Document Type

Conference Proceeding

Publication Date



Tessellations Publishing


Wallpaper patterns have been shown to be decomposable into standing waves of plane vibrations [6]. Previously unexplored are the sounds that arise from these vibrations. The main result of this paper is that each wallpaper type (square, hexagonal, rectangular, generic) has its own distinctive family of pitches relative to a fundamental. We review the method to make wallpaper with wave functions and describe new musical scales for each type, including initial attempts to use the scales: a movie showing vibrations of wallpaper patterns with 3- and 6-fold symmetry inspired a new piece by American composer William Susman, commissioned by the San Jose Chamber Orchestra, Barbara Day Turner, conductor. The piece, “In a State of Patterns,” was premiered on March 25, 2018.


BRIDGES STOCKHOLM 2018 Mathematics, Art, Music, Architecture, Education, Culture The National Museum of Science and Technology (Tekniska museet) Stockholm, Sweden 25–29 July 2018 Family Day: Saturday, July 28th, afternoon Excursion: Sunday, July 29th

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.