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Faculty Advisor

Karl Liechty, PhD

Abstract

The Spiral Array is a geometric model of musical tonality and exists as a tool in computer-aided music analysis. The model was first published in 2000 by Elaine Chew, PhD, in her thesis, Towards a Mathematical Model of Tonality. This project aimed to restructure the Spiral Array, limiting user ambiguity and optimizing the application of musical key finding. The existing model defines pitch, chord, and key location to form a series of spirals dependent on a set of flexible weights. In our research we were able to identify potential issues with the pitch definitions themselves and experiment with methods of addressing concerns by modifying existing pitch definitions and key algorithms produced by the model’s original creator. Additionally, we were able to improve the model’s potential for musical key finding by modifying these weights through gradient descent, given parameters derived from the Overtone Series and observations of common tonal practice. Our current model and algorithm allow users to analyze the key center of a musical excerpt in a way that is largely consistent with the overtone series and common tonal practice. This paper will highlight the journey of troubleshooting an existing model, demonstrate our successes, and provide insight into the field of Music Information Retrieval.

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