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世纪初到17世纪初从事音乐来源工作的人所面临的一个中心问题，无论是作为编辑、分析师还是表演者。当时流行的节奏记数法系统是与背景高度相关的；不同于现代的普通记号法，所有的音符只能被两个整除(有明确定义的例外情况称为“元组”)，因此在持续时间上是确定的，而在断续记数法中，许多音符可以被二分或三分，没有视觉上的区别，它们的持续时间要根据它们的上下文进行进一步的常规处理。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约翰尼斯·廷克托里斯(Johannes Tinctoris，C.1435-1511)的教学，该系统将以未解释的计量符号的文件作为输入，并以确定的持续时间输出它们。丁克托里斯的理论通过他严谨的方法和意图详尽地实例化他的规则，从而适合于这样的处理。拟议的系统是由同一项目组(http://earlymusictheory.org/Tinctoris).)制作的廷克托里斯著作的在线评论版的自然产物结果可以以各种格式输出：原始记数法或通用记数法、分数或单独的部分。我们的系统将接受其他项目制作的未解释的测数符号的输入；我们的解释输出将用于其他项目开发的分析软件。我们将使用机器学习技术来提高系统的性能。这将需要用一系列实际的十五世纪音乐作品进行分级培训：(1)廷克托里斯为说明他关于测音法和对位的论文而创作的所有音乐范例；(2)廷克托里斯的所有实用作品，我们将为此制作一个新的批评版；(3)廷克托里斯两位作曲家的作品选集，纪尧姆·杜·费伊和安东尼·布斯诺伊斯，他们的音乐创作与廷克托利斯所表达的那些有所不同的记谱惯例。我们希望这个系统能够解释从十五世纪初到十七世纪初的几乎所有音乐的符号(十四世纪提供了我们不应该有时间处理的变体)。现在的中世纪晚期和早期现代音乐的学生不像以前那样精通月牙符号的复杂性，同时越来越多的音乐家对从原始来源的复制品中演奏这种音乐感兴趣。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使用它来练习解释更年期符号所涉及的认知过程。该工具将呈现渐进的练习以及目标结果和注释机制，并将能够反馈进度并提供提示。我们预计，我们软件系统的开发将产生关于丁克托里斯理论的完整性及其与他那个时代更广泛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传达这些信息。该项目的一个特别有价值的方面是在伯明翰、牛津和伦敦举行的一系列公开研讨会，随着软件学习工具的发展，形成对软件学习工具的渐进介绍。该项目的主要受益者将包括所有参与中世纪晚期和现代早期音乐曲目的表演、编辑和学术研究的人。对所有用户来说，将大大提高和丰富对原始、复杂符号含义的认识，并提供一个高度创新的实用工具来帮助学习过程，以及能够制作这一西欧音乐关键时期由用户主导的新版本的作品。

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.