The new AHRC project described

Our new AHRC-funded project started work on 1 October 2017. We thought it would be a good way to inform our followers what we propose to do by posting the Case for Support, the most detailed and extensive component of our application to the Research Council. This is long, but it will give those interested a clear idea of our intentions over the next four years. (It should be pointed out that the timetable towards the end has been put out of joint by the lead time between submitting the application and beginning the project, which turned out to be several months longer than expected; we have adapted it as necessary and are using the revised version as our work plan.)

 

Interpreting the Mensural Notation of Music: an Expert System Based on the Theory of Johannes Tinctoris

Case for Support

Interpreting the Mensural Notation of Music is a 48-month interdisciplinary collaborative research project that brings together experts in music history, music theory, and digital musicology to develop a twenty-first-century response to a challenge posed by the notation of late-medieval music and addressed by the fifteenth-century music theorist Johannes Tinctoris (c.1435–1511). The problem is to interpret the context-dependent mensural system of rhythmic notation, prevalent from the early fourteenth century to the early seventeenth, in terms of definite durations. The aim of the project is to model Tinctoris’s fifteenth-century theory of musical notation, written in Latin prose, as a twenty-first-century formal system, capable of being encoded as a computer program that can perform such interpretation. This project fits into a wide range of current research aimed at automating the reading of musical sources, the editing of the music they contain, and the digital analysis of that music. Our core focus is on the interpretation of musical notation with a view to editing and analysis. We seek to discover whether Tinctoris’s theory is as complete as it seems, how the articulation of his theory relates to the practice of interpretation, and how his theory (and practice as a composer) relates to the practice of other composers of his time. Our modelling of music theory in digital terms represents a new application of artificial-intelligence technologies within the humanities. Birmingham Conservatoire has an established record of research in these areas, and the Principal Investigator, Co-Investigator, and Researchers are internationally recognized in their respective fields.

We will pursue three interrelated goals in applied musicology. First and foremost, we propose to develop an expert system – a computer system that emulates the decision-making ability of a human expert – to convert the rhythmically ambiguous notation into definite rhythmic values, permitting co-ordination into score and translation into modern, context-independent notation. Secondly, to complement our existing critical edition of his theoretical works (see Research context), we will produce a new critical edition of Tinctoris’s complete practical compositions, which will form part of the training material for the expert system. Finally, as a key part of our pathway to impact we will develop an interactive learning tool, with which students, performers, or others can practise the cognitive processes involved in interpreting mensural notation. In principle, our system ought to be extensible to all music written in mensural notation. Coverage of the full evolution of the mensural system from the early fourteenth century, when the minim was invented, until the early seventeenth, when triple subdivision of undotted notes was finally limited to the triplet, would not be achievable in the time we have, but we expect our system to be applicable to nearly all music from about 1400 onwards. Other editors will be able to use our system for their own purposes.

The outputs and outcomes of this project will provide significant benefits for historians, editors, and analysts of fourteenth- to sixteenth-century music, and for professional, semi-professional, and amateur singers and instrumentalists.

Research questions

We expect to learn unexpected things in the course of building our expert system, and in so doing to create new historical knowledge. Our key research questions are:

  • Are there inconsistencies or gaps in Tinctoris’s putatively exhaustive music theory?
  • How can these inform the foundation of an expert system?
  • How can the differences between Tinctoris’s theory and practices he explicitly criticized be rigorously characterized?
  • How do the various rule systems and notational practices interrelate?
  • What is the prioritization and hierarchy of these parameters for constructing the expert system?
  • What is the logical structure of the expert system?
  • How does this affect our understanding of Tinctoris’s music theory?

The intellectual and practical challenges of this project are considerable. Modelling a late-medieval music theory as a computer program involves much more than machine translation. The project draws upon the expertise of a renowned, established interdisciplinary team, and world-leading scholarship on Tinctoris, the mensural system, and advanced techniques of digital musicology.

