Greek and Latin Music Theory: Principles and Challenges
2022; Duke University; Volume: 66; Issue: 2 Linguagem: Inglês
10.1215/00222909-9930913
ISSN1941-7497
Autores Tópico(s)Linguistics and language evolution
ResumoIT IS A rare occurrence to find a genre bender among the offerings of the academic press. Not a monograph, nor a textbook, nor exactly a collection of essays, Edward Nowacki's Greek and Latin Music Theory: Principles and Challenges originates in lecture notes amassed over twenty years of teaching the history of ancient and medieval music theory at the University of Cincinnati. The book-cum-archive contains materials ranging from general overviews, new translations, “how-tos” for music-theoretical procedures, line-by-line commentaries on treatises, to essays with new research—all addressing topics from ancient Greek and medieval Latin music-theoretical traditions, starting with Plato and ending with Zarlino. A reader expecting the comprehensiveness of a modern textbook, the through arguments of a monograph, or the rigorous bibliographical and disciplinary framing conventions for a set of new scholarly essays could easily find him- or herself confused as to how to read or make use of the book. Taken as the outgrowth of pedagogical materials interspersed with nuggets of new research and argued discourse, the book comes into focus as generically similar to those medieval texts that Nowacki himself lovingly unpacks: Greek and Latin Music Theory constitutes a thematically coherent assemblage curated through the expertise and personal interests of a master pedagogue, a treasury stuffed with an assortment of useful aids—tables, definitions, notes, and excerpts from primary sources (including, as mentioned, several new translations). The collection will be an especially valuable resource for graduate seminars and for nonspecialists wishing to gain their bearings in some core principles undergirding ancient and medieval melodic theory.Although the title Greek and Latin Music Theory: Principles and Challenges provides no further hints to its contents than the language of the texts with which it is concerned, the collection is circumscribed by the overarching focus on melody and the intervallic and mathematical principles undergirding melodic theory. (Contrapuntal and rhythmic theory find no place in the discussions.) Part 1, “The Ancient Greek Tradition in Practice and Theory,” covers how melody was theorized and recorded—the ancient harmoniai, the tonoi, and Alypian notation. Part 2 deals broadly in the mathematical foundations shared by ancient Greek and medieval Latin musical writers, commencing with a prose explication of how to calculate harmonic ratios from the octave, proceeding to a handful of mathematical issues in Boethius and Aristoxenus that present problems for the modern reader, followed by an overview of the three mathematical means in selected writings, and closing with a commentary on Guido's division of the monochord. Part 3, “Emerging Theories of the Ecclesiastical Modes,” tackles several complicated issues in understanding early medieval modal theory including transposition and “the misunderstood confinalis” (92–110), a new translation of Bern of Reichenau's Prologus in tonarium, and translations and commentaries on portions of the Alia musica and the Musica of Hermannus Contractus. Nowacki includes a glossary of terms at the end of the book.Part 1: “The Ancient Greek Tradition in Practice and Theory” is a welcome new introduction to important concepts in the world of ancient Greek theory. Writing perhaps with a graduate-level survey of the history of music theory in mind, Nowacki provides an overview of the ancient Greek melodic tradition more inviting and approachable to a nonspecialist than the usual bibliography—for example, Thomas Mathiesen's (1999) Apollo's Lyre, M. L. West's (1992) Ancient Greek Music, and Andrew Barker's (1984–89) Greek Musical Writings (authorities whom Nowacki certainly cites heavily). In particular, his presentation of the mysterious ancient harmoniai (chap. 1), by means of a succinct survey of not solely music-theoretical, but also literary and philosophical texts, clearly articulates them not only as systems of tuning, but also as idioms that encompassed the conduct (agogē) of pitch collections in addition to poetic and instrumental genre. The reader of this chapter and chapter 2 will possess a firm historical grasp of their distinction from tonoi—a point of confusion and conflation for so many students and nonspecialists. Though not averse to plunging into careful technical explanations, Nowacki is careful to keep big questions up front and to take a long view of the history of Western music theory. Nowacki's choice to use modern naming conventions for pitch—though sometimes cumbersome—allows a nonspecialist to grasp the fundamental conceits, puzzles, and problems of the systems at hand. In particular, in chapter 2, Nowacki's tables of Ptolemy's tonoi, as overlapping double-octaves with thetic spelling and as revolving double-octaves with dynamic spelling, all translated into modern alphabetic conventions, are very welcome classroom resources. The flip side of the pedagogical character of Part 1, however, is that nuances important for a curious student or specialist are sometimes left unflagged, and the most relevant bibliography for follow up is sometimes lacking.1Parts 2 and 3, “Mathematical Foundations” and “Emerging Theories of the Ecclesiastical Modes,” contain notes on music-theoretical fundamentals (chaps. 4, 8, and 10), brief commentaries on and summaries of several texts (chaps. 6, 7, 9, and 14), new English translations with commentaries (chaps. 12 and 14), and two argued essays (chaps. 