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Contents

Music from the Earliest Notations to the Sixteenth Century

TONARIES

Chapter:
CHAPTER 3 Retheorizing Music
Source:
MUSIC FROM THE EARLIEST NOTATIONS TO THE SIXTEENTH CENTURY
Author(s):
Richard Taruskin

Among the earliest documents we have for the Carolingian reorganization of the liturgy and the institutionalization of Gregorian chant are the manuscripts, which begin to appear soon after Pepin’s time, that group antiphons (represented by their incipits or opening words) according to the psalm tones with which they best accord melodically. These lists, which began to appear long before the Franks had 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 (Ex. 3-1).

Tonaries

ex.. 3-1 The four species of fifth and the “four finals”

The ending notes of these four species-defining segments—D, E, F, and G—were dubbed “the four finals” in Frankish tonal theory and named (in keeping with the Byzantine derivation of the mode system) according to their Greek ordinal numbers: protus (first), deuterus (second), tritus (third), and tetrardus (fourth) respectively. (The fifth A–E was considered a doubling, or transposition, of the first segment; hence A was functionally equivalent to D as a final.) Full correspondence between the chant-classification and the preexisting eightfold system of psalm tones was achieved by invoking the category of ambitus, or range. Chants ending on each of the four finals were further broken down into two classes. Those with the final at the bottom of their range were said to be in “authentic” tonalities or modes, while those that extended lower than their finals, so that the final occurred in the middle of their range, were called “plagal,” from the Greek plagios, a word derived directly from the vocabulary of the oktoechos, where it referred to the four lower-lying scales.

Thus the four finals each governed two modes (protus authenticus, protus plagalis, deuterus authenticus, and so on), for a total of eight, in exact accordance with the configuration (but only in vague accordance with the content) of the eightfold system of psalm tones. In elaborating this system, the basic fifth (or modal pentachord, from the Greek) whose diatonic species defined the final’s domain was complemented with a fourth (or tetrachord) to complete the octave. (According to the terminology of the day, the tetrachord was said to be conjunct—rather than disjunct—with the pentachord because its first pitch coincided with the last one in the pentachord rather than occupying the next scale degree.) The authentic scales were those in which the pentachord was placed below its conjunct tetrachord, so that the final was the lowest note. In the plagal scales the tetrachord was placed below the pentachord, so that the final came in mid-range. The result was a series of seven distinct octave species or scales with particular orderings of the diatonic tones and semitones. There are only seven possible octave species but eight modes; hence the last scale in Tabl. 3-1 (tetrardus, plagal) has the same order of intervals as the first (protus, authentic), but they are split differently into their component pentachord and tetrachord. Although their octave species coincide, the modes do not, for they have different finals: D and G, respectively.

TABLE 3-1 Modes and Octave Species

TETRACHORD

PENTACHORD

TETRACHOD

Protus (D)

Authentic

T-S-T-T

T-S-T

Plagal

T-S-T

T-S-T-T

Deuterus (E)

Authentic

S-T-T-T

S-T-T

Plagal

S-T-T

S-T-T-T

Tritus (F)

Authentic

T-T-T-S

T-T-S

Plagal

T-T-S

T-T-T-S

Tetrardus (G)

Authentic

T-T-S-T

T-S-T

Plagal

T-S-T

T-T-S-T

In Ex. 3-2 this table is translated into modern staff notation, giving the full array of so-called “medieval church modes.” They will henceforth be numbered from one to eight, as they are in the later Frankish treatises, and they will be given the Greek geographical names that the Frankish theorists borrowed from Boethius, the authority of authorities. Boethius had adopted these names from late Greek (Hellenistic) sources, where they had referred not to what we would call modes but to what the Greeks called tonoi, transpositions of a single scale rather than different diatonic scales. Thus the familiar Greek nomenclature of the medieval modes was actually a misnomer, first perpetrated by an anonymous ninth-century treatise called Alia musica (literally, “More about Music”); but there is not much point in trying to rectify that now. (Note that the Greek prefix hypo-, attached to the names of the plagal scales, is roughly synonymous with the word plagal itself: both mean “lower.”) Ex. 3-2 also includes the tubae of the corresponding psalm tones, for these were sometimes claimed by contemporary theorists to pertain to the church modes as well. The tuba of an authentic mode lies a fifth above the final, as already observed in chapter 1. The tuba of a plagal mode lies a third below that of its authentic counterpart. Note that wherever, according to these rules, the tuba would fall on B, it is changed to C. This was evidently because of an aversion to reciting on the lower note of a semitone pair. Note, too, that the tuba of the fourth tone is A rather than G by the regular application of the rules: it is a third lower than its adjusted counterpart (C in place of B transposes to A in place of G).

Tonaries

ex.. 3-2 The eight medieval modes

Perhaps the most important thing to bear in mind regarding this array of medieval modal scales is that the staff positions and their corresponding “letter names” do not specify actual pitch frequencies, the way they do in our modern practice. Thus one must try to avoid the common assumption that the Dorian scale represents the piano’s white keys from D to D, the Phrygian from E to E, and so on. Rather, the “four finals” and their concomitant scales represent nothing more than the most convenient way of notating intervallic patterns, relationships between pitches that can be realized at any actual pitch level, the way singers (unless cursed with “perfect pitch”) can at sight—or rather, by ear—transpose the music they are reading, wherever it happens to be notated, to a comfortable tessitura or “placement” within their individual vocal ranges. What we are now conditioned to regard as fixed pitch associations (e.g., “A-440”) were at first no more than notational conventions.

If this is a hard idea to get used to, imagine a situation in which all pieces in the major were written “in C” and all pieces in the minor “in A,” regardless of the key in which they would actually be performed. Only instrumentalists, whose physical movements are coordinated with specific pitches, or singers with perfect pitch, who have memorized and internalized the relationship between specific frequencies and the appearance of notated music, would be seriously discommoded by such an arrangement. Such musicians can only transpose by mentally changing clefs and signatures. And as we shall see, it was the rise of an extensive independent repertory of instrumental music in the seventeenth century that brought about our modern “key system,” in which actual pitches were specified by notation and in which key signatures mandated specific transpositions of the standard scales.

Citation (MLA):
Richard Taruskin. "Chapter 3 Retheorizing Music." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 20 Sep. 2017. <http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-003002.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 3 Retheorizing Music. In Oxford University Press, Music from the Earliest Notations to the Sixteenth Century. New York, USA. Retrieved 20 Sep. 2017, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-003002.xml
Citation (Chicago):
Richard Taruskin. "Chapter 3 Retheorizing Music." In Music from the Earliest Notations to the Sixteenth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 20 Sep. 2017, from http://www.oxfordwesternmusic.com/view/Volume1/actrade-9780195384819-div1-003002.xml