invented any sort of neumatic notation, at first took the form of prefaces and appendices to the early
Frankish graduals and antiphoners that contained the texts to be sung at Mass and Office. (The earliest
appendix of this kind is found in a gradual dated 795.) By the middle of the tenth century, these lists had
grown large enough to fill separate books for which the term tonarius or “tonary” was coined.
These books served an eminently practical purpose, since in every service newly learned antiphons
had to be attached appropriately to their full cursive psalms (in the Office) or at least to selected stichs
(in the Mass) as a matter of basic operating procedure. In the Vespers service, for example, there were for
any given day of the week five unchanging “ordinary” psalms and literally hundreds of ever-changing
“proper” antiphons that had to be matched up with them in daily worship. To achieve this practical goal,
large stylistic generalizations had to be made about the antiphons on the basis of observation. Classifying
the Gregorian antiphons was thus the earliest European exercise in “musical analysis,” analysis being
(literally and etymologically) the breaking down of an observed whole (here, a chant) into its functionally
significant parts. The generalizations thus produced constituted a new branch of “music theory.”
The earliest analysts and theorists, like the earliest composers of medieval chant, were Frankish
monks. The most extensive early tonary was the one compiled around 901 by Regino of Prüm, the abbot of
the Benedictine monastery of St. Martin near the German town of Trier. It contains the incipits of some
thirteen hundred antiphons as well as five hundred introits and offertories (performed in those days with
psalm verses), all keyed to the ending formulas (differentiae) of the eight psalm tones. To achieve this
abstract classification of melody types, the compiler had to compare the beginnings and endings of the
antiphons with those of the psalm tones.
In effect, a corpus of actual melodies inherited from one tradition (presumed to be that of Rome, the
seat of Western Christianity) was being compared with, and assimilated to, an abstract classification of
melodic turns and functions imported from another tradition (the oktoechos, or eight-mode system, of the
Byzantine church). The result was something neither Roman nor Greek but specifically Frankish—and
tremendously fertile, a triumph of imaginative synthesis. What was actually abstracted through this
process of analysis by observation and assimilation was the intervallic and scalar structure of the chant.
Specifically, antiphons were compared with psalm tones to see how the interval was filled in between
their ending note (finalis) and the pitch corresponding to the psalm tone’s reciting tone (tuba), normally a
fifth above. (Since most often the last note of a Gregorian chant is the same as the first, Regino actually
classified antiphons—or so he said—by their first notes; the concept was refined slightly later.) There are
four ways a fifth can be filled in within the aurally internalized diatonic pitch set, with its preset
arrangement of tones (T) and semitones (S). In the order of the tonaries these were (1) TSTT, (2) STTT,
(3) TTTS, and (4) TTST. What is identified in this way are scale degrees. The notion of scale degrees,
and their identification, thus constitutes from the very beginning—and, one is tempted to add, to the very
end—the crucial “theoretical” generalization on which the concept of tonality in Western music rests.
These intervallic “species,” as they came to be called, could be demonstrated in various ways. One
method was by the use of the monochord, the medieval theorist’s laboratory instrument, which consisted
of a sound-box surmounted by a single string, under which there was a movable bridge. The surface of the
box was calibrated, showing bridge placements vis-à-vis one end of the string or the other, by means of
which one could exactly measure off (or “deduce”) the various intervals. Another, more abstract, way of
demonstrating the species was notation—at first by means of Daseian signs as illustrated in the previous
chapter (see Fig. 2-2), later (from the eleventh century) by means of the staff. When one writes things
down, one can demonstrate or discover that the diatonic scale segment descending from A to D (or
ascending from A to E) corresponds with the first species of fifth listed above; that the segment
descending from B to E corresponds to the second species; that the segment descending from C to F
corresponds to the third species; and that the segment descending from D to G corresponds with the fourth