Alan Marsden

Schenkerian Analysis by Computer: A Proof of Concept

Abstract A system for automatically deriving a Schenkerian reduction of an extract of tonal music is described. Schenkerian theory is formalized in a quasi-grammatical manner, expressing a reduction as a binary-tree structure. Computer software which operates in the manner of a chart parser using this grammar has been implemented, capable of deriving a matrix of reduction possibilities, in polynomial time, from a representation of the score. A full reduction of the extract can be discovered by selecting a tree from this matrix. The number of possible valid reductions for even short extracts is found to be extremely large, so criteria are required to distinguish good reductions from bad ones. To find such criteria, themes from five Mozart piano sonatas are analysed and samples of ‘good’ reductions (defined by reference to pre-existing analyses of these themes) are compared with randomly sampled reductions. Nine criteria are thereby derived, which can be applied in the process of parsing and selecting a reduction. The results are promising, but the process is still too computationally expensive—only extracts of a few bars in length can be reduced—and more extensive testing is required before the system can be properly claimed to perform automatic Schenkerian analysis.

Generative Structural Representation of Tonal Music.

Abstract The usefulness and desirability of representation schemes which explicitly show musical structure has often been commented upon. A particular aim of music theory and analysis has been to describe and derive musical structure, and this article discusses computational systems based on this work. Six desirable properties of a structural representation are described: that it should be constructive, derivable, meaningful, decomposable, hierarchical, and generative. Previous computational work based on the generative and reductional theories of Schenker and of Lerdahl and Jackendoff is examined in the light of these properties. Proposals are made for a representational framework which promises the desirable properties. The framework shares characteristics with earlier work but does not use pure trees as a representational structure, instead allowing joining of branches in limited circumstances to make directed acyclic graphs. Important issues in developing a representation scheme within this framework are discussed, especially concerning the representation of polyphonic music, of rhythmic patterns, and of up-beats. An example is given of two alternative representations within this framework of the same segment of music used to exemplify earlier work: the opening of the theme of Mozarts piano sonata in A major, K.331.

Representing Melodic Patterns as Networks of Elaborations

Previous discussions of musical pattern haveunderlined difficulties in seeking pattern as asequence of pitches, or of intervals or of other localand atomic features. This paper describes a manner ofrepresenting melodies through a hierarchical structureof elaboration, derived from concepts common in musictheory (in particular, the concept of reduction foundin the work of Schenker and of Lerdahl & Jackendoff).The fundamental structure is a planar directed acyclicgraph, each node of which represents a musical note(not necessarily as it is present in the actualmelody) and an elaboration which generates that noteon the basis of two parents. These graph structurescan be converted to trees, aiding processing andcomparison, in two ways. Firstly, any graph can betransformed into a set of binary trees in which eachnode represents an interval between two notes and anelaboration of that interval. Secondly, in the planargraph, the link of a node to one of its parents oftenprovides no useful information and can be disregarded,resulting in a reduction of the graph tending towardsa set of trees. From this arises a new approach to thequestion of melodic segmentation. Examples of melodicfragments represented in this manner demonstrate howthe representation makes explicit similarities betweenfragments which would not be found by an approachusing sequences of features.

Tools for Searching, Annotation and Analysis of Speech, Music, Film and Video—A Survey

This article examines the actual and potential use of software tools in research in the arts and humanities focusing on audiovisual (AV) materials such as recorded speech, music, video and film. The quantity of such materials available to researchers is massive and rapidly expanding. Researchers need to locate the material of interest in the vast quantity available, and to organize and process the material once collected. Locating and organizing often depend on metadata and tags to describe the actual content, but standards for metadata for AV materials are not widely adopted. Content-based search is becoming possible for speech, but is still beyond the horizon for music, and even more distant for video. Copyright protection hampers research with AV materials, and Digital Rights Management (DRM) systems threaten to prevent research altogether. Once material has been located and accessed, much research proceeds by annotation, for which many tools exist. Many researchers make some kind of transcription of materials, and would value tools to automate this process. Such tools exist for speech, though with important limits to their accuracy and applicability. For music and video, researchers can make use of visualizations. A better understanding (in general terms) by researchers of the processes carried out by computer software and of the limitations of its results would lead to more effective use of Information and Communications Technology (ICT).

