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Cents

ByGary

Musical notes can be mapped onto many different spaces. The two I find useful so far are: — Harmonic space, the space of the lattice, organized by harmonic connections (ratios of whole numbers). — Melodic space, the space of the scale, organized by pitch, or frequency. Both maps show the location of a note relative…

The Lattice

ByGary

In 1739, the great mathematician Leonhard Euler published something he called a Tonnetz, German for “tone network.” It looked like this: Euler’s Tonnetz organizes the notes into a matrix, instead of a scale. Moving down and to the left represents motion by an interval of a fifth (V) in musical space. Down and to the right…