To make the system work effectively, we shall incorporate machine-learning elements to train the system to co-ordinate multiple rule sets and to resolve apparent conflicts. This will make use of a graded series of pieces of actual fifteenth-century music to train and test the system, comprising:

  • the copious music examples expressly composed to instantiate the rules in Tinctoris’s theoretical writings, which can be expected to be fully compliant with his teachings;
  • Tinctoris’s practical compositions (high in quality and moderate in number), which we will test to see how far his practice complied with his theory;
  • selected compositions by two composers highly regarded by Tinctoris – Guillaume du Faÿ (1397–1474) and Antoine Busnoys (1430–1492) – to investigate Tinctoris’s criticism of Busnoys’s notational ‘errors’ and to test whether Du Faÿ’s practice does comply with Tinctoris’s precepts or not.

The music examples have already been edited and published online (see Research context). The new critical edition of Tinctoris’s complete musical works is a logical outcome of our project, since the existing edition is inadequate. We must re-edit Du Faÿ’s and Busnoys’s pieces on the basis of their original notation, but we shall speed the process with reference to good existing critical editions in modern notation. We expect to learn much from extending the rule base of our expert system to incorporate self-consistent but mutually inconsistent practices, modelling what a musicologist does when editing fifteenth-century music.

The interactive training module will become the basis of our interactive learning tool. The module will present progressive exercises in mensural notation together with target results and a mechanism for annotation, and will be able to give feedback on progress and to offer hints. This is an important and timely means for our work to extend beyond specialist academic research, to help support performing musicians as well as undergraduate and postgraduate students. This addresses an increasing dearth of technical expertise in pre-modern music studies rooted rigorously in contemporaneous theory. Such a self-directed learning tool, ideally suited to distance learning, will also offer high-quality guidance for those performers who are starting to perform medieval and Renaissance repertories from original notation in facsimile, but who are not necessarily equipped with the theoretical knowledge required to understand the fine detail of that notation.

At Birmingham Conservatoire, we are in a particularly strong position to advance a case for bringing scholarship of mensural notation into serious dialogue with the world of performance. Although some performing groups in Europe and the US have recently been exploring performance directly from original mensural notation, in the UK there is a gap in investment in, and promotion of, this kind of activity, for which the present proposal offers even richer intellectual, historical, and performative layers of support. Rather than polarizing practice into those who insist on performing only from original notation and those who prefer easier common-practice editions, the project will explicitly mediate, with a view to better, deeper understanding on both sides. It makes good sense to combine the Conservatoire’s established academic expertise in this field with its obvious performance-training remit (especially its growing Early Music department), potentially creating a UK hub for such activities, all underpinned by the latest in machine-aided interpretation and research.

Research context

The late-medieval mensural notation of musical rhythm, unlike its modern counterpart, is context-dependent in complex ways. In modern or common-practice notation, every note level is consistently divisible by two (with special, familiar exceptions called ‘tuplets’, always clearly marked), so there are two minims to the semibreve, two crotchets to the minim, etc. (other values can be obtained by using a following dot, which adds 50% to the value of a note, or ‘tying’ notes together with a curved stroke). In the late middle ages, however, all levels above the minim could be divided either by two or by three, as determined by a mensural signature in the composition or inferred through specialist recognition of the context. When one level was divided by three, a note equal in duration to two of the smaller level could be achieved by manipulating either level through processes called ‘imperfection’ and ‘alteration’. Depending on its context within such a mensuration, a larger note might be worth either three (perfect) or two (imperfect) of the next smaller, or a smaller one might be either equal to or double (altered) its regular value, without any notational distinction. Dots functioned in three distinct ways to affect durations (augmentation, perfection, or division), but ties had not yet been invented. In the extreme case, depending on its circumstances, one of the longest notes (a maxima) might be worth any value between 16 and 81 times the note four levels smaller (the minim). There were complex rules for construing the context of notes in practical music to determine their actual duration, since the visual forms of the notes did not encode this information.