A Study of Cognitive Demands in Listening to Mozart's Quintet for Piano and Wind Instruments, K.452

The objective of the paper is to study complexity in the music of Mozart. A scheme of modelling the cognitive representation of music is proposed, based on the theories of Schenker and Komar. The hierarchical structures of these theories are expressed as networks of elaborations. Such networks are produced for each phrase of the exposition of the allegro moderato of Mozarts quintet K.452. The number of elaborations in each network is found to be constrained to a limited range, and when plotted against the number of notes in each phrase a weak negative correlation is found. This is taken as evidence that the cognitive demand on the listener is maintained at a more or less constant level throughout the movement. Complications concerning recurrent material and different tempi are discussed.

Music, Intelligence and Artificiality

The discipline of Music-AI is defined as that activity which seeks to program computers to perform musical tasks in an intelligent, which possibly means humanlike way. A brief historical survey of different approaches within the discipline is presented. Two particular issues arise: the explicit representation of knowledge; and symbolic and subsymbolic representation and processing. When attempting to give a precise definition of Music-AI, it is argued that all musical processes must make some reference to human behaviour, and so Music-AI is a central rather than a peripheral discipline for musical computing. However, it turns out that the goals of Music-AI as first expressed, the mimicking of human behaviour, are impossible to achieve in full, and that it is impossible, in principle, for computers to pass a musical version of the Turing test. In practice, however, computers are used for their non-human-like behaviour just as much as their human-like behaviour, so the real goal of Music-AI must be reformulated. Furthermore, it is argued that the non-holistic analysis of human behaviour which this reformulation entails is actually informative for our understanding of human behaviour. Music-AI could also be fruitfully concerned with developing musical intelligences which were explicitly not human. Music-AI is then seen to be as much a creative enterprise as a scientific one.

Big Data Optical Music Recognition with Multi Images and Multi Recognisers

In this paper we describe work in progress towards Multi-OMR, an approach to Optical Music Recognition (OMR) which aims to significantly improve the accuracy of musical score digitisation. There are a large number of scores available in public databases, as well as a range of different commercial and open source OMR tools. Using these resources, we are exploring a Big Data approach to harnessing datasets by aligning and combining the results of multiple versions of the same score, processed with multiple technologies. It is anticipated that this approach will yield high quality results, opening up large datasets to researchers in the field of digital musicology.

Towards a connected distributed model of musical listening

Abstract A reappraisal of modelling approaches to musical behaviour is undertaken in the light of both recent general work in cognitive modelling and a study of musicians’ responses to Weberns piano variations, op. 27. A distributed framework of rule‐based systems is proposed in which the nature of communications between and among expert modules is of primary consideration in enabling the model to respond gracefully to differing musical demands.

Timing in music and modal temporal logic

Abstract ‘In-time’ representations of music in which the time represented is the same time as inhabited by the agent making or using the representation are contrasted with ‘out-of-time’ representations. Temporal logics with a similar ‘in-time’ perspective, and in particular those using operators S and U for ‘since’ and ‘until’, are explored as a means of representing musical situations, with particular reference to a paradigm ‘triangle-player problem’. Illustrative implementations are given in the music software Pd. New versions of the operators S and U are defined to accommodate the musically important phenomena of regularly occurring events associated with metre, and to allow representations to reflect actual timings rather than relations of temporal order. Nesting of out-of-time representations within in-time representations then becomes possible and arises naturally as a way of representing certain kinds of musical situations.

Analysing Symbolic Music with Probabilistic Grammars

Recent developments in computational linguistics offer ways to approach the analysis of musical structure by inducing probabilistic models (in the form of grammars) over a corpus of music. These can produce idiomatic sentences from a probabilistic model of the musical language and thus offer explanations of the musical structures they model. This chapter surveys historical and current work in musical analysis using grammars, based on computational linguistic approaches. We outline the theory of probabilistic grammars and illustrate their implementation in Prolog using PRISM. Our experiments on learning the probabilities for simple grammars from pitch sequences in two kinds of symbolic musical corpora are summarized. The results support our claim that probabilistic grammars are a promising framework for computational music analysis, but also indicate that further work is required to establish their superiority over Markov models.