5Repertoire: Mensural Notation

This chapter describes the module for encoding mensural notation from the late 13th century to about 1600. Historically, mensural notation preceded the development of Common Music Notation (CMN) and it included a wide range of features that persist in CMN and that can be encoded in a standard manner in MEI. In mensural notation, pitches are notated as in CMN, leaving out here the major exception of musica ficta. The pitch is given by the position of the note on the staff and the current clef as in CMN, and the mensural module introduces no modification to MEI regarding how pitches are encoded.

There are a certain number of differences, however, regarding the representation of duration in mensural notation. The mensural module introduces specific attribute values for notes and rests for appropriately encoding mensural durations. One of the main particularities is that the actual duration of a note is not given only by its symbol but also by position and the context in which the symbol appears. The general context is given by one of the 16 mensural species provide four levels of division: modus major, modus minor, tempus and prolatio. Depending on the context, certain rules must be applied in order to determine the duration of a note. In these cases, encoding both the sign and its actual duration is highy desirable.

Another particularity of mensural notation is the use of proportions that are indicated by numeric proportions or by specific mensuration signs. The proportions indicate that the durations have to be modified accordingly and they can be combined in a very complex manner. Over time, proportions and mensuration signs were simplified and became time signatures in CMN. The attributes and elements that are necessary for encoding proportions and mensural signs are made available by the module.

In mensural notation, notes can also be notated in ligatures that regroup two or more notes. Ligatures were a legacy from an earlier notation system that were still widely used in Renaissance music notation. They gradually disappeared during the seventeenth century. The mensural module provides multiple ways of encoding the ligatures.

5.1Durations

When the mensural module is included, dur on note, rest, and other elements takes the following values (from the Latin names of notes):

maxima: Two or three times as long as a longa

longa: Two or three times as long as a brevis

brevis: Two or three times as long as a semibrevis

semibrevis: Half or one-third as long as a brevis

minima: Half or one-third as long as a semibrevis

semiminima: Half as long as a minima

fusa: Half as long as a semiminima

semifusa: Half as long as a fusa

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Notes and Rests</title>
</titleStmt>
<pubStmt>
<date>2020-03-02</date>
</pubStmt>
<notesStmt>
<annot>The upper staff shows the different mensural note shapes and the lower staff shows the different mensural rests.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="notes" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2"/>
<staffDef n="2" label="rests" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="maxima"/>
<note dur="longa"/>
<note dur="brevis"/>
<note dur="semibrevis"/>
<note dur="minima"/>
<note dur="semiminima"/>
<note dur="fusa"/>
<note dur="semifusa"/>
</layer>
</staff>
<staff n="2">
<layer>
<rest dur="maxima"/>
<rest dur="longa"/>
<rest dur="brevis"/>
<rest dur="semibrevis"/>
<rest dur="minima"/>
<rest dur="semiminima"/>
<rest dur="fusa"/>
<rest dur="semifusa"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 207.

Normally, longa rests are vertical strokes occupying two or three spaces in the staff, depending on the mensuration. For instance, in modusminor=3, they take up three spaces; and in modusminor=2, they take two. However, there are situations where both types of longa rests can be present in the same piece, regardless of the modus minor. For this reason, the dur attribute can take on two other values when used within rest elements:

2B: Two-breve rest

3B: Three-breve rest

The example below illustrates this case in a passage in perfect modus from the triplum voice of a motet in the Roman de Fauvel music manuscript. The blue arrows on the image are pointing to the two-breve and three-breve rests in this passage.

Figure 52. Inflammatis invidia / Sicut de ligno / Victimae paschali detail from F-Pn 146, fol. 22r (https://gallica.bnf.fr/ark:/12148/btv1b8454675g/f55.image).

