Music Theory

Audio Note: Companion to “The geometry of musical keys”

The relationships between musical keys can be described either by means of the triangles in the “Tonnetz”, or by carefully designed geometric…

May 23 •

1:11

The geometry of musical keys

The Tonnetz (German for “tone network”) is a diagram representing musical tonal space, in which each vertex represents a musical note, and each small…

May 21 •

Maximally even musical scales

Given a musical scale, is there any way to measure the extent to which the notes are evenly spaced?

Aug 5, 2024 •

Generalizations of Euler’s Tonnetz

The picture above by Konstanze Rietsch shows a Tonnetz of type G2. This is an infinite tessellation of 30°–60°–90° triangles whose edges are labelled by…

Feb 4, 2024 •

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