Trees and musical tuning

These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.

A mathematical tree is a graph in which any two distinct vertices are connected by a unique path. If the vertices of a tree are in bijection with the notes of a piece of music, and the edges are labelled by frequencies, then we have associated to each note X of our piece a frequency, by taking the unique path from the first note in the piece to X and multiplying together a root frequency and all the frequencies corresponding to the edges in the path. These frequencies determine a tuning of our piece of music. A couple of examples, in which the tree and frequencies associated to the piece of music are related to the harmonic structure of the piece of music they are representing, have been overturned by the first supervisor. The music resulting from the tuning is related to that of the original piece but sounds somewhat different.

The project is to investigate these techniques in further detail, and perhaps find more examples of trees associated to musical pieces via musical analysis. Some computer programming will be required to realise the music.

The project could not be pursued in distance mode.

Informal enquiries can be made by contacting Dr W Turner (w.turner@abdn.ac.uk).

Decisions will be based on academic merit. The successful applicant should have, or expect to obtain, a UK Honours Degree at 2.1 (or equivalent) in Mathematics. Some musical background is also essential – eg. stave notation, intervals, octaves, cycle of fifths, transposition.

We encourage applications from all backgrounds and communities, and are committed to having a diverse, inclusive team.

Application Procedure:

Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php.

You should apply for Degree of Doctor of Philosophy in Mathematics to ensure your application is passed to the correct team for processing.

Please clearly note the name of the lead supervisor and project titleon the application form. If you do not include these details, it may not be considered for the project.

Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts.

Please note: you do not need to provide a research proposal with this application.

If you require any additional assistance in submitting your application or have any queries about the application process, please don't hesitate to contact us at researchadmissions@abdn.ac.uk

Funding Notes

This is a self-funding project open to students worldwide. Our typical start dates for this programme are February or October.

Fees for this programme can be found here Finance and Funding | Study Here | The University of Aberdeen.