For the better part of the past two centuries, the critical editing of music composed between the early fourteenth and the early seventeenth centuries has required editors to apply these rules in order to discern the intended durations, to put the separate parts into score (visually co-ordinating them so their temporal interrelationships are immediately apparent), and to translate the context-dependent original notation into the context-independent modern notation (even when ‘original note values’ are preserved). Editors avail themselves not only of the rules of mensural notation but also of the rules of counterpoint, which govern the pitch relations between simultaneous parts. The most comprehensive and detailed expression of all these rules is contained in the theoretical writings of Johannes Tinctoris. Like verbal translation, however, this norm of transcription is not a reliably reversible procedure; important information relating to the fundamental nature and structure of the original compositional conception is lost in the process. For instance, a number of important works (like Busnoys’s L’homme armé mass; see Research methods) present a Tenor part, repeatedly stated, whose notation is invariant but whose durations vary when subject to different mensurations and proportional relations to other parts, something distorted or imperceptible in modern notation.

This project builds on the intellectual and practical foundations of our AHRC-funded project, The Complete Theoretical Works of Johannes Tinctoris: A New Digital Edition (AHRC AH/I003827/1, 2011–14, henceforth JT:CTW), which established an intellectual infrastructure that can be used in many ways. We made the resulting editions and software of this earlier research available for many other scholarly purposes, and the proposed project is not so much a continuation as one possible sequel, developing this material in one particular, extremely important new direction. The critical editions and English translations produced in JT:CTW of all Tinctoris’s most pertinent treatises provide the textual foundation on which we will build our expert system. We will also adapt and extend the new software developed for the music examples in JT:CTW, which interprets data input in alphanumeric form as musical notation that can be displayed online in high quality, for the much more complex demands of the present project. The project will be hosted as an open-access online resource as part of our existing Early Music Theory web site (http://earlymusictheory.org), alongside our still-evolving JT:CTW edition.

We shall be working throughout with the developing standard for machine-readable musical notation, the Music Encoding Initiative (MEI: http://music-encoding.org); both the uninterpreted input files and the interpreted output will constitute compliant MEI encoding. We aim to integrate our system with research being carried out by others; in principle, it will be applicable to all music of the fourteenth, fifteenth, and sixteenth centuries. ‘Upstream’ of our system, various projects are producing uninterpreted mensural MEI through optical music recognition (e.g. Gamera, http://gamera.informatik.hsnr.de/addons/; Aruspix, http://www.aruspix.net; the Marenzio Online Digital Edition, http://www.marenzio.org; the early-music component of Transforming Musicology, http://www.transforming-musicology.org); ‘downstream’, others are automating the digital analysis of music in modern notation (e.g. music21, http://web.mit.edu/music21/; The Josquin Project, http://josquin.stanford.edu; The Lost Voices Project, http://digitalduchemin.org; Gesualdo Online, https://ricercar.gesualdo-online.cesr.univ-tours.fr). We shall bridge this gap, permitting (in suitable cases) a fully computerized process from acquisition of the notation through to analysis of the music. The files we produce can also be exported into other data formats to enable postprocessing in music-engraving software for high-quality printed output, making the music available to performers, editors, and publishers, as well as other scholars working on these repertories.

Machine learning, an approach to Artificial Intelligence that allows a system to learn from provided training data, has a long association with music through music composition, optical music recognition, and classification tasks (primarily on sound recordings). Despite this, there has been little direct work on applying these approaches within music theory. We have three key requirements of any machine-learning system used in this project. First, it must model the features and rules that we predefine. Secondly, it must be possible to subject decisions that it makes to introspection, that is, it must be possible after a decision has been made to view the rules that were brought to bear in that case, and how they were evaluated. Thirdly, the system must operate globally rather than linearly. Since a decision about any given note can affect or be affected by notes either earlier or later, and in any voice of a polyphonic work, there is no note-by-note order in which the piece can be ‘solved’. These constraints, along with the complexities of modelling music-theoretical features in logical terms, represent a new application of artificial-intelligence technologies within a humanities discipline.

