A crucial link between mathematics and music is nicely illustrated by the Tonnetz, a geometric diagram representing the harmonic relationships between the notes of the musical scale.
An early version of the Tonnetz appeared in Leonhard Euler’s book Tentamen Novae Theoriae Musicae (a new theory of music), published in 1739. A modern development of the diagram appears in the accompanying illustration. Closely related notes are grouped together: the C major triad, C–E–G, appears as a dark red triangle.
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