<!--With @modusminor equal to "3" in the <staffDef> element-->
<layer n="1">
<!--First system in the image-->
<!-- ... -->
<rest dur="2B"/>
<ligature>
<note dur="semibrevis" oct="4" pname="d"/>
<note dur="semibrevis" oct="4" pname="c"/>
</ligature>
<ligature>
<note dur="semibrevis" oct="4" pname="d"/>
<note dur="semibrevis" oct="4" pname="e"/>
</ligature>
<ligature>
<note dur="semibrevis" oct="4" pname="d"/>
<note dur="semibrevis" oct="3" pname="a"/>
</ligature>
<note dur="longa" oct="3" pname="b"/>
<dot form="div"/>
<ligature>
<note dur="semibrevis" oct="4" pname="c"/>
<note dur="semibrevis" oct="4" pname="d"/>
</ligature>
<ligature>
<note dur="semibrevis" oct="4" pname="c"/>
<note dur="semibrevis" oct="3" pname="b"/>
</ligature>
<ligature>
<note dur="semibrevis" oct="3" pname="a"/>
<note dur="semibrevis" oct="3" pname="g"/>
</ligature>
<note dur="longa" oct="3" pname="a"/>
<note dur="semibrevis" oct="4" pname="d"/>
<note dur="semibrevis" oct="4" pname="e"/>
<!--Next system in the image-->
<note dur="longa" oct="4" pname="f"/>
<note dur="brevis" oct="4" pname="e"/>
<dot form="div"/>
<note dur="brevis" oct="4" pname="d"/>
<ligature>
<note dur="semibrevis" oct="4" pname="c"/>
<note dur="semibrevis" oct="3" pname="b"/>
</ligature>
<ligature>
<note dur="semibrevis" oct="4" pname="c"/>
<note dur="semibrevis" oct="4" pname="d"/>
</ligature>
<note dur="longa" oct="4" pname="e"/>
<rest dur="3B"/>
<!-- ... -->
</layer>
Listing 208.

5.1.1Alteration and Imperfection

In ternary mensurations, the ambiguity between the note shape and its actual duration requires specific attention. The rules of mensural notation can require the alteration or the imperfection of a note; that is, an increase or reduction in its performed duration. In these cases, if the encoding is intended to be used for more than just graphically representing the notation, encoding only the note shape by means of the dur attribute alone is insufficient. In that case, in addition to encoding the duration sign in the dur attribute, it is recommended to encode its performed duration in the dur.quality attribute. The dur.quality attribute specifies the length of a note according to the contextual rules of mensural notation. Its values, listed below, are adopted from the original Latin terms:

perfecta: Three times the duration of the note in the next smaller degree

imperfecta: Two times the duration of the note in the next smaller degree

altera: Twice the original duration of the note (only usable in perfect mensurations)

minor: Category of a regular semibrevis in Ars antiqua, equivalent to a third of a brevis

maior: Category of an altered semibrevis in Ars antiqua, equivalent to two minor semibrevis

duplex: One of the three categories of a longa in Ars antiqua ('duplex', 'perfecta', and 'imperfecta')

The last three values are to be used exclusively in Ars antiqua mensural notation, where "maior" and "minor" refer to types of semibreves, and "duplex" refers to a type of longa. Examples of each of these six values are presented below. In these examples, the ‘voice’ staff renders the notes in the code snippet, and the ‘reference’ staff, together with the dotted barlines, are shown to help to visualize the relative values of the notes in the ‘voice’ staff.

The following example illustrates an alteration (the second brevis) in modus minor perfectus. Notice that the second brevis has doubled its regular value, it has been altered, unlike the first one.

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of 'alteration'</title>
</titleStmt>
<pubStmt>
<date>2019-11-15</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" dur.quality="perfecta"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis" dur.quality="altera"/>
<barLine form="dashed"/>
<note dur="longa" dur.quality="perfecta"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 209.

It is possible to omit the dur.quality attribute in a note when the performed duration of the note is the default value provided by the mensuration. In this case, the longas are perfect, just as the mensuration (perfect modus minor) indicates. Therefore, the dur.quality attribute can be omitted for the two longas.

<!--With @modusminor equal to "3" in the <staffDef> element-->
<layer>
<note dur="longa"/>
<note dur="brevis"/>
<note dur="brevis" dur.quality="altera"/>
<note dur="longa"/>
</layer>
Listing 210.
The same applies to the examples that follow.

