end, so to speak, can now fulfill the implications of the beginning). It sounds the B above the final so that
the full modal pentachord of mode 4 is represented. It expressly avoids a modal cadence at the end, of
course, so that it will flow imperceptibly into the antiphon it is introducing. But it has very perceptibly
enhanced the conformity of the actual Gregorian antiphon with the Frankish definition of its mode.
Although it is the shorter and the simpler of the introit tropes for Easter shown in chapter 2, “Psallite
regi” is by far the most radical in its transformation of the melody to which it is appended. Ex. 2-8b is
more obviously an imitation of the Gregorian antiphon. Its prefacing phrase begins, like the antiphon, with
a feint toward D, and ends, again like the antiphon, with a cadence on the final. It even mimics the Introit’s
ambitus (C up to A) instead of, like Ex. 2-8a, completing the modal pentachord with a B.
The Quem quaeritis trope (Ex. 2-9) is modally whimsical. It actually takes the initial feint to D at its
word, so to speak, and prepares it with an actual melody in mode 2 (Hypodorian). It is the descent to the
bottom of the lower tetrachord at the very beginning of the “Interrogatio” that establishes the melody as
plagal, even though the “Responsorium,” as befits the heavenly voice that sings it, ascends into the upper
tetrachord (though not all the way to the top of it). Melodies that encompass more than two primary scale
segments (or that have ranges of more than an octave) exemplify what medieval theorists called
commixtio, or modus commixtus. The term is often “translated” into a nonexistent English cognate:
“commixture” or “commixed mode.” In any case, it needs to be distinguished from the modus mixtus
defined above. “Mixed mode” denotes a mixture of different octave species. “Commixture” refers to the
extension of a melody so as to encompass both authentic and plagal scales.
The hymn melodies in Ex. 2-7 were chosen, among other reasons, to exemplify “modern” Frankish
melodies in various modes. Ave maris stella (Ex. 2-7a) is a wonderfully clear example of post-Gregorian
Dorian melody. Its composer most assuredly knew all about abstract modal syntax, and about the
relationship between antiphon modes and psalm tones as laid out in the tonaries. Note how the first phrase
leaps up from the final to the upper tetrachord, which it fully describes, meanwhile emphasizing the note
dividing the pentachord and tetrachord (the tuba, so to speak) with a turn figure. The second phrase
completely describes the pentachord. The third phrase cadences on the “note added on below,”
introducing it with a veritable flourish. And the fourth phrase returns to the uncluttered pentachord for the
final cadence. This kind of clearly delineated structure can hardly be found in the original corpus of
Gregorian chant. It is the product of “theory,” and of a single composer’s shaping hand. For the first time,
it seems, we are looking at a piece not merely maintained but composed within the literate tradition—
composed, that is, in the sense we usually have in mind when we use the word.
Pange lingua (Ex. 2-7b), in the third mode (authentic Phrygian), also gives its “modernity” away, this
time by giving cadential emphasis to the note C, high above the final. (Third mode melodies in the
original Gregorian corpus often emphasize this C, but not as a cadence.) By the time Pange lingua was
composed, theoretical rationalization had made such emphasis common. The same point may be made,
even more emphatically, about Veni creator spiritus (Ex. 2-7c). It is assigned to the eighth mode (rather
than the seventh), but not for any reason having to do with its ambitus or final. The final, G, is common to
all tetrardus melodies. The range could be described as the modal pentachord with a “note added on”
either above or below, again suggesting that the authentic and the plagal scales have an equal claim on the
tune’s allegiance. What clinches things for the plagal is the cadential emphasis on C, the tuba of the
corresponding psalm tone. (The authentic tuba, D, also gets a cadence, but C gets two.)
Thus these hymn melodies graphically illustrate the synthesis of Roman and Byzantine elements that
made up Frankish mode theory and its perhaps unforeseen compositional influence. (The regularity of
structure in the hymns may of course also reflect the influence of popular genres that have left no written
trace and are consequently beyond our historical ken.) The style and the effect of these tunes is altogether
different from those of the true Gregorian corpus. Where the older melodies were discursive, elusive, and