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

这个创新的项目解决了那些从14世纪早期到17世纪早期从事音乐资源工作的人所面临的核心问题，无论是编辑、分析还是表演者。当时流行的“计量”节奏记谱系统是高度情境化的；与现代的“常规”记谱法不同，所有的音符都只能被两个音符整除（除了定义明确的“二连音”），因此在持续时间上是明确的，测量记谱法中的许多音符可以被两个或三个音符分开，没有视觉上的区别，它们的持续时间是根据它们的上下文进行进一步的常规操作的。我们将构建一个在线软件专家系统，模拟15世纪最重要的音乐理论家之一Johannes Tinctoris （c.1435-1511）的教导，该系统将以未解释的测量符号作为文件的输入，并以确定的持续时间输出它们。廷托里斯的理论由于其严谨的方法和详尽地实例化其规则的意图而适合于这种处理。这个提议的系统是tintoris作品的在线评论版的自然产物，由同一个项目团队制作（http://earlymusictheory.org/Tinctoris）。结果可以以多种格式输出：原始测量符号或常用符号，分数或单独的部分。我们的系统将接受其他项目产生的未解释的计量符号的输入；我们的解析输出将可用于其他公司开发的分析软件。我们将使用机器学习技术来提高系统的性能。这将包括对一系列15世纪实际音乐作品的分级训练：(1)丁托利斯为说明他关于节拍记谱和对位法的论文而创作的所有音乐例子；(2)丁托里斯的所有实用作品，我们将为此制作一个新的评论版本；(3)丁托利斯高度评价的两位作曲家纪尧姆·杜·费伊和安托万·布斯诺瓦的作品选集，这两位作曲家的音乐与丁托利斯所表达的符号惯例有些不同。我们期望这个系统能够解释从15世纪早期到17世纪早期的几乎所有音乐的符号（14世纪呈现的变体我们应该没有时间讨论）。如今，研究中世纪晚期和早期现代音乐的学生不像以前那样精通测量记谱法的复杂性，而与此同时，越来越多的音乐家对根据原始资料的复制品演奏这些音乐感兴趣。因此，我们将开发一种新的在线互动学习工具，学生、表演者或其他人可以用它来练习解释测量符号所涉及的认知过程。该工具将呈现渐进式练习以及目标结果和注释机制，并将能够对进度进行反馈并提供提示。我们期望我们的软件系统的发展能够产生关于廷托里斯理论的完整性及其与他那个时代更广泛的实践的关系的不可预测的历史发现。我们将以标准学术出版物的形式进行交流。该项目的一个特别有价值的方面将是在伯明翰、牛津和伦敦举办的一系列公共研讨会，随着软件学习工具的发展，形成一个渐进的介绍。该项目的主要受益者将包括所有参与中世纪晚期和早期现代音乐剧目的表演、编辑和学术研究的人。对于所有用户来说，将提高对原始复杂符号含义的高度和丰富的认识，并提供一个高度创新的实用工具，以协助学习过程，并能够制作新的用户主导版本的作品，这些作品来自西欧音乐的关键时期。

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.