a "modal compass" diagram showing each mode as a tonewheel, representing the 12 equally-tempered chromatic pitch classes, arranged into two semi-circular arcs of wheels, one for descending scales (left) and another for ascending scales (right), with the inversion symmetry indicated by a mirror plane (vertical centerline). root positions of all scales is at 12 o'clock, regardless of where their tonewheel appears along the arcs. the inversion symmetry between pairs of modes, with dorian as its own inverse, can be seen by comparing the two pitch constellations at each vertical position. the seven modes are arranged into sequences of single-note semitone alterations, using sharps for ascending scales (right) and flats for descending scales (left). note that there is no single-note semitone alteration connecting the lydian and locrian modes, hence the disjoint arcs. however, the lydian and locrian modes are connected by inversion symmetry, since descending lydian intervals and ascdending locrian intervals are identical (and vice versa). the semicircular axes, from "dark/cold" to "light/warm", imprecisely convey an idea of how modulations between keys might be used to evoke particular feelings within a piece. shading within each tonewheel represents tritone quality: dark gray indicates exact tritones (three whole steps), light gray indicates split tritones (two whole steps and two half steps). tritone angles shift & qualities alternate for each step along the compass' arcs.
"modal compass" diagram. see alt text for a description.