The following example illustrates an imperfection (the two longae) in modus minor perfectus with the same longa-brevis-brevis-longa sequence but with an additional dot of division between the two breves. Notice that here the longae have been imperfected, unlike the previous example in which they kept the perfect value indicated by the mensuration.

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of 'imperfection' and 'dot of division'</title>
</titleStmt>
<pubStmt>
<date>2019-11-15</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" dur.quality="imperfecta"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<dot form="div"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="longa" dur.quality="imperfecta"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 211.

The following example in modus minor imperfectus illustrates the use of a dot of augmentation following the longa. Notice that the longa, which is supposed to be imperfect according to the mensuration, has a perfect value due to the augmentation dot.

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of 'augmentation'</title>
</titleStmt>
<pubStmt>
<date>2019-11-15</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="2"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="2"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" dur.quality="perfecta"/>
<dot form="aug"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="brevis" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 212.

Finally, the following example illustrates the dur.quality values related to the Ars antiqua style, for perfect modus, with the breve equivalents notated in the lower staff for reference (as in the previous examples).

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of 'imperfection' and 'dot of division'</title>
</titleStmt>
<pubStmt>
<date>2019-11-15</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.black" lines="5" clef.shape="G" clef.line="2" modusminor="3" tempus="3"/>
<staffDef n="2" label="reference" notationtype="mensural.black" lines="5" clef.shape="G" clef.line="2" modusminor="3" tempus="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" dur.quality="perfecta"/>
<barLine form="dashed"/>
<note dur="semibrevis" dur.quality="minor"/>
<note dur="semibrevis" dur.quality="minor"/>
<note dur="semibrevis" dur.quality="minor"/>
<dot form="div"/>
<barLine form="dashed"/>
<note dur="semibrevis" dur.quality="minor"/>
<note dur="semibrevis" dur.quality="maior"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="longa" dur.quality="duplex"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="brevis"/>
<note dur="brevis"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<note dur="brevis"/>
<note dur="brevis"/>
<barLine form="dashed"/>
<note dur="brevis"/>
<note dur="brevis"/>
<note dur="brevis"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 213.

Note: In Ars Antiqua, only the longa could be "perfecta" / "imperfecta" and the brevis could have a regular value ("recta") or be "altera". In the Ars nova, principles of imperfection and alteration were extended into the other note levels (brevis-semibrevis and semibrevis-minima). This means that the breves in Ars antiqua do not have a "perfecta" / "imperfecta" quality, and this is why there is no dur.quality attribute for the breves in the previous example. However, the brevis can have a ternary division (indicated by tempus=”3”), being divided either into three (equal) minor semibreves or into a minor-maior pair of semibreves. The encoding also allows for the possibility of encoding a binary division of the breve in Ars antiqua notations: the indication tempus=”2” indicates the breve is divided into two equal semibreves. This is why in this example with tempus="3", the semibreves do have a dur.quality attribute (with values "minor" or "maior").

An alternative encoding---removing the dur.quality attributes for notes which lengths are not modified from their default values (i.e., the perfect long and the minor semibreves)---would be:

<!--With @modusminor and @tempus equal to "3" in the <staffDef> element-->
<layer>
<note dur="longa"/>
<note dur="semibrevis"/>
<note dur="semibrevis"/>
<note dur="semibrevis"/>
<dot form="div"/>
<note dur="semibrevis"/>
<note dur="semibrevis" dur.quality="maior"/>
<note dur="brevis"/>
<note dur="longa" dur.quality="duplex"/>
</layer>
Listing 214.

The conjunct use of the dur and dur.quality attributes is generally enough to encode the duration of a note—and, as indicated before, one could even remove dur.quality when its value is in agreement with the mensuration. However, there are cases (e.g., partial imperfection) where the values of dur.quality are not enough to provide the note's duration.