Research methods

Tinctoris’s own intellectual method and the structuring of his notation treatises will inform the process of mapping his theory isomorphically to a formal system capable of computational expression. His careful delineation and articulation in verbal terms of his rule system, and his intention to instantiate it exhaustively, will make his theory easier to work with than those of other, less systematic late-medieval writers.

There are a number of Artificial Intelligence approaches that might be applicable to the task, depending on how complex and explicit Tinctoris’s rule system proves to be, along with the amount of musical context required by each rule. Before exploring our options in detail, we will create a general framework that applies a supplied algorithm to an input file to generate an interpreted output and then optionally compares the result to an expert-supplied ‘correct’ version. This will provide a test framework for experimentation and comparison, allowing us to try multiple approaches without substantial recoding. Candidate approaches, starting with simpler, lower-risk systems and then with growing complexity, will be implemented and tested in successive development iterations. Since being able to inspect the process of deduction is important to us, neural-network and other black-box systems may not be entirely suitable. We will aim to publish our interpretation of Tinctoris’s formal rules using Semantic Web technologies, allowing us to more easily disseminate our interpretations and algorithms, compare them with others and indicate provenance for completed interpretations, all in a sustainable, standards-compliant manner.

Training and testing materials: (1) Music examples from Tinctoris’s treatises De notis et pausis, De regulari valore notarum, De imperfectione notarum, De alteratione notarum, De punctis, and De arte contrapuncti. (2) A new critical edition of Tinctoris’s practical music: 3 complete masses, 1 incomplete mass (Gloria/Credo/Sanctus), 1 Lamentations setting, 3 or 4 brief Latin pieces, 9 songs. (3) New editions in original notation of Du Faÿ: Missa L’homme armé, Supremum est mortalibus, Ave regina celorum (4vv), Salve regina; Busnoys: Missa L’homme armé, Anima mea / Stirps Jesse, Regina celi I, Conditor alme siderum. We have selected compositions that are likely to require adapting the rules taught by Tinctoris to apply to notations he would not have admitted. The L’homme armé masses of both composers can be directly compared to Tinctoris’s own, and the chosen motets present interesting proportional relationships. The materials for (1) are online and exportable as uninterpreted MEI in JT:CTW. The sources for producing (2) and (3) are nearly all available in printed facsimile editions or online digital facsimiles; digital images will be sought from the libraries holding those manuscripts that are not yet available (Copenhagen, Kongelige Bibliotek; Edinburgh, National Library of Scotland; Florence, Biblioteca Nazionale Centrale; Munich, Universitätsbibliothek; Vatican City, Biblioteca Apostolica Vaticana; Zwickau, Ratsschulbibliothek). As these images will be used for research purposes and not published by us, no issues of intellectual property arise; the music itself is all in the public domain.

Technical summary

This project will produce three types of digital output – musical corpora, software and web pages.

The musical corpora will be used for training and testing the software, and as core learning materials. They will be encoded using the Music Encoding Initiative file format (MEI) and will be made freely available online, both as files for download and as rendered scores for viewing and printing using Verovio, an in-browser score viewer (http://www.verovio.org/). Corpora will be entered by team members either using a score editor and then exporting the results or using the input system developed as part of JT:CTW. The resulting encodings will then be marked up with information about durational interpretation.

Standalone software will be developed to provide durational interpretation and analysis. Where this builds on existing machine-learning libraries, they will be selected to be free and open source. Any software developed by us will be distributed under an open-source license on the Conservatoire’s GitHub site. Learning materials and academic output in the form of web pages will be made freely available and any source code used to generate the pages will be placed on GitHub.

We will extend the functionality of Verovio to support our pedagogical needs and to ensure that all the notational features we require are appropriately handled. We may also need to extend MEI, where its representation is incomplete. In the first instance, these extensions will also be made available on our GitHub site, but we would expect that some of these will be incorporated into the official versions of Verovio and MEI where appropriate.

