page_title: Mensural notation
section_title: Proportions and colorations
hierarchical_section_title: Mensural notation / Proportions and colorations
context_page_description: Mensural notation is the musical notation system used for European vocal polyphonic music from the later part of the 13th century until about 1600. The term "mensural" refers to the ability of this system to describe precisely measured rhythmic durations in terms of numerical proportions between note values. Its modern name is inspired by the terminology of medieval theorists, who used terms like musica mensurata or cantus mensurabilis to refer to the rhythmically defined polyphonic music of their age, as opposed to musica plana or musica choralis, i.e., Gregorian plainchant. Mensural notation was employed principally for compositions in the tradition of vocal polyphony, whereas plainchant retained its own, older system of neume notation throughout the period. Besides these, some purely instrumental music could be written in various forms of instrument-specific tablature notation.
  Mensural notation grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200.
context_section_description: An individual composition was not limited to a single set of tempus and prolatio. Meters could be shifted in the course of a piece, either by inserting a new mensuration sign, or by using numeric proportions. A "3" indicates that all notes will be reduced to one-third of their value; a "2" indicates double tempo; a fraction "" indicates three in the time of two, and so forth. The proportion 2 is usually understood to have the same effect as the use of a cut sign with a vertical stroke ( = ).
  The use of numeric proportions can interact with the use of different basic mensurations in fairly complex ways. This has led to a certain amount of uncertainty and controversy over the correct interpretation of these notation devices, both in contemporary theory and in modern scholarship.
  Another way of altering the metrical value of notes was coloration. This refers to the device of literally marking a note as rhythmically exceptional by writing it in a different color. In the earlier period, when normal notes were black, the exceptional ones were written in red, or sometimes hollow. In the later period, the practice was reversed; as the normal notes were now hollow, the exceptional ones were filled out in black. In either case, "colored" notes are understood to have ​²⁄₃ of their normal duration, and are always imperfect with respect to their next smaller sub-divisions.
  Coloration applied to a group of breves (ex. [a]) was known as color temporis, while that of a group of semibreves (ex. [b–c]) was called color prolationis. The resulting rhythmic effect, as expressed in modern notation, differs somewhat according to whether the affected notes were normally perfect or imperfect according to the basic mensuration of the music. Applied to perfect notes (ex. [a–b]), coloration creates the effect of a hemiola: three binary rhythmic groups in the space normally taken up by two ternary ones, but with the next smaller time units (semibreves in [a], minims in [b]) remaining constant. When applied to notes that were already imperfect according to their normal values (ex. [c]), coloration results in the effect of a group of triplets, with all rhythmic units reduced by two thirds. Another special form of coloration was that applied to a group of a single semibreve and a following minim, called minor color (ex. [d]). Whereas it would logically be expected to result in a triplet group (), it was instead conventionally executed as a dotted group equivalent to a dotted minim and a semiminim (note that in the context of white notation, the colored – i.e., blackened – version of the minim in the minor color group happened to look just like a normal semiminim  anyway, even though nominally it was considered a different type of note.)
  The use of colored notes (at that time written in red) was introduced by Philippe de Vitry and flourished in the so-called ars subtilior of the late 14th century.
  The example above, the chanson "Belle, bonne, sage" by Baude Cordier, written in a heart-shaped manuscript, is a rhythmically complex piece of ars subtilior. It uses several notation techniques for shifting between rhythms:
  red notes: diminution ​²⁄₃
  shift to prolatio maior: here with implied augmentation minim→semibreve
  white notes: diminution ​¹⁄₂ (two breves in the time of one)
  proportion "3": diminution ​¹⁄₃
  proportion "": eight notes in the time of nine notes of the preceding bar
caption: Upper voice, transcribed. (Full score; About this soundlisten (help·info))