Composition Practice

The aim of this study is to present the decimal values of square roots as potentially infinite melodies. This can aid the user of this system ideas to create new works for the 21st Century. While there are pieces written with square root models, this exercise will combine the works of Schenker(1), Schoenberg(2), Kirnberger(3), Slonimsky(4), and Hellmer(5). This writing exercise can also operate as a method for understanding square root values in general. The method used for converting square root values to music is called Cartesian Mapping of Chords and Scales(6).The method allows for integers in a sequence, much like the square roots, to have a one-to-one correspondence to the 12-tones. 

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1. Mapping Theory and Working Proof

   • Example of Inversions (A Major)

   • ii-V-I's in Root Position

2. In Practice

   • Marimba

   • Strings

   • Brass

3. Implications

   • Square Root Melodies as Applied to Instrumental Technique

   • Combination of Rudimental Coordination and Mapping Techniques

   • Analysis of Mapping via Topology 

1. Schenker, H., Jonas, O., & Borgese, E. M. (1954). Harmony. Chicago: University of Chicago Press. 

2. Schoenberg, A. (1978). Theory of harmony. Berkeley: University of California Press.

3. Kirnberger, J. P. (1981). The art of strict musical composition. New Haven: Yale University Press.

4. Slonimsky, N. (1947). Thesaurus of scales and melodic patterns. New York: Coleman-Ross.

5. Lawn, R., & Hellmer, J. L. (1996). Jazz: Theory and practice. Alfred Pub. Co.

6. Wesley, A. (2022, February). (pdf) White Paper Cartesian Music Theory for Math and ... ResearchGate. https://www.researchgate.net/publication/358441319_White_Paper_Cartesian_Music_Theory_for_Math_and_Music_Integration/download