With this volume Jan Herlinger resumes his project of editing the theoretical works of Prosdocimo de' Beldemandis, bringing to new light two more works of one of the most influential authors of early fifteenth-century Italy. The Tractatus plane musice (written in 1412) and the Tractatus musice speculative (1425) are the fourth and fifth of Prosdocimo's works published by Herlinger, which follow his previous excellent editions of the Contrapunctus (1412) and of the Brevis summula proportionum (1409, published along with the short treatise on the division of the monochord of 1413).Footnote ¹ Prosdocimo's treatise on Musica plana has remained unpublished so far, while the Musica speculativa was available in an earlier edition not easily accessible outside Italy and not entirely reliable. The two treatises appear as the fourth volume of Studies in the History of Music Theory and Literature, a series recently started by the University of Illinois Press. These volumes, under the general editorship of Thomas Mathiesen, carry on the endeavour, begun with an earlier series directed by Mathiesen, of making available major theoretical works with English translation, scholarly introductions and commentaries.

Prosdocimo's biography is not heavily documented, but colophons and a few archival references consistently point to a master who spent most of his life in his hometown Padua, and in the nearby region. Briefly in Bologna as a student, he graduated in artibus in 1409 at the University of Padua, where he later taught, at least between 1422 and 1428. He also received a degree in medicine in 1411, a step required to pursue an academic career in Padua, where the arts and medicine were united in the same college. However, Prosdocimo appears as the quintessential arts scholar of his time, writing treatises on the four branches of the Quadrivium: arithmetic, astronomy, geometry and music. His music production is distinctive for devoting an individual treatise to each component of the theory of music, instead of dealing with the traditional partition into plainchant and mensural music (the most influential example of which approach, among those circulating at the time, is represented by Marchetto of Padua's paired works, the Lucidarium and Pomerium). The two newly published treatises are characteristic of this attitude in Prosdocimo. They aim to cover issues that Marchetto dealt with together in his Lucidarium, written sometime around 1317–18. Prosdocimo's Musica plana is concerned solely with the theory of plainchant, while the Musica speculativa focuses on the mathematical foundations of tuning, which Marchetto had discussed in the first part of his Lucidarium.

Prosdocimo's aim of providing an alternative to Marchetto's bestseller is clear in both works, and it is most interesting to observe his twofold attitude towards the earlier Paduan theorist. On the one hand, he acknowledges the ‘most excellent’ clarity and ‘orthodoxy’ of Marchetto's exposition on the fundamentals of music and the theory of ecclesiastical modes; on the other, a firm disagreement with Marchetto provided the very reason for him to compose the Musica speculativa. The latter work was intended to amend Marchetto's deceptive account of the ratios of intervals, ‘so that the evils, lies and mistakes concerning music that had been brought forth and disseminated by one Paduan might be removed by another’. Before summarising the main deviations between the two authors, it must be noted that Prosdocimo, when referring to Marchetto, would seem to stand in an ideal position for giving us additional clues to Marchetto's identity (either a patronymic, or a family name, or a more accurate placement of his birth). However, he refers to ‘a certain person, Marchetto by name, my fellow Paduan citizen’, making clear that in Padua he had access to little more information than that provided by the treatises themselves. I take this as a further confirmation that Marchetto may have spent most of his life outside of Padua (Cesena and Naples are the places hitherto suggested by colophons – and by the recent research of Carla Vivarelli).Footnote ² One other interesting point here is how Prosdocimo reconciles his own opposite views, the praise and the blame, for the author of the Lucidarium. Marchetto was, he tells us, ‘a simple performer, totally lacking in his theoretical side, which, mistakenly, he thought he understood most perfectly’. These echoes of the Boethian dualism between musici and cantores remind us that it is indeed plausible that Marchetto's career was in fact that of a composer and performer, on which we happen to have much less evidence than we have on his contribution as a theorist.

As is customary, a brief summary on the sources with inventories of their content accompanies the edition. The two treatises are extant together in manuscripts in Bologna and Lucca, and a further source in Cremona preserves the Musica plana alone; all three manuscripts transmit almost exclusively works by the Paduan theorist. The Bologna manuscript is a very accurate and authoritative source which transmits not only all of Prosdocimo's known musical treatises, but also a few arithmetical and astronomical ones, all arranged in chronological order by date of presumed composition. The Lucca source is most relevant in that it contains later ‘revisions’ of the treatises, presumably by Prosdocimo himself; sadly, the Cremona manuscript has not come down to us in its entirety. A few circumstances surrounding these manuscripts would deserve further scrutiny. First, while actually not copied in Padua but in the outskirts of Ferrara, the Bologna manuscript appeared in a Paduan collection in the seventeenth century. This may raise the question of whether its scribe, an Antonio degli Obizzi from Lucca, might have been only temporarily resident in Ferrara, and perhaps more closely associated with Padua, where a branch of the Obizzi family was based. Second, another ‘Antonius’, also possibly from Lucca (styled ‘de Luca’) is found among the reader–compilers of music theory manuscripts of the period: he is the Servite friar responsible for an expanded version of Johannes de Muris's Ars practica mensurabilis cantus (the Libellus) found in Brussels, Bibliothèque Royale Albert 1^er, MS II.785. Third, if the Lucca manuscript can also be associated with Padua through its provenance (there is evidence that it was owned by the monastery of San Giovanni of Verdara), any clues about the origin and provenance of the Cremona manuscript are less informative. However, it is worth mentioning that the manuscript now Florence, Biblioteca Medicea Laurenziana, Ashburnham 206, an autograph of Prosdocimo, contains astronomical tables relating to the cities of Bologna (where Prosdocimo was a student) and Cremona.