5.1.2Partial Imperfection

In opposition to regular imperfection, which is caused by a note of the next smaller degree (e.g., a perfect brevis imperfected by a following/preceding semibrevis), partial imperfection is caused by a note of two or even three orders apart. As an example, consider an imperfect longa made up of two perfect breves. This longa can be "partially imperfected" by a following/preceding semibrevis. This semibrevis causes part of the longa—one of its perfect breves—to be imperfected, taking away one-third of one of its two halves. In this case, the longa's value changes from 6 semibreves (two perfect breves) into 5 semibreves. Partial imperfection is not supported by the dur.quality attribute—because there can be many cases of partial imperfection, as will be seen in the following examples. To encode a partial imperfection, the num and numbase pair of attributes are used instead. Given the change in the longa's value from 6 semibreves to 5 semibreves, the corresponding attributes to encode this particular case of partial imperfection would be num="6" and numbase="5" as shown below in the code snippet and its rendering.

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of "partial imperfection of an immediate part" (ad partem propinquam)</title>
</titleStmt>
<pubStmt>
<date>2020-03-03</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" num="6" numbase="5"/>
<barLine form="dotted"/>
<note dur="semibrevis"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 215.

Partial imperfection can also happen from both sides of a note at once, as shown below:

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of "partial imperfection" from both sides (ad partes)</title>
</titleStmt>
<pubStmt>
<date>2020-03-03</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="semibrevis"/>
<barLine form="dotted"/>
<note dur="longa" num="6" numbase="4"/>
<barLine form="dotted"/>
<note dur="semibrevis"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<note dur="semibrevis" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 216.

An example of partial imperfection caused by a note three orders apart is given next. Here the longa is partially imperfected by a minima (instead of by a semibrevis).

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of "partial imperfection of a remote part" (ad partem remotam)</title>
</titleStmt>
<pubStmt>
<date>2020-03-03</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted and dashed barlines, is used here to help visualizing the durational values of the notes in the upper staff. Dotted barlines in the bottom staff show the minim groups equivalent to a semibreve, and the dashed barlines show the groups of semibreves equivalent to a breve.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="2" prolatio="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="2" tempus="2" prolatio="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" num="12" numbase="11"/>
<barLine form="dotted"/>
<note dur="minima"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dotted"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dotted"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 217.

In the next example, the longa is also imperfected by a minima. However, the num and numbase ratio is different from the example above because the default value of the longa here (18 minimas) is different from that of the previous example (12 minimas).

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of "partial imperfection of a remote part" (ad partem remotam)</title>
</titleStmt>
<pubStmt>
<date>2020-03-03</date>
</pubStmt>
<notesStmt>
<annot>The bottom staff, together with the dotted barlines, is used here to help visualizing the durational values of the notes in the upper staff. Dotted barlines in the bottom staff show the minim groups equivalent to a semibreve, and the dashed barlines show the groups of semibreves equivalent to a breve.</annot>
</notesStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" label="voice" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3" tempus="2" prolatio="3"/>
<staffDef n="2" label="reference" notationtype="mensural.white" lines="5" clef.shape="G" clef.line="2" modusminor="3" tempus="2" prolatio="3"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note dur="longa" num="18" numbase="17"/>
<barLine form="dotted"/>
<note dur="minima"/>
<barLine form="dashed"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dotted"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dotted"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dashed"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dotted"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<note dur="minima" pname="a" oct="4"/>
<barLine form="dashed"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 218.

5.2Mensuration

Using the mensural module, mensuration signs can be indicated with the attributes available on the scoreDef and staffDef elements. Mensuration signs encoded using attributes on scoreDef are regarded as default values which may be overridden by values attached to individual staffDef elements.

The division levels corresponding to modus maior, modus minor, tempus, and prolatio can be encoded in the modusmaior, modusminor, tempus, and prolatio attributes respectively. Their value must be 3 (perfect) or 2 (imperfect).

@
modusmaior (att.mensural.shared)
Describes the maxima-long relationship.
@
modusminor (att.mensural.shared)
Describes the long-breve relationship.
@
Describes the breve-semibreve relationship.
@
Describes the semibreve-minim relationship.

The mensur signs themselves can be encoded in the mensur.sign attribute with a possible value of "C" or "O". Its orientation can be encoded in the mensur.orient attribute, for example, with the value "reversed" for a flipped C sign. The number of slashes (up to 6) can be given in the mensur.slash attribute. There is also a mensur.dot attribute for indicating the presence of a dot through the boolean values "true" or "false".

