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

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This innovative project addresses a central issue confronting those who work with musical sources from the early fourteenth to the early seventeenth century, whether as editors, analysts, or performers. The 'mensural' system of rhythmic notation, then prevalent, was highly contextual; unlike modern 'common-practice' notation, in which all notes are divisible only by two (with well-defined exceptions called 'tuplets') and are therefore definite in duration, many notes in mensural notation could be divided either by two or by three without visual distinction, and their durations were subject to further conventional manipulation according to their context. We will construct an online software expert system, modelling the teachings of one of the foremost fifteenth-century music theorists, Johannes Tinctoris (c.1435-1511), that will take files in uninterpreted mensural notation as input and output them in terms of definite durations. Tinctoris's theory lends itself to such treatment by virtue of his rigorous method and intention to instantiate his rules exhaustively. The proposed system is one natural outgrowth of the online critical edition of Tinctoris's writings produced by the same project team (http://earlymusictheory.org/Tinctoris). Results may be output in a variety of formats: original mensural notation or common-practice notation, score or separate parts. Our system will accept the input of uninterpreted mensural notation produced by other projects; our interpreted output will be available to analytical software developed by still others.We will use machine-learning techniques to improve the system's performance. This will involve training with a graded series of pieces of actual fifteenth-century music: (1) all the music examples Tinctoris composed to illustrate his treatises on mensural notation and counterpoint; (2) all Tinctoris's practical compositions, for which we will produce a new critical edition; (3) selected works of two composers Tinctoris regarded highly, Guillaume du Fay and Antoine Busnoys, whose music was composed with somewhat different notational conventions from those articulated by Tinctoris. We expect the system to be able to interpret the notation of nearly all music from between the early fifteenth century and the early seventeenth (the fourteenth century presents variants we should not have time to address).Students of late-medieval and early-modern music nowadays are less well versed than formerly in the complexities of mensural notation, while at the same time more and more musicians are interested in performing such music from facsimiles of the original sources. Accordingly, we will develop a new online interactive learning tool, with which students, performers, or others can practise the cognitive processes involved in interpreting mensural notation. The tool will present progressive exercises together with target results and a mechanism for annotation, and will be able to give feedback on progress and to offer hints.We expect the development of our software system to generate unpredictable historical discoveries concerning the completeness of Tinctoris's theory and its relation to the wider practice of his time. We will communicate these in the form of standard academic publications. An especially valuable aspect of the project will be a series of public workshops in Birmingham, Oxford, and London, forming a progressive introduction to the software learning tool as it evolves. Principal beneficiaries of this project will include all those involved in the performance, editing, and scholarship of late-medieval and early-modern musical repertories. For all users a much heightened and enriched awareness of the implications of the original, complex notations will be raised, and a highly innovative, practical tool made available to assist with the learning process, as well as to enable the production of new user-led editions of works from this pivotal period of western European music.