Prosdocimo's Musica plana relies heavily on Marchetto for the theory of plainchant. Herlinger, in his introduction, points out the deviations of the newer treatise from its model, including an extended set of rules for distinguishing between the tones. A few details are quite revealing of the fact that the professor of arts, proud of his speculative background, was not the experienced performer that Marchetto was. Approaching the fivefold Marchettan classification of tones as perfect, imperfect, pluperfect, mixed and intermixed, Prosdocimo merges the latter two in a single quality of a tone that ‘adopts the nature of another tone and composes a third nature’. As Herlinger observes, it is one thing to ‘mix the nature’ of an authentic tone and its plagal partner, but another to mix two non-partner tones, with a different final. The distinction, obliterated in Prosdocimo's simplification, would have been quite obvious, albeit important, to a practitioner; on the other hand, a performer would not have been in much need of the extended explanation of the use of the hand that opens the treatise. Moreover, compared with the Lucidarium, the Musica plana discusses a very limiting use of mutations, and of the alternation of melodic inflections between B flat and B natural. Prosdocimo, in fact, confines the determination of the use of accidentals to the consideration of hexachords, and also gives no account of the use of accidentals other than B flat. In sum, his approach to the theory of plainchant must be seen as a rather conventional one. However, Herlinger notes that this treatise contains one point of great interest, also for scholars and performers interested in the polyphonic repertory. After introducing the four original and four plagal tones, it states that any ‘manner of singing’ either ‘in plainchant or in measured song’ belongs to one of these eight tones. Prosdocimo is then one of the very few masters, including the anonymous author of the opening treatise in the Berkeley manuscript, as well as Amerus and Jacques de Liège, who either explicitly recommend, or imply, the application of modal theory to mensural music.

Prosdocimo's disagreement with the earlier theorist is, as I mentioned, the very programme of his Musica speculativa. On many occasions he ridicules Marchetto for his inaccurate use of terminology (a tone is a ratio, not a number; the semitones should not be called enharmonic, diatonic or chromatic, as these definitions are for hexachords, etc.) and for some logically and mathematically wrong statements. Beside these, his main point of criticism concerns Marchetto's division of the tone into five equal parts as an alternative to the Pythagorean major and minor semitones. As Herlinger puts it, while Marchetto tried an ‘imaginative attempt’ to introduce a non-Pythagorean conception of tuning, Prosdocimo strives to stay within pure mathematical orthodoxy (hence not allowing the geometric division of any superparticular ratio, such as the sesquioctave 9 : 8 representing the tone). Also, when discussing other controversial issues such as the placing of the perfect fourth (his ‘minor fourth’) midway between consonant and dissonant intervals, as a quasi-consonance, Prosdocimo insists upon invoking the ‘ancients’ against those he never calls by name but simply dismisses as the ‘Marchettinos’. It is worth recalling that Herlinger has shown elsewhere (curiously choosing not to refer to his own work in this edition) that among the latter we should also include his near contemporary fellow citizen (by adoption) Johannes Ciconia, certainly guilty of reiterating some of Marchetto's mistakes in his Nova musica.Footnote ³

The treatises presented in this book offer these and other points of departure for both scholars and informed performers, not restricted to the theory of plainchant and tuning. Herlinger, a foremost authority on late-medieval music theory and on Marchetto and Prosdocimo in particular, draws attention to these in his clear-cut and thought-provoking introduction. The texts and the critical apparatus are thoroughly accurate, and the English translation provides a smoother but reliable access to Prosdocimo's texts. A number of learned footnotes provide insights into the nuances of the text, link it with related treatises and scholarly discussions, and also help to decipher the sometimes complex calculations involved in the argument. While these texts are not yet included in the Thesaurus Musicarum Latinarum database, it is also a blessing to find a rich Index verborum in which to look for references to individual terms. In sum, the structure, layout and overall quality of this volume do not differ, apart from some graphical improvements, from the two previously published by Herlinger on the same author: so the three can happily sit side by side on the shelf, awaiting a possible fourth, it is to be hoped, in the form of a new edition of the earliest of Prosdocimo's musical writings, the Expositiones tractatus practice cantus mensurabilis Johannis de Muris.