The Critical Nexus: Tone-system, Mode, and Notation in Early Medieval Music

“The notes are so arranged that each sound, however often it may be repeated in a melody, is found always in its own row. And in order that you may better distinguish these rows, lines are drawn close together, and some rows of sounds occur on the lines themselves, others in the intervening intervals or spaces. All the sounds on one line or in one space sound alike”

(p. 229).

These lines, certainly familiar to medievalists, may well be reckoned among the most important in Western music history. They represent the first description of the line diagram known as the staff, and are taken from Guido of Arezzo’s Prologus in antiphonarium (1030). The quotation stands at the end, and at the apogee, of Charles Atkinson’s study of early medieval tone systems, mode, and notation, because, as Atkinson explains,

with this simple step, the fusing of the ancient Greek Immutable System (ametabolon systema) with the tonal matrix of medieval music and its embodiment in practical notation was complete. There was now available to the West a practical method of notating music that was fully diastematic, whose intervals represented precise numerical ratios that could be converted directly into sound via the monochord. That notation, however, preserved a systemic architecture based on the mathematical principles of ancient Greek harmonic theory […], rather than upon the flexible melodic shapes of the plainchant sung in the Western church.

(pp. 229–30)

How many musicologists, even those scholars in the fields of medieval studies, music theory, or liturgical chant, are familiar with the music and music theory of antiquity? The language and concepts of these texts may seem forbidding, and far away from the repertory known to most of us. Yet, as the quotation above indicates, the implications of this theoretical heritage for the development of early medieval music theory, its system of the eight modes (oktoèchos), and its dealing, and sometimes struggling, with the intricacies of the chant melodies and their notation, are of paramount importance.

Charles Atkinson, professor of musicology at Ohio State University, has written a book that spells out these implications methodically and with admirable accuracy. The study, dedicated to the memory of the German musicologist Fritz Reckow (1940– 1998), is the expanded version of a conference paper read by the author in Kiel in 1985, at Reckow’s invitation.

The book is amply illustrated with figures, texts, and examples. This “didactic” approach, complemented with a very rich footnote apparatus, enables the reader to study the book without burdening his reading table with additional reference works, studies and editions. Moreover, Atkinson’s profound knowledge of the theoretical writings of the period—ranging from Boethius’s De institutione musica (ca. 500) to Guido of Arezzo’s Micrologus (ca. 1026–28) and Prologus in antiphonarium (1030), with an epilogue expanding the spectrum to Marchetto da Padova’s Lucidarium in arte musice plane (1317–18)—allows him to select from the treatises exactly those passages that pertain to his argument. Introductory and contextual considerations about the theorists and their writings are limited to what is essential for the discussion; the reader can refer to the footnotes for more background.

After a brief prologue, chapter 1, entitled “The Heritage of Antiquity,” sets the scene by demonstrating convincingly that music in antiquity belonged to two disciplines, harmonic theory and grammar. Consequently, the concept of tonus has two meanings: one referring to the tone-systems discussed by Boethius, Martianus Capella, and Aristides Quintilianus; the other referring to textual accents as an element of grammar, discussed by such authors as Donatus. It is precisely this set of accents, acutus, gravis, and circumflex, that will allow Atkinson to make the connection to the earliest forms of plainchant notation in chapter 3.

Chapter 2, “The Reception of Ancient Texts in the Carolingian Era,” opens part 1, entitled “The Eighth and Ninth Centuries.” It clearly illustrates the importance of the ancient texts in general, and of the glosses added to them in particular for the medieval conceptualization of music. In accordance with the main topic of his study, Atkinson focuses on the glosses commenting on tonus as a grammatical and harmonic concept and reflecting the Carolingians’ attempts to understand these ancient texts. Glosses written by famous authors such as Johannes Scotus Erigena and Remigius of Auxerre did not reflect the ancient Greek modes accurately, but were “consonant with a different kind of modal relationship” (p. 73), that of the theory of the modesfound in Hucbald or in treatises such as Musica enchiriadis and Alia musica.

