Purves, Ross M.; (2001) A computer program for investigating transformation geometry concepts in musical and visual form: from theory to realisation. Masters thesis (M.A), University of London (Institute of Education).

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Abstract

This study begins with the hypothesis that music, like the Logo Turtle, can function as an object-to-think-with. It asserts that an extensible, ‘microworld’ computer environment is best placed to facilitate and develop a transitional relationship between music and mathematics. Transformation geometry is proposed as an area of mathematics that exhibits conceptual parallels with musical composition techniques. It is a subject rich in creative potential. A survey of research into the development of transformation geometry concepts in childhood is compared with existing models of musical development. It is suggested that exposure to symmetrical phenomena, both in the world around them and through education, may engender a tendency for children to ‘symmetrize’ melodies and drawings. Since transformation geometry and music have so much in common, it is hypothesised that children may be able to use their understanding of one domain to inform their understanding of the other. A computer program – GeoMusE – is developed to explore these issues. GeoMusE allows learners to enter melodies or shapes (collectively known as phrases) on a co-ordinate grid. The horizontal axis represents time and the vertical axis represents pitch. Phrases can be reflected and translated to develop musical and graphical material. Since it is written entirely in Logo, GeoMusE can be extended by the user to perform further transformations. The results of a school trial of GeoMusE are reported. Six Year 8 students attempted tasks such as composing palindromic melodies and canon, and creating music using shapes and patterns. The students moved fluidly between the musical and mathematical domains to produce some interesting compositions. Analysis of questionnaire data shows that the students were able to transfer their knowledge from one domain to another. It also shows that through the provision of feed back, audio-visual representational modes, and the facility to edit work, the computer environment cultivated this transfer.

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