Geometry of Chords and Melodies Based on Atomic and Molecular Models

Abstract

This dissertation proposes a geometrical model of musical chords and melodies based on the molecular bonding models, exploring music through a piano performer’s synesthetic mind that integrates auditory perception with visual geometrical shapes oriented in different dimensional spaces. The musical note itself is modeled as a solid sphere, two- note chords as two solid spheres bound linearly, three- and four-note chords as polygons inside a hollow spherical space, and the melodies as contouring lines of a helix. These shapes are based on the atomic and the VSEPR (valence shell electron pair repulsion) molecular geometry model used in chemistry, considering each of the musical pitches as atoms. Because an atom is the basic unit of chemical connection in chemistry, a musical note, in my model, is the basic unit of musical composition.Chapter One introduces the connection between music, mathematics, and geometry with some example illustrations of spatial reasoning of musical notes. Chapter Two explores theoretical systems that use geometrical shapes and spaces, such as Tonnetz and orbifold by music theorists, as well as alternative ideas of visualization of music by scientists. Chapter Three shows how to illustrate geometrical shapes of musical chords, relating to the VSEPR molecular model. The world-famous Pythagorean experiment that led to the development of the Western musical tuning system is the starting point of any chord models. The musical interval, often expressed as a fraction or decimal, is the basis to draw the interval edges of triangles by applying the trigonometric function. Amalgamating these concepts, I draw geometrical shapes of melody, intervals, and chords progressively into two-dimensional, three-dimensional, and possibly four- dimensional shapes. Chapter Four employs the musical geometrical models in selected excerpts of piano solo music. Prominent and repetitive musical themes or patterns, which function like the blueprint or DNA of a particular composition, are selected and illustrated. Lastly, Chapter Five provides a summary of this study and suggests future projects that would help to find further connections between music and physical science. This study aims to demonstrate that music can be interpreted and visualized with geometrical figures that originate from the pianist’s scientific mind and performance perspective. In addition, this helps both musicians and scientists to integrate music, mathematics, geometry, and chemistry by linking isolated dots, thus making more sense of the study of music and/or science. The ability to integrate music with associated visual geometrical shapes would open up the senses, expand the mind, and stimulate the imagination of the audience with perceptions beyond the musical sound, emotion, and aesthetic.