Sofia di Mambro presents a new critical edition of Nicomachus’ Harmonicon Encheiridion, accompanied by an Italian translation, critical notes and commentary, and a substantial introduction. This publication is particularly welcome, since the last edition of the text dates back to Karl von Jan’s Musici Graeci Scriptores (Teubner, 1895).
The volume is clearly and coherently structured. The introduction is divided into three main parts: the first offers an overview of Nicomachus and a general analysis of the Encheiridion; the second is devoted to the textual tradition and manuscript relationships; and the third consists of three appendices. I shall comment on the introduction before offering some shorter comments on the edition, translation, and commentary.
The first part of the introduction advances the claim that Nicomachus is ultimately less concerned with music and harmonics per se than with the philosophical issues they raise. Di Mambro argues convincingly that harmonics is treated as propedeutics to propedeutics: the Encheiridion functions as an introduction to the (now lost) Harmonicon Eisagoge, while harmonics itself is conceived as a preparatory discipline leading towards (Neoplatonic) philosophy. Assessing Nicomachus’ philosophical agenda in the Encheiridion is no easy task, given the brevity of the treatise and the particular circumstances of its composition. It is unusual for such an introductory work to include a significant amount of personal information, yet there is little reason not to take it at face value. Nicomachus writes for an unnamed lady, while abroad and without access to his library, and presents the work as a brief prelude to a more extensive treatise. The addressee must have been familiar with Plato’s Timaeus, as suggested by Nicomachus’ treatment of the psychogony; this may also explain why quotations appear to be drawn from memory and often take the form of close paraphrase. At the same time, Di Mambro rightly emphasizes—particularly in the commentary—that such transformations of quotations may reflect a deliberate authorial strategy aimed at adapting sources to Nicomachus’ own agenda. The Encheiridion must therefore be read with caution, and with one eye on the Introductio Arithmetica and another on the lost Eisagoge, later used extensively by Boethius in his De Musica.
Di Mambro further situates Nicomachus’ work within a certain philosophical milieu shaped primarily by Plato’s Timaeus, the apocryphal Timaeus Locrus, Theon of Smyrna, and probably Adrastus of Aphrodisias. She argues that Theon was not a direct source for Nicomachus, and that similarities between the two authors are better explained by a shared intermediary, identified as Adrastus’ commentary on the Timaeus. Since this commentary can only be reconstructed indirectly through parallels between Theon and Calcidius, our sole witnesses to Adrastus, Nicomachus’ precise debt to Adrastus must remain uncertain.
By examining the status of music within Nicomachus’ philosophical system, Di Mambro concludes (pp. 24–25) that his primary interest lies in the mathematical perspectives opened up by musical theory, particularly those concerning the centrality of number and the opposition between continuity and discrete quantity. Working within a broadly Platonic framework enriched by Pythagorean material, Nicomachus thus rejects “the subordination of number to forms” in favour of a “mathematization of form” (p. 26). The Encheiridion should therefore be read not as a musical treatise stricto sensu, but as a specialised philosophical reflection on musical questions: Nicomachus is neither an Aristoxenus nor a Ptolemy.
The discussion of the textual tradition forms the largest and most detailed section of the introduction. Di Mambro’s examination of the manuscripts is very thorough; moreover, she proposes five new identifications of hands, either independently or in collaboration with Ciro Giacomelli (per litteras). Her analysis of stemmatic relationships is careful and methodologically sound, though, as is often the case, the conclusions are constrained by the necessarily limited scope of the investigation. While the focus on a single treatise is justified, taking into account parallel philological work on other texts transmitted within the same codicological units might have helped clarify certain issues.
One example may illustrate this point. In comparing the variant readings of Marc. gr. 318 (Ma) and Vat. gr. 1772 (Vt), Di Mambro rightly identifies two substantial lacunae in Vt that are difficult to explain as ordinary copying errors. In my own work on the transmission of Manuel Bryennios’ Harmonica in these same manuscripts, I have encountered two comparable lacunae in Vt, each coinciding with a page turn in the apograph and resulting in an automatic and erroneous page turn in the antigraph. On this basis, it seems unnecessary to posit a lost intermediary manuscript that must have suffered some damage and was missing pages. It would be worth investigating whether the same phenomenon applies to Nicomachus, although this could not be tested for the purposes of the present review, since Marc. gr. 318 is not available online.
The difficulties encountered in the analysis of Paris. Suppl. gr. 59 (Ph) also highlight the limits of a strictly philological approach. Ph is a highly peculiar manuscript, whose anonymous compiler would merit further study. It presents an atypical version of ancient Greek musical treatises, produced by blending in parts of Pachymeres’ Quadrivium. In the case of Bryennios, entire chapters are reorganised, and some similar parts of the two treatises are replaced with Pachymeres’ phrasing. Ph appears to be a fair copy subsequently revised by its compiler, as evidenced by marginal annotations. Since Pachymeres himself used Nicomachus and incorporated the Eisagoge into his own Quadrivium, Ph reflects a circular process of cross-contamination that exceeds the simple antigraph–apograph model. Di Mambro concludes that both Pachymeres and Ph derive from a contaminated apograph of y (her proposed archetype), excluding y itself on the basis of certain variant discrepancies. Given, however, that she also notes several agreements with C (Coisl. 173), the working manuscript of Nicephorus Gregoras and itself an apograph of y, and considering the relative chronology of Pachymeres and Gregoras, it might be more economical to regard y as the common source of both Pachymeres and C, attributing minor variants to the autonomous interventions of individual scholars. The argument would have benefited from stemmatic diagrams indicating the chronological sequence of manuscript production.
