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Algebraic Methods in Musical Composition

Department of Mathematics

About the Project

Algebraic operations have been used as compositional tools for centuries. For example, the group theoretical operation of translation on the integers can be identified with the musical operation of transposition. This sort of operation, as well as other more complex operations, are implicit in the fugal form as well as other forms founded on repetition.

The aim of this project is to develop algebraic techniques for musical composition, to be played using modern musical software. Such software presents the possibility of great precision in performance, which means frequencies away from those that correspond to points on the stave can be utilised, as well as frequencies that correspond to points on the stave.

Of particular interest are compositions that are constructed via similarity, To give an example, in one approach we consider algebraic operations, like transposition, that map sounds to similar sounds. The sound resulting from the application of a sequence of such operations to a sound are concatenated to create a further sound. A sequence of operations is applied to this sound in turn, and the resulting sequence of sounds is concatenated. And so on.After a number of iterations we stop and our composition is complete.


• Apply for Degree of Doctor of Philosophy in Mathematics
• State name of the lead supervisor as the Name of Proposed Supervisor
• State ‘Self-funded’ as Intended Source of Funding
• State the exact project title on the application form

When applying please ensure all required documents are attached:

• All degree certificates and transcripts (Undergraduate AND Postgraduate MSc-officially translated into English where necessary)
• Detailed CV

Informal inquiries can be made to Dr Will Turner () with a copy of your curriculum vitae and cover letter. All general enquiries should be directed to the Postgraduate Research School ()

Funding Notes

This project is advertised in relation to the research areas of the discipline of mathematics. The successful applicant will be expected to provide the funding for Tuition fees, living expenses and maintenance. Details of the cost of study can be found by visiting View Website. THERE IS NO FUNDING ATTACHED TO THESE PROJECTS

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