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Algebraic Methods in Musical Composition

   Department of Mathematics

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  Dr W Turner, Prof R Levi  Applications accepted all year round  Self-Funded PhD Students Only

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.

Selection will be made on the basis of academic merit. The successful candidate should have, or expect to obtain, a strong 1st Class degree in mathematics from a UK university, or international equivalent. Knowledge of group theory, linear algebra, combinatorics, music (including music written on a stave).

Formal applications can be completed online:

• 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, Personal Statement/Motivation Letter and Intended source of funding

Informal inquiries can be made to Dr W Turner ([Email Address Removed]) with a copy of your curriculum vitae and a brief description of why you are interested in this project, along with full undergraduate transcript (and Masters transcript, if applicable). All general enquiries should be directed to the Postgraduate Research School ([Email Address Removed])

Funding Notes

This PhD project has no funding attached and is therefore available to students (UK/International) who are able to seek their own funding or sponsorship. Supervisors will not be able to respond to requests to source funding. Details of the cost of study can be found by visiting
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