Computational resource requirements are expected to be small for this project, and servers and backup and archives services will be provided by Birmingham City University for a minimum of 10 years following the end of the project.

Project management

Project team
Dr Jeffrey J. Dean will act as 0.5 FTE Principal Investigator. He has spent over two decades as a free-lance project manager in academic publishing, including seven years as a Senior Editor of the New Grove Dictionary of Music and Musicians. Dean’s publications provide evidence of his international reputation in the history of fifteenth- and sixteenth-century music and music theory, with particular attention to Tinctoris as both a theorist and a composer. On JT:CTW he was responsible for source transcription, first-draft editing, and translating of Tinctoris’s texts, finalizing them in consultation with Woodley, and worked with Lewis on the software development of the project. He has worked as a software technician in the past and is familiar with computational thinking. Principal responsibilities: Working with Lewis on modelling Tinctoris’s theory in software; working with Woodley and Goursaud on editing music by Tinctoris, Du Faÿ, and Busnoys, and assisting them as needed with development of the learning module; other original research arising from project results.

Professor Ronald Woodley will act as 0.5 FTE Co-investigator. His CV and publications testify to his project management experience, his international reputation for musicological expertise in late-medieval music theory, and his world-leading research on the life and writings of Tinctoris. He has extensive experience of editing medieval texts. On JT:CTW he finalized editions and translations of Tinctoris’s texts in consultation with Dean and produced commentary material of various kinds. Principal responsibilities: Leading the development of the learning module in association with Lewis and Goursaud; mentoring Dean and advising on Tinctoris’s theory; leading the editing of music by Tinctoris, Du Faÿ, and Busnoys in association with Dean and Goursaud; other original research arising from project results.

Mr David Lewis will act as 0.5 FTE Researcher. He is an established expert in digital musicology, with a growing record of accomplishment, especially in connection with early music. On JT:CTW he was responsible for the project’s software implementation, and, as his CV demonstrates, he has contributed to other projects whose results are relevant to this one. Principal responsibilities: Software development; other original research arising therefrom.

Dr Christian Goursaud will act as 0.5 FTE Researcher. He was Project Student on JT:CTW, completing his doctoral thesis on the codicology of two central Tinctoris manuscripts; he has particular experience in the fine detail of manuscript study, musical palaeography, and the cultural context of musical production in the fifteenth and early sixteenth centuries, and is also an active professional consort singer with experience of performing from mensural notation. His role will provide vital academic development as a postdoctoral researcher. Principal responsibilities: Working with Woodley and Dean on the editing of music by Tinctoris, Du Faÿ, and Busnoys; working with Woodley and Lewis on development of the learning module; other original research arising from project results.

The project team will meet face to face at Birmingham Conservatoire once each term, by videoconference monthly, and they will communicate frequently by e-mail. Good value for taxpayers’ money will be ensured by careful project management to the timetable below, by a lean, efficient, and expert research team, and by the dissemination of a rich, varied, and useful set of outputs.