@
mensur.sign (att.mensural.vis)
The base symbol in the mensuration sign/time signature of mensural notation.
@
mensur.dot (att.mensural.vis)
Determines if a dot is to be added to the base symbol.
@
mensur.slash (att.mensural.vis)
Indicates the number lines added to the mensuration sign. For example, one slash is added for what we now call 'alla breve'.
@
mensur.orient (att.mensural.vis)
Describes the rotation or reflection of the base symbol.

mensur elements can also be used instead of staffDef and its attributes. In mensur, the division levels are encoded with the previously mentioned modusmaior, modusminor, tempus, and prolatio attributes, while the attributes to indicate the mensur signs are: sign, orient, slash, and dot. mensur can be a child of the staffDef and layer elements.

(mensuration) – Collects information about the metrical relationship between a note value and the next smaller value; that is, either triple or duple.

@
modusmaior (att.mensural.shared)
Describes the maxima-long relationship.
@
modusminor (att.mensural.shared)
Describes the long-breve relationship.
@
Describes the breve-semibreve relationship.
@
Describes the semibreve-minim relationship.

@
The base symbol in the mensuration sign/time signature of mensural notation.
@
Specifies whether a dot is to be added to the base symbol.
@
orient (att.mensur.vis)
Describes the rotation or reflection of the base symbol.
@
Indicates the number of slashes present.

5.2.1Change in mensuration

The following example illustrates a change in mensuration. In this case, the element mensur is used within the layer element, preceding the stream of notes affected by the new mensuration defined by it.

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title>Example of 'mensuration changes'</title>
</titleStmt>
<pubStmt>
<date>2020-03-03</date>
</pubStmt>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef>
<staffGrp>
<staffDef n="1" notationtype="mensural" lines="5" clef.shape="G" clef.line="2" mensur.sign="O" mensur.dot="true" mensur.slash="1" mensur.color="red"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note/>
<note/>
<note/>
<mensur loc="3" sign="C"/>
<note/>
<note/>
<note/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 219.

5.2.2Implicit mensuration

It is common in Ars antiqua and some Ars nova pieces to have no mensuration signs. In this case, the mensuration—the division levels corresponding to modus maior, modus minor, tempus, and prolatio—is given by the context. The next example shows the incipit of a four-voice piece, Josquin's Tu solus qui facis mirabilia, where only two of the voices (Cantus and Tenor) have a mensuration sign. The other two (Altus and Bassus) have no mensuration signs, and the mensura is given by the context. Therefore, while only the Cantus and the Tenor have attributes for encoding the mensuration sign (in this case, mensur.sign and mensur.slash), all four voices include attributes to encode the mensura (tempus and prolatio).

