Analysing Musical Structure: Harmonic-Contrapuntal Reduction by Computer

Lead Research Organisation: Lancaster University
Department Name: Lancaster Inst for the Contemporary Arts


The combinations of notes which make up a piece of music form, in the minds of listeners, interrelated lines and segments somewhat in the manner in which letters form words, phrases and sentences. These lines and segments carry the meaning of the music, and musicians read them from a score as words and sentences are read from text. Based on the music theory of Heinrich Schenker, this project has dual objectives, one theoretical--to examine the principles by which such 'reading' is possible--and one practical--a computer program which 'reads' musical structures automatically from a representation of the score.

While music theory has, for centuries, given explanations of musical structure, it is only in the past few decades that researchers have asked how structures are discovered and recognised. A typical research paradigm has been to develop computer programs to derive musical structure, and programs now exist to derive information such the key of a piece and where the strong beats fall. However, none yet gives a full structural parsing of a piece without intervention from a musician.

The 'rules' of musical 'grammar', as currently conceived, allow many different possible structural interpretations of even a short passage of music, though most of them a musician would rule out as absurd. Indeed, it is the 'combinatorial explosion' of possibilities which has hampered previous efforts to implement Schenkerian analysis by computer. The solution adopted by researchers has usually been some numerical system of selecting the most likely or most preferred interpretation at each point. Success has been limited because the indices of preferred or likely interpretations are not well understood, and there is rarely a paradigm to find them other than trial and error. This project instead adopts a solution similar to 'dynamic programming', a technique applicable to problems where possibilities increase exponentially. Instead of deriving analyses directly, a table of possibilities is created from which actual analyses can be derived by following specific paths through the table. The information by which to decide at each point which is the best path is already derived in the table, and so is immediately evident. The final step in this project (which requires the empirical work which is the object of this period of research leave) is to establish the information which must be gathered when making the table of possibilities. This will be done by relating the tables derived by the software with a corpus of already completed analyses, where possible by Schenker himself.

Current computer tools for music generally deal only with the notes or the sounds which form the surface of a piece of music. Musicologists are usually concerned with the underlying structures and patterns, and so need tools which look deeper. With the software which will be the outcome of this project, sophisticated searches within a database of music for such things as all occurrences of variations of a particular melodic pattern will become possible.

The following improvements have been made to the previous submission (rated A+):
1. The title is more immediately meaningful.
2. The potential benefits have been more explicitly elaborated.
3. Recent personal communications from Keiji Hirata, Panayotis Mavromatis (colleague of Matthew Brown), and Darrell Conklin concerning the current state of their related research projects have confirmed my claims about the research context.
4. Prototype demonstration software has been written and can be viewed on my web pages.
5. Sources of existing music analyses to be used as research materials have been identified.
6. Details of journals and conferences for dissemination are more precise, and dissemination of the software has been discussed with the AHRC ICT Methods Network and the OMRAS2 project.
7. Project costs are more precise, and slightly lower. 8. Two items have been added to my list of publications.


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Marsden A (2010) Schenkerian Analysis by Computer: A Proof of Concept in Journal of New Music Research

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Marsden A (2011) Software for Schenkerian Analysis in N/A

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Marsden A. (2010) Recognition of variations using automatic schenkerian reduction in Proceedings of the 11th International Society for Music Information Retrieval Conference, ISMIR 2010

Description The research demonstrated that it is possible to analyse music in the manner of Schenkerian analysis by computer, but it is only practical to do so for short segments of music, because it is very complex. Through attempting to match the analyses of experts, the research demonstrated indirectly that when experts analyse music they draw on a great deal of uncodified information in making their decisions.
Exploitation Route A follow-up project collaborating with computer scientists to use more sophisticated programming methods is in development. The findings could be applied in music-educational software, and in music-processing software.
Sectors Creative Economy,Education

Description This was a theoretical research project which has not yet had a clearly demonstrable impact outside academia.
Description Information-theoretic techniques to Schenkerian Analysis 
Organisation University College London
Country United Kingdom 
Sector Academic/University 
PI Contribution I contributed data generated in the course of the original project for new experiments concerning information content and Schenkerian analysis.
Collaborator Contribution Dr Nicolas Gold of UCL conducted experiments on data supplied by me, and he and Samer Abdallah (also of UCL) have subsequently developed proposals for Schenkerian analysis using probabilistic programming.
Impact A jointly authored chapter is to be published in a forthcoming book on computational music analysis. The collaboration is between a musicologist and computer scientists.
Start Year 2012
Description Intelligent search and Schenkerian Analysis 
Organisation Goldsmiths, University of London
Department Department of Computing
Country United Kingdom 
Sector Academic/University 
PI Contribution I adapted the software from the original project to use best-first search in the analysis process.
Collaborator Contribution Prof. Geraint Wiggins designed experiments in Schenkerian analysis using search.
Impact Schenkerian Reduction as Search, paper at Conference of Interdisciplinary Musicology, 2008. This was a collaboration between a musicologists and a computer scientist.
Start Year 2008