than does the upper neighbor to the fifth above; hence we may conceptualize the octave species with the
pentachord below the tetrachord; and in additional confirmation, the vast preponderance of melody notes
lie above the final, establishing the mode as authentic.) With the two Graduals in Ex. 1-7, we are back in
ambiguous territory. The final, A, is accommodated to the theory of the four finals by the back door, as we
have seen, on the basis of the congruence between its modal pentachord (TSTT) and that of the protus
final, D. Its complementary tetrachord (STT) differs from that of the protus modes, however, resembling
the deuterus instead. So the assignment of these melodies to the second mode is more or less arbitrary,
especially in view of that pesky B-flat—over cedrus in Ex. 1-7a, and over the very opening word, Haec,
in Ex. 1-7b—preceding a cadence on A that would seem to invoke (if anything) a transposed deuterus or
Phrygian scale. There is a considerable gap here between the reality of the chant and the theoretical
abstraction of a modal system.
It was noted in chapter 1 that these Graduals come from an old, distinguished formula-family that is
suspected of being among the most ancient on record. Thus it is really no surprise that its melody
conforms so little with a body of generalizations (that is, a theory) that arose many centuries later—the
more so as Graduals, not being antiphons, were not much taken into account by the tonarists. The Frankish
mode theory did have a way of accounting for melodies that were wayward by its standards: they were
classified as being of “mixed mode” (modus mixtus), meaning that some of their constituent phrases
departed from the basic octave species of the melody as a whole. But that is just another effort to dispel
an anomaly by giving it a name—something on the order of an exorcism.
MODE AS A GUIDE TO COMPOSITION
What a difference we will observe when we look at melodies written after the Frankish chant theory had
been formulated! For that theory, modest in its intention, was huge in its effect. While it may have begun
as a way of improving the efficiency with which a body of ancient music was mastered and memorized, it
quickly metamorphosed into a guide to new composition, achieving a significance its early exponents may
never have envisioned for it. From a description of existing music it became a prescription for the music
of the future.
The first composer whom the chant theory “influenced” may have been Hucbald himself, its chief
early exponent. His surviving compositions include a set of antiphons for the Office of St. Peter, as well
as the famous set of laudes or Gloria tropes. They are all modally systematic in a way that earlier chant
had never been. The Office antiphons, for example, are arranged in a cycle progressing through the whole
array of church modes in numerical order—Hucbald’s own numerical order! The trope, Quem vere pia
laus, does not employ the common melodic formulae of the existing Gloria chants—in other words, it
eschews the old concept of mode as a formula-family—but instead exemplifies the more abstract features
of scalar construction.
In Ex. 3-4, Hucbald’s set of laudes is embedded in a Gloria that shares its mode (the sixth, or
Hypolydian) and seems, on the basis of its sources as well as its style, to date from within, or shortly
after, Hucbald’s lifetime. In both, the tonal focus is sharp, with the final, F, located in the middle of the
melody’s range, providing a clear line of demarcation between the modal pentachord and the plagal
tetrachord below. Hucbald uses three pitches to end the constituent (and, remember, nonconsecutive)
phrases of his laudes. Only the last ends, as might be expected, on the final. A plurality, five, end on the
reciting tone, namely A. The other four, which end on G, seem to have picked up the influence of some
secular genres, especially dance songs, which, as we will see in the next chapter, frequently use the
“supertonic” degree to create half (or “open”) cadences, to be fully closed by the final at the end of the