The three appendices constitute a particularly welcome and relatively uncommon feature in a critical edition. Appendix 1 consists of three tables summarising (1) the other musical content of the manuscripts, (2) their material features, and (3) the stemmatic relationships among the treatises they transmit. These tables usefully complement the earlier catalogue of manuscripts, allowing it to be kept short. The stemmatic chart, however, is more problematic in its realisation, although the underlying idea is a very clever one. While it shows that different treatises within the same codex may derive from different antigraphs, it reproduces stemmatic relationships drawn from earlier editions without always reflecting the conclusions reached in the preceding discussion, and therefore, some relationships do not indicate the current state of knowledge. In the case of R (Vat. gr. 198), for instance, the chart retains a relationship that Di Mambro herself rejects on p. 66 for chronological reasons.[1] An explicit clarification of this discrepancy would have been helpful. The blank entry for Leid. Voss. Misc. 22, reflecting the absence of comparable treatises, might more straightforwardly have been omitted.
Appendix 2 offers a concise and valuable study of the Philolaus fragment as transmitted by Nicomachus, compared with its other indirect source, Stobaeus. Di Mambro carefully weighs the possibility of contamination between the two traditions, especially given that the oldest manuscripts of each may have passed over the same scholarly desk, that of Maximus Planudes. While manuscript circulation makes such contamination plausible, the presence of independent corruptions in both traditions ultimately prevents a firm conclusion.
Appendix 3 provides a particularly important contribution in its critical examination of the so-called Excerpta Nicomachi. Di Mambro demonstrates that, as for the Encheiridion, all surviving witnesses ultimately derive from a single manuscript, M (Marc. gr. app. class. VI.3), where both the Encheiridion and the Excerpta appear as marginal additions. She convincingly argues that the Excerpta are commentary notes on the Encheiridion, reflecting a late antique dossier on musical theory (both rhythmics and harmonics) that gradually incorporated additional scholia. Identifying M as the sole archetype of the extant tradition, she offers a new edition that restores the original chapter divisions disrupted in Jan’s edition.
The critical text of the Encheiridion is accompanied by a clear and efficient apparatus criticus, combining positive and negative apparatus in light of the fact that the entire tradition ultimately depends on a single manuscript. The apparatus is intentionally concise. Occasional loci paralleli point to later works reproducing substantial portions of the text, chiefly Pachymeres’ Quadrivium and Bryennios’ Harmonica; it is organized as an apparatus fontium secundarum. These references seem to apply to entire pages and do not take into account minor quotations; given that some variant readings are sometimes given, we may infer that there are no discrepancies when nothing appears. The Italian translation is accurate and closely reflects the editor’s textual choices, as far as my Italian allows any statement on the subject.
The final section provides detailed notes and commentary, organised with clear lemmata. Following a brief introduction to each chapter’s main themes, Di Mambro offers philological, lexical, philosophical, historical, and musical notes. This section will be particularly helpful for readers less familiar with ancient musical theory. One might nevertheless have welcomed—admittedly from the perspective of personal interest—a discussion of the term διάγραμμα, translated as scale in Chapters 11 and 12. In the last occurrence, the term refers explicitly to the list of notes that follows; while such a list does convey the structure of a scale, the concept itself is arguably anachronistic and not usually designated by the term diagramma.
In sum, this volume represents a careful, ambitious, and wide-ranging piece of scholarship whose scope extends far beyond the publication of a well-known Greek text. By foregrounding the interplay between musical, mathematical, and philosophical concerns, Di Mambro highlights the scientific and epistemological tradition to which the Encheiridion belongs. The substantial and well-chosen bibliography, together with six detailed indices, will undoubtedly establish this edition as the new standard reference for Nicomachus’ Harmonicon Encheiridion.
Notes
[1] Ingemar Düring, Die Harmonielehre des Claudios Ptolemaios, Göteborg 1930, p. XXXVI (with stemma at p. LXIX) : ms G. Doubts about the relationship R>C were raised by Anne Tihon first, and she was proven right by D. Bianconi and I. Pérez Martín (see bibliography given in Daniele Bianconi, « La biblioteca di Cora tra Massimo Planude e Niceforo Gregora. Una questione di mani », Segno e Testo 3 (2005), p. 400 and Inmaculada Pérez martín, « El ‘estilo Hodegos’ y su proyección en las escrituras constantinopolitanas », Segno e Testo 6 (2008), 389-458 at 450).