Benchmarks (Dean) / Woodley / Goursaud Dean / (Woodley) / Lewis
 3 months Ensure compliant uninterpreted mensural MEI of all Tinctoris music examples; annotate examples from De not. et paus., De reg. val.; begin editing Tinctoris’s shorter works; lightning paper introducing project at Med-Ren conference (Prague) Begin developing formalism for musical rules; select and evaluate machine-learning techniques
 6 months Annotate examples from De imperf.; complete edition (including annotation) of Tinctoris’s shorter works Develop software infrastructure, including test suite and experimental setup
 9 months Annotate examples from De alt., De punct.; complete edition of Tinctoris’s Lamentations; begin editing Du Faÿ’s L’homme armé mass Develop and test initial rule set; identify areas in MEI that require extension; identify missing notational elements in Verovio
12 months Begin annotating examples from De contr.; complete edition of Du Faÿ’s L’homme armé mass; begin editing Tinctoris’s L’homme armé mass Extend MEI and Verovio for representation and display of music examples
15 months Complete annotation of examples from De contr.; complete edition of Tinctoris’s L’homme armé mass; begin editing Busnoys’s L’homme armé mass Begin development of learning tool; test machine-learning system
18 months Complete edition of Busnoys’s L’homme armé mass; begin editing Tinctoris’s Missa [secundi toni irregularis]; feed into development of learning tool Continue testing and refinement with music as it becomes available; presentation at ISMIR (Paris)
21 months Complete edition of Tinctoris’s Missa [secundi toni irregularis]; begin editing Tinctoris’s Missa [quinti toni irregularis]
24 months Complete edition of Tinctoris’s Missa [quinti toni irregularis]; begin editing Tinctoris’s Missa [primi toni]; first workshop on learning tool (Birmingham) Complete first test cases for all systems; complete second iteration on learning system
27 months Complete edition of Tinctoris’s Missa primi toni and Du Faÿ’s Supremum est mortalibus; work-in-progress presentation at Med-Ren (Basel) Subsequent iterations of systems will be timed to coincide with workshops; presentation at MEC (place tbc, probably Europe)
30 months Complete edition of Du Faÿ’s Ave regina celorum and Salve regina Implement other machine-learning approaches for comparison
33 months Begin editing Busnoys’s motets; second workshop on learning tool (Oxford)
36 months Complete edition of Busnoys’s motets; continue testing and refinement of learning tool during final year
39 months Themed session at Med-Ren (place tbc, probably UK)
42 months Third workshop on learning tool (London); presentation at AMS Annual Meeting (Minneapolis)
45 months Tie up loose ends and prepare final published outputs
48 months Release software outputs

If a key member of the project team should become unavailable, we shall appoint a replacement with the appropriate skill set. Birmingham City University can offer expertise both on mensural notation and on machine learning.

Dissemination

Principal beneficiaries of this proposed project will include all those in the early-music world involved in the editing, performance, study, and scholarship of late-medieval and renaissance musical repertories (in principle all music of the fourteenth to the sixteenth centuries), for whom a much heightened and enriched awareness of the implications of the original, complex notational parameters will be raised, as well as giving clearer view of the limitations to understanding of most conventional modern editions in overly simplified common-practice notation. The system outlined here will provide a practical computer-aided resource for the output of comprehensible and performable editions of these repertories, whilst at the same time highlighting and embedding the underlying structures and intellectual context of the original notations, and the issues involved in their translation into other, more modern notational schemas. In an educational context, the project will offer students and course leaders of early-music programmes a new resource for handling primary manuscript and early printed source material from this period of music history, which can feed into their own editing, performing, and historical projects at various levels of ability, catering for the needs of the student assignment as well as those of the fully professional ensemble or scholar.

The software we develop will be published online with open access as a comprehensive system incorporating graphical music input, durational interpretation of the rhythmic notation, display of the music in score or parts, interactive user refinement of the machine results, and export for music-engraving software. There will also be an online, open-access learning module. Source code for the software will be freely accessible through GitHub; all materials will have a Creative Commons CC-BY-NC license (free non-commercial use with attribution).

Aside from the new editions of Tinctoris, Du Faÿ, and Busnoys outlined above, musicological materials produced will include articles, reports, and a project blog covering analytical, technical, historical, and theoretical conclusions or speculations, as they evolve from both the input and output processes of the project. These will expose distinctions, problematics, inconsistencies, or gaps in the sources under scrutiny, in order to achieve a finer grain of understanding in the relationships between theoretical and practical musical sources of the late medieval and early renaissance period. Specialist conference papers and presentations, on both the musicological and technological aspects of the project, will be paced carefully, especially from Years 2 to 4, at high-profile events in the UK, USA, and continental Europe, especially the annual conference on Medieval and Renaissance Music (Med-Ren) and the Annual Meeting of the American Musicological Society. We also intend to make full use of existing professional contacts with individuals and performing ensembles already working at a high scholarly level from both mensural and common-practice notation, such as Stratton Bull of Cappella Pratensis (Leuven), Jesse Rodin of Cut Circle (Stanford), and Peter Urquhart of Capella Alamire (New Hampshire).

