13-Note Modes in a 18-Note Octave
The 6188 modes containing 13 notes embedded in an octave divided into 18 notes. Each mode, represented as a colored square, is attributed a unique pair of coordinates, similar to a GPS position on a map.
The vertical axis orders scales. Each row contains either a single symmmetric scale (no change under inversion), or a pair of mirror scales. The diatonic scale appears on the North pole (1) and the chromatic cluster (252) on the South pole.
The horizontal axis orders modes from the brightest (most “major”) in the column on the far West (30) to the darkest (most “minor”) on the far East (-30).
Color denotes symmetry: rows entirely in pink contain a single symmetric scale; different shades of blue distinguish between pairs of mirror scales, common modes appearing in pink.