User:Holger Stoltenberg/sandbox

Expanding tonal space

This article describes how to visually arrange a set of overtone scales in order to expand a particular plane of tonal space.

Why expand tonal space in this way?

The concept is a step towards building an electronic keyboard instrument that allows the player to interactively map sequences of rational intervals to consecutive keys – in real time, even live on stage. Therefore, the player needs convenient and intuitive access to the mapping process, which becomes an integral part of the musical performance.

[math]\displaystyle{ \displaystyle r=\frac{n+m}{n} }[/math]

[math]\displaystyle{ \displaystyle r = (n + m)/n }[/math]