In terms of external engagement, an important aspect of the project will be the organization of a series of at least three public workshops, to be held in Birmingham, Oxford, and London, which will function as a progressive introduction of the software learning tool as it evolves, and to obtain valuable feedback from other performing musicians, students and scholars, which will help refine the later stages of the tool’s development.

Select bibliography

Margaret Bent, Counterpoint, Composition, and Musica Ficta (New York and London, 2002): esp. ‘Editing Early Music: The Dilemma of Translation’; ‘Resfacta and Cantare super librum

Bonnie J. Blackburn, Composition, Printing and Performance: Studies in Renaissance Music (Aldershot, 2000): esp. ‘Tinctoris and the Art of Composition: A Lost Guide to Tinctoris’s Teachings Recovered’; ‘On Compositional Process in the Fifteenth Century’; ‘Did Ockeghem Listen to Tinctoris?’

Bonnie J. Blackburn, ‘The Sign of Petrucci’s Editor’, in Venezia 1501: Petrucci e la stampa musicale / Venice 1501: Petrucci, music, print and publishing [Venice 2001], ed. Giulio Cattin and Patrizia Dalla Vecchia (Venice, 2005), 415–29

Benjamin W. Bohl, ‘Fingerprinting the Rule: Towards Interconnecting Music Treatises by Means of an Encoding Scheme for Compositional Rules’, Music Encoding Conference, Mainz, 2013: http://music- encoding.org/archive/program2013 (not yet published)

Antoine Busnoys, Collected Works, parts 2–3: The Latin-Texted Works, ed. Richard Taruskin, Master and Monuments of the Renaissance, 5 (New York, 1990)

Anna Maria Busse Berger, Mensuration and Proportion Signs: Origins and Evolution (Oxford, 1993)

A Correspondence of Renaissance Musicians, ed. Bonnie J. Blackburn, Edward E. Lowinsky, and Clement A. Miller (Oxford, 1991)

Guillaume du Fay, Opera omnia, ed. Alejandro Enrique Planchart (Santa Barbara, 2008– ): http://www.diamm.ac.uk/resources/music-editions/du-fay-opera-omnia/

James Grier, The Critical Editing of Music: History, Method, and Practice (Cambridge, 1996)

Kate Helsen et al., ‘Optical Music Recognition and Manuscript Chant Sources’, Early Music, 42 (2014), 555–8

Frauke Jürgensen and Ian Knopke, ‘A Comparison of Automated Methods for the Analysis of Style in Fifteenth-Century Song Intabulations’, Musicae Scientiae (Special Issue 2005–6), 139–160: https://jyx.jyu.fi/dspace/handle/123456789/19344

Ian Knopke and Frauke Jürgensen, ‘A System for Identifying Common Melodic Phrases in the Masses of Palestrina’, Journal of New Music Research, 38 (2009), 171–81

Laurent Pugin and Tim Crawford, ‘Evaluating OMR on the Early Music Online Collection’, in Proceedings of the 14th International Society for Music Information Retrieval Conference (ISMIR) (Curitiba, 2013), 439–44: http://ismir2013.ismir.net/wp-content/uploads/2013/09/65_Paper.pdf

Johanni [sic] Tinctoris Opera omnia, ed. William Melin (Corpus Mensurabilis Musicae, 18; n. p., 1976)

Rob C. Wegman, ‘Miserere supplicanti Dufay: The Creation and Transmission of Dufay’s Missa Ave regina celorum’, The Journal of Musicology, 13 (1995), 18–54

Rob C. Wegman, ‘Mensural Intertextuality in the Sacred Music of Antoine Busnoys’, in Antoine Busnoys: Method, Meaning, and Context in Late Medieval Music, ed. Paula Higgins (Oxford, 1999), 175–214

See also relevant writings by project team members in attached publication lists.

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