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The pitch of a note is a quantity which, in its natural form, can vary continuously.  However, we usually define a scale, which replaces the continuum of pitches with a discrete set of notes.  The difference is analogous to the difference between viewing matter as a homogenous substance or as a crystal structure with atoms at each lattice point.

For my project, I explored the results of viewing the notes of a traditional musical scales as points on a two-dimensional square lattice.  Along each row, the notes increase chromatically in pitch going from left to right.  Pitch also increases chromatically going from down to up along a column.  This results in a lattice where each row is identical to the row below it but shifted one lattice spacing to the left.  The result is shown below, with that green line marking a line of constant pitch (slope = -1).

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