Guillaume de Machaut, The Boethian Poems: Music Glossary
NOTE SHAPES AND VALUES
[Musical notation coming soon] Minima (pl. minimae): Officially the smallest rhythmical unit available in this style. It is transcribed into the modern eighth-note (but note that in some contexts, the medieval notational rules require it to be realized as a quarter note in modern transcription).
[Musical notation coming soon] Semibrevis (pl. semibreves): The next rhythmic level up from the from the minima, and (in the newer, Ars nova notational style) the most likely candidate for the counted ‘beat.’ The relationship between semibreves and minimae (i.e., how many of the latter fit into the former) is called prolatio (or the modernized ‘prolation’) and can be either maior (major, that is, three minimae per semibrevis) or minor (that is two minimae per semibrevis). It is, therefore, transcribed into either a quarter note or a dotted quarter note depending on the prolatio and local context (but note that in some cases the medieval notational rules require it to be realized as a half note or even dotted half note in modern transcription).
[Musical notation coming soon] Brevis (pl. breves): The next rhythmic level up from the semibrevis. The relationship between breves and semibreves (i.e., how many of the latter fit into the former) is called tempus (or the modernized ‘time’) and can be either perfectum (perfect, that is, three semibreves per brevis) or imperfectum (that is, two semibrevis per brevis). As a result, a standalone brevis can contain four, six, or nine minimae. Other context-based notational rules enable its realization to encompass also five, seven, or eight minimae, making its value in modern transcription rather unstable (but not shorter than a half note). In the Ars nova notational style (applicable here to the last four musical interpolations), the brevis is the prime organizational unit, causing a full brevis to be transcribed as the measure unit (without implying the stressing patterns inherited in many modern barrings). In the mode archaic notational style of the first three songs (Ars Antiqua), the measure unit is larger than the brevis, and it becomes the most likely counted ‘beat.’
[Musical notation coming soon] Longa (pl. longae): The next rhythmic level up from the brevis. The relationship between longae and breves (i.e., how many of the latter fit into the former) is called modus (or the modernized ‘mode’), and like the tempus, it can be either perfect or imperfect. As with the other units, it can comprise either two or three breves, and like the brevis, its realization possibilities are numerous. In pieces using the Ars Antiqua notational style, this level has been taken to represent the measure.
Triplum: Within the song repertoire, this is a secondary (or tertiary), textless counterpoint voice to the structural duo, which operates within the same range or above the cantus.
Cantus: Within the song repertoire, this is the main text- and melody-carrying voice whose cadences usually define also the main harmonic goals of the work.
Contratenor: Within the song repertoire, this is a secondary (or tertiary), textless counterpoint voice to the structural duo, which operates within the same range as the tenor. In this period their functions are non-interchangeable. In a fifth-octave perfect sonority, for example, the contratenor cannot fulfill the tenor role and hold the fundament of the chord while the tenor and the cantus sound the remaining upper fourth.
Tenor: Within the song repertoire, this is the primary, textless, counterpoint to the cantus, forming a structural duo that is harmonically self-sufficient and functional even when other voices are stripped away from a larger setting. It usually operates in a range a fifth lower than the texted cantus.
Fa-sign: The precursor to the modern flat sign, but with a different theoretical justification. Its meaning is not as straightforward as its modern counterpart, with both the duration of its effect and its potential effects on notes other than the one it is appended to remaining open to interpretation. On rare occasions and when used to cancel the operation of another sign, it can represent a modern natural sign.
Mi-sign: The precursor to the modern sharp sign, but with a different theoretical justification. Its meaning is not as straightforward as its modern counterpart, with both the duration of its effect and its potential effects on notes other than the one it is appended to remaining open to interpretation. When placed in front of the notes B or E, or when used to cancel out a fa-sign, it can also represent the modern natural sign.
Formal section: A musical-poetic structural unit smaller than a strophe. It usually involves a musical repetition matching patterning in the rhyme scheme, or section marked out by their exclusion from such practices. The Chanson Roial, for example, has two formal sections: the first encompassing the repeating music and text-structure of the first four lines, and the second, the through-composed single iteration of the remaining five poetic lines. Sometimes divisions are not as clear cut, as in the Lay, where some but not all musical and structural repetitions are written out fully. Formal sections end with structural cadences. These are usually referred to as ouvert (open) or clos (closed). The latter implies the cadence is stable and occurs on the main note of the mode, while the former suggests an open-ended, unstable cadence on a different sonority. Repeating formal sections tend to have alternate endings, with the first iteration ending with an ouvert cadence (leading the ear on) and the second one with a clos cadence (marking the end of a more substantial structural caesura).
Ligature: The combination of breves, longae, or certain groups of two semibreves into a physically unified shape. As in theory ligatures should not be set to more than one syllable, they were originally used for specifying underlay division. Later on they became instrumental in the development of rhythmic notation, but by the fourteenth century (and especially in the song repertoire), there is no technical necessity to use them. As a result, they can be seen as a visual tool aiding the quicker transmission of information, as an aesthetic preference, a space-saving device, or simply as a scribal habit. Nonetheless, they still had relevance for text underlay, and by showing groupings could affect melodic interpretation.
Melisma: The performing of more than one note to a single text-syllable. The opposite arrangement (i.e., each syllable being set to a single note in the music) is referred to as syllabic recitation.
Mensuration: The overall rhythmic organization arising from the combination of the different rhythmic levels, operating as a precursor of the modern time signature. The Ars nova style combines the tempus and prolatio levels (see discussion of note-shapes above). When transcribed into modern notation, this results in time signatures equivalent to 2/4, 3/4, 6/8, and 9/8. When longae appear, they are usually imperfect. The Ars antiqua style combines the tempus and modus levels, but in the songs, the modus level is more dominant and the tempus rather unstable. This results in 3/2 and 2/2 measures, with occasional triplets.
Plica: An ornament appended to a brevis or a longa through the manipulation of the note-shape. While it specifies direction (i.e., whether the ornament should move above or below the note it is appended to), it is not clear how far it should move away from its given starting point. Some medieval commentators say up to a fifth, whether it should be a single note or a backwards and forwards vibration, or what the character of the sound should be (some medieval commentators mention the use of the glottis, while in some of Machaut’s works — Motet 2, for example — it seems to be used to enhance a sighing motif).