The Zone of Musical Creativity: Harmonic Series Structures - From Pictorial Representation to a Method of Teaching

Abstract

For any pitched sound in nature, there is an inner structure of that sound displaying a series of harmonics, or partials, that vibrate with different frequencies. Due to the mathematical underpinnings of those frequencies, the pitched sound may be visualized with a Cartesian (logarithmic) spiral design [16]. The language of mathematics and music can therefore be pictorial, and so the elements of music - e.g., intervals, rhythmic and harmonic structures, these originate in the harmonic series (THS), and can be matched against spiral and circle designs. This paper discusses such visualizations suggesting from preliminary findings that pictorial representations of music are beneficial to: I. Explain the form in a musical piece, II. Facilitate students' understanding of compositional processes in music, III. Enhance memorization in music performance, IV. Develop such visualizations into a method of teaching in music and coaching for music performance. Narrative enquiry is the framework for an envisaged qualitative study [5], [23] which engages creativity and visualization in music performance, teaching, learning, coaching, music composition and analysis.