The latter were of four main types. There are lengthy passages in syncopation initiated by innocent-
looking little “dots of division,” like the one that comes after the second note in the cantus. There is
interplay of perfect and imperfect note values, represented by contrasting ink colors (red standing for the
opposite of whatever the prevailing mensuration happens to be). The groups of three red semibreves near
the beginning of the contratenor (third line from the bottom), and in the tenor (its single color shift), show
this relationship of perfect and imperfect in most basic terms: the three red (imperfect) semibreves equal
the same length of time as two black (perfect) ones. This very common and characteristic 3:2 proportion
was called hemiola (from the Greek) or sesquialtera (from the Latin), both meaning “one-and-a-half.”
There are superimposed and juxtaposed time signatures throughout. Most of them involve the two
signatures that represented the extremes of mensural practice: which denoted perfection at every
specified level, and, C, which denoted imperfect divisions at every specified level. The latter signature,
moreover, is reversed to , a diminution (reduced value) sign that could have various meanings
depending on the context. Here it means that all values are halved, so that there are four minims rather
than two in the time of a normal semibreve. There is a lovely little passage in which the three voices all
go into diminished imperfect time, but not together: first the cantus (near the end of the first line in Fig. 9-
5 , on the words “en laquel”); then the contratenor, near the end of its first line (third up from the bottom of
the page); and, finally, even the tenor, as if nudged by the other parts, bestirs itself for just four notes, its
one and only signature change.
Finally, there are the ad hoc note shapes without which no self-respecting ars subtilior composition
would be complete. There are two such shapes in En remirant, both borrowed, as it happens, from the
Italian-style notation at which we will take a look in the next chapter. What seem like minims with stems
down (near the end of the “A” section in the cantus, and again on its “rhyming” repeat near the end of the
“B” section) are sesquitertia semibreves, meaning that four of them take the normal time of three. And the
curious red notes with stems both up and down (called dragmas) near the end of the second line in the
cantus are sesquitertia minims, reproducing the same 4:3 relationship at a higher level of rhythmic
activity.
Perhaps you have noticed that the red dragmas mean the same thing as minims under. Such redundancy
is typical of ars subtilior notation and proves that notation as such was for composers like Philippus a
focus of “research and development” in its own right.