<mei meiversion="4.0.1">
<meiHead meiversion="4.0.1">
<fileDesc>
<titleStmt>
<title> Example of omitted mensuration signs </title>
</titleStmt>
<pubStmt/>
<notesStmt>
<annot>In this choir book, only the verso parts have a mensuration sign, whereas Altus and Bassus on the recto don't.</annot>
</notesStmt>
<sourceDesc>
<source>
<bibl>FlorPanc27, 79v-80r</bibl>
</source>
</sourceDesc>
</fileDesc>
</meiHead>
<music meiversion="4.0.1">
<body>
<mdiv>
<score>
<scoreDef key.sig="1f">
<staffGrp>
<staffDef n="1" label="Cantus" lines="5" notationtype="mensural.white" clef.shape="C" clef.line="1" tempus="2" prolatio="2" mensur.sign="C" mensur.slash="1"/>
<staffDef n="2" label="Tenor" lines="5" notationtype="mensural.white" clef.shape="C" clef.line="4" tempus="2" prolatio="2" mensur.sign="C" mensur.slash="1"/>
<staffDef n="3" label="Altus" lines="5" notationtype="mensural.white" clef.shape="C" clef.line="3" tempus="2" prolatio="2"/>
<staffDef n="4" label="Bassus" lines="5" notationtype="mensural.white" clef.shape="F" clef.line="4" tempus="2" prolatio="2"/>
</staffGrp>
</scoreDef>
<section>
<staff n="1">
<layer>
<note pname="b" oct="4" dur="brevis"/>
<note pname="b" oct="4" dur="brevis"/>
<note pname="a" oct="4" dur="brevis"/>
<note pname="g" oct="4" dur="brevis"/>
<note pname="g" oct="4" dur="semibrevis"/>
<note pname="g" oct="4" dur="semibrevis"/>
</layer>
</staff>
<staff n="2">
<layer>
<note pname="g" oct="3" dur="brevis"/>
<note pname="b" oct="3" dur="brevis"/>
<note pname="c" oct="4" dur="brevis"/>
<note pname="c" oct="4" dur="brevis"/>
<note pname="c" oct="4" dur="semibrevis"/>
<note pname="c" oct="4" dur="semibrevis"/>
</layer>
</staff>
<staff n="3">
<layer>
<note pname="d" oct="4" dur="brevis"/>
<note pname="d" oct="4" dur="brevis"/>
<note pname="f" oct="4" dur="brevis"/>
<note pname="e" oct="4" dur="brevis"/>
<note pname="e" oct="4" dur="semibrevis"/>
<note pname="e" oct="4" dur="semibrevis"/>
</layer>
</staff>
<staff n="4">
<layer>
<note pname="g" oct="2" dur="brevis"/>
<note pname="g" oct="3" dur="brevis"/>
<note pname="g" oct="3" dur="brevis"/>
<note pname="c" oct="3" dur="brevis"/>
<note pname="c" oct="3" dur="semibrevis"/>
<note pname="c" oct="3" dur="semibrevis"/>
</layer>
</staff>
</section>
</score>
</mdiv>
</body>
</music>
</mei>
Listing 220.

5.2.3Italian Divisiones

The division of the breve in Italian trecento notation can be encoded using the divisio attribute, which provides the values: ternaria, quaternaria, senariaimperf, senariaperf, octonaria, novenaria, duodenaria. The divisio attribute would usually replace the use of the tempus and prolatio set of attributes.

@
Describes the divisions of the breve in use in 14th-century Italy.

The signs for the Italian divisiones can be encoded in the sign or mensur.sign attribute (to be used with mensur or staffDef respectively), with the values: "t" for ternaria, "q" for quaternaria, "si" and "i" for senaria imperfecta, "sp" and "p" for senaria perfecta, "oc" for octonaria, "n" for novenaria, and "d" for duodenaria. And the additional values for senaria gallica, "sg" and "g", and senaria ytalica, "sy" and "y".

5.3Proportions

Proportions can also be indicated within the staffDef element. The proport.num and proport.numbase attributes are available for encoding the numerator and the denominator of the proportion, respectively. There is also a proport element that can be used as an alternative, with the corresponding num and numbase attributes.

(proportion) – Description of note duration as arithmetic ratio.

5.4Ligatures

Ligatures can be encoded using the ligature element. The form attribute is available for specifying if the ligature is recta or obliqua.

Figure 53. Recta and obliqua ligatures
<layer>
<ligature form="recta">
<note dur="semibrevis" oct="4" pname="d"/>
<note dur="semibrevis" oct="3" pname="g"/>
</ligature>
<ligature form="obliqua">
<note dur="semibrevis" oct="3" pname="g"/>
<note dur="semibrevis" oct="4" pname="c"/>
</ligature>
</layer>
Listing 221.

In cases where the ligature contains both recta and obliqua notes, the lig attribute of the note element can be used to specify the form of the ligature at the note level.

Figure 54. Ligature with more than two notes with recta and obliqua
<ligature form="recta">
<note dur="longa" oct="3" pname="a"/>
<note dur="longa" oct="4" pname="e"/>
<note dur="semibrevis" lig="obliqua" oct="4" pname="d"/>
<note dur="semibrevis" lig="obliqua" oct="4" pname="c"/>
<note dur="brevis" oct="3" pname="b"/>
<note dur="brevis" oct="4" pname="e"/>
</ligature>
Listing 222.

