Applying the phi ratio in designing a musical scale
Date
2005-03
Authors
Smit, Konrad van Zyl
Journal Title
Journal ISSN
Volume Title
Publisher
Stellenbosch : University of Stellenbosch
Abstract
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.
Description
Thesis (MMus (Music))--University of Stellenbosch, 2005.
Keywords
Ratio analysis -- Data processing, Consonance (Music) -- Data processing, Musical intervals and scales -- Data processing, Cognition -- Data processing, Psychoacoustics -- Data processing, Pi-calculus -- Data processing, Dissertations -- Music, Theses -- Music