¶ Isomorphic tessellations for musical keyboards

pdf link

¶ BibTeX

@inproceedings{maupin2011isomorphic,
  title={Isomorphic tessellations for musical keyboards},
  author={Maupin, Steven and Gerhard, David and Park, Brett},
  booktitle={Proceedings of Sound and Music Computing Conference},
  pages={471--478},
  year={2011}
}

¶ Abstract

Many traditional and new musical instruments make use of an isomorphic note layout across a uniform planar tessel- lation. Recently, a number of hexagonal isomorphic key- boards have become available commercially. Each such keyboard or interface uses a single specific layout for notes, with specific justifications as to why this or that layout is better. This paper is an exploration of all possible note layouts on isomorphic tessellations. We begin with an in- vestigation and proof of isomorphism in the two regular planar tessellations (Square and hexagonal), we describe the history and current practice of isomorphic note layouts from traditional stringed instruments to commercial hex keyboards and virtual keyboards available on tablet com- puters, and we investigate the complete space of such lay- outs, evaluating the existing popular layouts and proposing a set of new layouts which are optimized for specific mu- sical tasks.

¶ My Notes

Very interesting paper. But I was dissapointed that:

• They don’t actually enumerate all possible note layouts
• They don’t treat note layouts as equivalent if they are rotations or reflections of another.

(Likely the first failing a necessary consequence of the second.)