Maple based music application featured in international virtual exhibition - User Case Studies - Maplesoft

User Case Study: Maple based music application featured in international virtual exhibition
Kenneth Rubenstein, a long time Maple user, university mathematics professor, composer and guitarist uses Maple to illustrate math based music applications

Mathematics of Planet Earth 2013 (MPE) is an initiative that was started by mathematical sciences organizations around the world. Its aim is to showcase ways in which mathematics can be used to understand geophysical, biological, artistic and human processes that make up the earth. More than a hundred scientific societies, universities, research institutes, and organizations all over the world have banded together to understand how the world functions and find solutions to challenges faced by our planet.

Maplesoft is a supporter of this initiative and has connected with this movement through the sponsorship of MPE events. Supporting MPE 2013 is part of Maplesoft’s commitment, as part of its 25th anniversary celebrations, to support initiatives that promote the use of mathematical and scientific tools.

One of the highlights of MPE 2013 is a virtual exhibition. MPE exhibition is a collection of open source material on the web that can be used by museums and schools around the world to stage their own exhibitions or to learn more about MPE topics. Entries for the exhibition are collected through a competition to design virtual or physical museum-quality exhibits (modules). The best modules are awarded, and exhibited at museums around the world. These modules form the basis of a virtual and real exhibition that is hosted by the IMAGINARY platform of the Mathematischen Forschungsinstituts Oberwolfach (MFO), an international research center based in Germany.

University mathematics professor, composer and guitarist, Kenneth Rubenstein, is a long time Maple user whose work was displayed at IMAGINARY.

As part of his teaching work, Kenneth uses Maple to help students understand mathematical theories and concepts. Music is his passion, and he often pulls examples from the world of music as illustrations for his students. For example, he has his students use math to explore the relationships between the placements of guitar frets and the 12-tone chromatic scale, based on the relationships of intervals and pitch first discovered by Pythagoras.

Being a musician himself, Kenneth uses Maple to create attractive animations that bring his music to life visually. “These images are generated through the mathematic software Maple, and are typically rendered in spherical or cylindrical coordinates,” said Kenneth. “Much of this amounts to extreme experimentation, premised upon a strong understanding of domain and range. I am basically sculpting with mathematics, using as my chisel trigonometric, group and number theoretic functions (and composed functions) so as to meticulously surf texture, scale and graphical behavior.”

A collection of Kenneth’s music videos that feature Maple can be found here:

The idea behind Mathematics of Planet Earth is to showcase how math and science can impact our lives, our community and the planet we live in. Kenneth’s applications of math using Maple touch people’s emotions and senses, providing insights into how mathematics and art come together to shape our observations, thinking and decisions.

Kenneth is not the only one to combine music, mathematics, and Maple. Another Maple user, George Articolo, published a book in 2013 that addresses the connection between music and math. In his book titled “Mathematical Concepts in Music: Scales, Harmony and Ratio”, George uses a mathematical approach to the numeric representation and quantitative analysis of musical objects. Maple was used in writing the text’s mathematical material and graphics. Use of Maple permitted the export of worksheets to PDF files in order to embed sound files into the text.




  • Kenneth Rubenstein uses Maple to "sculpt with mathematics", creating animations that complement his musical compositions
  • Examples of his mathematical sculptures are on display at IMAGINARY
  • Mathematics of Planet Earth is a showcase of how math and science can impact our lives, our community and the planet we live in