5.5Music Data Organization

The data organization based on measure elements that usually prevails in MEI is not appropriate for mensural notation because most music until 1600 does not have measures (bars) as we understand them today. Even though it is not defined by the mensural module, a more suitable alternate data organization without measures is available: staff elements may occur directly within the section element without being organized into measures first. The organization of events (notes, rests, etc.) within the staff and layer elements remains unchanged.

<section>
<staff n="1">
<layer>
<note dur="longa" oct="5" pname="c"/>
<note dur="brevis" oct="4" pname="g"/>
<note dur="brevis" oct="4" pname="e"/>
</layer>
</staff>
<staff n="2">
<layer>
<note dur="maxima" oct="3" pname="c"/>
</layer>
</staff>
</section>
Listing 223.

This feature may also be used to encode measured music without using the measure element. That is, the same data organization described above may be used, but with the addition of barlines, indicated by the barLine element, for those situations where a measure-by-measure organization is not appropriate, for example, when measures are not coincident in all the staves of a score.

5.6Other Features

Other features included in the MEI schema that allow for the encoding of various mensural notation properties are presented below:

5.6.1Notation Type

The notationtype attribute, part of the MEI module, can be used within the staffDef element to specify which dialect of mensural notation is in use.

@
notationtype (att.notationType)
Contains classification of the notation contained or described by the element bearing this attribute.

At the moment, three values are in use for mensural notation:

mensural: For mensural notation in general

mensural.black: For black mensural notation, this is in reference to the use of filled-in note heads

mensural.white: For white mensural notation, this is in reference to the use of void note heads, which became most widely used in the Renaissance period

The values of the notationtype attribute can indicate notation types other than mensural, such as common (Western) music notation, neume notation, and tablature.

The attribute notationsubtype can be used, together with the notationtype attribute, to provide more specificity regarding the type of notation encoded. This attribute can be used, for example, to specify if a piece in black mensural notation (notationtype=mensural.black) is written in Ars antiqua or Ars nova style. Currently, the values allowed in the notationsubtype attribute consist of any sequence of characters provided by the user.

@
notationsubtype (att.notationType)
Provides any sub-classification of the notation contained or described by the element, additional to that given by its notationtype attribute.

Important: An element with a notationsubtype attribute must have a notationtype attribute.

5.6.2Stems

The characteristics of a note's stem can be encoded within the note element, using the attributes:

@
stem.dir (att.stems)
Describes the direction of a stem.
@
stem.len (att.stems)
Encodes the stem length.
@
stem.pos (att.stems)
Records the position of the stem in relation to the note head(s).
@
stem.x (att.stems)
Records the output x coordinate of the stem's attachment point.
@
stem.y (att.stems)
Records the output y coordinate of the stem's attachment point.
@
stem.form (att.stems.mensural)
Records the form of the stem.

PLACE-HOLDER FOR EXAMPLE OF ONE NOTE WITH ONE STEM: IMAGE & ITS ENCODING

Sometimes notes have two stems. In this case, the stem element can be used as a child of note to define the individual characteristics of each stem with the following attributes:

A stem element.

@
Describes the direction of a stem.
@
form (att.stem.vis)
Encodes the form of the stem using the values provided by the data.STEMFORM.mensural datatype.
@
Encodes the stem length.
@
Records the position of the stem in relation to the note head(s).
@
flag.form (att.stem.vis)
Encodes the form of the flag using the values provided by the data.FLAGFORM.mensural datatype.
@
flag.pos (att.stem.vis)
Records the position of the flag using the values provided by the data.FLAGPOS.mensural datatype.
@
x (att.xy)
Encodes an x coordinate for a feature in an output coordinate system. When it is necessary to record the placement of a feature in a facsimile image, use the facs attribute.
@
y (att.xy)
Encodes a y coordinate for a feature in an output coordinate system. When it is necessary to record the placement of a feature in a facsimile image, use the facs attribute.

PLACE-HOLDER FOR EXAMPLE OF A NOTE WITH TWO STEMS: IMAGE & ITS ENCODING

5.6.3Plicas

Plicas can be encoded using the plica element as a child of note. The direction of the plica, as well as its length, can be encoded using the following visual-domain attributes:

Plica

@
Describes the direction of a stem.
@
Encodes the stem length.