First Name:
Alison
Last Name:
McClay
Major Department:
Mathematical Sciences
Thesis Director:
Vicky Klima
Date of Thesis:
May 2014
Using Brian J. McCartins "Prelude to Musical Geometry" as a guide, we will look at the geometric link between mathematics and tonal music. When a collection of pitches is heard, either successively (melodically) or simultaneously (harmoni- cally), forming scales or chords, we find varying intervallic relationships. One of our main goals in investigating this musical link is to understand the mathematical implications of the interval relationships among the members of any set of pitches and systems. Arranging the pitches of an n-tone system in a circle of pitches similar to a clock, we are able to plot the pitches of a chord on our musical clock to see the geometric distances, or semitones, between each note. These pitches are joined together by line segments, forming a polygon that we then try to rotate (trans- pose) and/or reflect (invert). From what is known about the 12-tone system, we hope to see the same geometric and mathematical representation in a 20-tone and then other general n-tone systems. We ultimately hope to find analogies between different n-tone systems the applications of the same geometric and mathematical representations in order to see which, if any, microtonal systems preserve the same chordal structure and properties present in the 12-tone system that makes up the musical world we know.
Complete Thesis (PDF, 355KB)