These treatises, the earliest to comment on the system of the eight modes, are discussed in the longest chapter of the book, chapter 3, “The Heritage of the Church,” in which Atkinson traces the emergence of this system in several types of sources. The first are the tonaries, as exemplified by the earliest of its kind with musical notation, the tonary of Regino of Prüm. The tonaries are the first sources to connect several differentiae to each mode, a recurrent theme in Atkinson’s discussion from this chapter on. Furthermore, the most influential of the music manuals in circulation was undoubtedly Aurelian of Reome’s Musica disciplina (840–59), which, in its nomenclature of the modes (the authentic and plagal protus, deuterus, tritus, and tetrardus), was informed by its Byzantine counterparts, the singers’ manuals known as the papadikai. Similarly, the Musica enchiriadis opens with the presentation of the four tones (phtongi) forming the roots (origines) of the modal system. One of the most fascinating parts of the book follows when Atkinson demonstrates that the precise notation of pitch becomes a central preoccupation for music theorists. This is apparent from the daseia notation used in Musica enchiriadis, Hucbald’s combined use of (“pseudo-Alypian”) letters and neumes, the letter of Notker Balbulus to Lantpertus on the meaning of the litterae significativae, and especially from the correlation between Aurelian’s description of notation and the Paleofrankish neumes (pp. 106–13).

Part 2, “The Synthesis of Ancient Greek Theory and Medieval Practice,” opens with a discussion of two theorists already mentioned, Hucbald of St. Amand and Regino of Prüm (chap. 4). Hucbald’s classifications of the toni are related to the ancient Greek tone system, and thus form the “first witness to the direct conjunction of ancient Greek theory and chant notation” (p. 160). Moreover, because Hucbald announces the tensions between tone systems and notation, he is “also our first witness to the possible necessity of transposing chant, introducing the notion of socialitas (comradeship) of notes a fifth above the final (the “affinities” or alternative finals)” (p. 160). This necessity is demonstrated in the notation of the early-eleventh-century manuscript Montpellier H. 159, famous for its double notation in letters and neumes. The chapter concludes by a brief discussion of the tension and, indeed, dichotomy between singing practice (labeled “cantus theory” by Atkinson) and the influence of ancient Greek harmonic theory, as it is reflected in Regino of Prüm’s Epistola de harmonica institutione.

Chapter 5, devoted to the anonymous treatise Alia musica, is probably one of the most innovative. Atkinson thoroughly reassesses existing scholarship on the treatise, and presents a revised table of contents, in which he distinguishes four different authors, identified by the first four letters of the Greek alphabet. This last author, the compiler of the final version of the Alia musica, resolves the problem of the eighth mode (with the same ambitus as the first, and the same final as the seventh) by defining a meta (mediam chordam) specific to every mode: G is the “mean pitch” of the eighth mode, as opposed to a in the first.

Chapter 6, “Pseudo-Bernelinus, Berno, Pseudo-Odo, and Guido d’Arezzo,” shows that only gradually were the modes interpreted as conjunctions of species of fourths and fifths, which made it possible to distinguish between the modes on a systematic basis, found for the first time in an interpolated version of the Prologus in tonarium of Bern of Reichenau (d. 1048). The emergence of these developments is contemporaneous with the rise of diastematic notation. From Pseudo-Odo on, the tone system consisting of the lowest tone, represented by an uppercase gamma, followed by the letters A-G, and their octave equivalents a-g and aa-gg, forms the standard system of Western music until well into the Renais sance. Odo defines the (co)determinants of a chant as the final, the distinctiones (intermediate cadences), and the ambitus; Guido of Arezzo still acknowledges the importance of the initium, but likewise gives greater weight to the final. An interesting notion highlighted by Atkinson is Guido’s transformatio: the use of B instead of B transforms a chant from one mode into another; when it is used in a chant on G, for example, this chant will sound as in the protus (p. 223). Similarly, the technique of partial transposition forms a means to notate “nonsystemic pitches” (p. 227), in particular the low B not included in the tone-systems of Pseudo-Odo or Guido. (As Atkinson points out (pp. 129–33), the Scolica enchiriadis had already introduced the technique of the vitia to allow for “foreign” pitches such as F or E .)

The epilogue takes the liturgical chants’ occasional incongruities with tone systems and notation as its point of departure, and compares the solution offered by Bern of Reichenau (transposition with a fourth upwards) to those of three post-tenth-century authors, Johannes Affligemensis, Marchetto da Padova, and the anonymous author of the first treatise in the Berkeley manuscript. The book concludes with a list of manuscripts, editions, and literature, indexes of chants and manuscripts, and a general index.

A modest book review cannot possibly convey the richness of a study such as The Critical Nexus. Charles Atkinson analyzes his sources with wonderful precision and constructs his argument with great clarity, always careful to do justice to the authors, to highlight their specific contributions, and to show the evolution of the recurrent Leitmotive throughout this fascinating history. All readers, regardless of their level of specialization, will find their understanding both broadened and deepened. To be sure, this is a work that merits to become a classic, that deserves to be read and reread, studied and discussed among students and scholars time and again, and is therefore highly recommended to all musicologists and libraries.