11 and 15). The chapters of notes are some of the most useful pedagogical material, explaining fundamental though confusing concepts often passed over as being too elementary in specialist writing. “Pythagorean Harmonic Ratios from the Octave to the Comma by Continuous Subtraction” (chap. 4) takes the reader through the mathematical operations necessary to derive the proportions of the fourth through the comma—demonstrations fundamental for understanding Western speculative theory and which are rarely fully explicated. In fact, I wish that Nowacki would have expounded the operations even more thoroughly by showing proofs for the use of division for subtracting ratios—a straightforward proof for the modern mathematician, but not for most modern music students.“The Three Mathematical Means in the Theories of Euclid, Boethius, Glarean, and Zarlino” (chap. 8) delineates the fundamental kinds of mathematics employed in ancient and medieval music theory and points to puzzles and problems they generate across the centuries. The broad historical timeline of this chapter underscores the transhistorical importance and interest of just a few mathematical means (geometric, arithmetic, and harmonic). “Transposition and the Doctrine of Modal Affinity” (chap. 10) summarizes the early medieval practice of transposing a chant to its mode's affinis against a stationary background of tetrachords, offers observations for each standard transposition, and distinguishes this kind of early medieval transposition from the hexachordal transposition that began to coalesce in the eleventh century. Nowacki concisely summarizes at the conclusion of the chapter, “As historians of music theory, we have inherited in the word ‘transposition’ a pair of terminological homonyms. Each is the correct terminus technicus for its respective repertory and era. When we use the term, we must simply take care to specify the particular sense in which we use it” (91). Here, as elsewhere in this book, Nowacki balances concise technical summary and references to primary source with big-picture issues and important takeaways, which can be retained even if the infilling details may soon be forgotten. The pedagogical merit of this kind of writing is evident to any teacher.Nowacki's translations of the first Quidam of the Alia musica (ca. 900) and Bern of Reichenau's Prologus in tonarium (1021–36) are useful additions for the seminar leader or nonspecialist. The first Quidam is significant for the history of music theory because it analyzes chant, perhaps for the first time, “by observing how all melodies in their various movements present the horizontal unfolding of certain normative intervals” (116).2 To my knowledge, Nowacki supplies the only full English translation of the first Quidam: Edmund Heard's (1966: 120–230) dissertation includes a translation main text of the Alia musica, but excludes the appended first Quidam. Charles Atkinson's The Critical Nexus (2009:179–84) contains just the passage on the first tone from this section. Nowacki's translation and commentary (111–30) is most profitably read in parallel with Atkinson's chapter on the Alia musica (2009: 171–201), to which Nowacki responds and which prints the source's relevant musical examples not included in Nowacki's translation. Nowacki's translation of Bern of Reichenau's Prologus in tonarium is likewise, as far as I am aware, the only published English translation of the full text, significant as an early instance of tying modal identity to species of diatessaron and diapente, an approach which would become normative for modal theory in later centuries.3The chapters providing commentaries and summaries of primary sources are a grab bag. Some chapters constitute a few pages of prose taking the reader through quite a short passage from a primary source: chapter 6, “Aristoxenus's Proof That the Perfect Fourth Is the Sum of Two Tones and a Semitone,” which guides one through a thought experiment at the end of the second book of Aristoxenus's Elmenta harmonica, and chapter 9, “Guido and the Monochord,” which charts Guido's two methods for dividing the monochord ruler, are of this kind. Other chapters are more like short commentaries or responses to secondary scholarship: chapter 7, “Aristoxenus's Anticipation of the Logarithmic Logic of Music Cognition,” summarizes Malcolm Litchfield's 1988 article, which argues for Aristoxenus's classification as a speculative rather than empirical thinker based on that ancient theorist's putative inability to perform the experiments adequate to generate of hard data (Litchfield 1988). Nowacki disagrees with this assessment and suggests that Aristoxenus's intuitive approach to musical perception may indeed be classified as empirical observation—indeed, as “cognitive science.” Although Nowacki's reactions to Litchfield's article are perceptive and provocative, he does not offer a robust argument for his conclusions, and recent relevant scholarship (esp. Barker 2007; Creese 2012) on Aristoxenus's methodology does not appear. As a specialist, I did not find this chapter particularly helpful for research, although it does perhaps suggest routes for seminar discussion. I was also rather puzzled by the inclusion of chapter 5, “Boethius's Error in the De institutione musica, 4.6.” In this short chapter, Nowacki demonstrates the practical efficacy of utilizing arithmetic means to approximate the values of certain intermediate intervals over the more complex operations necessary to ascertain their true values by geometric means. But, as Nowacki himself writes, it was Andrew Hicks (2016: 7–8) who first noted the phenomenon in Boethius, that, “the discrepancy between the geometric and arithmetic means, while great in the case of large intervals such as the octave, fifth, and forth, becomes vanishingly small in the case of the semitone, the quarter tone, and the comma” (58). Hicks, as Nowacki notes, even discusses De institutione musica 4.6 (Hicks 2006:12–5). It is hard to see, then, the purpose of this chapter