Wolfram Computation Meets Knowledge

Wolfram Summer School


Katarina Miljkovic

Summer School

Class of 2010


Katarina Miljkovic has written for symphony orchestra, string orchestra and various other groupings, including works for amplified solo instruments and electronics, saxophone quartet, electric guitar and percussion. Ms. Miljkovic has been exploring the relationship of music, science and nature. This initially led her to the Benoît Mandelbrot essay “The Fractal Geometry of Nature”. The study resulted in her cycle, “Forest”, for two prepared pianos and percussion, released by Sachimay Records. Currently, Ms. Miljkovic is working on mapping elementary rules from A New Kind of Science by Stephen Wolfram to sound. She presented her exploration in this new field at the NKS international conferences in 2004, 2006, and 2007, NKS Summer School 2004 and 2009, the 2005 Wolfram Technology Conference, soundaXis 2006 in Toronto, the 2007 International Conference on “Mathematics and Computation in Music”, held in Berlin, and Cambridge Science Festival, 2009 and 2010.

Katarina Miljkovic established her carrier as a composer in Belgrade, former Yugoslavia. In 1992, she moved to Boston for doctoral studies in music composition at the New England Conservatory of Music. Currently, Katarina Miljkovic is a full time faculty member at New England Conservatory of Music, where she has been teaching since 1997.

Project: Equal Temperament Tuning

Music making in Mathematica has mostly been limited to 12-tone equal temperament, 12-tone chromatic scale, and MIDI output. This summer, I decided to expand the available range of frequencies to various systems of equal temperament utilized in music of the past as well as to open the ways for generating new tuning systems. The variables within the code will enable a user to explore all possible cases of equal temperament. Combining different tuning systems is the second part of the project. Combining unequal interval steps may require a longer time for creating satisfying solutions, but it is certainly an interesting topic to explore. In terms of sound output, this approach requires work with sine waves, which has been somewhat neglected within the Mathematica community.

Once the choice of tuning is made, steps for generating non-contextual sonorities and building a palette of sounds will be proposed. The last step will be proposing application of a chosen range of frequencies to music making using cellular automata.

Favorite Four-Color Totalistic Cellular Automaton

Rule 397