly the same as in CMN. In CMN this value is more absolute (with the exception of augmentation dots or tuplet modifications); however, in mensural music this duration value can be "perfected" (normally 2 time units changes to 3; i.e., performance duration increased by 50%), or "imperfected" (normally 3 time units changed to 2 units; performance duration decreased by 33%), or "altered" (normally 1 time unit changed to 2; performance duration increased by 100%).

Notice that there are two groups of mensuration signs in the table. This grouping is related to which two rhythmic levels that the mensuration signs describe. For the first four signs, the @modusminor and @tempus levels are explicitly indicated (numbers highlighted in red):

The C/O of the mensuration indicates the @modusminor level, which is the number of breves that are equivalent to a long. C means there are two breves for each long, or equivalently C means the modus minor is imperfect. O means that there are three breves for each long, meaning the modus minor is perfect.

The number following C/O gives the number of divisions at the tempus levels (number semibreves that a breve splits into). 2 means imperfect tempus, and 3 means perfect tempus.

The other rhythmic levels of @modusmaior and @prolatio are not explicitly given by these four mensuration signs. The default divisions for these mensuration signs are given in the table, but perhaps you would need to look at the music to see what perfect/imperfect state should be for these levels. The @prolatio should probably always be imperfect for the first four mensuration signs in the table. Groupings of long rests into twos or threes will be a clue to the @modusmaior perfection.

The four mensuration signs on the right side of the table describe the divisions at the @tempus and prolatio levels (numbers highlighted in red):

The C/O symbols describe the @tempus divisions, while the dot or lack of dot inside the main symbol indicates the @prolatio divisions. A dot mean there are three minims for each semibreve, while lack of a dot means two minims for each semibreve. Also note that the C and O symbols are systematic representations of the numbers 2 and 3. The circle represents the "perfect" 3, while the C represents an "imperfect" 2. Think of the C as being two-thirds of a circle, with one of the units missing from the three that represent a full circle.

The shortest rhythm in the table is the minim (analogous to the half note in CMN). Rhythm divisions for notes shorter than minims are always 2 and never 3 (i.e., always imperfect) in all mensurations. The minim is divided into two semiminims (looks like a quarter note of modern notation), the semiminim is divided into two fusa (looks like an eighth note iof modern notation), and the fusa is divided into two semifusa (looks like a sixteenth note of modern notation). Here are the list of these rhythmic levels used for note@dur in MEI mensural music: https://music-encoding.org/guidelines/v4/data-types/data.duration.mensural.html

[craigsapp]

Not central to the basic meanings discussed above, but here is a discussion of the main difference between the four signs on each side of the table in the previous post:

The main obvious difference is which two levels the mensuration signs describe. Related to this is what the "beat" or "tactus" of the mensuration is. For the first four mensuration signs, the beat is at the breve level, while in the last four it is at the semibreve level. Notice that the C3 and O mensurations both have the same level divisions of 2,2,3,2, so the only difference is what level the beat is at, similar to the bottom number in modern time signatures, or the difference between common time and cut time in modern music (although these two are more closely related to mensural music proportions).

The first four signs are generally found in older music (say roughly early 15th century), and later music (roughly later 15th century and 16th century) tend to use the last four mensuration signs. This is part of a general trend towards using shorter rhythmic levels, which continues to modern music, that typically has the beat on the quarter note level which is analogous to the semiminim level of mensural music.

An exception to this general timeline is that masses from the latter half of the 15th century often notate the tenor part in one of the first four mensuration signs (because the tenor is often a quotation of an earlier melody written in that mensuration sign), while the other parts use one of the four mensuration signs on the right. In such cases there is almost always an additional proportion (time scaling) between the tenor and other parts, which is not notated within the mensuration sign itself, but typically described in a textual note above the mensuration sign.

It is also useful to note that the numbers after the main sign for the first four mensuration signs are not related to proportions. And to make things confusing, there is a different interpretation of C3 where the 3 is referring to a proportion modification at the semibreve or minim level. (This should be discussed further in a thread about mensuration sign proportions).

When converting the two groups into CMN, the Josquin Research Project sets the modern "measure" to the breve. For the first four mensuration signs, the music notated in a hypermeter style, where the long divisions are notated with solid barlines and the breve divisions are notated as dotted barlines. As an example, here is a CMN transcription of Josquin motet "Preter rerum seriem":

https://josquin.stanford.edu/cgi-bin/jrp?a=notationEditText&f=Jos2411

For O2, the divisions are 2, 3, 2, 2 (with O meaning @modusminor="3" and 2 meaning @tempus="2"). Notice that there is a solid barline every three measure which is the long cycle, and there are two dashed barlines between the solid ones, since there are three breves for each long in O2 mensuration. Also notice that the imitation between the bottom two voices is three measures apart, which represents a long, which is probably related to the mensuration sign describing divisions of the long/breve. Also in this case the beat is probably not really at the breve level, perhaps because this composition is from the latter half of the 15th century when the four mensuration signs on the left side of the table are less common.

[craigsapp]

The above description of mensural signs is the dominant system used for mensural music, at least in the fifteenth through early seventeenth centuries. There are earlier alternate systems in the fourteenth century that allows for more than two or three subdivisions for each rhythmic levels. Perhaps someone familiar with these alternate systems can describe them in this thread.