other than to serve as a summary for a student unable to read Hicks's article for him- or herself. (Admittedly, this article would be challenging for most students.)Chapter 14, “Reading Hermannus,” comments on portions of Hermannus Contractus's Musica—the opening fundamentals, the division of the monochord in four steps, species of perfect consonances, and the sedes troporum and the modi vocum. Nowacki offers several important corrections to the English translation in John Snyder's reprint of Leonard Ellinwood's (2015) The Musica of Hermannus Contractus and seeks to defend the Musica from accusations of “willful and idiosyncratic speculation” by inferring Hermannus's cognitive or perceptual approach at several junctures.4 Despite the varied material and genres of writing in Nowacki's volume, the vindication of ancient and medieval theorists by suggesting a psychological, cognitive, practical, or empirical motivation is something of a recurring theme. Chapter 15, “Idealist and Empirical Perspectives in Theories of the Ecclesiastical Modes,” fittingly then, closes the collection with a meditation on modern and medieval methodologies in modal analysis, framed as a rebuttal to Harold Power's characterization of medieval modal as predominantly rationalist (162). Nowacki collates and comments on examples from the Musica enchiriadis, Alia musica, and John of Afflighem to demonstrate that “indigenous medieval theories of the ecclesiastical modes exhibit a variety of perspectives ranging from idealized descriptions deduced from general principles to more empirical descriptions based on observation of mundane practice” (170). Here, some of Nowacki's inferences seem a bit of a stretch, or at least too simplistic; moreover, the characterization of Power's position is a bit of a straw man. By Nowacki's account, the mere inclusion of musical examples of chant from the ninth century repertory in the Musica enchiriadis, given the absence of a highly developed analytical language, “exemplifies an empirical approach to musical analysis” (164). But this begs the question, as if musical analysis eo ipso or even perhaps any mention of actual repertory whatsoever were a badge of an “empirical approach” to modal analysis. Is Nowacki simply treating “empirical” as equivalent to “practical”? I found myself wondering why Nowacki had adopted an ideal/empiricist dichotomy as the framework for many of his observations when the usual categories of speculative and practical seem neater descriptions.Chapter 11, “The Misunderstood Confinalis,” moves away from what is purely pedagogical toward through argumentation on the basis of new research. In this chapter, Nowacki distinguishes the theoretical concept of the confinalis as used from the ninth through fifteenth centuries—“a note in the gamut five steps above the finalis to which entire compositions could be transposed”—from a later concept of the confinalis—the fifth step of the modal octave and an alternative to the final as a note suitable for concluding whole compositions (92). This chapter narrates a history of how this change in meaning came about. Nowacki first demonstrates, through close readings of music-theoretical texts and musical analyses that refer to the confinalis, that theoretical works preceding the sixteenth century assume at least a partial transposition, or transpositio ex parte, of the chant in question. Nowacki points to Franchino Gaffurio's Practica musice as defining confinalis, for the first time, as the note that divides the authentic modal octave at the harmonic mean and forms the upper boundary of the mode's proper species of fifth in both authentic and plagal octaves.5 Gaffurio's ambiguity as to the confinalis's ending function (does it end a transposition ex parte, or may it end an untransposed chant?) precipitates a gradual withering of the term's original sense. Zarlino's treatment of the confinalis drives the nail in the coffin. As is characteristic of this volume, the articulation of a rather esoteric subject is lucid and approachable. I was surprised, though, that Nowacki did not at least mention the place of polyphonic composition in the conceptual change, as this has been previously claimed as central to the concept's development (cf. Atcherson 1970).As the author himself declares, Greek and Latin Music Theory: Principles and Challenges is not a textbook nor a monograph. It cannot replace the usual secondary texts and textbooks for the teaching of ancient and medieval theory. But it does offer far more succinct and inviting introductions to many important principles and challenges of Greek and Latin music theory than are, for the most part, contained in the standard bibliography. It widens the horizons of access to primary sources by its translations. It kindly guides novice readers in their first approaches to medieval texts. The work well warrants its addition to any history of theory syllabus. And while some of Nowacki's observations and inferences may seem a bit off the cuff, they all serve the purpose of probing why any of this theory is studied in the first place—a basic question too often forgotten in the seminar room among the twists and turns of specialist arcana. To read Greek and Latin Music Theory, then, is a bit like overhearing the discussions, debates, questions, and discourses of a beautifully crafted seminar. For readers of this journal, the text may supply materials for courses, or a lucid introduction for nonspecialists in ancient and medieval theory. But it also may serve as an inspiration and model for excellence in pedagogy—from the seriousness with which Nowacki manifestly treats the questions and observations of students, to his willingness to start from basics when necessary, and to his balance of precise and fine analysis with broad awareness of big questions.
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