Applying the phi ratio in designing a musical scale

Smit, Konrad van Zyl (2005-03)

Thesis (MMus (Music))--University of Stellenbosch, 2005.


In this thesis, an attempt is made to create an aesthetically pleasing musical scale based on the ratio of phi. Precedents for the application of phi in aesthetic fields exist; noteworthy is Le Corbusier’s architectural works, the measurements of which are based on phi. A brief discussion of the unique mathematical properties of phi is given, followed by a discussion of the manifestations of phi in the physical ratios as they appear in animal and plant life. Specific scales which have found an application in art music are discussed, and the properties to which their success is attributable are identified. Consequently, during the design of the phi scale, these characteristics are incorporated. The design of the phi scale is facilitated by the use of the most sophisticated modern computer software in the field of psychacoustics. During the scale’s design process, particular emphasis is placed on the requirement of obtaining maximal sensory consonance. For this reason, an in-depth discussion of the theories regarding consonance perception is undertaken. During this discussion, the reader’s attention is drawn to the difference between musical and perceptual consonance, and a discussion of the developmental history of musical consonance is given. Lastly, the scale is tested to see whether it complies with the requirements for successful scales.

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